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Hands-on PID autotuning

1. Status Ready Controller mode Automatic Set point 94 737 Relay parameters Height 1 000 Hyst 0 100 Limit cycle Last P 34 000 32 877 0 Controller_Output 29 60 z nn Fi Start Tune D F2 Download i F3 Move SP Figure 31 CAD software screen dump showing evaluation of PI controller The MasterTune software incorporates many attractive features that provide an automatic medium for PID controller parameter determination Another attractive feature is the ability to download the parameters directly into the actual process controller once the values are ac cepted When this stage is complete the PC is disconnected form the controller A new tun ing cycle with a different controller begins once the communications link is again estab lished 7 Soft Computing methods for PID Autotuning A novel alternative and a very promising research field 7 1 What is Soft Computing Soft computing is a relatively recent collection of methodologies which have been inspired by natural phenomena The term soft was coined by L A Zadeh Zadeh 1965 as opposed to conventional hard computing in order to emphasise their tolerance for imprecision and uncertainty The core methodologies of soft computing are fuzzy logic neural networks and evolutionary computing Although these methodologies have different genesis they can be seen as complementary rather than co
2. As a consequence this volume does not lead to a selection table but to a set of concepts that once mastered allows to evaluate how much a product fits an application We have proposed a classification of autotuners that is slightly different from the one most widely adopted in the academic literature This must not be taken as a criticism to that classi fication however Our point is that the proposed one reflects more precisely the operational aspects of autotuning being based on the three questions a what type of process informa tion it uses b how is the desired behaviour of the control system specified c how does it act for achieving its objectives As such we think that this classification may be less suited for methodological discussions but is more useful for selecting a product The monograph has devoted a significant space to the review of PID control principles This has been done essentially for less experienced readers We did not intend to provide a com plete treatment of PID control rather to recall the most relevant facts with a notation consis tent with the rest of the work The same rationale is behind the section devoted to tuning methods with the difference that mastering these is very important not to say crucial for selecting an autotuner properly Some industrial products have been presented to illustrate how the concept introduced for classifying and selecting autotuners reflect in the real world Some samp
3. Another possibility not requiring a model is to choose the regulator parameters so that some expected closed loop characteristics computed using the process description which is not a model reflect the user s desires an example of a characteristic is the request that the open loop Nyquist curve contain a prescribed point which is typical of relay based autotuning In this case we have a non model based characteristics following autotuner A third way to construct tuning rules is trying to emulate human reasoning This leads to the so called rule based tuning methods In rule based tuning both the process behaviour and the desired closed loop behaviour descriptions can be in the form of a model or not since human reasoning can be used thus imitated in any case All these approaches involve more or less explicitly solving some system of equations This can be accomplished in many ways from analytical methods to numeric approximations In particular characteristic based tuning can lead to a number of techniques for pursuing its goals including pattern recognition based methods and soft computing It is worth emphasising that the classification we are proposing is slightly different from that commonly adopted in the literature which distinguishes only model based and rule based auto tuning the former is when a process model is involved explicitly the latter when no model is used explicitly and the tuning system tries
4. More complex models If the model must represent complex dynamics it must be correspondingly complex For ex ample some of the responses shown at the beginning of this section apparently call for the presence of zeros In addition it is not always a good practice to use a model with delay if it is physically known that no delay exists thus that the observed dead time is due to high order rational dynamics Approximating such processes with delay models permits surely to achieve the regulator tuning but generally with worse performance than could be obtained Unfortunately for more complex models less general and simple estimation methods exist It is then often necessary to employ numerical parameter optimisation and even scratching the surface of this subject would extend far beyond the scope of this volume However almost any package for engineering mathematics nowadays offers such features included in a rea sonably friendly interface so that identifying a model given its structure is an ability that can be learned with moderate effort 3 1 2 Characteristic based process description Time domain characteristics Time domain characteristics are in synthesis those sketched out in Figure 4 the gain or the presence of an integrator the settling and rise times the overshoot and undershoot and so on naturally completed with the times at which any relevant response fact e g the maximum occurs Apparently all these characteristics are al
5. especially in process con trol which is in some sense the preferred domain of autotuning to be considered not really a structure surrounding a regulator but an extension of the regulator itself This is the Smith predictor used for controlling processes with significant delay and at present offered by sev eral industrial controllers and autotuners The Smith predictor is then presented in the following together with a somehow simplified version of it called the predictive PI which is also offered by several autototuners The aim of this section is not to provide complete theoretical coverage on these extensions rather to make the reader understand their rationale possibilities and pitfalls so as to be able of evaluating the operation of an autotuner encompassing them 2 8 1 The Smith Predictor The Smith predictor has been first proposed in Smith 1957 Since then it has been exten sively applied to the control of processes with significant dead time 1 e when in the process response the delay dominates the rational dynamics The Smith predictor is shown in the scheme of Figure 13 28 Figure 13 the basic scheme of the Smith predictor The rationale is as follows Suppose the process is described by a rational model P s cas caded to a delay L If an almost exact approximation M s of P s and an almost exact estimate Lm of L are available then in the scheme of figure 13 the transfer function from the control
6. formative for knowledgeable users by convincing them that this can make a product more successful e Learning to ask themselves the questions above to seek their answers in the documenta tion and if they are not there to find them by experimenting with the autotuner In fact in the authors experience once the user has clarified to himself what he wants to know on a given autotuner simple experiments with it in a laboratory are enough As a further remark experiments in the field are not always the right way to answer these questions nor to evidence general thus conceptually reusable facts The second need is to gather information on the control relevant process dynamics This task is even more difficult because contrary to steady state information it is necessary that some clue on what are the control relevant dynamics be provided by the user or by the identifica tion In fact the concepts of dominant and control relevant dynamics are often confused by many users and this too leads to poor autotuner utilisation Also in this case we illustrate the idea with an example Consider the process 1 0 5s 1 s Identifying a FOPDT model for it with the method of areas leads to the result depicted on the left in Figure 22 on the right are the results of different PID tuning operations P s Identification method of areas Closed loop load dist step responses 1 2 0 5 0 45 i 0 4 0 35 a IMC A T 0
7. many of the industrial PID controller structures often quoted in the technical literature It is clear that this is an important prerequisite However because of space limitations this section is necessarily brief If the reader feels completely unfamiliar with the content of section 2 then it is recommended that the references identified in the monograph be consulted before addressing the core of the subject Once a firm grasp of PID control basics is achieved Section 3 can be digested This section explains how PID controllers can be tuned on site This introduces the importance of ex perimentation especially when this leads to the derivation of a description of the process be haviour from measured I O data The rationale of Section 3 is to clarify that once a process description has been obtained there are many methods available for determining the PID controller parameters Another important feature is that at the end of this section the reader has all of the information required to tune the PID controller by hand This kind of knowl edge should be invaluable later when assessing the various autotuner functionalities In summary at this stage the reader will have encountered several tuning methods presented so as to be implemented by a human not yet automatically The main goal of this section is to understand the range and variety of the various tuning methods that are available to the prac titioner Section 4 address
8. the PID is essentially due to the prompt response in the first instants which requires a bigger control spike while the settling time increases Closed loop error step response Settling time versus HF loop gain dashed PID t setPl setPID solid and e oO aN SS eS Norm alized time o t HF loop gain dB Figure 25 PI versus PID tuning with ISE minimisation In this case minimising the same index means different things if different controllers are se lected Generalising then we can say that e Optimising integral indexes like the ISE is a good policy for achieving compromise solutions where no tight objective dominates all the others but can sometimes produce unexpected results It must be kept in mind that an optimiser achieves its goal whatever this means and that if one has desires not directly reflected into an index problems like this are quite likely to arise e In general autotuners based on index minimisation and more generally on lexical specs require the user to select the correct index or spec and the correct regulator structure for the problem at hand Index and structure selection is often done automati cally as already discussed but autotuners like these are not the best choice if tight con trol is required 59 4 2 3 Autotuners with numeric specs These al
9. with the body itself and or to heater losses In a very simplified case this means assuming either that the air temperature increases linearly with time or that the temperature of far off air stays constant while that of surrounding air increases due to the exchanges with the body and with far off air These two situations correspond to the models dT 04 C pody Pa Piai K podyair Ty T la To I t agrad and dT cay K T _T body d t heater bodyair body surrair dT C ais ra 7 K poayair Ty E D Kn T urair E T pair Liri Tao Implementing and simulating these two models where the meaning of symbols should be self explanatory in the Simulink environment produces the results depicted in Figure 23 where the first model and its transients are reproduced in the upper half while the lower half is devoted to the second model and to the transients obtained with it It can be easily observed that when the air thermal capacity is bigger than that of the body even if the thermal exchange coefficient from body to surrounding air is larger than that from surrounding air to far off air a quite realistic situation the surrounding air temperature re sponse is slow So slow in fact that in the time scale of the body temperature response it is 55 practically a straight line As a result without quite detailed process knowledge it is appar ently impossible to distinguish one case from the other Tbody sdid and
10. 8 am b IMC A T 10 c IMC 2 T 100 0 6 0 25 AL d one point 3 6 60 5 Process dashed and model solid IMC dashed and one point solid Figure 22 different tuning operations on the same process Setting T 1 74 captures the dominant dynamics well enough However this requires the in troduction of a delay which is not physical Moreover the FOPDT structure hides the ef fect of the zero As a result the cancellation policy of the IMC method will always produce al an integral time larger then needed so that only the gain will be used for opening the band width to achieve good disturbance rejection The gain is however limited by the delay so that even very demanding speed specifications e g A T 100 will not push the obtained re sult beyond a certain limit Notice also the saturation in the achieved performance the 1m provement obtained between A T 10 and A T 100 is smaller than that from A T to A T 10 It is also apparent that in this case tuning with a one point method i e using e g a relay based autotuner can achieve far better results provided one stipulates a good specification in terms of and m Taking some general lessons also from this example then leads to the following statement e Not always do the dominant and control relevant dynamics coincide The latter depend also on what are the control needs The problem is particularly relevant for processes with complex dyna
11. Approximate Reasoning 22 pp 73 91 Hong H P S J Park S J Han K Y Cho Y C Lim J K Park and T G Kim 1992 A Design of Autotuning PID Controller using Fuzzy Logic 1992 Int Conf on Industrial Electronics Control Instrumentation and Automation pp 971 976 Isermann R K H Lachman and D Matko 1992 Adaptive Control Systems Prentice Hall Iwasaki T A Morita and H Maruyama 1993 Fuzzy Autotuning with Model Classifica tion Japanase Journal of Fuzzy Theory and Systems 5 3 pp 435 446 Jones A H and P B Oliveira 1995 Genetic Auto Tuning of PID Controllers Galesia 95 13 pp 141 145 Jones A H and P B Oliveira 2000 Co Evolutionary Design of PID Control Structures Proc IFAC Workshop on Digital Control Past Present and Future of PID Control PID 00 Terrassa E pp 205 213 Kessler C 1958a Das Symmetrische Optimum Teil I in German Regelungstechnik 6 11 pp 395 400 Kessler C 1958b Das Symmetrische Optimum Teil II in German Regelungstechnik 6 12 pp 432 436 Leva A 1993 PID Autotuning Algorithm Based on Relay Feedback IEE Proceedings D 140 5 pp 328 338 Leva A and A M Colombo 1999 Method for Optimising the Set Point Weights in ISA PID Autotuners IEE Proceedings Control Theory and Applications 146 2 pp 37 146 Leva A and A M Colombo 2000 Estimating Model Mismatch Overbounds for the Robust Autotuning of Industrial Regulators Automatic
12. HF conversely the noise N s will be attenuated while the disturbance D s will pass through Recall that in this frequency range L jw 1 hence Soj 1 1 L j 1 and T G L j A L L G e In the boundary area between these frequency ranges i e around the cutoff frequency range MF there is usually some amplification of both noise and disturbance As for the set point its frequency components below the cutoff frequency will pass through on the controlled variable making the error small in that band while those at higher fre quencies will be attenuated allowing a larger error in that band see again figure 9 This 1s by the way another explanation of the connection between cutoff frequency and response speed From these considerations we will now show that performance and robustness speci fications can be given in terms of desired shapes of S j and T j in a very straight forward and expressive way Nominal performance The first issue to deal with is nominal performance which means requesting that in nominal conditions i e without model errors disturbances and uncertainty the error produced by any set point signal belonging to a characterised set be smaller than a prescribed amount One way of characterising such a set is to say that the set point signal has finite energy and that its frequency distribution is quantified by a function W j More precisely this means that the set point signals of
13. Lefebvre 2000 Neural and Adaptive Systems Fundamen tals through Simulations John Wiley amp Sons Rohrs C E J L Melsa and D G Schultz 1993 Linear Control Systems McGraw Hill Ruano A E P J Fleming and D I Jones 1992 A Connectionist Approach to PID Autotun ing IEE Proceedings D 139 3 pp 279 285 Ruano A E and A B Azevedo 1999 B Splines Neural Networks Assisted PID Autotuning International Journal of Adaptive Control amp Signal Processing 13 4 pp 291 307 Sanchez Pena R S and M Sznaier 1998 Robust Systems Theory and Applications John Wiley amp Sons Scattolini R and N Schiavoni 1995 Regolatori PID e Metodi Classici di Taratura in Italian Proc ANIPLA Workshop on Advanced PID Regulators for Industrial Processes Milano 1 82 Smith O J M 1957 Close Control of Loops with Dead Time Chemical Engineering Pro gress 53 pp 217 219 Swiniarski R 1990 Novel Neural Network based Self Tuning PID Controller which uses Pattern Recognition Technique Proc IEEE Automatic Control Conference 3 pp 3023 3024 Takagi T and M Sugeno 1985 Fuzzy Identification of Systems and its Applications to Modelling and Control IEEE Transactions on Systems Man amp Cybernetics 15 1 pp 116 132 Van Doren V J 1997 PC based Control Package Includes Everything Control Engineer ing November 1997 Visioli A 1999 Fuzzy Logic Based Set point Weighting for PID Contr
14. Software Tools There has been an explosion in the number of loop tuning packages designed to facilitate both novice and experienced user A limitation of some of the earlier systems was that con nection between the PC containing the tuning software and the controller relied on an ADC DAC interface card in the PC and knowledge of the controllers communication proto col which was not always easily accessible Some systems also used current clamps that had to be physically connected to the input and output terminals of the controller to provide the necessary tuning information Traditionally each software or application developer was required to write a custom interface to allow data exchanges between the various hardware devices Most modern systems still provide one or both of the above options but much more reliance is placed on exploiting OPC server technology OPC is the standard for plant floor communications between data servers and client applications The OPC specification is a non proprietary technical specification that defines a set of standards based upon Microsoft s OLE COM technology The application of the OPC standard makes process interoperability straightforward by defining a common high performance interface that can be reused by 65 SCADA control and custom client applications Some of the features present in these new tools include Data conditioning prior to modelling outlier and bad data removal Process mo
15. Tair dashed Power unit step Exogenous variation of Tair Cbhody 1 Kbodyair 0 1 Tbody 0 25 Tair 0 25 Tagrad 0 005 Variation of Tair caused by heater Cbhody 1 Kbodyair 0 1 Cair 190 Ksunfar 0 01 Tfarair 25 Tbody 0 25 Tair 0 25 Tbody sdid and Tair dashed Ta2 Figure 23 trends caused by exogenous and endogenous phenomena In the autotuning context detailed process knowledge is seldom available and strictly speak ing assuming its availability is in contradiction with the principle itself of autotuning So the problem is not to understand the reasons of a trend or to distinguish it from the effects of unmodelled dynamics corresponding in the example to the air thermal dynamics if the first model is used rather to recognise the presence of a trend and to eliminate its effects on the identification of the process behaviour description Coming back to the example it should be clear that when controlling the body temperature the relevant dynamics are those of the body These do emerge from the step response but considering the time scale of the body temperature response it seems that no steady state 1s reached So trends may be viewed as another reason why detecting static characteristics may be tricky The effects of absent or incorrect detrending can vary a lot depending on all parts of the autotuner s operation It is important to remember that in any case they must not be
16. and of the model respec tively Note that the feedback signal is the difference Ym I which motivates the method s name in that the regulator the grey blocks contains a model of the process explicitly Note also that the IMC scheme closely resembles that of a Smith predictor In fact the IMC is a generalisation of the Smith and of many other schemes casting them all together in a unified framework The IMC scheme corresponds to a classical 1 d o f feedback one if the regula tor 1s R s FOO 1 F 8 Q s M s and it can be proven that under the hypothesis P s M s it is internally asymptotically sta ble iff M s Q s and F s are asymptotically stable Hence the IMC provides a parameteri sation of all the regulators which stabilise a control system containing a known asymptoti cally stable process Coming to its practical use the IMC synthesis method is a two step procedure all the details omitted here can be found in Morari and Zafiriou 1989 First Q s is determined to optimise the system s response to the reference signal of interest without any robustness considera tion assuming P s M s and with the sole constraint that Q s be asymptotically stable The best policy is to choose Q s as an approximated inverse of M s namely that of its mini mum phase part Then to ensure robustness the low pass IMC filter F s is introduced The structure and the parameters of F s are chosen to achieve a reasonable balance
17. are different types of fuzzy models The most common are the Mamdani fuzzy model Mamdani 1975 whose global structure was described above and the Takagi Sugeno model Takagi and Sugeno 1985 where the consequents are polynomials There are various excellent introductory books in fuzzy systems such as Driankov et al 1993 Evolutionary algorithms are founded on Darwinian principles of evolution of species Dif ferent algorithms follow under this umbrella such as Genetic Algorithms GAs Evolution Strategies and Evolutionary Programming Among these GAs have been since their intro duction by Goldberg Goldberg 1989 the mostly used and actually the only ones used for PID autotuning GAs are a powerful stochastic method for performing global search and op timisation Instead of working with only one solution which is evolved iteration by iteration they employ a population of possible solutions to the problem and it is this popula tion that is evolved over different generations Each particular individual is expressed in a particular genetic code and is assigned a fitness value which describes how well it performs for the problem at hand Evolution is performed by applying genetic operators for the cur rent population These include selection based on the fitness values assigned to the indi viduals within the current population only some of them are selected for propagating its genes for subsequent populations crossover w
18. born in 1939 in Kingston on Thames England His sub sequent life and education was mainly in the North East of England He received a BSc Hons Degree in Electrical and Electronic Engineering in 1963 from the University of Durham and a MSc in Control Engineering from the University of Newcastle in 1996 He is presently Professor of Control Engineering at the University of Sunderland He is a Chartered 7 f Engineer Member of the IEE and Fellow of the Institute of Measurement _ of Control His main research interests include tuning of traditional and predictive control system identification and intelligent instrumentation with particular emphasis on chemical dosing philosophies at clean and dirty water treatment works He also has an interest in the development of tools for the edu cation of undergraduate students He has acted as an editor for a number of special features and his reviewer experience has been very diverse including journals such as the IEE Pro ceedings Control Theory and Applications Simulation Industrial and Engineering Chemis try Research and International Journal of Condition Monitoring and Diagnostic Engineering Management Antonio Ruano was born in 1959 in Espinho Portugal He received the First Degree in Electronic and Telecommunications Engineering from the University of Aveiro Portugal in 1982 the MSc in Electrothecnic Engi neering from the University of Coimbra Portugal in 1989 and the PhD degree in E
