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user`s manual - Control Systems Engineering Laboratory

1. Time Sequences Noise in Y 9 41972 14 9255 dB 0 4F T T T 10 4 y 5 Y e o S Y Y 990 p 0 46 1 1 1 H A 0 500 1000 O iii Noisy 2500 10 4 ae Noise free Pi AR o eL el P 3 10 0 4L f f f ite H e s LE RARO A 0 500 1000 1500 2000 2500 r r r r r 10 2 10 F 3 gt o Js CD 10b f 0 500 1000 1500 2000 2500 10 4 r r r r 1 10 gt o0 7 10 d 10 L L fi 10 X 0 500 1000 1500 2000 2500 Frequency rad min Time min a Input PSD b Time Sequences Figure 42 Experiment of identification test monitoring for the Jacobsen Skogestad high purity distillation column a standard zippered power spectrum design a and time series of input and output data b Input State Space Output State Space 0 4 15F 4 e 03 la 31 a pe 10 st J oF 4 0 2 tho pa 1HE ld E tt st oot a F Ft 0 1 AE r the aF EN Tye qt a a 9 Fe agp t E 4 F gt get gt ee teh at ee E t e ER ae t 0 1 F 5 fa 4 4 CN Aer t tF E ET FE a 02 go AR ES F z He tae af tt e T 10 F 4 Py Sn 0 3 F qe t i a 0 4 1 1 1 1 1 1 1 1 1 15 10 5 0 5 10 15 0 4 0 3 0 2 0 1 0 0 1 0 2 0 3 0 4 U Y a Input State Space b Output State Space Figure 43 Experiment of identification test monitoring for the Jacobsen Skogestad high purity distillation colu
2. Unweighted MFD 100 150 Time min 200 PH 35 MH 5 Ywt 1 1 and Uwt 0 05 0 03 0 13 51 Singular Value Plot True Plant 2 Unweighted MFD tere Weighted MFD 10 Frequencies Rad Min Figure 49 Experiment of identification test monitoring for the Jacobsen Skogestad high purity distillation column singular values of true plant vs estimated models in frequency domain MPC tuning set PH 35 MH 5 Ywt 1 1 and Uwt 0 05 0 03 0 13 Additive Uncertainty Norm Bounds 10 dd cn AN is ie R a E Y a Ne iH 3 S T 10 C M 1 7 a 4 O v a t i Wo A Stage 3 14 cycles nwi PE joth im A Stage 3 10 cycles Ya d donas 1A Stage 3 5 cycles 1 Vy Vn 29 107 10 Frequency rad min Figure 50 Experiment of identification test monitoring for the Jacobsen Skogestad high purity distillation column additive uncertainty norm bounds at 5 10 and 14 cycles 52 Spectral Radius Analysis p E H Robust Loopshaping with Weighted CR MFD G w r a E 0 10 me Pag dd gt an 10 E e Se ar i n Ss a 3 ETS 10 z F 10 unweighted MFD weighted MFD mima Smax Wy S maxll d 1 T 10 107 Frequency a Small Gain condition p E
3. CRIDENT_Toolbox_release4 Sele ae Q sxx amp P Search e Folders Ez Address C hyunjinisysID CRIDENT_Toolbox_releaset Y Go Folders E O CRIDENT_Toolbox_release4 5 example E 5 fregestgui o 8 IT Kernel O Test multisine_design E mvparest robustloopshaping 5 uncertain_estm D statbx42 A ne ewe m Figure 2 Directory structure for CR IDENT Toolbox The toolbox is designed using Matlab R14 with Service Pack 3 Version 7 1 and requires the Signal Processing Control System System Identification and Model Predictive Con trol Toolboxes as well as Simulink Installation of the CR IDENT Toolbox is accomplished by the following steps 1 Copy CRIDENT Toolbox releasexx zip at a directory 2 Uncompress CRIDENT Toolbox releasexx zip from the current directory If it is properly uncompressed the main directory contains the same sub directories as Fig ure 2 3 Start Matlab on your computer and open Set Path window from File menu on the Matlab command window 4 Click Add with Subfolders and select CRIDENT Toolbox releasexx directory Then 1t will automatically include the sub directories 5 Hit the Save button and close the Set Path window Although the CR IDENT toolbox should work in all Matlab plaforms its development has been primarily done using PC Windows 3 Getting Started with the CR IDENT Toolbox Now CR IDENT is
4. Model Predictive Control Tuning for Weighting toWorkspace MPC Tuning A PH Yt r MPC Evaluation gt MPC Object MFD Model MH Paes MPC Simulink Model MDL file setting End Time O CRPEP Model o using Unweighted Model Input Change r mec rest O using Weighted Model i Example Cases True Plant optional enter Model CRMFD ESTIMATE A Modified Shell Heavy Oil Fractionator Jacobsen Skogestad Distillation Column Hyunjin Lee amp Daniel E Rivera Figure 23 Control Relevant Parameter Estimation GUI The curvefitting relies on frequency dependent pre and post weight functions meaningful to MPC control Rivera and Gaikwad 1995 The control relevant weighting functions sys tematically shift the model error into regions that are less significant to closed loop control performance Sanathanan Koerner iteration and Gauss Newton minimization are applied to successively improve the model estimate robustness criteria such as the Small Gain The orem can be specified from the GUI to monitor the control relevancy of an MFD model If a closed loop Simulink model is available users can test the estimated model with respect to setpoint tracking directly from the GUI 7 1 Entry Data Format for Control Relevant Parameter Estimation GUI The necessary components for the entry data structure to the control relevant curve
5. Multisine Type Shifted Signals Zippered Signals Modified Zippered Signals Low Frequency Interval delta 0 Low Frequency Ratio If 01 Harmonic Suppression hs 0 High Frequency Ratio hf 05 Correlated Harmonics Design for Mofidied Zippered PSD gamma 72 direction 1 1 or PRBS Inputs C Inverse Repeat Sequence Figure 6 Input signal type selection on the Input Design GUI First the user determines an input signal type between Multisine or PRBS The GUI will disable some components depending on the user selection Multisine Inputs Phases should be either Guillaume Phasing Guillaume et al 1991 or Schroeder Phasing Schroeder 1970 The crest factor minimization algorithm using Guillaume Phasing takes more time to compute than Schroeder Phasing 11 Multisine Type should be given among Shifted Zippered or Modified Zippered design that specifies an input power spectrum for multiple input channels If the number of input channels is one they are all identical Low Frequency Interval 6 creates the given number of channel groups in the input power spectrum at low frequency grids using Low Frequency Ratio If lt 1 The coef ficients in the lower frequency grids in Figure 4 that correspond to Lf High Frequency Ratio hf lt 1 defines Fourier coefficients at higher frequencies out side the primary bandwidth The coefficients in t
6. _ 3 020305 E SAVE Process Source Select O Frequency Responses LOAD a source Unweighted MFD model CLEAR for P w E Weighted MFD model Isto IHG II HCI F 110 11 Uncertainty Estimation Frequency Response TYPE Confidence Level O ETFE Spectral Analysis 95 0 gt et aa el a i 10 10 10 o Biene O High Order ARX Transfer Function Plots Sensitivity Function Specification Merged Response O Piw 7 wpiw 7 esq How Design C11 St Design 1911 wu w V cHiw NUM i T Performance Weights liS E y DEN Wp Weighting C Wu Weighting IICS w eae ae do metal Refresh Plot Evaluate mb 4 mbe wh 0 001 3 whe A 0 000001 Abc obust Performance Weighting hn J yunjin Lee aniel E Rivera Loto osa Robust Perf Weighti FULTON H Lee amp D lE Ri CSEL 4 ciheal af cepinesting ma Lava Figure 31 Robust Loopshaping GUI a parametric model is performed using robust loopshaping considering both uncertainty bounds and model estimation error If the model satisfies the loop bounds the procedure can be terminated otherwise the user needs to change performance weights and otherwise iterate on the control relevant parameter estimation and robust loopshaping procedures 8 1 Entry Data Format for Robust Loop