19. characteristic The operator only needs to specify the maximum process variable swing allowed by the closed loop system Further it should be noted that this stage may only be required when tuning a process for the first time In subsequent sessions the relay parameters can be entered directly based on previously recorded values AutoTune PI strategy When the autotune in invoked the relay and integrator force the process variable to oscillate with the specified amplitude see figure 30 When the tuning phase is completed as indicated by a flag a PI controller is calculated which will result in a system with the requested level of overshoot Status Tuned Process Variable 174 7 units Controller mode Manual Set point 160 000 Relay parameters Height 1 000 Hyst 0 100 Limit cycle Last P Ave P i Last A Ave A PI parameters 233 462 8 748 0 000 Controller_Output 51 00 z Comms Cycle n a eS ke E Figure 30 CAD software screen dump showing Autotuning in process 70 Evaluation Once the appropriate controller has been selected and tuned the evaluation stage can be im plemented Here the controller is put into automatic mode and if desired a step change can be induced in the set point see figure 31 This as well as each other stage in the tuning cy cle can be logged and saved in a data file to provide a full record of the tuning cycle Tue Oct 28 16 39 24 1997
20. characteristic is compensated for in terms of the others and how minimising an index reflects on the shape of the achieved transients This is particularly true if the regulator structure is selectable as we now show with an ex ample Consider a process described by a delay free first order transfer function If a PI regu lator is tuned for it no matter which synthesis policy is adopted the open loop transfer func tion will be approximated around by L s s If a PID is adopted L s will have a sec ond zero above 1 e it will be approximated by L s 1 sa s where a e 0 1 is the high frequency open loop gain Suppose now that the lexical spec is to minimise the ISE for a step variation of the set point which in the PI and PID cases turn out to be 58 1 ISE edt ISEpp 0 C lf 2 gt Je 20 a 5 OE l a dt _ I 20 1 a _ It is apparent that the ratio between the PI and the PID ISE is 1 a thus the PID appears bet ter in any case It is also apparent however that this ISE improvement is paid in terms of a higher value of the open loop high frequency gain Moreover the bigger this reduction is the longer and closer to the 0 dB axis the plateau of LG after has to be which means poor robustness Coming to the quality of the output transients the situation 1s depicted in Figure 25 where a normalised time t t has been introduced for convenience The ISE reduction provided by
21. configur able Some systems determine it automatically by recording the process output while the control is kept constant If the filter is configurable it must be considered that any identifica tion procedure will identify the process in series with the filter so that an incorrect choice of it may deteriorate the identification results 54 On the basis of considerations similar to those made for outliers it is intuitive that the poten tial negative effects of filtering are more noticeable in model based autotuners and espe cially in those that employ optimisation or prediction based techniques Detrending A process response is said to have a superimposed trend if it is affected by very slow phe nomena lasting more than the dynamics that are relevant to the response itself It is impor tant to note that these phenomena may be completely exogenous or depend at least partially on the possible stimulation given to the process In other words the qualifying aspect of a trend is only the fact of being slow and typically of modest entity not the fact of being ex ogenous To explain this with an example we may consider the response of the temperature of a body to a step in the power of its heater If this response is measured while the temperature of the surrounding air is varying very slowly it will have a trend However the air temperature variation could be mostly exogenous or be also significantly due to the thermal exchange
22. fail and that the absence of detrending is a fairly evident symptom of dumbness Closed loop response to a unit SP step a Closed loop response to a unit SP step b 26 2 26 2 25 8 25 8 25 6 25 6 25 4 25 4 25 2 25 2 25 25 0 20 40 60 80 100 0 2 4 6 8 10 time s time s x 10 Figure 24 closed loop responses with and without detrending To generalise from the example we can easily state that the solution to this problem is to in struct a possible autotuner as follows I know that a steady state must be reached by the step response so when you record it and see it goes asymptotically to a straight line consider this as a steady state because there must be something else I don t care what that acts like moving some base value for the response note that observing the phenomenon from the body that is exactly what happens with the air temperature in both cases So identify the Slope of this trend and use it to subtract a straight line from the response you have that is the response to consider for describing the process because that is the one containing the rele vant phenomena For doing this it suffices to say the process is not integrating which is an information that most advanced autotuners accept and that it is important that the user be able of providing consciously Note that the same could be said if a slowly oscillating trend were observed due say to cyclic climatic variations throughout the experiment
23. interest are all both Fourier and Laplace transformable which implies that the two transforms coincide on the imaginary positive semiaxis and that denot ing these transforms by Y j 21 Y ja lt W go Vo holds Requesting that in nominal conditions any frequency component of the set point signals of interest produce an error frequency component with amplitude in the corresponding unit of measure less than unity simply means imposing that SE W jo S jo lt This condition can also be understood visually by looking at figure 9 and stating that shap ing S jo in the frequency range where any set point signal of interest may have compo nents is a performance specification because the plot of S j expresses how much the fre quency components of the set point are attenuated on the error Of course requesting that the error frequency components amplitude be less than the unity is purely conventional for a tighter constraint on the error it is enough to select a proportionally larger W j It follows then that the designer can specify performance by defining desired the shape of S j Moreover from the definition of S j the previous inequality may be expressed as W j lt l L jo Vo 8 In words this inequality will be satisfied if a circle of radius Wj j centred on the point 1 of the s plane does not include the point L jo for all Equation 8 specifies necessa
24. must be dealt with This makes industrial products adopt in extreme situations one of the three approaches described in the following together with their advantages and potential pitfalls 4 2 1 Autotuners with no specs Such autotuners are extremely simple to use do not aim at particularly sophisticated results but can cope with most problems satisfactorily The only way to make them fail is to use them in a situation where their identification mechanism which is normally very simple can fail significantly like we have shown in the body temperature example Fortunately in prac tical cases this is not a difficult precaution to take on the sole basis of conscious common sense 4 2 2 Autotuners with lexical word specs These products allow more user control in that they accept specs like minimise the over shoot achieve the shortest settling or minimise an index like e g the ISE This normally reflects in characteristic following tuning made by optimisation where the spec dictates the cost function to be used Some autotuners of this kind allow the user to select the regulator structure others choose it on the basis of measured data For these autotuners the identifica tion phase is more critical than in the previous case and that is why more sophisticated tech niques are used It is important to note that this approach is not suited for tight control be cause in general it is not easy to forecast how achieving a
25. on line operation consisted on applying a reference step determining the identification measures using the output or the output and the control signals apply those to the MLPs and finally the PID values to the controller Figure 32 illus trates an example of this method Output oS 45 ao R0 206 250 300 Time seconds Figure 32 results of PID autotuning The plant was allowed to change between steps once the transients related to the previous step had vanished The initial value of the PID parameters was computed from the open loop step response Further PID values were computed from the closed loop step response The following sequence of changes to the plant was investigated e e l l s 1 4 s 05s 1 s 1 0 5841 74 At time 0 the loop was closed and step I was applied to the reference input The transfer function of the plant was S e stl When step II was applied the plant had been changed to S s 1 Since the PID parameters were tuned for the first plant a considerable overshoot is present The plant remains unchanged when step III is applied and better results are obtained since the PID has retuned as a consequence of the observation of the results of the last step In step IV a plant with transfer function of oe s 1 0 5s 1 is assumed The response is now typically overdamped The controller retunes and a faster response is now obtained in step V In step VI the plant had chang
26. problems can be substan tially smoothed by the adoption of standardised procedures in this respect a systematic use of autotuning can be very useful 1 2 3 The process knowledge that can be gathered from the use of autotuning Finally we would like to focus on an often neglected advantage provided not by autotuners directly rather by the adoption of a systematic control system design and maintenance policy where they are used extensively and cleverly Quoting from str m and H gglund 1995 p 232 poor behaviour of a control loop can not always be corrected by tuning the regulator It is absolutely necessary to understand the reason for the poor behaviour Remember no amount of so called intelligence in equipment can replace real 3 process knowledge This can lead to two interpretations First autotuning must be employed with the awareness that invoking it unconditionally every time a loop behaviour is not satisfactory can actually hide process malfunctions For example if an actuator is progressively reaching an unserv iceable condition adapting the regulator over and over can keep the loop inside its operating limits up to the moment when the actuator definitely trips This is by the way one of the major reasons why continuous adaptation features must be used sparingly and wisely On the other hand every autotuning operation gathers process information and is a snapshot of process operating cond
27. the process physical characteristics and limits evidenced by its description In particular specifi cations must take into account what is the control effort required for their satisfaction Speci fications may involve 1 requirements on the controlled variable s behaviour typically expressed in terms of set tling time maximum overshoot response time rejection of disturbances bandwidth and so on 11 requirements on the control variable s behaviour basically aimed at keeping the control energy as low as possible iii requirements on the loop degree of stability and robustness typically in terms of a re p deg y yp y quired phase gain and or magnitude margin iv constraints on the controlled variable e g alarm levels v constraints on the regulator dynamics given by measurement noise which typically calls for reducing the high frequency gain vi constraints on the control variable in terms of value and rate saturations It is worth pointing out that for autotuner designers control specifications are one of the most difficult issues In fact rigorously speaking specifications should take into account not only the process information obtained in a but also the objectives of the tuning and the role of the regulator in the overall control system which cannot be determined from experiments This leads to some important considerations which are relevant not only for designing an autotuner but also for selecting
28. to resort to more complex and or specialised controllers which are not treated in this volume An excellent and far more detailed discussion on the matter of this section can also be found in str m et al 1992 and in the papers quoted therein to which the interested and control theoretically curious reader is referred The discussion starts by defining some dimensionless quantities that can be used for indicating a preferred controller structure and also for predict ing the main characteristics of the closed loop behaviour Though referring to regulators tuned with the closed loop Ziegler Nichols rules this discus sion can be used for drawing first cut conclusions on the preferred controller structure also in the general case provided that the process dynamics can be described by low order models precisely enough It must be kept in mind that in any case these are just first cut rules it 1s in 46 no sense guaranteed that the suggested controller structure is the best one but if an auto tuner allows to choose the structure the one provided by these rules is a good first guess In the following we shall then resume the guidelines given in str m et al 1992 which at the authors experience can be used effectively in all the cases of practical interest The first thing to note in this respect is that user guided controller structure selection is seldom avail able in autotuners but can be very useful if properly employed Fu
29. too complex to be presented here As a consequence autotuners can accept specifications at very different levels of com plexity some do not require them at all some provide the user with basic control e g asking whether a fast or low overshoot tuning is preferred some allow the user to input numeric specifications e g a desired settling time directly In synthesis an important characteristic of an autotuner is the level of specifications control it allows the user to have It must be noted that the validity of user specifications must somehow be checked thus that full control is normally available only on products conceived for complex and or large scale control sys tems where the presence of skilled personnel can be assumed On the other hand tuning a regulator which is part of a more complex control system also requires tackling the problem of loop interactions This has a number of consequences start ing from the fact that one has to decide the order in which loops need tuning For example in cascade control anybody would tune the inner loop first and then the outer with the inner closed such that the outer bandwidth is sufficient for the correct process operation but lower than that required for the inner However such choices clearly require knowledge of the overall control system structure It is then apparent that autotuner designers have to face some very tough problems in making their products usable Quite natural
30. 2 42 e Decide whether rational dynamics dominate the delay or vice versa This can be made e g by computing the normalised delay and assuming the delay as dominant if it is greater than a given threshold one is a good threshold see str m et al 1992 e Ifthe delay is not dominant say if t lt 0 25 set to a fraction of the model time constant e g 1 10 to 1 2 depending on the required acceleration e Ifthe delay is moderately dominant say if 0 25 lt t lt 0 75 set A 1 5 L T e Ifthe delay is definitely dominant consider delay compensation e g with a Smith Pre dictor scheme or with a pPI if possible otherwise choose a greater than in the previ ous cases 3 L T 1s a fairly good first guess It must be noticed that these are only rules of thumb In every practical case performance can be improved by trying different values of in the field For apparent stability reasons this should be made starting with a high 1 e conservative value and then reducing it Optimisation methods There are a number of methods sharing the following simple rationale If the closed loop behaviour must be made similar to that of a given model tune the PID by minimising with respect to its parameters a cost function J containing the difference between the response of the loop forecast with the process model and that of the model to be followed A frequently used function is the ISE 1 e tend 2 J en t E Y mod t
31. 8 0 019 0 76 Bo 8 9 89 52 B 66 66 25 15 17 0283 B 30 30 14 093 069 0 0089 e oso Jos T o o desy Jas L a a ee Ee a a D 081 048 o4 022 033 078 p fon on lois os 25 19 m fio oas 28 oosr a9 2 These coefficients were derived by applying dominant pole design to many different proc esses and then interpolating the results to obtain compact tuning relationships Thus this is a model following method with the peculiarity of using interpolation One important remark is that the normalised delay sometimes called the controllability index can be taken as a measure of how difficult to control a process is 40 The KT method is a very good tool simple to use and suitable for many different situations Also a frequency response version of this method exists The Internal Model Control IMC method The IMC scheme first proposed in Morari and Zafiriou 1989 has found a number of suc cessful applications To briefly explain its rationale consider the block diagram of Figure 19 D s N s Figure 19 IMC block diagram where P s is the transfer function of the process which we assume to be asymptotically sta ble thus excluding integrating processes M s is the process model Q s and F s are as ymptotically stable transfer functions at this stage arbitrary Ym and y are the true measured and nominal controlled variables i e the outputs of the process
32. Honeywell AccuTune This autotuning method described in str m et al 1993 is implemented in several con trollers see e g Honeywell controllers where several powerful devices are described with trend removal capabilities set point programming and so on It can only be used for stable processes It is initiated by setting the controller to manual then driving the controlled variable to a steady state a little away from the set point before switching to automatic This initiates a step experiment where the control step amplitude is calculated but no information is sup plied on how in order to force the process variable back to the set point The experiment leads to a first or second order model the selection is automatic from which the PID pa rameters are computed by convenient rules based on cancellation and influenced by the 62 process order and by the presence of a significant process delay The PID is then set to automatic and once the set point is reached a fine tuning of its parameters is carried out on the basis of steady state levels The user can decide whether tuning must be made only on set point changes or also on transients that are assumed to be caused by load disturbance and which is the minimum set point change that will trigger the tuning Thus the AccuTune is model based with automatic structure selection It also is experiment based and characteristic following it cancels the model poles aim
33. IFAC IFAC PROFESSIONAL BRIEF Hands on PID autotuning a guide to better utilisation A Leva leva elet polimi it Dipartimento di Elettronica e Informazione Politecnico di Milano Italy C Cox chris cox sunderland ac uk Control Systems Centre School of Computing Eng and Technology University of Sunderland UK A Ruano 2tuano ualg pt Centre for Intelligent Systems Faculty of Science amp Technology University of Algarve Portugal Abstract PID regulators are the backbone of most industrial control systems The problem of deter mining their parameters then is of great importance in the professional control domain To simplify this task and reduce the time required for it many PID regulators nowadays incor porate autotuning capabilities i e they are equipped with a mechanism capable of comput ing the correct parameters automatically when the regulator is connected to the field Due to the importance of the problem a very wide variety of PID autotuners have been developed and are currently available on the market This monograph is aimed at control professionals who want to approach the problem of choosing and applying a PID autotuner in a knowledgeable and effective way This goal is pursued by inducing an understanding of the theory of autotuner operation rather than by presenting an exhaustive menu of techniques and commercial products As a consequence this volume does not lead to a mere selection guide but t
34. In this case the user should instruct the autotuner that the process has no oscillatory dynamics and a periodic trend would have to be detected and subtracted To help non specialists advanced autotuners normally do not ask whether the process is in tegrating oscillating or not Instead they adopt the same policy described for model or char acteristics structure selection requesting the user to provide some basic information on the nature of the loop This information can also be used for deciding which aspects of the re sponse used for the identification are probably spurious and correspond to trends that must be removed We can then notice again that for judging an advanced autotuner it 1s important 57 to understand as completely as possible what assumptions on the process dynamics thus on the expected responses it makes depending on the information provided by the user 4 2 Accepting and checking user specifications Contrary to inexperienced intuition this is one of the most important parts of an autotuner Specifications concern stability robustness disturbance rejection and set point tracking The first thing to know in this respect is whether the autotuner exploits the 2 d o f structure of the PID or not because only in the former case can stability robustness and disturbance re jection issues be separated from tracking ones In any case the main problem for autotuners is that possible inconsistent user requests
35. a 36 pp 1855 1861 8 1 Leva A and A M Colombo 2001a Implementation of a Robust PID Autotuner in a Con trol Design Environment Transactions of the Institute of Measurement and Control 1 pp 1 20 Leva A and A M Colombo 2001b JIMC based Synthesis of the Feedback Block of ISA PID Regulators Proc ECC 2001 Porto P Lima J M and A E Ruano 2000 Neuro Genetic PID Autotuning Time Invariant Case IMACS Journal of Mathematics and Computers in Simulation 51 pp 287 300 Lightboby G and G Irwin 1991 Neural Networks for Nonlinear Adaptive Control Proc 1 IFAC Conference on Algorithms and Architectures for Real Time Systems Mamdani E H and S Assilian 1975 An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller Int J of Man Machine Studies pp 1 13 Morari M and E Zafiriou 1989 Robust Process Control Prentice Hall Nishikawa Y Sannomiya N Ohta T and Tanaka H 1984 A Method for Auto tuning of PID Control Parameters Automatica 20 3 pp 321 32 Omatu S M Khalid and R Yusof 1995 Neuro Control and their Applications Springer Verlag Omatu S T Fujinaka Y Kishida and M Yoshioka 1999 Self Tuning Neuro PID for SIMO systems Proc European Control Conference in CD Rom Pfeiffer B M and R Isermann 1994 Self Tuning of Classical Controllers with Fuzzy Logic Mathematics and Computers in Simulation 37 pp 101 110 Principe J N Euliano and W
36. actical applications this is common only when a model has to be identified by parameter optimisation techniques see later Fi nally several experiment based autotuners use the so called relay identification As will be explained later almost any stable process subject to relay feedback enters a permanent oscil latory state from which some characteristics in the time or especially in the frequency do main are straightforward to obtain Relay feedback has the important feature that it does not require one to open the loop which makes it particularly useful in some applications 31 3 1 1 Model based process description In the great majority of process loops applying a step to the control variable causes the con trolled variable to reach a steady state and does not provoke an instantaneous variation of it This means that the process model seen by the regulator can be described by an asymptoti cally stable strictly proper transfer function In a few loops a control step causes the con trolled variable to asymptotically assume a ramp like behaviour this case is commonly re ferred to as runaway integrating or non self regulating processes and can be described by models with a pole at the origin of the s plane These facts are in good accordance with experience since any practitioner would classify the step responses he may encounter more or less as depicted in Figure 15 Other cases e g an oscillatory response w
37. acts and the knowledgeable user must be able of understanding if these facts are the right ones to learn about for solving his problem In the great majority of cases where the authors have seen autotuners not behav ing satisfactorily some wrong assumptions in this respect had been made when selecting the autotuners themselves Second when thinking of how an autotuner obtains the description of the process behaviour users tend to focus their attention primarily on what it does to the process and to worry mostly about the required perturbations This is important but is not the only aspect it is equally important to figure out what it learns about the process and to discriminate whether the information learned are enough and adequate for solving the control problem In other words first one has to worry about what the autotuner must know then select one that learns what is required with the minimum process upset doing the reverse i e limiting the accepted upset a priori is keen to limit the achievable results and in the authors knowledge it is another very frequent flaw in control systems design involving the use of autotuners Third one of the reasons why a skilled human can outperform any autotuner is that gathering process information and converting it into a description of the process behaviour automati cally is a very difficult task Any human looking at any response can learn much more than any automatic system This m
38. amics are From now on to simplify the presentation we shall employ the simplified scheme of figure 1 instead of figure 8 and almost always refrain from analysing the effects of disturbance and noise and the difference between the real and apparent error Nevertheless we strongly encourage readers to become familiar with the subject of the preceding sections and to em ploy this knowledge for evaluating the results of tuning operations or at least of critical ones In fact if the results obtained with a given autotuner have not been satisfactory it is always a good idea to examine these results with the analysis methods presented 2 Realistic PID Structures str m and H gglund 1995 have covered PID control in great detail They have explored different algorithms besides the ideal control law 2 provided detailed solutions to the inte gral wind up problem and looked in some depth at several important operational scenarios This brief section is simply intended to introduce three important themes that will be rele vant in different parts of this book Here we shall briefly concentrate on antiwindup con troller properness and set point weighting 2 1 Antiwindup It is perhaps unrealistic to assume that the system actuator will never ever hit an end stop One possible effect of such a constraint on the PID controller is that the integrator may wind up and produce a very large signal usually leading to poor dynamic system p
39. antifying the response of the final closed loop control system 2 2 Controller Modes The PID control law computes the control signal as the sum of three contributions which are termed the Proportional P Integral 1 and Derivative D actions Quite often the P I and D actions are also referred to as control ler modes Figure 1 generic PID control scheme Throughout the volume we shall refer to the generic PID control scheme of Figure 1 Here y is the reference signal u is the control signal and is assumed to be limited by two bounds Umin and Umax y is the controlled variable Ym is the measurement of it fed back to the PID regula 10 tor d and n a are a disturbance and a measurement noise respectively Note that in a real control system there are usually more than two sources of disturbances and noise However for our purpose it is effective to classify all of them in the two categories suggested by figure 1 More precisely then we can state the following e There are disturbances that do not make y differ from y These include all the actions on y not y other than the control signal u thus correspond to physical actions on the system and not to phenomena that just affect measurements For analysis and synthesis purposes all these disturbances can be treated as output disturbances 1 e as d in figure 1 For example if the process is described by a transfer function P s a load disturbance i e an additive
40. arning rate employed for the PID network 4 and the ITAE network A were 0 02 and 0 5 respectively and the green symbols the case where 0 05 and 0 2 D eee 4 4 4 Ny 1 6 K Se Sk 15 yY 4 f 124 Kok RRR PREPS J 1 3 H Pekk E Pee eee 1 254 1 1 l l l l 0 10 20 30 40 50 60 70 80 90 100 iterations Figure 33 On line performance of the PID autotuner It can be seen that the ITAE is converging to its optimal value indicated by the three solid lines each one for each plant in the figure 7 3 Fuzzy Logic approaches to PID autotuning There are a significant number of contributions related with fuzzy PI or PID like controllers which will not be mentioned here As in the neural network approaches most of the applica tions focus in adaptive PID control The interested reader can consult for instance the works of Zhao et al 1993 Pfeiffer and Isermann 1994 Visioli 1999 Visioli 2001 the LabVIEW PID Control Toolset User Manual and a commercial controller Honeywe
41. ation point minimally affects the information stored for the whole application domain and can be interpreted as fuzzy systems Fuzzy systems were first introduced by Zadeh Zadeh 1965 as a means for handling and processing vague linguistic information as humans do It allows variables to be partial members of a particular set and uses generalisation of conventional Boolean algebra to ma nipulate this information Fuzzy information is represented by a set of fuzzy rules IF x is Ai AND AND x is Ai THEN yis B c The terms A are linguistic variables which represent vague terms such as small medium or large defined on the input and output variables Each rule maps the antecedent formed by the intersection of the n univariate linguistic statements 1S Ai to the consequent formed by a single univariate linguistic statement yis B Associated with is rule is a variable c which describes the confidence in the particular rule being true To implement 12 a fuzzy algorithm the fuzzy sets need to be defined and the functions used to implement the fuzzy operators chosen To be used in the real world a numerical crisp value needs to be fuzzified i e the degree of membership of each of the linguistic fuzzy sets needs to be calcu lated and on the other hand a real valued output is obtained by defuzzifying the fuzzy out put set which is formed from the contributions of each fuzzy rule There
42. atisfied if a circle of radius W j centred on the point L j of the s plane does not include the point 1 for all see again Doyle et al 1992 for a complete discus sion Robust performance The result of equations 8 and 10 can be combined to yield e g W j S Jo W G T Go lt 1 Vo If this is satisfied it is guaranteed that the system achieves the required performance under nominal conditions expressed with W jq and that stability is preserved for any model un certainty or perturbation not exceeding the limits expressed by W j It must be noted that the problem of combining equations 8 and 10 is far more complex than the very simplis tic sketch presented herein see Doyle et al 1992 once again Nevertheless this is the prac tical condition usually specified for robust performance of SISO systems This condition can be expressed graphically requiring that the two discs in figure 10 do not intersect for all 23 R W 9 Figure 10 assessing robust performance on the basis of S j and T jo 2 6 Concluding remarks on stability performance and robustness assessment It should now be apparent that the problem of assessing the stability performance and ro bustness characteristics of a control system has been continually evolving since its first in tuitive setting in the time domain and also since the introduction of the stability and per formance indexes in the frequency doma
43. between robust stability and performance For simplicity F s is often chosen of the first order and of course with unity gain 1 e 4 l F s s l str Parameter can be interpreted as the closed loop time constant of the control system if P s M s and if P s is minimum phase More in general it can be thought as the dominant closed loop time constant In any case is the design parameter of the method which deter mines the control system bandwidth and degree of robustness Being in the ideal case T s F s Q s M s the IMC is a model following method trying roughly speaking to can cel M s with Q s so as to impose the closed loop dynamics F s Applying the IMC approach to PID tuning is very straightforward Here we present a modi fied version Leva and Colombo 2001b of the original IMC PID method reported in Morari and Zafiriou 1989 This method computes the parameters of the 2 d o f ISA PID 11 apart from the weights b and c but including N which can improve the sensitivity see Leva and Colombo 2001b for a discussion If the objective is disturbance and noise rejec tion then this method does all the job If also set point tracking is an issue several methods exist for computing the weights which do not interact with stability and disturbance rejec tion as discussed One such method is proposed in Leva and Colombo 1999 but also computing them with the simpler KT formula has proven to be sati
44. cessively or lead ing it to the stability boundary as required e g by the closed loop Ziegler Nichols method treated later on Finally a step experiment lasts as long as the process takes to settle thus it is one of the shortest ways of getting all the required information In some cases the step is applied in closed loop to the set point or to the control signal but this requires that a regulator be already present Hence this is only used for refining an exist ing tuning or in autotuners with a pretune mode Closed loop step experiments clearly pro vide a description of the closed loop system That of the process must be obtained from it which is a nontrivial task and is not treated in this work For a more extensive discussion in cluding closed loop identification frequency domain methods and so on the reader can refer to str m and H gglund 1995 and to the references given therein particularly in the bibli ography of chapter 2 Step experiments are very common both in model based autotuners because it is straight forward to identify a model on the basis of a step response record and in characteristic based ones since several interesting features of the process dynamics emerge clearly from some features of the step response such as the apparent delay the settling time and so on Another widely used method for stimulating the process is the use of random like signals e g a PRBS Pseudo Random Binary Sequence In pr
45. consid ered a marginal aspect Suppose for example that in the simple case described a PI had to be tuned from a first order model that the time constant T of this model be computed as 1 5 of the measured settling time that its gain u be obtained from the steady state value of the step response and that tuning be made by pole zero cancellation so that the closed loop set tling time is equal to half the measured open loop one This implies that T T and K 2 u Note that this is a quite crude procedure but especially for very low end products it is not so far from reality In the example which is deliberately extreme the response of the body temperature in the second more realistic model settles when that of the air temperature does in approximately 1 2 10 seconds The amplitude of the corresponding transient of the body temperature is ap 56 proximately 110 degrees This means u 110 and T 24000 while the detrended response of the body temperature provides approximately u 12 and T 10 Denoting with a the PI con troller tuned with the detrended response and with b the other the closed loop responses to a unit set point step are shown in Figure 24 notice the different time scales Apparently the PI b regulates the wrong dynamics but if nobody has told it what are the relevant ones it can only do what it has been tuned for Realistic cases are not so extreme but it should be clear that a dumb tuning policy can easily
46. d by the control ler manufacturers The second explores some of the new software environments that gener ally offer analysis and diagnostics as well as loop tuning capabilities In either case the lists are not extensive but simply represent examples typical of those likely to be encountered by practicing control engineers An excellent review of the loop tuning tools available about five years ago was presented in an article in the November issue of Control Engineering VanDoren 1997 This section complements that article and also provides web site details of the controllers and tuning en vironments cited for those readers who wish to obtain more information 5 1 Controllers with built in tuning capability 5 1 1 The Foxboro EXACT In this historical autotuner Bristol 1986 the tuning operation is initiated automatically whenever the error exceeds a user specified threshold When this occurs it is assumed that either a set point change or a disturbance might have occurred In both of these cases the er ror transient may resemble that of Figure 26 a and b respectively Heuristic logic de tails are not published is used to decide whether a proper transient has occurred and to compute the peaks e e2 and e by means of pattern recognition techniques 6l Figure 26 examples of error transients for a a set point change and b a load disturbance Tuning is completed once specified values of damp
47. d for automating the PID synthesis Their rationale is to impose a decay ratio of 0 25 to the set point step response assuming that the process can be very roughly described by an integrator plus a time delay at least in the band of interest As such this is a characteristics following method Ziegler and Nichols proposed some for mulae for computing the PID parameters on the basis of characteristic values of either the process open loop step response or the sustained oscillation induced by a proportional regu lator of convenient gain The first method consists in determining the quantities a and b based on an open loop step response record as depicted in figure 20 tangent in the point of maximum slope Figure 20 the Ziegler Nichols method Then the PI D parameters can be computed from the following table P Ma O L Pi 09a 3b The second method requires to apply proportional control and increase the controller gain until the process output reaches a sustained oscillation Denoting with T the period of the oscillation and with K the regulator gain yielding it the PI D parameter are computed as 44 Po fOSKy S o PIE OAK 08T PID Relay based methods A number of methods exist for PID tuning that are termed this way because they use the typical information provided by a relay experiment i e one or more point of the process Ny quist curve As such they are all characteristics based methods and in the g
48. del derivation transfer function or frequency response PID controller design including a empirical look up table b str m H gglund c IMC and d optimal methods Performance checking through system simulation Robustness analysis Looking simultaneously at more than one loop Process diagnosis to detect a hysteresis b stiction c oversized undersized valves d excessive measurement noise e need for gain scheduling What if simulations Report preparation facilities Lots of excellent graphics support Because of space restrictions the intention is to identify some of the more well known prod ucts by their web site addresses and this information is tabulated below At these sites a con siderable amount of information is available plus downloads of the software Tune Wizard www tunewizard com SS ae Mina RaPID www mathworks com PROTUNE www protuner com Complete software hardware system that records troubleshoots and analyses dynamic data EXPERTUNE www expertune com PID tuning analysis and simulation software or 169 207 153 173 Control Arts Inc www controlartsinc com Model Identification and PID tuning software Rockwell Software www software rockwell com ee O O BESTune bestune 50megs com O Poceo OOOO O e 66 6 Some samples of the current research How advanced autotuning concepts are put into operation This section is aimed at presenting some research autotuners taken basically f
49. der rational dynamics causes the estimation of a larger delay which can deteriorate the subsequent tuning results SOPDT models of the type 16 can be identified from the step response in several ways The simplest one is to determine u as in the FOPDT case then L as the intercept on the time axis of the tangent drawn from the unit step response in the maximum slope point Finally the remaining parameters T and T are computed by fitting two points of the model unit step response whose expression with T gt T gt is tL _tL T T T u t Tae DeL to the measured response recall that at this stage u and L are known This must be done numerically but is not a complex task Traditionally the two points used for the fitting are the ones where the measured response reaches 33 and 67 of its final value For oscillatory responses that cannot be described well enough by FOPDT models 1 e when the oscillation is evident and cannot be confused with a moderate overshoot models in the form 17 are to be used To identify them it is necessary to measure the period T of the os cillation and the first two peaks a and a as indicated in figure 17 u is to be determined as above By the way the presence of a visible second peak is a good clue for suggesting that this is the right model to use time Figure 17 estimating second order oscillatory models Once these quantities are available the remaining parameters of the model are com
50. dominance of tracking or rejection degree of nonlinearity and so on In particular identify loops that require gain or parameter scheduling because performing several auto tuning operations in different conditions is one of the most efficient ways for selecting the scheduling characteristics e Find out the really critical ones taking into account also past process experience Con centrate efforts on these since for the others the choice of the autotuner will not be cru cial This means that for non critical loops regulators can be chosen in any other way and the autotuner they encompass if any can be used without worrying particularly of its characteristics e Identify who will use the autotuners for the critical loops which provides information on what level of knowledge the autotuners to be chosen can or cannot require on the part of the user e At this point all the information is available for choosing the best autotuning policies for all the critical loops with the guidelines provided along this volume plenty of product information and the consciousness required for interpreting it e If this choice appears to call for adopting too many different types of product figure out the cost of system complexity versus performance and flexibility This means pondering whether adopting the same product for two different problems one more suited for it than the other is likely to produce so big a performance loss to make the added com p
51. e amount of overshoot the closed loop system will exhibit when compensated by the tuned PI controller The percentage overshoot is used to determine the phase margin required by the design equations e The relay characteristics the amplitude to control the size of the limit cycle oscillations during tuning and the hysteresis used to prevent false switching caused by noisy sig nals e Tolerance between peaks used by the software to detect when the tuning phase has been completed e Constraints control over the allowable level variations of both the process and manipu lated variables The process analysis phase is the preliminary step of the tuning procedure Here an open loop step test is conducted and a FOPDT model automatically calculated using the character istic area method Nishikawa et al 1984 The process inputs and outputs are visually dis played to the process operator throughout this phase On completion of the test the model is overlaid onto the process reaction curve allowing an informed judgement to be made about the quality of the model figure 29 Process Wariahble 5 00 10 00 15 00 20 00 25 00 30 00 35 00 40 00 Time tsecss Estimated process paraneters Gain 3 299 Tau 3 8555 Dead time 3 381is Recommended relay paraneters hysteresis 1 005 height 2 991 Predictive PI settings Hp 325 916 Ti 3 8555 Est cycle period 31 270 Figure 29 typical process analysis result PI QuickTune If th
52. e associated documentation and establish when tuning occurs and how it is initiated Under this point of view we shall distinguish four cases 1 Tuning is initiated by the user as a deliberate decision either explicitly or by making some manoeuvre which the documentation states to initiate a tuning e g turning up power or modifying the set point If this is the case it is important that the connection between the manoeuvre and the tuning phase can be broken if desired 1 e for example that the tune when set point is changed option can be disabled in the regulator con figuration and inhibited temporarily with some signal from outside the regulator to pre vent e g that necessary plant manoeuvres cause two interacting loops to begin a tuning operation together 2 Tuning is initiated by the user as a deliberate decision but the regulator can suggest a retune If this is the case it is important that the suggestion logic be documented and configurable 3 Tuning occurs automatically when some condition occurs e g the error becomes too big for a certain time If this is the case it is even more important that the logic be precisely documented and configurable Moreover it must be possible to disable this functionality in the regulator configuration and to inhibit it temporarily from outside the regulator 4 Tuning occurs continuously Cases 1 and 2 are to be classified as autotuning case 4 is clearly c
53. e data for obtaining the process model An extremely wide variety of model types are used in autotuning ranging from state space models to transfer functions convolution models stochastic models up to neural networks and so on To clarify the panorama then we can say that in the autotuning context a model is something that can be simulated and in so doing reproduces the process data it has be drawn from with sufficient accuracy so that it can be expected to cap ture the process behaviour precisely enough to allow forecasting that of the closed loop once the regulator is tuned In this case we have a model based autotuner The other approach is to employ the process data immediately for the subsequent tuning In this case we have a non model based auto tuner Also in the non model based case a wide variety of process descriptions are used points of the Nyquist curve points or characteristic values of some relevant responses in the time domain e g the static gain overshoot and settling time of the step response and so forth In our description the relevant fact is that these various representations cannot be simulated Non model based autotuners can also be termed characteristics based autotuners 1 1 2 The way specifications are accepted or produced Step b corresponds to agreeing the control specifications Clearly these can depend on what has been observed in a in that a given requirement can be realistic or not depending on
54. e time delay is not appreciable in relation to the time constant the software recommends that a PI controller be used This fast tune facility uses the transfer function obtained in the process analysis phase to calculate the controller settings using some empirical formula typically those recommended by Cox et al 1997 reference This feature can be used to es tablish a satisfactorily tuned control loop in a very short period of time relevant of course to the dynamics of the process 69 Predictive PI pPI If the time delay is large compared to the principal time constant then a PI controller will not be able to yield satisfactory performance In this situation the software recommends that the pPI strategy is used and calculates the controller parameters For implementation of the pPI algorithm it is recommended to use a programmable process controller Setting the relay characteristics If as recommended the fast tune procedure is by passed in favour of relay feedback autotun ing then the relay characteristics must be set The process analysis phase calculates a value for the relay height that will produce a limit cycle with an amplitude approximately equal to that set in the Set test parameters phase above Additionally the software will analyse the level of noise imposed on the process variable and use this value to suggest a level of hys teresis This stage relieves the process operator of the task of specifying the relay