7. button for the weighted curvefitting If it is successful the user can run the closed loop evaluation with MPC by hitting the MPC Test button with CRPEP Model selected The user may change the parameters in Ma trix Fraction Description Method to improve the numerical convergence for the loop iteration To use the true model during the curvefitting hit Load Model with putting shell_ss in the edit box and select True Plant optional For MPC relevant weights PH 35 MH 10 Ywt 1 1 and Uwt 15 22 1 605 MPC Eval uation is set as MPC Object mpc3 MPC Simulink Model Shell HOFP_MPC Input Change r 0 1 0 1 and End Time 1500 The use may iterate the last two steps until the estimated model shows desirable performance in the closed loop evaluation Otherwise the user may need to refine the frequency responses or to redo the input signal design and testing experiment 4 9 2 Illustration with Jacobsen Skogestad Distillation Column Utilizing the step wise procedures given in the previous section a modified zippered spec trum input design is utilized for the Jacobsen Skogestad Distillation Column The open loop Matlab Simulink simulation is provided at run jacobsen_skogestad_idtest in the Ex ample directory 1 Open the Multivariable Input Signal Design GUI 2 Hit Jacobsen Skogestad Distillation Column button and it brings the pre
8. tion Once the weighted model is obtained repeat the procedure with the Robust Loop shaping GUI and compute the robustness conditions based on the parametric model For a weighting fuction in the loopshaping W is used with mb 4 wb 0 001 and A 10 and Confidence Level is 95 When new robustness condition bounds are computed repeat the procedure in the Control Relevant Curvefitting GUI Find a controller tuning parameter set that can satisfy robustness conditions If a weighted model satisfies robust conditions in both Control Relevant Curvefitting and Robust Loopshaping GUIs the user can stop At last the obtained set of models based on the weighted model and uncertainty bounds may possess sufficient model adequacy for robust control system 44 9 3 Example Study of Jacobsen Skogestad Distillation Column The Jacobsen Skogestad column represents a highly interactive system and as a result a directional input signal design is considered to achieve balanced gain directionality in the data From a priori model information a steady state gain is obtained such that 0 785 0 771 18 0 966 0 978 and SVD analysis on K gives _ 0 6249 0 7807 rE 1 7609 0 yHe 0 7072 0 7070 0 7807 0 6249 7 0 0 0130 0 7070 0 7072 19 A y range is obtained using the above information as Ynin 54 25 lt Y lt Ymax 84 65 20 As a result Yayg 69 45 and v2 0 7070 0 7072 are selected f
9. 0 2 0084 8 2 6 Action Buttons 8 2 7 Sensitivity Function Specification o Illustrative Examples of CR IDENT 9 1 Illustration with Shell Heavy Oil Fractionator Problem 9 2 Illustration with Jacobsen Skogestad Distillation Column 9 3 Example Study of Jacobsen Skogestad Distillation Column 10 Remarks and Conclusions 11 Acknowledgements 33 34 35 35 35 36 36 37 37 38 39 40 42 45 49 49 1 CR IDENT Overview This document describes CR IDENT a Matlab based toolbox that implements a com prehensive framework for multivariable control relevant system identification aimed pri marily at process system applications CR IDENT consists of a series of graphic user interface GUI modules that accomplish 1 multivariable input signal design for multi sine and pseudo random binary sequences PRBS 2 frequency response estimation 3 control relevant frequency response curvefitting and 4 robust loopshaping The toolbox is intended to generate efficient models whose end use is the design of high performance model based control systems Rivera et al 2003 Lee 2006 An important component in the implementation of this design procedure is its reliance on a priori knowledge of the system of interest to design input signals meeting both theoretical and practical user requirements Data from identification testing using these signals are the basis for the subsequent steps of
10. forall other i up to m 6 n A frequency range of interest containing the bandwidth of the primary power spectrum should fall within the range specified by the inequality of 3 Braun et al 2002 Rivera et al 2002 a 10 amp lt 0 lt a 3 fe A Within the primary bandwidth sinusoidal harmonics perturb the dynamics of a system of Primary Excitation Frequency Bandwidth E Channel 1 O Channel 2 MBOAMBOCABOAHBOAHBOAHOA A Channel 3 hf HOAHOA Fourier Coefficients 2am l 8 2am n T E E OD O A A Se a IN E NT T Frequency s Figure 4 Conceptual design of a standard zippered spectrum for a three channel signal interest to produce informative datasets for system identification Consequently 2am 1 2mm ns T _ lt a lt wo lt ow lt lt N T N T o 4 which in turn translates into the following inequalities for the number of sinusoids the sampling time and the sequence length ns T and Ns respectively ns 6 gt 1 6 6 T lt mi T m nl 6 ES Eye 0 0 n 0 2mm 1 6 2mm ns The principal design guideline implemented in the CR IDENT uses a priori knowledge of dominant time constants of the system and speed of the response specifications to define a primary bandwidth for excitation in the signal Lee et al 2003b Lee and Rivera 20050 For users not wishing to use these guidelines the input GUI supports direct parameter spec
11. H b Robust Loopshaping on P MPC Setpoint Tracking Test T Singular Value Plot 0 15 r r 0 14 TENERE True Plant ra T ie Unweighted MFD e L veers Setpoint ff fee _ Weighted MFD 1 10 0 50 100 Weighted MFD 0 r T Unweighted MFD e Time min 10 107 Frequencies Rad Min c Setpoint Test d Singular Values Figure 51 Experiment of identification test monitoring at Neycies 5 for the Jacobsen Skogestad high purity distillation column Small Gain condition a robust loopshaping b MPC setpoint test c and singular values d with MPC tuning set PH 35 MH 5 Ywt 1 1 and Uwt 0 05 0 03 0 2 53 Spectral Radius Analysis p E H a 10 at pe pmo unweighted MFD Ss weighted MFD A Sma Wy S Say Lal 10 a y Ad ix 10 gt 10 1 10 10 a Small Gain condition p E H MPC Setpoint Tracking Test 0 15 i A AAA gt 0 05 0 sees Setpoint 0 50 100 Weighted MFD 0 i Unweighted MFD 0 05 4 gt 01 TR u7 0 15 ea 0 50 100 150 20 20 r i l 0 50 100 150 20 20 T T 7 S10 mre 0 f 1 0 50 100 150 20 Time min c Setpoint Test o 0 Amplitude Robust Loopshaping with Weighted CR MFD G w T Frequency b Robust Loopshaping on Singular Value Plot T I
12. Specification for Shifted Signals Nunmber of Sinusoids Sequence Length Frequency Bandwidth Specification Lower w lt Primary Bandwidth lt Upper w No of Sinusoids optional i Figure 10 Design parameter selection on the Input Design GUI Design Guideline a priori process information is utilized for this option which specifies the primary excita tion bandwidth as described before from 3 to 7 TdomL and TdomH indicate the low and high dominant time constants i e Ti H and Tiom 14 Alpha and Beta represent 0 and Ps for the speed of closed loop response and set tling time requirement respectively No of Sinusoids is an optional parameter allows the user to specify the number of sinusoids in the primary excitation bandwidth Direct Specification for Shifted Signals The options are changed based on Multisine and PRBS respectively such that 1 Multisine e Number of Sinusoids directly specifies the number of sinusoids for the pri mary bandwidth e Sequence Length directly specifies the sequence length for multisine input signals 2 PRBS e Switching intervals nsw indicates that the input magnitude will remain un changed for at least this time interval e No of shift registers specifies for the number of registers for the pseudo random binary sequence generator Frequency Bandwidth Specification T