55. eans that for evaluating an autotuner it is very important to see how rich flexible and possibly configurable the process description employed is Of course all these considerations apply to complex problems and where tight control is re quired There is no need to say that these cases are a minority and that in all the others al most any autotuner can do a decent job In other words the examples presented herein should not make the reader think that autotuners need an amount of human effort comparable to that required for tuning the regulators manually We are discussing these problems be cause the aim of this section is to identify difficult cases explain why they are difficult i e when and why the way an autotuner is selected and used may be critical and giving clues for solving them In this respect we can conclude that no process description is always good so that if an autotuner does not work properly also the identification phase and not only the specs or the tuning method must be diagnosed 4 1 2 Improving the accuracy in obtaining the process description On line outlier removal During the identification phase spurious phenomena may affect the measurements This must be counteracted somehow otherwise any process description may be erratic To give a scheme we can distinguish two main cases fast phenomena spoiling only a few samples and 53 slower phenomena acting for a time comparable with the process dynamics T
56. ection have been dealt with in the synthesis of Ra s b and c can be safely used for improving the set point tracking The ISA form is a good structure for considering N b and c as true regulator parameters and for taking profit from them in the synthesis phase This is a quite modern issue but some autotuners do start reasoning this way At present there is considerable research effort on this and other associated matters As a final remark note that the presence of the set point weights in the ISA PID can also be interpreted as a very specialised form of feedforward compensation because the scheme of figure 11 can also be drawn as 2l Ym S Figure 12 set point weighting viewed as feedforward compensation where 1 sT N b i Cels Ra S Ra s 1 K b 1 1 sT N 13 2 8 Two widely used extensions of the PID controller As anticipated many controllers are not applied to processes alone On the contrary these controllers are assembled to form more complex structures like cascade control feedfor ward feedback schemes and so forth In this volume there is not the space for treating con trol structures though this is a very important subject deeply connected with the recent re search on autotuning for a detailed discussion the interested reader can refer to str m and H gglund 1995 and to the bibliography given therein Nevertheless at least one control structure has become so popular
57. ed to 1 s 1 0 5s 1 and an oscillatory response is obtained The controller is again retuned for step VII and again a better response was achieved This approach has been subsequently refined in order improve its performance as a result of on line operation In the previous approach the neural networks were only trained off line their weights remaining fixed subsequently In Ruano and Azevedo 1999 an additional neural network the criterion network was incorporated to capture the mapping between the identification measures and the PID parameters to the performance criterion the ITAE As this criterion can be computed on line this neural network can be adapted on line therefore improving its knowledge about the system as a result of on line operation This enables to adapt the original neural networks PID networks responsible for delivering the parameters to the PID controllers using the optimal PID values resulting from an on line optimisation using the criterion network to supply estimates of the ITAE criterion as function of the PID parameters In this approach due to their useful properties for on line adaptation B spline networks are used Figure 33 illustrates the performance of the auto tuner when the plant time delay here a FOPDT plant is considered changes between 1 0 1 05 1 1 1 05 1 0 The transitions occur at every 10 reference step The purple symbols indicate the case where the le
58. ence as steady state is approached since at this point it is the I action that dominates Then if b 1 the P action is nonzero at steady state since there y y Finally since b can limit control bumps it is particularly useful in the inner loops of cascade controls where the set point is not under direct operator control Parameter b is sel dom considered in practice several regulators do not encompass it while others just permit one to select for it a value of 0 or of 1 Some advanced tuning techniques make use of b Set point weighing in the D mode means that the derivative action is computed as skT est No Y s U s where c is a further parameter whose role is to limit the control spike that may arise as a con sequence of an error step also with a proper controller Here too some remarks are useful Since in general y is seldom modified especially in process applications setting c 0 does not modify the controlled system dynamics significantly In fact c influences only the few instants when y varies because when it is constant its derivative is zero and computing the D action by deriving e or y is the same Clearly this does not hold e g for the inner loops of cascade controls or whenever y may vary continuously Some advanced tuning techniques use c Most often however it is set to zero leading to the so called output derivation PID 2 7 4 The ISA PID A number of PID structures have been propo
59. ency in order to follow the set point and reject disturbances then intro duce strong attenuation to prevent high frequency measurement noise from upsetting the system It is clear that frequency domain assessment can be used in model following autotuners the desired closed loop description being in this case a desired L jm Figure 7 has also sketched how it can be used in characteristics following autotuners since the desired characteristics can be turned into features of a desired L In any case this approach requires a process model unless the decision is taken to assess the desired characteristics of L j on the basis of some conveniently measured points of its Nyquist diagram this is typical of relay based tuning 2 5 Modern design issues and the accommodation of plant uncertainty Up to now it has been assumed that the process under control is perfectly described by a lin ear time invariant model In the real world this is rarely not to say never the case The process model will only ap proximately capture the real plant behaviour because of time variances nonlinearities un modelled dynamics sensor noise and unpredictable disturbances Doyle et al 1992 Rohrs et al 1993 Goodwin et al 2001 str m and H gglund 2000 For these reasons we must be aware of how modelling errors will influence the process description and then of course the performance of the closed loop control system These ideas have
60. ents then as y approaches y it tends to vanish unless set point weighting is used in it see later on 2 2 2 Integral Mode Integral or reset action produces a controller output that is proportional to the accumulated error The control law in this case is given by u felt u 0 4 where T is the integral or reset time constant and u 0 is the value of the controller output when t 0 Note that u also depends on the controller gain Because u is proportional to the sum of the system errors integral action is referred to as a slow mode str m and H g glund 1995 point out that integral action can also be viewed as a device that automatically resets the bias term u of a proportional controller This follows immediately by considering that at steady state with y y the P action is zero except for uy In other words the I action guarantees zero steady state error because whenever e is the input of an integrator there cannot be any steady state if e 1s nonzero The I action does not vanish with e on the contrary if e remains constant it varies linearly obeying to the principle that if y does not start moving towards y the control action ex erted must become stronger and stronger Thus the I action does not consider only the pre sent e but also its past history and that is another way of explaining how it provides the re set Note that at any steady state with y y the control will be made only o
61. erform ance The remedy is that the I action must never be allowed to exceed the control saturation limits This is the basic principle of antitwindup which can be implemented in several ways a complete discussion would not fit in this volume It is in any case a nonlinear regulator feature that is why it is seldom considered in autotuning being in general sufficient to rely on the antiwindup mechanism of the underlying regulator however it is implemented 25 2 2 Controller properness Another issue is that the D part of the PID controller in the ideal form 1 is not proper To overcome this it is commonly implemented as Up s E s sT N This is often referred to as using a real derivator In this way N becomes another parameter of the PID that has to be selected It is worth noting that a high N makes the implementation of the D action similar to a true derivative but it also increases the high frequency gain thus increasing noise sensitivity 2 7 3 Set point weighting in the P and D modes Set point weighting in the P mode means that the proportional action is computed as U s K bY s Y s where b is a further parameter whose role is to limit the control step that may arise as a con sequence of an error step An error step in turn is most likely to arise as a consequence of a set point step since the process response is rarely instantaneous Some remarks are now in order First b has practically no influ
62. es the problems that arise when the tuning is automated and briefly de scribes some of the solutions that are commonly exploited in industrial applications The im portance of obtaining steady state information is emphasised together with the need for sig nal conditioning to improve the accuracy of the process description The expectation is that the understanding gained from this section should lead to a more informed choice if the reader has to select a particular system The focus of Section 5 is a short presentation of a sample of industrial autotuners This re view is not meant to be exhaustive reference to product documentation is given when re quired but rather to illustrate how the autotuner features previously considered and the pro posed classification reflect in the real world If the goal of the monograph has been attained the reader should now be capable of reading a product description and understand the advan tages and disadvantages of that configuration when it is to be applied in a particular situa tion Sections 6 and 7 are devoted to brief descriptions of some research autotuners chosen to illustrate the authors experience Section 6 refers to research on classical autotuning while section 7 deals with the very promising alternative provided by the use of soft computing The purpose of Section 8 1s to provide a summary of the steps covered in the earlier sec tions that leads to a route map that s
63. est and that of the permanent oscillation are made by the user This type of interactivity where human insight is employed for decisions that are particularly difficult to automate seems to be a trend in new autotuners It can lead to good results but requires at least a minimum of in sight The second feature is that both for the controller and for the autotuner the source code in the G graphical programming language is visible This means that a conscious user can in spect it and learn a lot about the autotuner s operation see the LabVIEW PID Control Tool set User Manual 64 5 1 7 Additional Controller Information The following table reports a short and in no sense exhaustive list of other controllers with autotuning and or adaptation capabilities together with the web sites where additional in formation can be obtained ECA 600 http www abb com 1 16 DIN Athena http www athenacontrols com pages tempproc html Universal Process Controller ee ee Babcock intial ff tee Controllers rotherm Series 2000 FGH PID e e horeo OOOO Ns eee ee htt TEE RER com m amp i controllers_recorders s pecs_controllers htm htm PPS eae Ultra ll lem FP fo a orthrup http www omronsupport net knowhow NLS omronsupport net knowhow Eco Toshiba Pm e e tpufanwwcte toshibacom SLPC Sake po E E gawa Gain Scheduling a AutoTuning Ad Adaptation FF FeedForward 5 2 Independent
64. f I action unless 13 set point weighting is used see later The I action is slower in responding to e and cannot have abrupt variations being the state of an integrator However it plays a crucial role in governing the way steady states are reached 2 2 3 Derivative Mode The final mode is the derivative or rate action Here the control is proportional to the rate of change of the error signal It follows that whenever the error signal is constant the deriva tive signal contributes zero The control law in this case is given by de t up t KT dt 5 Where T is the derivative or rate time constant Problems may arise when the error signal is entrenched in high frequency noise or when step changes in the set point occur since in these cases derivative action will generate large amplitude signals However most real sys tems have simple fixes to limit any harmful effects a priori such as imposing that the D action cannot provide more than a specified percentage of the overall control u Derivative action is referred to as a fast mode that generally improves the loop stability It is often said that the D action anticipates the future This is another way of saying that it makes u de pend on the direction and speed of the variations of e In fact with reference to Figure 3 it can be stated that the D action depends on the forecast variation of e Ta ahead Ta then de termines how far in the future
65. f figure 13 M s being the model used for the tuning and L the delay estimate The main pitfall of this approach is that the model must be more accurate than normally required for model based tuning of standard PID regulators 2 8 2 The Predictive PI pPI A specialised version of the Smith predictor is even more widely employed in process con trol applications Recalling the definition of Rg s in 12 the 1 d o f pPI regulator in its simplest form is given by Sl 1 U s Khi tro Y s l l e Jus 14 29 where Lm is an estimate of the process delay This is a specialisation of the scheme in figure 13 with R s K 1 1 sT 1 e a PI and M s 1 sT The pPI can also be interpreted as a stan dard PI the first term in 14 plus a correction based on the effects of the control action that have not yet appeared on the controlled variable due to the process delay The resulting regulator block diagram is shown in Figure 14 Notice the similarity with the standard PI sLm that corresponds to the same scheme replacing the term e with the unity s Figure 14 the basic scheme of the predictive PI pPI Many variations of the pPI have been proposed see e g str m and H gglund 1995 For our purposes it suffices to say that this scheme is a less powerful but also less critical and easier to tune with commonly available process data declination of the Smith predictor idea often available in ind
66. h plant uncertainty The frequency domain design of robust feedback control systems involves fitting some con veniently chosen frequency responses to constraints derived from specifications and from some quantification of uncertainty and model errors To this end the functions S s and T s defined in 7 play an important role Let us have a look at them under this perspective assuming that both P s and L s have a low pass aspect and considering for simplicity the 1 d o f case 1 e Re s 1 With these hypotheses in nominal conditions the transfer function from Y s to the true er ror E s is S s that from D s to E s is S s and that from N s to E s is T s More over the transfer function from Y s to Y s is T s that from D s to Y s is S s and that from N s to Y s is T s see 6 and figure 8 Generalising the facts stated when talking about Bode diagrams see figure 7 three fre quency ranges of importance emerge as shown in Figure 9 20 dB Range MF Range LF Range HF IT Go IS Go Figure 9 important ranges in frequency domain design e At low frequencies range LF the disturbance D s will be attenuated while the noise N s will pass through on the controlled variable thus on the error with no attenuation Recall that in this frequency range L j 1 hence S j 1 1 L Q 1 L Q and T j L j 1 L j 1 e At high frequencies range
67. he form of the transfer function P s while R s is the transfer function of the PID regulator which is considered linear as well Moreover the regulator input is the apparent error This means that the regulator has one degree of freedom 1 d o f in that the transfer functions from Y s to U s and from Y s to U s differ only by sign so it is not possible to specify how the control will react to a set point change and to a measurement change i e for example to a disturbance separately Such regulators are frequently termed error input in the profes sional literature Y S N s Figure 2 generic linear 1 d o f PID feedback control scheme In the simplest PID regulator the control signal is then computed as de t t u t K e t K e t dt K or equivalently and with a more common notation as l de t u t KI e t e t dt T 1 t CORE 2 1 which corresponds when expressed in the form of the transfer function from e to u to l R p s Khi Ta 2 sT and is frequently termed the ideal PID 2 2 1 Proportional Mode The mode that is almost universally present is the proportional or P mode With reference to 1 then the control law in this case is given by u t Ke t u 3 12 where up t is the proportional controller output 1 e the P action itself K is the controller gain and w is a bias or reset value The P action makes the control propo
68. he former case is the typical effect of noise or transmission flaws the second may also occur when some other manoeuvre is made on the process during a tuning operation Of course the distinction between fast and slow is relative but in the majority of practical case it is quite easy to distinguish the possible sources of outliers and to classify them in these two categories We shall refer to them as instantaneous and lasting outliers Rigorously speaking there is a third type of outlier given by phenomena with a time scale onger than that of the process dynamics However this problem is traditionally treated in the framework of detrending so here it 1s dealt with in the corresponding section The effect of instantaneous outliers is relevant especially for model based autotuners and for the determination of process characteristics in the frequency domain In fact it is intuitive that a single spurious sample is more unlike to cause an erroneous detection e g of a settling time than to affect the result of the FFT of an output record In addition instantaneous out liers are quite easy to eliminate most autotuners impose a threshold on the measurement variation and reject samples that exceed it This threshold is normally computed on a statisti cal basis and in some cases this mechanism is configurable Also filtering see later may help Lasting outliers are more difficult to eliminate and can affect any ty
69. he process description determined in a into a de scription of the desired closed loop behaviour c decide what the regulator parameters must be to achieve this desired behaviour Formalising these steps will establish a procedure which from now on will be termed a tuning method Hence an autotuner is an implementa tion of a tuning method made so as to be capable of running automatically Let us now take a closer look at these steps 1 1 1 The way process data is obtained and treated Step a provides the process data This can be done by stimulating the process deliberately or just observing how it behaves during normal operation In the former case we have an ex periment based autotuner in the latter a non experiment based one Experiment based auto tuners can stimulate the process in various ways in open or closed loop with different sig nals injected in different places and so on Some approaches try to reduce the process per turbation by taking as experiments normal manoeuvres e g set point changes Whatever method is adopted it is necessary to ensure that process data are significant enough to allow regulator tuning This is a very complex and critical problem Suffice now to say that quite intuitively this problem is simpler in experiment based autotuners Once process data are available they must be turned into a description of the process To this end two main directions can be followed The first is to employ th
70. he two processes l 0 5 _ P s gt 1 F s i S Notice that at 1 both have magnitude 0 5 and phase 90 thus we can say that these two processes though they are completely different as for the static behaviour because one is in tegrating and one not in the frequency domain have the same local behaviour around w 1 P s Suppose the regulator must be tuned to achieve w 1 and 60 This can be done with a PI by imposing that RGDPGD e which by the way is the most common practice in relay tuning In both cases since P G1 P2 j1 the result will be K T 43 Figure 21 depicts the resulting open loop Ny quist plots the magnitude plot of the transfer function from the load disturbance to the con trolled variable the process output and the closed loop responses of the controlled variable to a set point and to a load disturbance unit step 49 O I Nyquist plots Mag of the t f from d to output dB C I set point step resp C I load dist step resp 0 0 4 1 5 40 0 1 1 5 f 0 5 0 0 5 10 10 10 0 10 20 0 10 20 P solid and F dashed P solid and R dashed P solid and B dashed P solid and R dashed Figure 21 different processes with the same local behaviour and local requests on LQ It is apparent that in both cases the required and have been attained that the resulting set point responses are quite different and that the load disturbance responses are not s
71. heme is being extended to accommodate additional criteria and integrated in the learning scheme proposed in Ruano and Azevedo 1999 As an example of this technique figure 34 illus trates an example of a closed loop step response of a SOPTD plant where the PID tuning was obtained from a multi objective genetic optimisation considering criteria such as the ITAE overshoot rise time control peak value and additional criteria related with noise re jection UNITARY DEGREE RESPONSE T T T Amplitude Figure 34 a step response obtained with MOGA PID autotuner T7 8 Selecting an autotuner How the concepts introduced can be joined to form a modus operandi Selecting an autotuner is never easy and the role of experience is so important that the knowledge gathered from any work like this can only serve as a starting point A way of thinking for this selection process can be obtained by recalling the numerous selection ori ented statements made throughout the volume but we think it is useful to complete this knowledge with some final guidelines Assuming that the problem is to choose one or more autotuners to be employed in a sufficiently well identified application or type of applications a quite realistic scenario experience recommends to proceed more or less as follows e Identify the characteristics of the control problem s involved in the application in the terms introduced here tight control or not
72. hich involves the exchange of genetic mate rial between two parents to create new off springs and mutation performing random changes to individual chromosomes Once the new generation is obtained the process goes on iteratively for a specified number of generations Genetic algorithms are robust algorithms which look for global optima instead of local op tima as gradient based algorithms do They have been found to cope well with noise discontinuities and are very well suited for performing multi objective MO optimisation The interested reader can be found more detailed information in another IFAC Professional Brief Genetic Algorithms in Control Systems Engineering Fleming and Purshouse 2002 and the references there within 7 2 Neural Networks approaches to PID autotuning The first historically approaches are due to Swiniarski 1990 and Lightbody and Irwin 1991 Both exploit the approximation capabilities of MLPs to approximate the mapping be tween samples of the step response to the PID PD in the second case gains The first ap proach uses the open loop output samples while the second uses the closed loop output un der PD control of a nominal plant Both approaches suffered from several problems the most important being requiring a very large of samples and hence neural network inputs and be ing obviously dependent on the sampling time 73 Several authors have employed neural networks for adaptive PID co