13. curvefitting If it is successful the user can run the closed loop evaluation with MPC by hitting the MPC Test but ton with MFD Model selected The user may change the parameters in Matrix Fraction Description Method to improve the numerical convergence for the loop it eration Model orders are na 1 nb 1 nk 1 and Iteration Options amp Error Criteria are SK Loop Iteration Max 20 Min 2 GN Iteration at a SK step 100 Abs Error 1e 12 Rel Error 0 001 Relatvie Parameter Difference 0 001 Hit CRMFD ESTIMATE button for the weighted curvefitting If 1t is successful the user can run the closed loop evaluation with MPC by hitting the MPC Test button with CRPEP Model selected The user may change the parameters in Matrix Fraction Description Method to improve the numerical convergence for the loop iteration To use the true model during the curvefitting hit Load Model with putting jacob_ss in the edit box and select True Plant optional For MPC relevant weights PH 35 MH 5 Ywt 1 1 and Uwt 0 05 0 03 0 13 MPC Evaluation is set as MPC Object mpe3 MPC Simulink Model Jacobsen_Skogestad_MPC Input Change r 0 1 0 1 and End Time 500 The user may iterate the last two steps until the estimated model satisfies the robust ness conditions and shows desirable nominal performance in the closed loop evalua
14. frequency response estimation and control relevant parameter estima tion A resultant representation is a discrete time state space model that can be used as the nominal model for Model Predictive Control or other forms of multivariable control design Improving the link between system identification and control design has been a subject of great interest in the control systems literature for nearly two decades Hjalmarsson 2005 There is a continuing need for control relevant identification methodologies focused on multivariable problems that appeal to both academic and industrial practitioners In princi ple such methodologies should be comprehensive in nature take full advantage of a priori knowledge of a system to be identified be as short and non invasive as possible to the process i e plant friendly and not make substantial demands on user skill levels in its implementation Rivera et al 2003 Based on recent research activities in the Control Systems Engineering Laboratory at Arizona State University CR IDENT has been devel oped with these goals in mind Rivera et al 2003 Lee 2006 The functionality implemented in the CR IDENT is summarized in Figure 1 Although aimed primarily at process system applications the methodology is broadly applicable and can be useful in multiple application domains These modules can be used independently or as part of an integrated procedure as shown in Figure 1 The functionality of e
15. given for a two output sys tem as 7 2 6 Action Buttons Close Figures Figure 29 Action buttons on the Curvefitting GUI Close Figures closes all the Matlab figures SAVE stores all the information from the GUI into a file LOAD opens a file and uploads it onto the GUI CLEAR ALL empties all the information on the GUI toWorkspace exports all the information to the Matlab workspace 7 3 Examples By the use of the Input Signal Design and Frequency Estimation GUIs two example cases for the curvefitting procedure available directly from the GUL The frequency responses can be uploaded by hitting the buttons in Figure 30 i Example Cases A Modified Shell Heayy Oil Fractionator Jacobsen Skogestad Distillation Colurnn Figure 30 Illustrative example cases on the curvefitting GUI A Modified Shell Heavy Oil Fractionator provides the two cases using phase shifted and standard zippered multisine input designs In addition the model is slightly modified from the Shell Heavy Oil Fractionator with longer time delays in transfer functions Jacobsen Skogestad Distillation Column provides the three cases using phase shifted standard zippered and modified zippered multisine input designs In particular the modi fied zippered spectrum is considered for the directional adjustment to enhance the low gain direction in the distillation column The frequency responses are estimated based o
16. identification test monitoring procedure O after 5 cycles is only available for the high frequencies Figure 51b After 10 cycles O S is computed for a wider range but is partly missing in the low frequencies Figures 52b All the low singular value plots show good estimation to the true plant Figures 51d to 52d Robust stability analysis is improved with increasing test cycles from 3 to 10 cycles see Figures 53 and 54 10 Remarks and Conclusions CR IDENT represents a software implementation of a comprehensive control relevant iden tification methodology that is motivated by the needs and requirements of process systems particularly strongly interactive ones such as high purity distillation The toolbox reduces the background and skill level required to implement this procedure since only a priori knowledge of a system in terms of time constants and steady state gains if available is required to initiate this toolbox Following identification testing the frequency response estimation and control relevant curvefitting modules work interactively with necessary it erations between the GUIs to produce a useful model leading to a high performance Model Predictive Controller This was demonstrated for a strongly interactive distillation column simulation As a result CR IDENT is able to provide an integrated framework that is highly demanded to achieve a systematic identification test monitoring procedure The most up dated CR IDENT t
17. method for multiple input implementation Inverse Repeat Sequence results in an even frequency grid harmonic suppression effect 4 2 2 General Signal Specs Although the user can determine general signal specs more often these parameters should be based on the system s physical characteristics General Signal Specs Sampling Time 8 min Number of Channels 2 y Number of Cycles gt d Amplitude 0 1 0 1 60 Figure 9 General input signal specs on the Input Design GUI Sampling Time is the minimum hold time of change for the input sequence which should 13 agree with the measurement sampling time in the output Number of Channels corresponds to the number of input channels in a given system The user can select a value between 1 and 20 on the current GUI or numerically specify a number larger than 20 Number of Cycles repeats one period of the input signal for the specified number of cycles Amplitude is the input magnitude that can be given in several ways for multiple chan nels For example when the user has two input channels the amplitude can be given either in string or number format e 1 1 1 1xones 2 1 1 0 5 4 2 3 Parameter Selection for Signal Bandwidth Parameter Selection Design Guideline TdomL 15 Alpha 2 No of Sinusoids optional TdomH 194 Beta 3 O Direct
18. ready to be started by the user Invoking the command gt gt crident calls a main menu see Figure 3 with options corresponding to each of the four GUIs that comprise CR IDENT The toolbox consists of modules for multi channel input signal design multisine and PRBS frequency response estimation control relevant frequency response curvefitting and robust loopshaping CR IDENT Control Relevant System Identification 2 0 A Toolbox for Control Relevant Identification Test Monitoring Hyunjin Lee amp Daniel E Rivera Control Systems Engineering Lab Department of Chemical Engineering Arizona State University Multivariable Input Signal Design GUI Frequency Response Estimation GUI Control Relevant Parameter Estimation GUI Robust Loopshaping GUI CQ CSEL 00 PSU Fion Contact Us by Email Daniel Rivera asu edu or peacernaple hotmail com Figure 3 The main GUI for CR IDENT a toolbox for multivariable control relevant iden tification To open each individual GUI the user needs to hit the buttons on the CR IDENT GUI which will then open the corresponding GUI window Currently it is not possible to run multiple instances of the same GUI Salient aspects for each GUI module are described in the ensuing sections 4 Multivariable Input Signal Design GUI 4 1 Background in Multisine Input Signal Design By enabling direct specification of the power spectrum multisine signals represent a ver satile class of inpu
19. CR IDENT CR IDENT A MATLAB Toolbox for Multivariable Control Relevant System Identification Hyunjin Lee and Daniel E Rivera Control Systems Engineering Laboratory Department of Chemical Engineering Ira A Fulton School of Engineering Arizona State University Tempe Arizona 85287 6006 January 2008 CS E j Control Systems Engineering Laboratory ira FULTON school of engineering Copyright Control Systems Engineering Laboratory ASU Currently with the Department of Chemical and Biological Engineering Rensselaer Polytechnic Insti tute Troy NY Email hlee6 rpi edu or peacemaple hotmail com 2To whom all correspondence should be addressed Phone 480 965 9476 Fax 480 965 0037 E mail daniel rivera asu edu Contents 1 CR IDENT Overview 2 Installing CR IDENT and System Requirements 3 Getting Started with the CR IDENT Toolbox 4 Miultivariable Input Signal Design GUI 4 1 Background in Multisine Input Signal Design 4 2 Generating Multi Channel Input Signals 42 1 Input Signal Type 2 3 2 pis ais do add SE Ske 4 2 2 General Signal Specs ovio 12 iia ss 4 2 3 Parameter Selection for Signal Bandwidth ADA PIOUS oe Se eh OM ee a a Oe ek BA ES A2 Acon Buttons os s eo E A Rae Rie Be 4 3 Data Structure from Input Signal Design GUI 44 Examples sl Y a e ss A eRe 5 Running Experiment from Input Design GUI 6 Frequenc
20. Design GUI The user can use the designed input data in variety of ways for simulation or experiment for identification testing To use the input signal on the Matlab workspace it can be available directly from the GUI using toWorkspace or using a command load filename on the Matlab command window With a designed input signal u Ns and T are used as essential information for running the testing experiment The user has to decide a number of cycles for the total test duration N should not be modified and will be the basis for calculating the test cycles The simulation or experiment styles may depend on the user However the input and output data should be collected properly for the further identification analysis Figures 14 and 15 show typical examples of the simulation set using Matlab Simulink HIGH PURITY DISTILLATION COLUMN FOR IDENTIFICATION TESTING Jacobsen 32 State Model Discretized Version Input Signal t1 u2 Input Signal E gt hnum z hden z di kd1 2 Filter 1 hnumiz gt Distllation Column hden z kd2 5 Filter 2 discrete Input Output Data Figure 14 A Matlab Simulink simulation for Jacobsen Skogestad Distillation Column 18 Shell Heavy Oil Fractionator KO nx1 ot Scope ma H nx2 TEA t1 ux1 Input Signal Input Signal1 Scopet On zo Int out a utput Data Figure 15 A Matlab Simulink simulation for a modified Shell Heavy Oil Fr
21. Put idtest02 on the data load box and Hit LOAD DATA button Select Spectral Analysis since the input signal is designed by a modified zippered power spectrum design Put 256 or 512 in the Window Lag box Select Response Amplitudes and Hit ESTIMATE button the user can choose different options Put fresptest02 on the edit box in the toWorkspace box and Hit the button Open the Robust Loopshaping GUI Put fresptest02 on the data load box and Hit LOAD DATA button Choose Frequency Responses on the Process Source Select a Confidence Level for the Uncertainty Estimation and then press the Esti mate button Select a Performance Weight and put appropriate parameters Once such case is W with mb 4 wb 0 001 and A 10 Hit the LOOP SHAPING and it computes the robustness bounds with respect to the nonparametric frequency responses Write rsloop02 in the edit box and Hit the toWorkspace Open the Control Relevant Curvefitting GUI Before loading rsloop02 on the GUI please Hit Jacobsen Skogestad Distillation Column and Choose Modified Zippered Case because by doing this the user can take advantage of preset curvefitting options for Jacobsen Skogestad Distillation Column case on the GUI 43 22 23 24 25 26 2T Hit MFD ESTIMATE button for the unweighted
22. Rivera L Ljung and T McKelvey 2000 On adap tive smoothing of empirical transfer function estimates Control Engineering Practice 8 2 1309 1315 57
23. Systems Prentice Hall New Jersey Morari M and E Zafiriou 1988 Robust Process Control Prentice Hall Englewood Cliffs N J Prett D M and C E Garc a 1988 Fundamental Process Control Butterworth Stoneham M A Rivera D E and S V Gaikwad 1995 Systematic techniques for determining modeling re quirements for SISO and MIMO feedback control problems Journal of Process Con trol 5 4 213 224 Rivera D E H Lee H D Mittelmann and M W Braun 2007 High purity distillation Using plant friendly multisine signals to identify a strongly interactive process JEEE Control Systems Magazine 27 72 89 Special section on Applications of System Identification Rivera D E H Lee M W Braun and H D Mittelmann 2003 Plant friendly system identification a challenge for the process industries In 3th IFAC Symposium on System Identification SYSID 2003 Rotterdam Netherlands pp 917 922 Rivera D E M W Braun and H D Mittelmann 2002 Constrained multisine inputs for plant friendly identification of chemical process In 5th IFAC World Congress Barcelona Spain paper T We A11 Sanathanan C K and J Koerner 1963 Transfer function synthesis as a ratio of two com plex polynomials IEEE Trans Autom Control 9 56 58 Schroeder M R 1970 Synthesis of low peak factor signals and binary sequences with low autocorrelation IEEE Trans Info Theory IT 16 85 89 Stenman A F Gustafsson D E
24. True Plant Unweighted MFD mur Weighted MFD Frequencies Rad Min d Singular Values Figure 52 Experiment of identification test monitoring at Neycies 10 for the Jacobsen Skogestad high purity distillation column Small Gain condition a robust loopshaping b MPC setpoint tracking test c and singular values d with MPC tuning set PH 35 MH 3 Ywt 1 1 and Uwt 0 05 0 03 0 2 54 Figure 53 Experiment at 5 cycles of identification test monitoring for the Jacobsen Skogestad high purity distillation column robust stability analysis Figure 54 Experiment at 10 cycles of identification test monitoring for the Jacobsen Skogestad high purity distillation column robust stability analysis Robust Stability 10 Frequency rad min Robust Stability 10 Frequency rad min 55 References Braun M W R Ortiz Mojica and D E Rivera 2002 Application of minimum crest fac tor multisinusoidal signals for plant friendly identification of nonlinear process sys tems Control Engineering Practice 10 301 Guillaume P J Schoukens R Pintelon and I Koll r 1991 Crest factor minimization using nonlinear Chebyshev approximation methods IEEE Trans on Inst and Meas 40 6 982 989 Hjalmarsson H 2005 From experiment design to closed loop control Automatica 41 393 438 Jacobsen E W and S Skogestad 1994 Inconsi