73. hod the SO one Kessler 1958a b which also refers to the ideal 1 d o f PID 2 contains several ideas that have been widely developed in the following years The most important one is to assume that the process model be are M s u 1 e either FOPDT m 1 or SOPDT m 2 but with some other poles accounting for unmod elled dynamics It is also assumed that the time constants Tx are dominant 1 e that T gt gt 5 1 sT Vk The quantity Tm L gt _ 1 sT can then be interpreted as the time constant of a transfer function representing the unmod elled dynamics which is a very clever albeit rough way to account for model mismatch The SO method takes as approximate model a 1 sT n LE 1 sT and designs the regulator so that the cutoff frequency be 1 2Tym thus reducing the demand as the mismatch increases and that the open loop magnitude R0 M Go has a slope of 20 dB dec in the frequency interval from 1 4mT m to 1 Tum Hence this is a characteristics fol lowing method For a SOPDT model with T T 2 the SO tuning formulae are M s p PID T228T um T T 4T AT T3t4T um 4T T TA gt T T The SO method performs very well provided that the process delay is small since the time constants T must also dominate L thus it is especially suited for electromechanical systems Moreover it is keen to generate low frequency regulator zeros 1 e overshoots in the set point 38 respo
74. hould be followed for the purpose of autotuner selec tion In Section 9 some brief concluding remarks are reported 1 Introduction The basic concepts of PID autotuning Many definitions of autotuning have been suggested For the purpose of this volume we pre fer to define the object devoted to the autotuning operation rather than the operation itself Thus we say that an autotuner is something capable of computing the parameters of a regulator con nected to a plant i e of tuning that regulator automatically and possibly without any user interaction apart from initiating the operation The autotuner may reside within the regulator or anywhere in the overall control system No matter where it is any regulator whose parameters can be computed automatically is said to have autotuning capability Note that strictly the autotuner is not part of the regulator when no autotuning is in progress the computation of the control signal in no sense depends on the autotuner s presence It is also sensible at this stage to distinguish between autotuning and adaptation or adaptive control In the latter case the regulator parameters are computed without operator intervention while in the autotuning context the system may at best suggest the operator to retune not initiate a tuning operation Complete treatment of adaptive sys tems can be found e g in Isermann et al 1992 In selecting an autotuner then the user is encouraged to read th
75. ice The problem is that several delay modifications may be required resulting in a long tuning phase A very important advantage of relay based methods however is that the local characteristics of the open loop Nyquist curve can be imposed exactly in that it is guaranteed that this curve contain the point e the problem is what the overall behaviour of this curve will be but having a way for imposing at least its local behaviour around the cutoff with great precision is a good feature 3 2 3 Rule based synthesis According to the proposed classification in rule based synthesis there is actually no explicit process description neither as a model nor as a set of characteristics The goal behind this class of methods is to mimic human intuitive reasoning rather than time or frequency domain computations Under this framework lie expert and fuzzy systems 45 These methods which are not suitable for manual tuning but can only be applied in an automated manner will be described further on in the section devoted to Soft Computing methods 3 3 Choosing the controller structure This section is aimed at giving some very basic guidelines for understanding when P PI PID or more complex control strategies are recommended Borrowing from section 3 9 of str m and H gglund 1995 where a deeper analysis is reported we can start with the fol lowing statements e PI control is sufficient when tight control is not requ
76. in the phase margin and the cutoff frequency The previous sections have just given a quick overview of recently established results a complete treatment on the matter can be found with specific reference to the PID case in str m and H gglund 1995 and more in general in Doyle et al 1992 and Morari and Zafiriou 1989 Under the restrictions of this volume if the goal of the previous sections has been attained the reader should now be able to master the following concepts e Assessment in the time domain typically refers either to local characteristics of a re sponse e g the settling time or the overshoot of the closed loop step response or to some integral index computed over time e g the ISE for a certain response It is very intuitive for the non specialist user but sometimes tricky to automate Autotuners using this approach may require no model of the process but in this case cannot provide rig orous guidance for modifying the specifications if the required result cannot be ob tained In addition issues like the degree of stability or the attenuation of noise are not easily cast into this framework e Assessment in the frequency domain with classical indexes the phase margin and the critical frequency can only be understood by people with at least a minimum of theo retical control engineering knowledge Autotuners using this approach can employ a process model or not and only in the latter case are they able to forecast
77. ing and overshoot are satisfied 1 e the two quantities e3 e2 e e2 and e e match given values User specifications are given in terms of these quantities notice that the terms damping and overshoot are not used with their normal interpretation The autotuner uses a complex set of heuristic rules also for this purpose The EXACT requires quite a lot of prior information for tuning For example it is necessary to tell it how long to wait for an error peak before concluding that it will not occur The most important thing however is in order to speed up convergence initial regulator controller pa rameters must be provided To help the user supply this information the EXACT has a pre tune mode based on an open loop step test and on the Ziegler Nichols rules The EXACT is not experiment based apart from the pretune phase and from the set point modification case It is characteristic based it uses the error response peaks as well as characteristic following maximum allowed damping and overshoot in the sense stated above It features a rule base it uses heuristics and pattern recognition and specifies a 1 d o f PID structure It is a good tool but difficult to completely understand and sometimes to drive given the complexity of the heuristics involved and the limited amount of documen tation on it see the Exact technical information and Foxboro for controllers using this technique 5 1 2 The
78. ing at fast response with constraints on the phase margin and on the high frequency regulator gain It uses steady state information and leaves quite limited user intervention possibilities It also refers to the 1 d o f PID structure and possesses a continuous adaptation feature For a list of controllers using this technique see Honeywell controllers 5 1 3 The Yokogawa SLPC This autotuner see e g Yokogawa 1993 is initiated on user demand and experiment based a step added to the control signal in closed loop It is based on a FOPDT model identified by optimisation on the basis of the captured response It requires the user to specify the type of the response in terms of maximum overshoot no overshoot 5 10 or 15 thus it is characteristics following Tuning is decided by rules developed statistically on a large number of simulations These rules minimise an integral index ITAE ISE and so on chosen on the basis of the response type requested The SLPC refers to a 2 d o f PID structure where R is set by the user and does not use steady state information It has a pretune mode based as usual on an open loop step test and has also a continuous adaptation feature For a list of controllers incorpo rating this technique see the Yokogawa page 9 1 4 The ABB ECA 600 The auto tuning mode has to be enabled by the operator The method is based on a relay ex periment with hysteresis in closed loop The value of con
79. int weight From this example we can learn the fol lowing and general lessons e Static process information is always useful though in general not easy to obtain and leads to longer identification phases e g it cannot come from a single relay experi ment e Static information can be more or less relevant depending on the regulator structure on the tuning policy and on the characteristics of the control problem at hand especially on whether tight control is required or not This means that a skilled user needing to select an autotuner should ask himself at least the following questions do I have mostly a set point tracking or a disturbance rejection problem Do I need tight control or not Do I have integrating processes to deal with or not Is the regulator 1 d o f or 2 d o f Does the autotuner use static information or not This means also that the autotuner should be documented well enough to allow these questions to be answered 50 It is very unlikely however that these autotuner characteristics do emerge from the product documentation clearly enough This is a pity since it adversely affects good product selection and utilisation which ends up in diminishing the users confidence in the autotuning tech nology as a whole However it can be counteracted by users at least in two ways which are in some sense two further lessons learned e Encouraging autotuner manufacturers to enrich their documentation so that it will be in
80. ired i e when the detailed aspect of the controlled variable and control signal transients is not an issue or when the proc ess dynamics exhibits an apparent first order behaviour single time constant and no dead time This is easy to guess from a step response and quite frequent in practice e g in level control of single tanks Moreover the I action can be excluded if zero steady state error is not required which sometimes happens e g in internal loops of cascade controls e PID control is sufficient when the process dynamics looks second order and 1s signifi cantly delay free A typical case is temperature control when one time constant comes from the body whose temperature is controlled and the other from the sensor The D ac tion is particularly beneficial if the two time constants differ significantly as is common in the case quoted It must be kept in mind that a large D action also amplifies meas urement noise unless properly filtered Thus if the regulator at hand does not allow con trol on the derivative filter 1t may be better to reduce bandwidth expectations and use a PI e For processes where one of the two previous statements hold and if tight control is not required there is a very little benefit in using more complex controllers e PID control may be inadequate when tight enough control is required for processes with long dead times high order dynamics or oscillatory modes If this is the case it 1s often necessary
81. ith significant de lay may exist but they are unlikely to appear in practice For simplicity in this section we do not consider noise and disturbances unless explicitly stated d Undershooting e Oscillatory f Integrating Figure 15 classification of step responses First order models Overdamped responses can be well represented with a first order model plus delay or dead time leading to the acronym FOPDT i e with a transfer function in the form a l sT M s p 15 Many methods exist for identifying such models an extensive review can be found in chap ter 2 of str m and H gglund 1995 Here we present one of the most widely used namely the method of areas Given the step response record y t one must first compute the gain u by dividing the response total swing by the input step amplitude A and the unit step re sponse y t as y t A Then denoting by tena the final experiment time i e assuming that from tena ON Yys t p it is necessary to compute in sequence the three quantities tend A f Ao fi B Ju t ktt to ma A yu tit 0 0 32 where the areas Ay and A motivate the method s name as depicted in figure 16a Finally the other two parameters of the model are obtained as _ eA estima u u T and setting L 0 should the computed value be negative which can happen if the real delay is small The method of areas is very powerful remarkably noise insensitive
82. itial one Figure 4 typical requirements for the closed loop step response in the time domain Quite intuitively similar requirements could be made on the load disturbance response and or on the transients of the control variable We omit details for brevity but it is worth noting that time domain assessment is very close to the way people not familiar with control theory tend to evaluate the control performance As such it is a very natural way of compil ing a specification Time domain assessment however may not be easy to automate because it often implies recognising local characteristics of a response that can be compromised by spurious meas urements An alternative is to use integral indexes computed over time like the ISE Integral of the Squared Error these are treated later on in this work In addition characteristics like the degree of stability are easier to assess in the frequency domain 2 4 Control performance assessment in the frequency domain Assessing the controller performance in the frequency domain is maybe less intuitive but in general leads to more powerful analysis and synthesis tools provided that the required proc ess information is available Moreover in this context also the degree of stability and the re 15 jection of noise and disturbances can be assessed within a unitary framework The block dia gram considered is that shown as figure 2 1 e the process and the regulator are assumed lin ea
83. itions If process data are made available by autotuners to the plant information system it is possible and not difficult to compare them during the various tuning operations Using autotuners systematically involves making many experiment on the plant Besides tun ing the regulators these can produce a wealth of process information thus refining the proc ess knowledge by completing qualitative human impressions with quantitative data This re quires that the autotuners employed be open towards the exchange of information and com patible in this respect with the total system This degree of compatibility is then another use ful parameter for selecting an autotuner 2 The basics of PID control Definitions performance features and design fundamentals 2 1 Introduction PID control research supports a massive literature It would be impossible to do justice to all the published results in a volume such as this In addition because of varying definitions as sumptions and terminology it is sometimes difficult to make a direct comparison of two seemingly similar algorithms A common result is that the improved features highlighted in a particular publication are not reproduced in the problem that one is examining The aim of this section is to establish our notation to agree and identify the different PID controller structure representations and to define and illustrate the key performance features that are regularly employed when qu
84. ive is to lead y not ym to y so the true error is defined as e t y t y t However the regulator can only act on the measurement Ym of y since n is by definition unknown in fact one could give for example a stochastic description of it but this is beyond our scope Hence we can define also an apparent error e t y t y t This is the error the regula tor will try to make as small as possible and is a good representation of e if n is small It is important to keep in mind the distinction between real and apparent error because it has some important consequences that will be discussed later Curiously enough however also this distinction is sometimes unclear especially in the literature concerning less sophisticated products To minimise possible confusion we shall adopt the following notation When referring to the error seen by the regulator which will be our point of view when describing all control laws and most tuning methods we shall use the symbol e and the reader must remember that this is the apparent error When the distinction is necessary we shall adopt the symbols 11 e and eg explicitly and the reader must remember that expectations are on e whilst avail able measurements are described by e A very common specialisation of the scheme in figure 1 is that shown as Figure 2 Here the process is assumed to be described by a linear time invariant dynamic system in t
85. ks for asymptotically sta ble processes It is based on the identification of a FOPDT model in the form 15 by an open loop step test and the method of areas Subsequently the IMC formulae 18 are used for synthesising the block R s see figure 11 67 Parameter can be chosen by the user but a limit on it is imposed on the basis of an esti mate of the additive model error magnitude obtained in the identification phase with the method described in Leva and Colombo 2000 The computation of this limit on A is dis cussed in Leva and Colombo 2001b in so doing A becomes a stability degree user request over a minimum forced by the autotuner on the basis of data After Rp s is tuned a convolution model of the loop part of the control system is computed This contains R s and the response data not the FOPDT model so that no structural hypotheses on the process dynamics are involved Finally Res is tuned by minimising with respect to b and c the ISE between the control system response computed with the convolution loop model and that of a first order trans fer function with unity gain and delay equal to that of the FOPDT model whose time con stant becomes the user set point tracking performance request and cannot interact with stabil ity robustness and disturbance rejection because it only affects R s This method for opti mising the weights b and c is described in Leva and Colombo 1999 This autotuner i
86. lectronic Engineering from the University of Wales in 1992 In 1992 he joined the Department of Electronic Engineering and Computing of the Faculty of Sciences amp Technology of the University of Algarve where in 1996 he become Associate Professor of Automatic Control His main A interests are neural control and particularly its applications to PID autotun ing environmental control and parallel processing techniques applied to real time control He is the Coordinator of the Centre for Intelligent Systems and has over 100 research publi cations He is Associate Editor for Automatica he is a member of the Editorial Board of In ternational Journal of Systems Science and serves as reviewer for other international jour nals and conferences 84
87. led initially to a range of investigations captured under the global heading of sensitivity analysis but nowadays presented under the more general framework of uncer tainty and robustness Sanchez Pena and Sznaier 1998 Central to the new formulations is the concept of plant uncertainty described in terms of a nominal plant model plus a multipli cative or additive perturbation This leads to definitions of robust stability and robust per formance Robust stability infers the capability of maintaining stability in the face of plant variations and modelling errors Robust performance preserves a specified level of response in spite of plant variations and modelling errors The following sections are based on extracts from the books and papers mentioned above The intention is to follow the framework introduced by str m and H gglund 2000 The purpose is to provide the reader with basic knowledge of modern controller design and as sessment methods that can account for model errors and uncertainty in a more complete and rigorous way than could be done with more classical indexes such as the cutoff frequency 18 and the gain and phase margins Control synthesis and assessment methods that account for model errors explicitly are often collectively called robust control This means that they can ensure some properties e g stability and performance in a robust way 1 e so that these properties continue to hold in spite of model er
88. les of the current re search have also been given based on the authors experience We sincerely hope that our intent has been successful 79 References str m K J and T H gglund 1984 Automatic Tuning of Simple Regulators with Specifi cations on Phase and Amplitude Margins Automatica 20 pp 645 651 str m K J and T H gglund 1995 PID Controllers Theory Design and Tuning Sec ond Edition Instrument Society of America str m and H gglund 2000 The Future of PID Control Proc IFAC Workshop on Digital Control Past Present and Future of PID Control PID 00 Terrassa E str m K J C C Hang P Persson and W K Ho 1992 Towards Intelligent PID Control Automatica 28 1 pp 1 9 str m K J T H gglund C C Hang and W K Ho 1993 Automatic Tuning and Adapta tion for PID Controllers a Survey Control Engineering Practice 1 4 pp 699 714 Bialkowski W L 2000 Control of the Pulp and Paper Making Process In S Levine Ed Control System Applications CRC Press pp 43 66 Bristol E H 1986 The EXACT Pattern Recognition Adaptive Controller a User oriented Commercial Success In Narendra Ed Adaptive and Learning Systems Plenum Press pp 149 163 Brown M and C Harris 1994 Neurofuzzy Adaptive Modelling and Control Prentice Hall Control Engineering May 1998 Single Loop Controllers Dominate Marketplace Cox C S W J B Arden and A F D
89. lexity of two products acceptable In these considerations be extremely careful in con sidering compatibility among products and preferably make sure they all respect a well established communication standard This is very important because using several auto tuners in an integrated process environment almost always requires them to communi cate somehow e In extremely complex cases consider that nowadays selecting an autotuning policy does not always mean selecting a product There are several SCADA environments providing off line tuning 1 e capable of making an experiment on the process and then compute the PID parameters in the computer running the SCADA with plenty of different meth 78 ods Parameters can then be downloaded to the regulator if the communication channel allows to do so otherwise input manually e In even more complex cases consider implementing a set of autotuning policies tailored for the application s at hand in a SCADA environment with user programming fea tures This can be done only with a deep knowledge of autotuning much deeper than that achievable from this volume but in some few cases it is the only realistic alterna tive 9 Conclusions The goal of this work is to help control professionals to select a PID autotuner effectively We have decided to pursue this goal by inducing consciousness on autotuners theory of op eration rather than by presenting a large number of products flatly
90. ll UDC 6300 incorporating fuzzy logic Hyeong Pyo Hong et al 1992 proposed a scheme where some characteristics of the step response first peak ratio of settling time ratio of time constant and ratio of the first peak were identified and converted into linguistic values Using a set of six fuzzy rules the fuzzy inference engine computes fuzzy values which defuzzified are used as adjusting multiply ing factors for the current PID parameters A similar scheme is presented in Iwasaki et al 1993 Again characteristics of the refer ence step response overshoot time duration of the overshoot ratio between the integral pa rameter and the rise time saturation time are fuzzified and used as an input to a fuzzy sys tem which outputs the PID parameters The main difference is that previously the process is classified according to the ratio of the delay time to the time constant a FOPDT model is as sumed in three different classes lag middle and dead time plant and for each case a spe cific fuzzy rule set is used An example of a neural fuzzy approach to PID supervision is described in Henriques et al 1999 Here they address the problem of the PID control of a solar power plant One charac 76 teristic of this problem is that the operating point varies throughout the day causing changes in the plant dynamics which can not obviously be controlled Different PID controllers were designed for different ope
91. low the maximum user control and are an almost obliged choice if tight control is required Identification is very important and specification correctness even more In fact this is the only case where user requirements can prove inconsistent This problem is more relevant in autotuners where specs are directly related with control theoretical characteristics For example where the user is allowed to select the cutoff fre quency and or phase margin explicitly There is no need to prove that these two specs which are quite common can easily be inconsistent so the autotuner must make a choice and fulfil only one of them The problem is that there is no way of ensuring that this choice will reflect the user requirements As such we can state the following e Autotuners with numeric specs are to be used wisely They are powerful tools for tight control especially if they use the 2 d o f structure but must be used by people capable of giving specs correctly or at least not in an inconsistent way e Before adopting such an autotuner test several others if possible selecting apparently inconsistent requests see what they do and choose the most reasonable one for the problem at hand here there is really no general criterion It would be appreciated that documentation were available to allow one to forecast the autotuner behaviour with an inconsistent request but this is rarely the case and we must admit it is very difficult to d