25. ach mod ule is accessed with a graphical user interface GUI to provide flexibility and convenience to the user The theoretical background behind CR IDENT is described in various papers by Lee et al 2003a 2003b Lee and Rivera 2004 2005a 2005b Rivera et al 2007 and the Ph D dissertation by Lee 2006 Input Signal Design Nonparametric Control relevant Control Design and High order Parameter E Execution Parametric Estimation Estimation Implementation Multisine Input Empirical Transfer Robust Model Predictive phase choice Function Estimate Loopshaping Controller MPC Schroeder phased Smoothing Guillaume phased or constrained min CF geometrically distributed Spectral Analysis Frequency Weighted Robust Decentralized Curve Fitting PID I MC Controller spectrum type phase shifted High Order ARX standard zippered Estimation modified zippered PRBS Input Uncertainty Bounds Low process knowledge Figure 1 Summary of the design procedure and functionality available in CR IDENT a comprehensive framework for multivariable control relevant system identification This document presents the general features of the CR IDENT and helps the users get started and acquire the experience of using this toolbox In the following we will intro duce the four main GUIs in the CR IDENT with step by step guidelines for the user More over two illustrative example cases are provided based on the Shell Heavy Oil Fractionator Problem P
26. actionator Problem 6 Frequency Response Estimation GUI 6 1 Background in Frequency Response Estimation The Frequency Response Estimation GUI Figure 16 enables estimating frequency re sponses from multisine generated data using both parametric and non parametric approaches The Empirical Transfer Function Estimate ETFE and Spectral Analysis SA methods are used for non parametric estimation while high order ARX models are utilized for paramet ric frequency response estimation For noisy ETFE responses a Model on Demand curve smoothing algorithm by Stenman et al 2000 is available The specific requirements cre ated by zippered frequency grids are considered for orthogonal ETFE computation this also includes the treatment of signals that involve harmonic suppression Since multisine signals with the modified zippered spectrum contain correlated harmonics ETFEs cannot be computed however SA and ARX estimation options are available instead 6 2 Entry Data Format for Frequency Response Estimation GUI Having completed experimental testing the generated dataset can be used for further anal ysis in CR IDENT The first cycle of the data is usually not used for the identification analysis in order to reduce the impact of transient effects 19 Multivariable Frequency Response Estimation GUI Loading DATA Analysis and Plot Enter Data Structure Array Name from Workspace 3 or Click LOAD ID DATA for mat Files Respons
27. ag 20 Frequency Bandwidth Specification i Lower w lt Primary Bandwidth lt F Upper w No of Sinusoids optional gt CSEL ari Multivariable Identification of the High Purity Distillation Column Hyunjin Lee Ouputs dyD dxB amp Inputs dL dY Disturbance dF Parameter Selection TdomH 194min TdomL 1 5min alpha 2 beta 3 T 8min Daniel E Rivera A gain matrix K is available for a modified zippered spectrum Arizona State University Nanan Inal ab thn ride tne thn em atinbae A Modified Shell Heavy Oil Fractionator Jacobsen Skogestad Distillation Column ESI Fu LT ON j denso of Snpineerin Figure 5 Multivariable Input Signal Design GUI in CR IDENT are shifted relative to each other in order to reduce the interactions between channels A similar feature is available for PRBS signals A zippered power spectrum design gives or thogonality to individual input channels so that only one input channel is excited at each frequency grid The result of this approach is longer signal lengths relative to shifted sig nals but with lower levels of cross correlation For the case of strongly interactive systems CR IDENT offers the multisine signal with a modified zippered spectrum that contains both correlated and uncorrelated harmonics over the frequency bandwidth A modified zippered spectrum enables a directional adjust ment that can be used to emphasize specific gain directions
28. atrix Fraction Description Model Orders The MFD model consists of a matrix polynomial fraction A model P is approximated into a linear parametric real rational transfer function formed by a left side fractional matrix polynomial description LeftMFD P amp A 0 B 7 0 13 where A and B denote parameterized polynomial matrices in the indeterminate 7 E j represents a continuous time model whereas e 7 represents the shift opera 28 tor It requires the model orders for the number of matrix polynomial in the B nb and A na respectively In addition the time delay nk can be specified Iteration Options amp Error Criteria SK Loop Iteration gives the minimum and maximum iteration numbers for the Sanathanan and Koerner 1963 method that updates the weighting functions utilizing the previous model parameter G N Iteration at a SK step specifies the number of Gauss Newton error minimization iteration at each SK step Extended from the original SK method an optimal model pa rameter set is considered simultaneously with the SK iteration Abs Error sets the absolute weighted error criterion for the SK and GN loop termi nation Rel Error sets the relative weighted error criterion for the SK and GN loop termina tion Relative Parameter Difference sets the relative parameter difference criterion with the previous and current
29. cy Response Estimation GUI 40 10 11 12 13 14 15 16 17 Put idtest01 on the data load box and Hit LOAD DATA button Select Spectral Analysis since the input signal is designed by the phase shifting method Put 256 in the Lag Window box Select Response Amplitudes and Hit ESTIMATE button the user can choose different options Put fresptest01 on the edit box in the toWorkspace box and Hit the button Open the Control Relevant Curvefitting GUI Before loading fresptest01 on the GUI please Hit Heavy Oil Fractionator and Choose Phase Shifted Case because by doing this the user can take advantage of preset curvefitting options for A Modified Shell Heavy Oil Fractionator case on the GUI Then proceed to load fresptest01 Hit MFD ESTIMATE button for the unweighted curvefitting If it is successful the user can run the closed loop evaluation with MPC by hitting the MPC Test but ton with MFD Model selected The user may change the parameters in Matrix Fraction Description Method to improve the numerical convergence for the loop it eration Model orders are na 1 nb 1 nk 1 and Iteration Options amp Error Criteria are SK Loop Iteration Max 30 Min 2 GN Iteration at a SK step 50 Abs Error 1e 12 Rel Error 0 0001 Relative Parameter Difference 1e 10 Hit CRMFD ESTIMATE