92. ltiplicative perturbation because it allows one to write L s L s 1 AW s where Lo s Rp s Po s which simplifies computations This information can be used to as sess closed loop stability in the presence of plant uncertainty Assuming the nominal loop i e the one described by L s to be internally stable it turns out that the robust stability condition is L jo 1 Ajo W jo L j lt 1 L jo Vo VIAGjo lt 1 1 e VO 10 T j lt To W 0o Also in this case a visual explanation can be given By the Nyquist criterion if the nominal closed loop is stable and for any W2 s and admissible A s there are no right half plane cancellations and P s and P s thus L s and L s have the same number of right half plane poles the perturbed closed loop is stable too iff the Nyquist plots of L j and of L j make the same number of turns around the point 1 If the perturbation is so big as to destroy stability then there must be at least one frequency for which the corresponding point L jw of the perturbed open loop Nyquist diagram is far away from the nominal one L j more than the distance from L j to the point 1 This means that the larger W gt j is in a certain band the further L j must stay from the point 1 to guarantee that stability 1s preserved In force of 10 this condition can be expressed on L j easily In words the inequality 10 will be s
93. ly the result is the availability of products that are more or less open with respect to the user control allowed thus more or less powerful if well used and dangerous if not When choosing an autotuner for a given application especially if several interacting loops are involved it is important to be able to select one that allows the right level of user control and to ensure that the human skills required for using that autotuner correctly are available 1 1 3 The way parameters are computed Step c corresponds to invoking a procedure having the process and desired closed loop de scriptions as input and the regulator parameters as output This procedure then implements what is commonly referred to as the tuning rules Tuning rules can be constructed in several ways One requires a process model and resorts to choosing the regulator parameters so that the expected closed loop behaviour that forecast using the process model either be as similar as possible to that of a reference model or enjoy some time or frequency domain properties such as a prescribed settling time or a prescribed position of its poles In the former case we have a model based model following autotuner the desired closed loop description being in fact a model in the latter we have a model based non model following one which since it imposes some characteristics of the closed loop and not a model for it could also be called model based characteristics following
94. mics where low order models may be inadequate In such cases if tight control is required it is better not to use model based autotuners unless they have the capability of selecting the model structure or the set of characteristics to detect and or measure or at least to let the user select these Note also that model or character istic structure selection is a very powerful feature but requires a significant degree of understanding e Advanced autotuners with model or characteristic structure selection typically hide this capability by asking the user what is the nature of the controlled variable e g tem perature level flow and sometimes some other basic information on the process e g whether the pressure of a liquid or of a gas is to be controlled On the basis of the user response they can then make some generally loose assumptions on the structure of the process dynamics in the model based case or on which characteristics have to be expected and quantified in the characteristics based case For example in level control the process is frequently integrating in pressure control there is frequently a quick over shoot followed by smooth convergence to the steady state and so on Apparently it is necessary to provide this information correctly It would be also useful to know which assumptions the autotuner makes but this is seldom revealed mostly due to justified know how protection and is also quite difficult to fig
95. most immediate to obtain from a step test For a human they are immediate de facto while in an automatic tuning process the only though not simple problem is to replicate human insight and to eliminate the effects of noise which can make the recognition of a characteristic more or less blurred Frequency domain characteristics Frequency domain characteristics conversely are very straightforward to obtain by means of a relay experiment The rationale is that if a process with Nyquist curve P j is subject as in figure 18a to relay feedback with amplitude D i e whose output is D and hysteresis E i e whose switching points are at E a permanent oscillation of the process output occurs This oscillation has the frequency where P j intersects the critical point locus of the 35 relay which is a straight line parallel to the real negative axis located in the third quadrant of the complex plane and depending on the hysteresis entity as shown in figure 18b Noise and disturbances are omitted here for simplicity Figure 18 relay feedback a and oscillation characteristics b This allows to identify one point of the process Nyquist curve since P j x is the point indi cated above with the circle its magnitude is related to the amplitude A of the controlled variable oscillation by G j x tA 4D and its phase can be easily deduced knowing that its real part is tE 4D Notice that if a relay without hysteresis is em
96. mpetitive Recently hybrids systems such as neuro fuzzy neuro genetic or even neuro fuzzy genetic systems have been proposed and it is our feeling that this trend will increase in the future Before describing some applications in PID autotuning let us briefly introduce each methodology Artificial neural networks were inspired by the human brain operation They consist of proc essing elements the neurons each one with very small processing capability densely inter 71 connected in a network through the use of weights each neuron acting independently of the others A neural network as the brain has the capability of learning There are a large vari ety of neural networks employed for different purposes and using different paradigms of learning the interested reader can consult for instance Haykin 1999 Principe et al 2000 Here we only mention the ones used in the chosen applications In PID autotuning they are used for nonlinear function approximation purposes The most widely know neural networks are Multilayer Perceptrons MLPs They have as the name indicates a layered structure consisting of an input layer a buffer one or more hidden lay ers where typically sigmoidal functions are used and an output layer where linear functions are usually employed Although different learning algorithms can be employed the most well known is the error back propagation BP algorithm This belongs to the class of su pervi
97. ncy where L jo 1 is termed cutoff fre quency and indicated in figure 6 with The frequency where arg L jm 180 is termed ultimate frequency and indicated in figure 6 with 39 Note that a low pass behaviour has been assumed for L s as suggested by physical considerations in any case of interest Also it has been assumed that is properly defined 1 e that there is only one frequency where LG 1 We omit theoretical details for brevity but a proper definition of how can be achieved by correct regulator design is a required feature for any control system 16 Log modulus dB IL jo WO Wiso Phase deg arg Li jo Figure 6 gain and phase margins as seen on the Bode diagrams The magnitude Bode diagram is widely used for regulator synthesis because many control specifications can be easily expressed using it In fact with reference to the scheme of figure 2 the transfer function from Y s to Y s is L s 1 L s that from D s to Y s is 1 1 L s and that from N s to Y s is L s 1 L s Hence for o i e where LG 1 Lg 1 LGo 1 and 1 1 LQG lt 1 LGo while for m i e where L 1 LG 1 LGo LG and 1 1 LQG 1 Thi
98. nformation should be gathered and used This is dealt with at present by several research paths As a final remark note that A tuning has significant relationships with the pPI control law an interesting discussion on this matter can be found in str m and H gglund 1995 pp 156 158 The kappa tau or KT method This method computes the parameters of the 2 d o f ISA PID control law 11 apart from N and in the output derivation case i e c 0 It requires to identify a FOPDT model if the process is not integrating or a FOPDT one plus a factor 1 s if it is 39 The information used is then given by the model parameters u T and L by the presence or absence of the term 1 s the parameters meaning is of course different and by the request of a PI or PID regulator A further specification is the required magnitude margin M defined as M S x ____ 1 L jo oO for which the two values of 1 4 conservative tuning or 2 0 more aggressive tuning are ad vised Given all this and defining the process normalised gain a and normalised delay t as L L Q U T T L T the PI D regulator parameters are computed as Ao olama O L LC ere b Derm K T _ LB e 22 where the coefficients A B Ci and D come from the following table taken from str m and H gglund 1995 M 14 20 14 20 14 20 As 029 o7 38 84 osi 0s fa 27 aa sa Jos oz lai A BI la 73 9
99. nses This can be avoided by filtering the set point or equivalently by set point weight ing Many evolution of the SO method have been proposed there is an extensive discussion e g in str m and H gglund 1995 pp 166 172 The Dahlin method or A tuning Given a FOPDT process model the Dahlin method Dahlin 1968 aims at making the trans fer function from the set point to the controlled variable resemble that of a first order model with unity gain the same delay as the process model and a specified time constant which becomes a design parameter Denoting this time constant with which motivates the method s name this corresponds to tuning the regulator so that it can be approximated by l sT R s sL ull sX e If the term e is replaced with its 1 0 Pad approximation i e 1 sL this approximation turns out to be a PI Conversely if a 1 1 Pad approximation 1 e 1 sL 2 1 sL 2 is used a PID is obtained In synthesis then the Dahlin tuning formulae are T LA for the PI and TH t yyy Tee u L 2 T L 2 for the PID The method refers to the ideal 1 d o f PID 2 and is apparently model follow ing It is a good technique but requires a reasonable choice of However experience would soon convince any user that a bigger A 1 e less performance is required when the process model mismatch is more significant Therefore for making these methods really useful some model error i
100. ntrol As this is not the theme of this work this route will not be detailed We shall just point out that they usually two different neural networks one acting as a plant model generally determined off line and that is used on line to back propagate the error between the reference and the plant out put to the second neural network which supplies the PID gains This latter network is adapted on line in order to minimise the square of the error between the reference and the output at each time instant References to approaches in this route can be found in Omatu et al 1995 and 1999 Ruano and co workers Ruano et al 1992 employed MLPs in a characteristic based auto tuner Here they evaluated the process transfer function in the real axis in specific points These were used as they can be obtained on line using integral measures of the reference step response in the open loop case or the step response and control signal under PID con trol This enabled to identify the plant on line that belonged to a large domain of plant transfer functions and for each transfer function type a large range of its parameters By sampling this plants domain and determining for each example the PID gains according to a user defined criteria in this paper the ITAE criterion was used a set of examples was obtained for off line training three MLPs each one responsible for a PID parameter After these steps were realized off line the
101. o a set of concepts that once mas tered allows the reader to evaluate the effectiveness of a specific industrial autotuner for a particular application A significant space is also devoted to the review of PID control prin ciples essentially for less experienced readers Some industrial products are presented to il lustrate how the concept introduced for classifying and selecting autotuners reflect in the real world and samples of current research are given based on the authors experience Foreword This monograph is principally aimed at professional engineers who want to know how to choose and apply much more effectively one of the many PID autotuners currently avail able In addition it should also be of interest to anyone who would like to improve their knowledge of PID control and autotuners The focus of the information is on how the various autotuners work The primary aim is to provide the right kind of detail users require in order to select the methodology most appropriate for their current application Let us begin by sketching out the monograph s organisation in order to help the reader understand the ra tionale behind this particular Professional Brief Section 1 features some basic concepts including the necessary definitions to establish the terminology employed Section 2 reviews the basics of PID control and pays particular atten tion to design issues and the formulation of a general transfer function that encapsulates
102. o be followed t dt 0 This reasoning can be extended to the characteristics following context provided that the cost function does not involve any model to be followed for example it may simple contain the error and be J O n Oat which can be viewed as a characteristic of the loop behaviour It is important to note that these methods require the user to specify what response must be considered For example minimising an ISE for the set point response may lead to different results than minimising it for the load disturbance response Also the ISE is not the only cost function employed Several examples of such methods can be found in str m et al 1993 str m and H g glund 1995 and in the references given therein 3 2 2 Characteristics based synthesis The key feature of non model based methods is that the process description is not a model rather some characteristic values of it in the time or frequency domain In deriving some 43 methods a model may be involved but this is not meant to represent the process so as to al low forecasting the tuning results Here too we present a brief and not exhaustive list of methods to improve the knowledge of them and of autotuners based on them For apparent reasons non model based synthesis methods are intrinsically non model following The Ziegler Nichols methods The Ziegler Nichols rules Ziegler and Nichols 1942 are the first thus historical example of a metho
103. o dif ferent All these facts are because a local request assigning one point of the open loop Ny quist diagram has been made and the effects of it depend on the overall loop dynamics i e on the overall aspect of P In particular the integrator makes the two Nyquist plots out side the unit circle 1 e at low frequencies completely different while this difference is sig nificantly smoothed the magnitude maxima are comparable and at similar frequencies in the transfer function from load disturbance to output unless at high frequency where it is not relevant in any case Observing the figure we can now make some remarks Should the tuning process have been made taking into account the presence or absence of the integrator it would have been pos sible e g to increase the requested phase margin so as to obtain a lower overshoot This however would also have slowed the load disturbance response Or the overshoot in the set point response could have been cured with set point weighting but this requires a 2 d o f regulator And in any case one point of P j which is the only information used in the ex ample for tuning is not enough if not only and m but also the aspect of the obtained transients are important 1 e if tight control is required In this case either static information must be gathered prior to tuning or it must be implicitly obtained after measuring the re sulting overshoot to compute the set po
104. ocument these facts satisfactorily 4 3 Computing and validating the regulator parameters At this point an autotuner can compute the PID parameters with the tuning method it is based on After this step it is necessary to check the obtained result against some validation criteria These can be broadly classified in two categories 4 3 1 Criteria for checking the tuning results Since in solving the equations required for tuning it is often necessary to employ numerical techniques and even quite crude approximations it is generally required to check that the de sired results have been attained In model based autotuners it is also possible to forecast the loop behaviour before actually modifying the regulator parameters For obvious reasons this is not possible in the characteristic based case In this case sometimes a small perturbation is given with the tuned regulator and if results are not satisfactory the previous tuning is re stored In the experiment based case this check is often done to recover from the experiment perturbation this is also useful in the model based case Product documentation normally says almost nothing on these checks which is sometimes a pity because their appreciation allows one to understand the autotuner s operation more precisely In some cases these checks require additional process perturbation 60 4 3 2 Criteria for checking the aspect of the obtained regulator As a final step the regula
105. odel is SOPDT a PID is selected and the tuning formulae are 2T T LT K 2A0 T gt Cig oe 3uL DEL The Haalman method is well suited for processes with overdamped response and significant delay In fact being inversely proportional to L the requested response might become too fast if L is small A modified version of the method has been proposed in Scattolini and Schiavoni 1995 so as to ensure for a FOPDT process model and with a PI regulator a minimum phase margin Pm and a maximum cutoff frequency taking of course the most restrictive constraint This leads to k mig 7 2 a To T T uL u where m and become design parameters A cue for selecting them is to fix m to a rea sonable minimum say 50 by default while can be computed by imposing that the ex pected closed loop settling time which equals 5 be B times smaller than that of the process model In the FOPDT case where the model settling time can be expressed as L 5T this means setting O 2 L 5T where B can range from 4 to 10 Note that it can be interpreted as an acceleration factor which makes its understanding quite easy also for non specialists The modified Haalman 37 method does not necessarily impose L s thus it is a characteristics following method where the characteristics providing the desired closed loop behaviour are m and e The Symmetric Optimum SO method Despite being older than the Haalman met
106. ollers IEEE Trans actions on Systems Man amp Cybernetics Part A 29 pp 587 592 Visioli A 2001 Tuning of PID Controllers with Fuzzy Logic IEE Proceedings D 148 1 pp 1 8 Zadeh L A 1965 Fuzzy Sets Inform Control 8 pp 338 353 Ziegler J G and N B Nichols 1942 Optimum Settings for Automatic Controllers Trans ASME 64 pp 759 768 Zhao Z M Tomizuka and S Isaka 1993 Fuzzy Gain Scheduling of PID Controllers IEEE Transactions on Systems Man amp Cybernetics 23 5 pp 1392 1398 83 About the authors Alberto Leva was born in 1964 in Milano Italy In 1989 he received the MSc Laurea Degree in Electrical Engineering from Politecnico di Mi lano Italy In 1991 he joined the Department of Electronics and Informa tion of the Faculty of Engineering at Politecnico di Milano where in 1997 he became Assistant Professor of Automatic Control His main research _ interests are process modelling and simulation especially of power gt plants automatic tuning of industrial regulators with particular emphasis on application oriented issues and the development of innovative tools for education in Automatic Control He serves as reviewer for several international journals in cluding Automatica Control Engineering Practice IEE Proceedings Control Theory and Applications IEEE Transactions on Education Journal of Process Control Simulation and for various international conferences Chris Cox was
107. one Consider the following short discussion on the matter The tuning objectives The goal of any autotuner is to achieve the best control However it is often unclear what is meant by best control Any control engineer knows that there are a number of trade offs when synthesising a regulator for example bandwidth and degree of stability are normally opposite desires Autotuners can accommodate such trade offs but there exist other choices that must be made to orient the automatic tuning Maybe the most important one is to decide exactly what the best control is Low overshoot Fast settling Quick set point tracking Ef ficient disturbance rejection In addition these desires often conflict with one another and a good autotuner must be so flexible in accepting specifications to allow the skilled user to ob tain exactly what he wants yet remaining simple enough to avoid confusing less knowledge able users and robust enough in the face of incorrect choices The role of the regulator in the overall control system When tuning the regulator in a single stand alone loop the main problem for the autotuner designer is given by the extremely variable level of understanding the users may have For example especially in very low end products so little user knowledge is commonly assumed that specifications must be generated entirely by the autotuner itself this is normally achieved on the basis of the process descriptions with methods
108. one on u with Laplace transform Djoag s we denote the Laplace trans form of signals with the corresponding uppercase letter is equivalent in figure 1 to an output disturbance D s with Laplace transform P s Djoaq s e There are disturbances that do make y differ from y We can group all of them under the collective name of measurement noise because noise is their most common source These disturbances do not correspond to physical actions on the system conversely they account for the imperfections of measurement whatever their reasons may be signal transmission and so forth All these disturbances can be treated as n in figure 1 Quite intuitively counteracting phenomena that affect a physical quantity and phenomena that only affect its measurement are different problems That is why in the analysis and in the synthesis of a control system d and n are treated differently as will be shown later It is worth noting that in the literature there are several other ways to classify disturbances and that in some products documentation there appears to be some confusion on the matter As a consequence the reader is encouraged to master this or any equivalent classification of disturbances because making wrong assumptions on how a disturbance must be counter acted may have a significant adverse affect on the controller auto tuning As for the error some definitions are consequently in order to clarify notation The control object
109. ontinuous adaptation case 3 is somehow hybrid but if the logic is properly configured it is much more similar to autotuning than to continuous adaptation It is important when selecting an autotuner to un derstand in which category it falls so as to forecast how it will possibly interact with the rest of the control system It is also necessary to read the documentation carefully since an ex pression like expert tuning mode supervised self adaptation or something similar does not provide any information on the actual mechanisms involved In this work we shall focus primarily on PID autotuning for single loop situations and say almost nothing on continuous adaptation and more complex structures This might appear a limitation so a justification is in order First the statistics reported in Control Engineering May 1998 state that single loop controllers contribute 64 of all loop controllers suggest ing that many customers still want a controller to handle only one or two loops so as to pro vide a more manageable process in case of failure In addition the two most desired fea tures of a loop controller are the PID algorithm and startup self tuning which in our ter minology means autotuning initiated at power up As such becoming familiar with autotun ing for single loop controllers means becoming proficient in a fundamentally relevant situa tion Then no matter how complex a plant is control system optimisa
110. ontrollers turned a simple problem into a very difficult one In fact when setting up the higher levels of the control system appears particularly difficult almost certainly a part of the responsibility falls on some underlying loops The problem is that these loops must be identified and above all that the only way for avoiding problems is to tune every loop as well as possible which is actually very time consuming Autotuners al low the user to spot these problems automatically to tune a loop quickly and even to per form cyclic loop retuning for progressively improving the system performance They can be used in the plant startup phase or during its operation providing flexible tools for mainte nance Of course especially in large scale systems it is important that autotuners be highly inte grated in the overall control and supervision system The main goal of these remarks is then to clarify that especially in complex systems loop autotuning must not be considered an an cillary functionality both when choosing a control product and when using it rather it is an important feature to observe when selecting a controller 1 2 2 The importance of having standardised tuning policies Repeatability is an issue in plant construction commissioning and maintenance It means clarity less errors reduced costs In one word it is necessary because also undesired situa tions are in some sense repetitive Briefly and intuitively these
111. oo lengthy to carry out here For the purpose of this work it is better to draw from it some operational cues for the selection and use of an autotuner Hence we can state the following e When the table dictates that the I action is optional recall that 1t must be included if zero steady state error is required e If tight control is not required the only significant recommendation is to use set point weighting with integrating processes that if the integrator is removed show a dynamics dominated by the time constant T case 5 Integrating processes whose dynamics re moving the integrator is dominated by the dead time can be managed with a P or PI regulator case 4 If tight control is required things are far more complex Also in this case however some di rections can be given 47 e When feedforward compensation is required recall that set point weighting is a very specialised form of it see 13 Hence in the single loop PID framework treated in this volume choose a PID with this feature e g an ISA one and possibly an autotuner em ploying the weights If the latter is not available tune for load disturbance rejection where feedforward has no influence and then try to adapt the weights manually recall ing again 13 e When dead time compensation is required it would be advisable to use regulators with this feature e g comprising a Smith predictor or a pPI There also exist autotuners for these regulators not
112. oonan 1994 CAD Software Facilitates Tuning of Tra ditional amp Predictive Control Strategies Proc ISA 94 Advances in Instrumentation and Control 49 2 pp 241 250 Anaheim CA Cox C S P R Daniel and A Lowdon 1997 QUICKTUNE A Reliable Automatic Strat egy for Determining PI and pPI Controller Parameters Using a FOPDT Model Control Eng Practice 5 10 pp 1463 1472 Dahlin E G 1968 Designing and Tuning Digital Controllers Instrumentation and Control Systems 41 6 pp 77 81 Doyle J C B A Francis and A R Tannenbaum 1992 Feedback Control Theory MacMil lan Driankov D H Hellendoorn and M Reinfrank 1993 An Introduction to Fuzzy Control Springer Verlag EnTech 1994 Competency in Process Control Industry Guidelines version 1 0 Fleming P J and R C Purshouse 2002 Genetic Algorithms in Control Systems Engineer ing IFAC Professional Brief 80 Goodwin G C S F Graebe and M E Salgado 2001 Control System Design Prentice Hall Goldberg D E 1989 Genetic Algorithms in Search Optimization and Machine Learning Addison Wesley Haalman A 1965 Adjusting Controllers for a Deadtime Process Control Engineering July pp 71 73 Haykin S 1999 Neural Networks a Comprehensive Foundation 2 edition Prentice Hall Henriques J A Cardoso and A Dourado 1999 Supervision and C Means Clustering of PID Controllers for a Solar Power Plant Int Journal of
113. p and maintain ing control systems provided that it is viewed as an aid to human skill not a substitute for it This improvement can take place in several directions and in the following we shall point out the three major ones 1 2 1 The importance of tuning PID loops correctly Several studies report that the majority of regulators are mounted in the field and set into op eration using their default parameters This often results in poor operation According to EnTech 1994 80 of the control loops not only do not provide any benefit but even in crease variability Of these situations 30 are due to incorrect regulator tuning As a conse quence many loops end up being left in manual mode This implies at least two things First the majority of applications do no appear to be critical at least as far as stability is concerned Second which is far more relevant to us the importance of having PID loops tuned correctly is often underestimated In fact few loops are independent A poorly tuned loop means more hassle for the upper lev els of the control hierarchy where intuition should be enough for guessing this interactions are even more evident Thus having a loop tuned incorrectly often results in the necessity of taking more complex solutions at the higher hierarchy levels or of reducing the overall ex pectations This might seem obvious but the authors have quite often came across situations where a few badly tuned PID c
114. pe of process description The first precaution to take is to ensure that during the identification phase nothing happens that affects the process output other than the possible input stimulation made by the auto tuner In the opposite case any identification method would try to explain these effects as input output process dynamics thus making an unavoidable mistake of unpredictable entity Of course this is a preventive approach but little else can be made It is however important that when using the autotuner these situations be detected usually by the user who must then be conveniently trained so that the autotuning process can be aborted simply and with out consequences which is another feature to look for when selecting an autotuner It is im portant to note that user training in this respect is simple but necessary the authors have seen a number of failed autotuning operations in which the only problem was that plant operators did not know that at least the loop they were tuning had to be left alone during the tuning operation This is very simple to explain and understand and solves the great majority of that kind of problem It is also obvious for anyone with a minimum knowledge on the matter but curiously is not always transmitted to operators Filtering Filtering 1s used mainly to eliminate the effects of noise including instantaneous outliers The filters used are normally lowpass and it is desirable that their bandwidth be
115. ployed this phase is r An extension of the basic relay feedback idea is to insert a time delay between the relay and the process Leva 1993 In this case the relay has no hysteresis or realistically has the minimum for avoiding spurious switchings due to noise its critical point locus being still ap proximated by the real negative axis Here the point identified is the intersection of the Ny quist curve P j with the real negative axis Due to the delay t however a point of P j o corresponds to the point of PQ given by P j w e Thus by modifying t several points of P j can be obtained This use of relay feedback then provides a set of characteristics in the frequency domain given by several points of the process Nyquist curve 3 2 Most common approaches to PID synthesis We now present some model based some characteristics based and more briefly some rule based methods for the synthesis of PI D regulators This is not meant to be an exhaustive list rather a reasoned selection of well established and useful techniques These methods and the autotuners that use them may require the user to select some design parameters An other aim of this section is then to explain at least the basic rationale of the methods so as to allow a conscious use of the autotuners based on them 3 2 1 Model based synthesis The key feature of model based methods is precisely that the process description is a model which is available a
116. puted as o 27 dy I lt 1 log a a Models for integrating processes It is very uncommon that integrating processes also exhibit oscillatory behaviours As such for describing them it is possible to use FOPDT or overdamped SOPDT models multiplied by 1 s Moreover an integrating process produces responses that are similar to those shown for asymptotically stable processes provided a pulse not a step is applied More precisely if 34 a model M s has no poles nor zeros in s 0 and y t is its response to a step of amplitude A then y t is also the response of M s s to an ideal pulse of area A Hence one can iden tify a model for an integrating process in two ways One is to apply a step and wait that the process output moves for say 5 times the previously observed noise band then remove the step thus overall applying a non ideal pulse and wait for settling The response is then used for identifying a FOPDT or SOPDT model as above remembering to normalise dividing by the area not the amplitude of the pulse The required model is the identified one multiplied by 1 s The other way is to apply a step and wait for the process response to become a straight line unfortunately this typically means more perturbation The response is then dif ferentiated numerically and treated as above for identifying a FOPDT or SOPDT model The required model is the identified one multiplied by 1 s
117. r and described by the transfer functions P s and R s respectively The most used media for frequency domain assessment are the Nyquist and Bode diagrams Given a transfer function G s the associated Nyquist diagram is the plot in the complex plane of the image through G of the positive imaginary semiaxis 1 e the locus defined by G j 0 lt a lt oo In closed loop control it is particularly interesting to observe the Nyquist plot of the open loop transfer function L s R s P s see figure 2 because this allows two very important definitions to be made These are the phase margin PM and the gain margin GM illustrated in Figure 5 Lo Figure 5 gain and phase margins as seen on the Nyquist diagram The GM is defined in dB as 20logj0 B whilst the PM is and is normally expressed in degrees The system is marginally stable when both GM and PM are zero For a system to be stable both GM and PM have to be positive The Bode diagrams are two graphs drawn to a base of logio If the frequency response of L s can be written as L j L j e then the vertical axis on one graph the magnitude diagram is the log modulus LM The LM is expressed in dB and defined as LM 20 log LGa The vertical axis on the second graph the phase diagram is simply the phase nor mally expressed in degrees Examples of Bode diagrams are presented as Figure 6 which also indicates how GM and PM appear The freque
118. rating points based on neural network plant models Based on measured data related with the solar radiation and the reference temperature a fuzzy super visor selects among the available controllers the one which achieves the maximum output value among the rules that have been fired simultaneously 7 4 Genetic approaches to PID autotuning Being genetic algorithms powerful optimisation methods it is not surprising that they have been applied for PID tuning The first known by the authors approach to PID autotuning is due to Jones and Oliveira 1995 Assuming that the process is modelled by an ARMA process they use first a genetic algorithm to estimate the model parameters based on the closed loop step response Then they use this model to determine again using genetic algo rithms the PID gains that minimise a cost function such as ISE IAE or ITAE The same au thors extended this work to use co evolutionary design in Jones and Oliveira 2000 Differ ent authors have used genetic algorithms for PID tuning the major problem being to auto mate the techniques for on line operation As mentioned before genetic algorithms are well suited for performing multi objective op timisation This approach was introduced in Lima and Ruano 2000 for PID autotuning where they compared genetic algorithms with standard optimizers for the simultaneous op timisation of criteria related with reference tracking and disturbance rejection This sc
119. reat majority of cases they are also characteristics following A somehow historical example can be found in str m and H gglund 1984 another is Leva 1993 In fact the most natural way of using one point of the process Nyquist curve characterised by a frequency a magnitude P and a phase is to impose that R jo P e sel This complex equation yields two real regulator parameters and means that the open loop Nyquist curve L j will contain the point e i e that the loop will have cutoff fre quency and phase margin m For tuning an ideal PID in the 1 d o f form a third equation is required which is typically obtained by imposing the T T ratio i e setting T aTa where a becomes a design parameter useful for limiting the high frequency regulator gain The main concern in using relay based methods is that the cutoff frequency emerges as a re sult of the relay experiment being the frequency at which the oscillation arises As such the amount of relay hysteresis adopted becomes relevant in determining the loop cutoff fre quency and the problem is that the relationship between these two quantities 1s far from triv ial Inserting a delay in series with the relay can help in this respect because modifying this delay along the experiment can make the oscillation arise at a prescribed frequency This means that the design parameters are the cutoff frequency and the phase margin which is a widely accepted cho
120. rom the au thors experience so as to provide the reader with at least some samples of what is being done The descriptions reported here tend to be longer than those of industrial products be cause the references provided are written in a more academic style 6 1 A relay autotuner exploring the process Nyquist curve This autotuner is presented in Leva 1993 It first performs a short double step test to see if the process is integrating then identifies one point of its Nyquist curve by a relay experi ment A delay is cascaded to the relay to explore several points as discussed This search is aimed at finding the frequency where the process magnitude is 1 10 of the static gain in the non integrating case or 0 1 in the integrating case Tuning is made by moving this point onto the unit circle with the user specified phase margin The method ensures a reasonable cutoff and a regulator magnitude of at least 20 dB at the cutoff which results in good disturbance rejection The autotuner is initiated on demand characteristic based characteristic following and uses static information An example autotuning session is shown in figure 27 SP responses with the tuned regulator Tuning phase Control signal 00 0 20 0 40 1 00 1 20 1 40 2 00 20 Figure 27 autotuning session 6 2 A robust autotuner based on the IMC and on optimisation This autotuner is described in Leva and Colombo 2001a and wor
121. rors process variations and or uncertainty provided these remain within quantified bounds 2 5 1 The block diagram and some important transfer functions The control systems we are dealing with are assumed to be characterised by the block dia gram of figure 8 Figure 8 generic feedback control scheme highlighting the true and apparent errors In figure 8 the process is assumed SISO Single Input Single Output and described as a linear system with transfer function P s We assume that P s is not perfectly known and that only an approximation of it is available When relevant we shall denote this approxima tion with P s and with the term nominal model The controller is also linear but notice with two degrees of freedom 2 d o f In fact the transfer function R s describes the feedback from the process output measurement Y s to the control signal U s while the series of Res and Rp s represents the feedforward from the set point Y s to U s Hence in the 2 d o f case these two signal paths can be made different and the control reactions to the set point and to disturbances can be dealt with in a partially separate way A 1 d o f formulation is obviously obtained by setting R s 1 see figure 2 Clearly in the 2 d o f case the open loop transfer function is defined as L s R s P s and in nominal conditions it is L s Rp s P s The choice of Rg s leads to the structure embraced by many of the tex
122. rthermore any recommen dation on the controller structure is deeply connected with some on the tuning policy This means quite intuitively that when a problem is so critical that the controller structure cannot be chosen arbitrarily this also indicates that some ways of tuning that controller are not rec ommended The quantities considered in str m et al 1992 refer to a FOPDT model in the form 15 if the process is not integrating or to one in the form a M s u s My Sda4sT 19 if it is integrating thus they are consistent with the simple model identification guidelines we have given before These quantities are the normalised process gain for processes with out integration k the normalised process gain for processes with integration kz the nor malised dead time for processes without integration 0 and the normalised dead time for processes with integration defined with reference to 15 or 19 as u Hy L L en a 0 gt Mjo Mjo T T i gt y Oy where u is the ultimate frequency 1 e the smallest one such that the model phase is z Note that names like these are used elsewhere with different meanings so we have adopted the quantity names and symbols used in str m et al 1992 to avoid confusion The directions for controller structure selection are given in the following table The com plete interpretation of this table would be t
123. rtional to the error Hence it obeys to the intuitive principle that the bigger e is the bigger the control action must be to lead y close to y The P action depends only on the instantaneous value of the error and is nonzero only if e is nonzero In other words the P action is ideally zero at steady state but only provided that the required steady state can be reached with zero control If this is not the case it will be neces sary to reset u 1 e to add a constant term to it so that it maintains the required steady state if only the P action is used this is the role of uy However the reset can also be accom plished by the I action and that is why the in older regulators this action is also called automatic reset Taking into account the control signal limitation it is possible to define the proportional band of the controller i e the range of error values where u can be made pro portional to e without exceeding the limits The proportional band P is then given by Umax Umin K Note that if K 1 the control output is only linear for small errors However the proportional controller s response is instantane ous and normally produces a quick response from the process Unfortunately the P action is very prompt in responding also to measurement noise Hence it must be used wisely since it can contribute to excessive actuator upset Finally note that the P action gives its main con tribution at the beginning of transi
124. ry and sufficient conditions for nominal performance see Doyle et al 1992 for a more extensive discussion Robust stability A similar condition can be derived for robust stability According again to Doyle et al 1992 a controller provides robust stability if it provides internal stability for a family of plants that embrace all of the conceived plant variations and modelling errors To define robust stability it is then necessary to introduce the idea of model uncertainty This is the difference between the nominal model and the true system Model uncertainty can be described either as an additive or multiplicative perturbation For the latter case the true and unknown plant transfer function P s can be written as P s P 9 1 A s W s 9 where P s is the nominal model the weighting function W jw provides a means of quanti fying the frequency distribution of the model uncertainty Sanchez Pena and Sznaier 1998 and AQG lt 1 It is worth noting that for a rigorous treatment of this matter some fur ther technical hypotheses are necessary For example it is required that P s and P s have the same number of right half plane poles for any W gt 2 s and admissible A s and that there be no right half plane cancellations between R s and P s for any W2 s and admissible A s see Doyle et al 1992 for a discussion that we omit for brevity 22 Here we prefer to express the model error as a mu
125. s a by product of the synthesis Thus these methods rely on some identi fication technique that must provide a simple fixed structure model due to the necessity of deriving simple tuning rules Albeit approximate however this model has to represent the process well enough to allow sensible forecasting of the tuning results When model based methods are used manually this is very useful for selecting the possible design parameters When they are used in an autotuner it is important to check whether the identification results 36 are made available to the user if this is the case they can be a valuable source of informa tion for process diagnosis The Haalman method The Haalman method Haalman 1965 refers to the ideal 1 d o f PID 1 e to the control law 2 Its basic idea is to start from a FOPDT or SOPDT model and to select the controller pa rameters so that L s 2e 3Ls which corresponds to a cutoff frequency of 2 3L and a phase margin m of 50 approximately The objective is then to make the closed loop behave like L s 1 L s Hence this is a model following method Once L s has been assigned the regulator parameters are computed by applying the rela tionship R s L s M s where M s is the process model transfer function which means that the model poles and zeros are cancelled If a FOPDT process model is used it is advised to select a PI tuned with the formulae K ELS I T 3uL while if the process m
126. s means that requirements in terms of re sponse speed disturbance and noise rejection can be expressed in terms of L j very natu rally as depicted in figure 7 while stability requirements are easily checked on the Bode phase diagram In detail if the closed loop dominant time constant must be between T and T if a disturbance D s in the band 2 must be attenuated at least by the quantity Ap in dB and if a noise N s in the band 3 4 must be attenuated at least by the quantity Ay in dB the Bode magnitude diagram of L j must fulfil the constraints of figure 7 Log modulus dB Figure 7 the Bode magnitude diagram as assessment tool Notice the different role of D s and N s Disturbances representing actions on the physi cal variable Y s can be counteracted by feedback if their frequency content does not extend 17 above the cutoff frequency and rejection is better if L j is bigger in that band Noises only affecting the measurement Y s can be counteracted if their frequency content is above the cutoff frequency and rejection is better if L Qj is smaller in that band A response speed requirement means that L jm must intersect the 0 dB axis in a given interval This formalises and quantifies the intuitive idea that the control loop must exert strong feedback up to the cutoff frequ
127. s then experiment based model based model following by cancellation for Rg and by optimisation for R initiated on demand The user interface of the autotuner has been designed so that the user can modify the stability and performance request and see the achieved results computed with the convolution model on line this has proven to be highly appreciated by several people with very different degree of control culture An example ses sion with the autotuner is shown in figure 28 Penance woe A busters Fre a b Figure 28 the autotuner s user interface a and results b 6 3 The MasterTune CAD Software The MasterTune software has been developed to help in the automatic tuning of PI PID and pPI controllers The kernel of the MasterTune software Cox et al 1994 for the PI and PID cases is the Astr m Hagglund 1984 autotuner However it has a family of additional refinements that make it easy to use whilst at the same time producing consistent behaviour at least equivalent to that obtained when using well tried empirical formulae Cox et al 1997 The main features of the software are briefly outlined next During the tuning 68 phase the values of the various test parameters used are normally set to default values by the software If the user so chooses these values can be modified to suit individual requirements The parameters which can be modified include e The percentage overshoot this is th