30. ding the dataset to the Robust Loopshaping GUI Once the dataset is loaded without errors data information is analyzed and printed in the box e g the number of inputs and outputs the number of sinusoids the sequence length and the sampling time If available it indicates the signal to noise ratio in dB 8 2 2 Process Source The Robust Loopshaping GUI computes robust loop bounds based on frequency responses or a parametric models The user can select a process source in Figure 33 If a parametric MFD model is selected the loopshaping procedure will consider model estimation error in addition to uncertainty bounds 35 Process Source Select Frequency Responses a source O Unweighted MFD model for P w Weighted MFD model Figure 33 Process Source for the Robust Loopshaping GUI 8 2 3 Uncertainty Estimation Uncertainty estimation relies on the same procedure implemented in the Frequency Re sponse Estimation GUI The user may change the confidence level during the iterative procedure of designing a robust control system Uncertainty Estimation Frequency Response Type O ETFE Spectral Analysis 95 0 High Order ARX O Merged Response Confidence Level Figure 34 Uncertainty Estimation on the Robust Loopshaping GUI 8 2 4 Performance Weights The two performance weights are considered for the robust control system 1 W perfor mance weight Figure 35 on
31. e 17 Load an input output dataset to Frequency Response Estimation GUI Once the experiment dataset is loaded the GUI determines the input signal type based on 21 1ts input power spectrum The user has no control over the Input Signal Type Quick Start runs a series of frequency response estimations with basic options available on the GUI 6 3 2 Freqeuncy Response Methods The user decides a method of frequency response estimation with the loaded input output data using the selection options in Figure 18 Frequency Response Method ETFE Analysis High Order ARX Analysis C Model on Demand na nb nk Curve Smoothing z C Spectral Aneivsie _ Order Selection Window Lag LOAD Lag min lt OS Residual Analysis C Conf Level s d 99 9 X C Conf Level s d 99 9 i Figure 18 Methods of frequency response estimation option ETFE Analysis computes non parametric Empirical Transfer Function Estimates Model on Demand Curve Smoothing is available for smoothing noisy frequency responses The ETFE of the h th element of G is obtained from a fraction of output and input DFT se quences Ljung and Glad 1994 such that 1 A 0 Sne Qj ee 8 Y 0 and Up represent the DFT sequences of y k and uy k at frequency respec tively and yak ya k s 1 N5 9 fork 1 N ands 1 r Spectral Analysis uses the spa command of
32. e Ampiludes emer C Response Phases QA C Time Sequences C Input Power Spectrum Input Signal Type anal Standard Zippered Signals O Output Power Spectrum Modified Zippered Signals Shitted Signals ESTIMATE Frequency Response Method 2 ETFE Analysis High Order ARX Analysis C Model on Demand ina nb nk Curve Smoothing l Spectral Analysis Window Lag alidetion Data C Order Selection Lag min se lt ag max C Residual Analysis Ej Conf Level s d 99 9 O Conf Level s d 99 9 Additive Uncertainty Estimation Confidence Level 99 9 y Additive Uncertainty Estimation Example Cases A Modified Shell Heawy 0il Fractionator Jacobsen Skogestad Distillation Column Welcome to Multivariable Frequency Estimation Toolbox Enter a Data Name For questions or more information Please contact us Hyunjin Lee asu edu or Daniel Rivera asu edu ee Hyunjin Lee amp Daniel E Rivera Pte ts CSEL Loco Arizona State University FULTON echoa l sf enginesrisg Figure 16 Frequency Response Estimation GUI The GUI takes iddata or struct format as input data whose essential components include the following input and output time series sampling time the sequence length for one cycle and the number of sinusoids only for struct see Table 2 Once the input data is loaded the GUI analy
33. eter Estimation GUI The goal of the control relevant frequency response curvefitting GUI Figure 23 is to op timally estimate a useful parametric model with satisfactory control relevance which can be used as a nominal for Model Predictive Control MPC The approach used here follows according to the analysis described in Lee and Rivera 2005a 2005b Users can rely on frequency responses from the previous GUI or import frequency responses in idfrd or struct format with the proper syntax The control relevant curvefitting algorithm approximates frequency responses into parsimonious discrete time state space model representations based on linear Matrix Fractional Descriptions MFD 26 Multivariable Control Relevant Parameter Estimation Toolbox Loading DATA Saas aS Unweighted Parameter Estimation Please a data name from Workspace System information t Close Figures or Click for loading a mat file No of Inputs MFD ESTIMATE No of Outputs SAVE EE Bandwidth LOAD D AT A j Control Relevant Parameter Estimation Matrix Fraction Description Model cae ha LOAR from Unweighted MFD Model L l CLEAR ALL Model Orders Iteration Options amp Error Criteria SK Loop Iteration Max 10 Min 1 GN kteration at a SK step 20 4 r L SS nb a Abs Error 18 12 Rel Error 1E 6 z T na 1 nk 1 Relative Parameter Difference 1E 6 f
34. fitting GUI are given as follows Components Description Gy Frequency response in complex valued form w Frequency grids T Sampling time in minute Table 3 Essential components for Control Relevant Frequency Response Curvefitting GUI 27 The components in Table 3 can be contained either IDFRD or struct format 72 Getting Started with Control Relevant Curvefitting 7 2 1 Loading DATA An estimated data is loaded using the block in Figure 24 The user can load the data from the Matlab workspace or a mat file From the workspace the user enters a data structure name on the edit block and hit the LOAD DATA button If the entered data is not available on the workspace an error mes sage will appear From a mat file the user just hits the LOAD DATA button with the empty edit box Then it prompts the file open window for selecting a data file Loading DATA Please a data name from Workspace or Click for loading a mat file System Information No of Inputs 2 il No of Outputs 2 Bandwidth 1 0 0016 and LOAD DATA w n 0 1340 Figure 24 Loading the dataset to the Control Relevant Curvefitting GUI Once the dataset is loaded without errors its information is analyzed and printed in System Information box e g the number of inputs and outputs and frequency bandwidth range 7 2 2 Specification for M
35. he control relevant weighting is considered for curvefitting the frequency response into a parametric MFD model In particular this requires more information than the unweighted curvefitting The weighted curvefitting needs an initial parameter model to obtain the pre post weighting functions Since the closed loop response is reflected on the weight ing functions the user should provide an appropriate tuning set for MPC Select Initial Weighting The current release version is only based on the initial model from Unweighted MFD Model for initial weights The future release will consider from Loopshaping bounds and from User Defined Weights Model Predictive Control Tuning for Weighting MPC Model Predictive Control takes a set of tuning parameters PH prediction horizon MH moving horizon Ywt output weighting and Uwt move suppression The detailed information can referred to the Matlab MPC Toolbox manual Moreover the weighting function also needs the Input Changes which is located in the MPC Evaluation panel Tuning Adjustment is a feature that draws the sensitivity and complementary sensitivity 30 functions using a parametric model and the given MPC tuning set for the user convenience True Plant is an option for the user to provide the true plant to the curvefitting GUL in the state space model or a Matlab transfer function object If provided true plant is used for the spectra
36. he higher frequency grid in Figure 4 have value hf Harmonic Suppression hs suppresses sinusoidal harmonics at the frequency grids of the multiples of prime number 2 3 5 in the input power spectrum Correlated Harmonics Design is for a modified zippered spectrum that requires two additional design factors gamma Y applies its ratio to the correlated harmonics e direction specifies a particular input directional vector in real or complex values of interest to the correlated harmonics This can be given directly by the user or can be computed from a steady state gain by hitting on the Gain Matrix button Then the following window will show up Directional Input Design Ea tx Enter a Gain Matrix or Enter a Variable Name of Gain Matrix Figure 7 Entering a gain matrix for design a modified zippered spectrum The user can directly enter a gain matrix or a variable name that exists in the Matlab workspace A general scheme of the modified zippered spectrum is illustrated in Figure 8 12 Primary Excitation Frequency Bandwidth a Channel 1 O Channel 2 a O a D B O O O Correlated D 2 a pa El i harmonics E i i E y 0 z i 3 De 20 0 Ouau OEB O hf E if 200208 10200 2am 1 0 D 2am n 0 T NT NT T Frequency Figure 8 Conceptual design of a modified zippered power spectrum for 2 channel signal PRBS Inputs PRBS inputs rely on the phase shifting
37. his is a simple specification relative to the previous selections It allows the user to specify a primary bandwidth for both multisine and PRBS inputs see Equation 3 Lower w indicates for the lower bound of a primary bandwidth Upper w indicates for the upper bound of a primary bandwidth No of Sinusoids is only available with the Multisine signal option which generates that amount of sinusoids within the specified bandwidth 4 2 4 Plots The GUI provides several plots for the input signal 15 e Time Series plots one cycle of the generated input signals e Input Power Spectrum draws the input power spectrum based on one cycle e Auto Cross Correlation takes the correlation analysis for input signals The user can specify the lag size Plots O Time Series O Power Spectral Density O Auto Cross Correlation Lag 20 Figure 11 Plotting options on the Input Design GUI 4 2 5 Action Buttons Analyze Plot SAVE LOAD CLEAR ALL Close Figures Figure 12 Action buttons on the Input Design GUI The GUI provides a series of the action buttons for signal generation and data management Analyze Plot generates input signals with selected user s choices and plot options A small bar window shows up for the progress status SAVE opens a window to save the current signal data to a file 16 LOAD opens a window t
38. i e the low gain direction This is a critical consideration in the identification of highly interactive systems Lee et al 2003b Lee and Rivera 2005b Rivera et al 2007 If users provide a gain matrix the GUI computes the system gain directions and adjusts the signal s input directions and power amplitudes to produce a more balanced distribution in the output state space Lee and Rivera 2005b For all multisine signal choices shown in Figure 5 the phases can be obtained through either the closed form formula by Schroeder 1970 or the iterative p norm optimization 10 approach that minimizes crest factor developed by Guillaume et al 1991 Signals can be validated in both time and frequency domains and be exported in struct format A mod ified Shell Heavy Oil Fractionator Prett and Garc a 1988 and Jacobsen Skogestad high purity distillation column Jacobsen and Skogestad 1994 problems are provided as ex amples with the CR IDENT When the user selects the example buttons on the GUI these bring up default parameters that represent sensible choices of design variables for each of the two example systems 4 2 Generating Multi Channel Input Signals The detailed procedure of how to generate input signals using the Multivariable Input Sig nal Design GUI is given here 4 2 1 Input Signal Type Input Signal Type Multisine Inputs Phases Guillaume Phasing Schroeder Phasing
39. ification with a verification routine to insure proper implementation The input design GUI Figure 5 offers various options for multi channel implementation such as phase shifted orthogonal zippered spectrum and modified zippered spectrum designs Lee and Rivera 2004 The phase shifted multisine input design adopts a tech nique well known in the literature for pseudo random signals in which multiple channels 9 Multivariable Input Signal Design Toolbox General Signal Specs Input Signal Type Sampling Time Multisine Inputs Analyze Plot Guillaume Phasing Schroeder Phasing Number of Channels Z Multisine Type LOAD 2 O Shifted Signals Zippered Signals Modified Zippered Signals Ps im goers SAVE CLEAR ALL Number of Cycles Low Frequency Interval delta 9 Low Frequency Ratio If 01 3 Harmonic Suppression hs 0 High Frequency Ratio hf 0 5 Correlated Harmonics Design for Mofidied Zippered PSD Amplitude 4 wa detec gamma 72 direction 1 1 or PRBS Inputs Oo Inverse Repeat Sequence Close Figures 0 1 0 1760 to Workspace Parameter Selection _ Plots Design Guideline O Time Series TdomL 15 Alpha 2 No of Sinusoids gt TdomH 194 Beta 3 optional J Power Spectral Density Direct Specification for Shifted Signals O Auto Cross Correlation Nunmber of Sinusoids Sequence Length E L
40. ision to start or stop experimental testing The experiment is tested for 14 cycles to reduce the norm bound of model uncertainty to a suitable level for robust loopshaping anal ysis Initially robust loopshaping on P is performed providing provides 0 4 and 5 as a preliminary tuning guideline to properly tune the MPC controller in control relevant curvefitting that are selected to satisfy G A and 6 bounds Figure 44a Relying on previously weighted models we can iteratively tune the weighted curvefitting algorithm until a weighted model meets the loopshaping bounds When a weighted model satisfies the loopshaping bounds its Small Gain condition shows sufficient levels of nominal sta bility as seen in Figure 44b The weighted model P is then taken into account again for robust loopshaping including the model error P The model estimation error and model uncertainty are incorporated into N and N structures for loopshaping As the bounds of 6 F1 and G S are satisfied with the weighted model a finalized model can be obtained that meets both control relevance and robustness requirements with an MPC tuning set of PH 35 MH 5 Ywt 1 1 and Uwt 0 05 0 03 0 13 Figure 47 A closed loop model evaluation of a satisfactory curvefit model using setpoint tracking is shown in Figure 48 With a faster set of MPC tuning parameters only the weighted model shows fast and over damped responses without offset the unweighted model suffe