128. se problems in industrial autotuners Understanding this material will then become another source of information for selecting an autotuner and for using it in the most effective way 48 4 1 Obtaining the process behaviour description automatically 4 1 1 The needs steady state and control relevant dynamics determination First it may be necessary to determine the static process behaviour Limiting the scope to situations that may arise in practice in a model based context this means sensing whether the process is integrating or not and in the latter case estimating its gain In a characteristics based context this may mean several things the gain or the steady state output value are normally considered as characteristics too and in most cases some lexical variable is used for stating that the process is integrating So as long as static behaviour is considered the model and the characteristics based contexts are quite similar However the matter is less trivial than it may appear for at least two reasons Under the point of view of the autotuner designer obtaining static information is not an easy task espe cially in noisy cases and when nonlinearities are involved Under the point of view of the user static information is always useful but its actual importance depends on the characteris tics of the specific control problem This fact which is the more relevant in this context will be now illustrated with an example Consider t
129. sed in the literature In this volume we have to choose one for discussing general aspects though we shall quote some of the others when 26 dealing with autotuners that use them As a general form for the realistic PID regulator we choose the ISA one str m and H gglund 1995 due to its great generality The general form of this control law is U s K bY s Y s Ys Y s aN OY Y s 11 1 The notation is as previously defined with the inclusion of the set point weights b and c in the proportional and derivative actions already introduced Similarly the derivative part is made proper by adding a pole with time constant proportional to Tg via parameter N as dis cussed above Another way of seeing that these additional three parameters give added flexi bility to the controller implementation is to notice that they correspond to the 2 d o f realisa tion shown as figure 11 Y s U s Ym S Figure 11 a PID regulator with 2 degrees of freedom where T R s K rn l sT 1 sT N 12 1 s bT T N s T T c b N Ry Ss 8 1 s T T N s T T 1 1 N Two facts are worth pointing out First R s is a real i e made proper with N 1 d o f PID Thus it can be tuned with virtually any method including the numerous old ones that refer to this structure Second once N is fixed by tuning Rg s b and c can only modify the zeros of Res Hence once stability and disturbance rej
130. sed learning algorithms supervised means that a set of desired outputs is available for a set of inputs and the role of the learning algorithm is to minimise the sum of the squared er rors between these two quantities and the BP algorithm performs its task that by comput ing in an iterative fashion the gradient of the criterion with respect to the weights and adapt ing them in the direction opposite to the gradient The name of the algorithm comes from the fact that the gradient is computed by propagating the error from the output towards the input therefore back propagating it If the set of examples is fixed through all the iterations and the gradient is computed for the whole set then we have batch learning or training other wise we have pattern based learning Of course for on line applications this is the procedure adopted and learning becomes adaptation B spline neural networks have also been employed for PID autotuning They have also a three layered structure but the basis functions employed have a compact support which means that they are active only for specific sub domains within the larger domain covered by the inputs A more detailed description of these networks is beyond the scope of this work and the interested reader is conducted to Brown and Harris 1994 for more information We only mention that these networks have interesting properties for adaptation performing on line learning in a neighbourhood around an oper
131. sfactory in practice In synthesis then the method consists of identifying a FOPDT model and then applying the IMC technique by choosing A Faye 1 1 s Q s and by replacing the process delay by its 1 1 Pad approximation 1 sL 2 1 sL 2 The regulator turns out to be a real PID given by L T T L A ALN ay ES ___ a T T ices i 2 L A w L A XT 2 L A 1 18 The main concern in using the IMC PID method is the choice of A This concern is shared by the Dahlin method which can be interpreted as an ancestor of the IMC procedure As antici pated is a knob for trading stability and robustness against performance It has been proven Leva and Colombo 2001b that given a process model and an estimate of the corre sponding model error a lower bound for A 1 e an upper bound for the performance request can be found beyond which stability cannot be ensured anymore There exist also methods for estimating the model error from measured data see e g Leva and Colombo 2000 but these would lead us beyond the scope of the volume thus we just quote the fact as a suggestion for interested readers As a practical rule of thumb anyway one can reason both for the IMC PID and for the Dahlin method as described in the follow ing A far more extensive discussion involving cues for selecting the most appropriate con troller structure is reported in str m et al 199
132. signal u to the feedback signal f is very close ideally equal to P s Moreover in the ideal case and without disturbances D s and N s YO UB oy poet ge _ ow U6 F s F s P s e PO F s e F s r Y s Y s Hence by using this scheme the PID regulator R s can be tuned taking into account only the rational dynamics of the process 1 e P s Without modelling errors noise and distur bances which implies that Y s Y s the resulting behaviour of Y s will be that of F s which would be the controlled variable if there were no delay just delayed by L The name predictor comes from the block M s 1 e which actually generates the prediction F s of Y s compensating for the delay Of course the Smith predictor cannot counteract disturbances D s and N s simply because it cannot predict their effects and it is not a robust scheme because all its rationale lies on the availability of a quite accurate process model Nevertheless it is widely used especially in process control so that several regulators and autotuners encompass it In fact as will be clarified later adopting the Smith predictor is a viable way to extend a model based auto tuner conceived for process with rational dynamics to cases where the delay is dominant With a very crude simplification once the rational model and the delay estimate have been obtained it suffices to tune a PID on the former and then insert it in the scheme o
133. since it uses integration and quite accurate Moreover it has the ability of estimating the delay without obliging the user to define thresholds for deciding when the process response has started moving This ability suggests its use also for moderately oscillatory undershooting or overshooting re sponses provided that after computing u the parts of y t greater than it be mirrored with respect to u and those below zero be truncated to zero This is in some sense a trick based more on empirism than on rigorous reasoning It is shown synthetically in figure 16b where the process response is indicated by the dashed line and that used for computing Ao and A by the solid line idinn P b o a i gt A ee to time Figure 16 the method of areas a and the response to be used b Second order models Second order models can describe both overdamped and oscillatory responses In the former case a delay can also be included for better fitting leading to a model in the form sL e M s u 16 EE st lesT a which with the same rationale as above is termed SOPDT For oscillatory responses conversely the advised model structure is M s 7 y 17 ea ware aes WO WO It is apparent that an overdamped response can be described also by a FOPDT model The advantage of the SOPDT is a better phase accuracy because in the FOPDT case any lag not 33 explained by the first or
134. the effect of a modification in the requirements In any case all the results provided by such autotun ers are based on the assumption that the process model if any is exact so the only way to achieve some robustness is to reduce the requirements on the cutoff frequency and or to increase those on the phase margin a priori 24 e Assessment methods accommodating model uncertainty are seldom used in autotuners because they require both a process model and some measurement of its uncertainty Obtaining this information automatically is very difficult However if an autotuner re veals the model that has been employed for the tuning some nowadays do a knowl edgeable user can determine the nominal system s characteristics and also quantify the amount of disturbances and model errors that can be tolerated According to the authors experience several people who tune regulators in the field appear to consider their parameters just as knobs to be moved depending on what characteristic of the loop response needs improving This may be enough in that context but does not suffice for evaluating an autotuner effectively For understanding how an autotuner will behave it is necessary to abandon ideas like the regulator gain must depend on the step response over shoot which are misleading because the entire regulator depends on the entire process dy namics facts like the overshoot being just an external evidence of what these dyn
135. this forecast is projected while K acts as a further proportional factor between the forecast and the corresponding action The D action is the quickest to react unfortunately also to measurement noise and helps only if the forecast is good 1 e if Tg is not too big with respect to the time scale of the error dynamics compare cases A and B in figure 3 That is why Ta must be limited and because T is a measure of the closed loop time scale Tg is normally requested to be quite a bit smaller than T e t de t Ne precast T d d 7 Aeru 5 e t T e t Figure 3 explanation of the role of the D action 14 2 3 Control performance assessment in the time domain The most natural way of assessing the performance of a controller is to formulate prescrip tions on the transients it must produce A variety of response characteristics can be used to this end such as the most common ones indicated in Figure 4 Or the requirements could be in the form that the closed loop response to a set point step must be as similar as possible to that of this model Thus time domain assessment can be used both in model following and in characteristics following autotuners Overshoot Steady state error Settling time time for entering a band of 2 around the final value without leaving it anymore Controlled variable response Rise time time for going from 5 to 95 of the final value minus the in
136. tion is a skyscraper whose foundations are the low level loops As such learning to auto tune the individual loops means mastering the very basic fundamentals of the overall construction Finally dis cussing the issues we have chosen to omit would really lead far beyond the scope and extent of this work so we must acknowledge that we are covering a small section of the competen cies required for setting up control systems in the general case An effective grasp of what we mean can be obtained e g from EnTech 1994 a short document that the authors strongly recommend to anyone involved in industrial control or from Bialkowski 2000 However accepting these limitations will allow for a self contained discussion some problems will necessarily be left open and it is the authors hope that the reader will be encouraged and stimulated by them Some suggestions for further reading will be given when useful to guide those who desire a wider or deeper knowledge 1 1 How autotuners work and how they can be broadly classified To start understanding how an autotuner works consider how a human would act when tun ing a regulator in the field Basically he would a observe how the process behaves maybe stimulating it somehow and more or less consciously turn this knowledge into a descrip tion of the process behaviour b convert his ideas on how the closed loop should function taking into account the limitations of t
137. to emulate human expertise str m and H gglund 1995 p 237 241 In our opinion this classification is well suited for classifying autotuners under a methodological point of view but especially if used by non specialists may introduce some confusing elements Hence we prefer a description that reflects the op erational aspects of autotuners more in detail and though remaining simple and broad al lows us to point out clearly those differences that may not be methodological but have a sig nificant relevance on what must be understood when using that autotuner A final remark on the classification we are proposing is that all the steps of the autotuning process are tightly coupled for model based autotuning a process model is in order for time domain character istics to be imposed the required process information must be available and so on More over a certain tuning policy is more suited for some purposes than for others e g pole zero cancellation tends to produce sluggish transients for load disturbance rejection It is then im portant when choosing an autotuner to understand at least the basics of the tuning rules it contains 1 2 Where and why PID autotuning is useful Before saying anything in this respect it must be made clear that a sufficiently skilled human with sufficient process knowledge data and time available can outperform any autotuner in any situation Autotuning can provide a tremendous improvement in setting u
138. to explain as an effect of the input some fact that is actually caused by something else and conclusions on the process dynamics drawn in this way can be far from reality 30 The simple structure of the PID regulator especially in the 1 d o f case calls for simple process descriptions so that first or second order models or small sets of characteristics are typically used In this section we present a very brief review of some modelling and identifi cation techniques used in autotuners limiting the scope to experiment based methods since they cover almost the totality of cases and treating the other methods would really not be practicable Since this presentation cannot be exhaustive for apparent reasons we only intro duce methods adopting the most common approaches 1 e involving an open loop experi ment the recording of the so obtained response and the processing of this for obtaining the process description In most cases a step response will be used Step experiments are the most common strategy in experiment based autotuners For the reader willing to experiment they are also easy to apply in the field it suffices to switch the regulator to manual wait until a reasonably steady state 1s reached then change the control variable suddenly by an amount sufficient to make the response obtained easily distinguishable from noise In addition step tests permit the process to be maintained under reasonable control without perturbing it ex
139. tor is checked against some parameter consistency rules for exam ple most autotuners verify that Ti gt Td Also the implementation feasibility is checked typi cally verifying say that no regulator time constant is smaller than few times the sampling time Finally very high end products also check the sensitivity of parameters to specifica tions to avoid the situation where a small change in requirements results in a completely dif ferent regulator This is not required strictly but nevertheless users are keen to think that the dependence of parameters on specs must be in some sense continuous Also these checks are normally documented up to a very limited extent but for selecting a product this is less im portant 5 Examples of industrial autotuners Applying the obtained knowledge to evaluate a product Throughout the previous sections we have acknowledged the features of the various types of autotuners with the aim of helping the reader understand their operation and above all to se lect one on the basis of the characteristics of his particular control problem In this section we briefly present some industrial products Firstly to show how the features that have been highlighted earlier can be detected in the manufacturers documentation Secondly to see how this information can then be evaluated as for its suitability for a given application This section is in two parts The first part looks at autotuners that are supplie
140. treated in this volume for space limitations If no predictor is avail able choose a tuning policy aimed basically at high damping and then try some manual adjustments e g slightly increasing the gain or decreasing the integral time Tight control Tight control required not required High measurement Low saturation Low meas noise noise limit and high sat limit 0 gt 1 k lt 1 5 por i FFCE DTCR PI FFCE DTCR PI FFCE DTCE 2 0 6 lt 0 lt 1 I or PI I FFCR PI FFCR PI FFCR DTCR or 1 5 lt k lt 2 25 PID FFCR DTCR 3 4 1 0 15 lt 0 lt 0 6 PI PI PI or PID PID 2 25 lt k lt 15 0 lt 0 15 k gt 15 P or PI PI PI or PID PI or PID or 0 gt 0 3 k lt 2 0 lt 0 3 k gt 2 PD SPWE PPTR PD SPWE PD SPWE FFCR Feed Forward Compensation Recommended FFCE Feed Forward Compensation Essential DTCR_ Dead Time Compensation Recommended DTCE Dead Time Compensation Essential SPWE Set Point Weighting Essential PPTR Pole Placement Tuning Required 4 The typical autotuning process Automating the steps of tuning methods In this section we shall describe the most important aspects of the autotuning process That is after the reader has been provided with the background of how a PID can be tuned on the basis of process information gathered from the field it will be explained how this operation can be automated what are the major problems that arise in doing this and what are the solu tions taken for the
141. trolled variable should be close to the set point when the auto tuner is initiated The procedure starts by inserting a small step to the system and this causes the system to oscillate The step value has to be selected in ad vance The tuning function itself has similarities with the manual Ziegler Nichols method precise information about the tuning method is not available The auto tuner adjusts the amplitude so that the process value will not be greater than the level that 1s necessary to isolate the meas urement noise The auto tuner is able to judge if the derivative element is necessary An adaptive procedure is available which can be used as a fine tuner For further details see the ABB web site 63 9 1 5 The OMRON ESAK E5EK The Omron E5AK ESEK calculates suitable PID parameters using a fuzzy self tuning func tion The controller itself determines when tuning is necessary Three different modes are se lectable step response tuning SRT disturbance tuning DT hunting tuning HT In the SRT mode the controller parameters are tuned when a new or different set point change oc curs In the DT mode the PID parameters are adjusted so that the controller output stays within the target range that has to be specified in advance In the HT mode the controller pa rameters are amended once hunting occurs HT will be enabled when four or more extreme control values occur provided SRT is not being executed 5 1 6 The National Instrumen
142. ts Autotuning PID This quite recent autotuner is initiated on user demand experiment based it uses relay feed back on the set point characteristics based the process description is given by the ultimate gain and frequency see e g str m and H gglund 1984 characteristics following with lexical specs the user has to select the controller type P PI or PID and normal fast or slow tuning Parameters are computed by Ziegler Nichols like formulae described in the product docu mentation The regulator has an ISA like form there is no derivative filter but a fixed one on the process variable output derivation is used and set point weighing in the P action is available in the online help the weight is called relative emphasis of disturbance rejection to set point tracking Gain scheduling and a static nonlinear characteristic on the error are also available While presenting all the advantages and pitfalls of autotuners obtaining local process infor mation from relay feedback see the corresponding section this one has two peculiar fea tures that are worth pointing out First tuning is accomplished by the used via a wizard 1 e a sequence of interactive steps guided by windows carrying the necessary instructions and the usual next previous cancel buttons to navigate back and forth in the procedure Interest ingly enough in this wizard the recognition of the steady state prior to the relay t
143. ts introducing analysis and design methodologies at undergraduate level The relationships between the external input signals Y s the disturbance D s and the measurement noise N s and the control system outputs the process output Y s its meas urement Y s and the control signal U s can be expressed in nominal conditions by 19 Y s S s T 8 Ry s T s DOs Ya f S9 S89 Re S T s NG 6 U s 8 8 Re SC s Y The transfer functions S s Co s and T s are called the nominal sensitivity the nominal complementary sensitivity and the nominal control sensitivity respectively and are defined as follows l __Ra 9P 8 LOTR OPA T C s 89 1 R a s P s h 1 R 8 P 8 7 2 5 2 Stability definitions The classical concept of stability of a linear time invariant system described as a transfer function is well known This will be defined here as input output stability and demands that the roots of the nominal characteristic equation 1 R s P s 0 all lie in the left half of the s plane The second concept is that of internal stability The requirement for internal stability is that the nine transfer functions in 6 are stable This corresponds to requiring that the nominal system is input output stable and also that in it there is no pole zero cancellation in the right half plane 2 5 3 Frequency domain design definitions for SISO systems wit
144. ure out by experimenting with the autotuner The advice when selecting one is then to try providing some of the re quested information incorrectly This should not be done in the field of course but is very useful when testing the autotuner e g simulating the transfer function seen by the regulator with a PC In so doing one can always obtain a quite clear idea of which in formation is more critical and sometimes with good knowledge of the control theory and some luck also imagine at least the basic assumptions made by the autotuner e If one has a clear idea on what some closed loop characteristics must be it is better to use a characteristics following autotuner having those among the ones it is capable of ensuring e If one has no well defined desires a good idea is to use a model based autotuner which may sometimes achieve modest results but is very unlikely to provoke e g instability and observe its outcome In our example it would have been evident that the IMC pro duced too large an integral time and that the disturbance transient could be accelerated 52 After the autotuning operation an experienced user could easily refine the tuning an easier job than doing it from scratch Three remarks are now in order First the considerations we have made apply both to model based and to characteristics based autotuning No matter what the description of the process behaviour is certain quantities yield information on certain f
145. ustrial regulators 3 The basics of PID tuning Obtaining simple process descriptions from data and computing the PID parameters To select an autotuner it is of great help if one is capable of tuning Hence after the review of PID control principles made in the previous section here we shall illustrate the major PID tuning methods These can be used by a human and it is recommended that anyone involved in control have some experience of these and when automated form the backbone of many of the more common autotuners The tuning process as sketched out in the introduction will be the path followed in this section We shall first describe how to obtain a description of the process behaviour and then how to compute the PID parameters on the basis of it and of the desired specification 3 1 The extreme basics of data based process description The process descriptions used for autotuning must be obtained from I O data In the great majority of cases a process description is obtained by performing an experiment on the pro cess 1 e by stimulating it deliberately In other cases it is obtained by merely observing the process input and output during normal operation This approach is far less frequent because it requires one to make sure that the observed output behaviour is actually caused by the input which is not easy and may require measuring additional signals If there is no certainty in this respect the identification mechanism may try

Hands-on PID autotuning

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