41. l radius analysis and the comparison with frequency responses and paramet ric models Control Relevant Parameter Estimation Select Initial Weighting from Unweighted MFD Model Model Predictive Control Tuning for Weighting MPC Tuning PH Ywt MH Uwt using Unweighted Model i Tuning Adjustment using Weighted Model J True Plant optional enter Model Load Model CRMFD ESTIMATE Figure 27 Control relevant weighted curvefitting into MFD model 7 2 5 MPC Evaluation Taking advantage of the estimated parametric model a closed loop evaluation with the MPC tuning parameters used for the weighting function that can be performed It requires a Matlab Simulink Model MDL file in MPC Simulink Model and the user is required to assign a name for an MPC object in MPC Object In addition the user should specify End Time in the same unit with the sampling time Input Change is considered for generating the weighting function and a reference change 31 MPC Evaluation MPC Object mpc3 MFD Model CRPEP Model MPC Simulink Model sen_Skogestad_MPC End Time Input Change r 1 1 0 1 600 MPC Test Figure 28 Preparation for MPC closed loop evaluation in the closed loop evaluation with MPC For example it can be
42. mn input a and output b state space plots 47 10 10 107 107 A x 10 10 10 10 10 10 10 1 True Plant o x Go G Unweighted MFD i 22 oo penn Weighted CR MFD 10 10 10 10 107 10 x 2 2 10 10 10 10 107 10 10 10 107 10 a Frequency Responses and Curvefits Spectral Radius Analysis p E H r r gt gt e a a a e ps e e 10 F mm pa a 3 e unweighted MFD p va weighted MFD D Ee rr Cmax Wy S mall d So 1 S 10 F Sen 7 2 1 10 10 b Small Gain Condition p E 4 Figure 44 Experiment of identification test monitoring for the Jacobsen Skogestad high purity distillation column frequency responses and curvefitting a with MPC tuning set PH 35 MH 5 Ywt 1 1 and Uwt 0 05 0 03 0 13 a and Small Gain condition for the unweighted and weighted curvefit models b 48 are all under the unity around 107 over the bandwidth Figures 51a to 52a which is much lower than those of unweighted models With the increasing number of cycles the levels of uncertainty bound are lower and have very similar values at 10 and 14 cycles see Figure 50 The robust loopshaping bounds are changed dynamically along testing cycles 0 H is always lower than the unity in this case therefore G S is only considered for applicable robustness bound in the
43. model parameters for the SK and GN loop termination The curvefitting loop terminates only when all three user error specifications are met If the loop is not numerically converging properly the curvefitter will terminate abruptly Curve fitting noisy frequency responses requires a more relaxed set of error criteria to keep it from abrupt termination Over parameterization could result in crashes in the loop iteration On the other hand the user can try setting some relaxed error criteria while monitoring model performance with the Small Gain Theorem analysis and closed loop MPC evaluation 7 2 3 Parameter Estimation by Unweighted Curvefitting Model estimation error is minimized iteratively without using weighting functions Cur rently the input change weighting is not implemented in the routine This will considered for the future release version 29 Matrix Fraction Description Model Model Orders r Iteration Options amp Error Criteria 1 SK Loop Iteration Max 10 Min na G N iteration at a SK step 20 nb Abs Error 18 12 Rel Error MES nk 1 Relative Parameter Difference 1E 6 Figure 25 Specification options for MFD model on the curvefitting GUI Unweighted Parameter Estimation MFD ESTIMATE Figure 26 Unweighted curvefitting into MFD model 7 2 4 Parameter Estimation by Weighted Curvefitting T
44. n the ETFE for a standard zippered spectrum signal and Spectral Analysis for phase shifted and modified zippered spectrum signals 8 Robust Loopshaping GUI The goal of the Robust Loopshaping GUI is to design a set of models that can meet the requirements of robust stability and performance Figure 31 shows the necessary compo nents for this robust loopshaping procedure The robustness bounds for the sensitivity and complementary sensitivity functions involve performance weight s and uncertainty bound Those conditions of robust stability and performance are computed using Structured Sin gular Value analysis For successful robust control system design it is necessary to iterate between control relevant parameter estimation and robust loopshaping this follows a procedure we call identification test monitoring Rivera et al 2003 Initially frequency responses with un certainty bounds are considered to compute robust loop bounds that are used as a prelimi nary guideline for controller tuning in the control relevant curvefitting The evaluation of 33 Robust Loopshaping GUI Loading Data Structure Enter a data structure name or click on LOAD DATA button for Mat File rscrloop 3f LOAD DATA ini A os Mu Analysis Test Close Figures rscrloopO3ff is loaded Process contains 2 output s and 2 input s we A Data has ns 27 Ns 316 and 34 cycles we LOOP SHAPING Output constains noise signal at 2 1814 AP
45. o load a signal data file to the current GUI CLEAR ALL clears all the data information on the GUI Close Figures closes all the open Matlab figures toWorkspace transfers the input signal data to the Matlab workspace with a variable name on the text box given by the user 4 3 Data Structure from Input Signal Design GUI The data structure from the Input Signal Design GUI has a number of components that are needed for the internal operation of the GUI The essential components for executing an identification testing experiment as well as being useful for subsequent portions of CR IDENT are as follows Components Description u Inputs T Sampling time Ns One cycle sequence length Ns Number of sinusoids in the primary bandwidth Table 1 Essential components of the data in struct format from Multivariable Input Signal Design GUI 4 4 Examples The input design GUI provides two example cases based on the Shell Heavy Oil Fraction ator Prett and Garc a 1988 and the Jacobsen Skogestad Jacobsen and Skogestad 1994 high purity distillation column problems Preset values are loaded on the GUI when but tons for these examples are selected the user can then analyze these examples within the GUI as desired 17 A Modified Shell Heavy Oil Fractionator Jacobsen Skogestad Distillation Column Figure 13 Illustrative examples on the Input Signal Design GUI 5 Running Experiment from Input
46. oolbox and its documents can be accessed from the ASU CSEL website using the link http www fulton asu edu csel Software html 11 Acknowledgements Funding for this work was provided by grant number PRF 37610 AC9 from the Ameri can Chemical Society Petroleum Research Fund and general support from the Honeywell Foundation to the Control Systems Engineering Laboratory 49 Additive Uncertainty Norm Bounds T lla I Frequency rad min Figure 45 Experiment of identification test monitoring for the Jacobsen Skogestad high purity distillation column additive model uncertainty norm bound with 33 cycles a Robust Stability 10 r T T 10 10 Frequency rad min Figure 46 Experiment at 14 cycles of identification test monitoring for the Jacobsen Skogestad high purity distillation column robust stability analysis 50 Amplitude Figure 47 Experiment of identification test monitoring for the Jacobsen Skogestad high purity distillation column robust loopshaping bounds on P with MPC tuning set PH 35 Robust Loopshaping with Weighted CR MFD G w T Frequency MH 3 Ywt 1 1 and Uwt 0 05 0 03 0 13 u2 Figure 48 Experiment of identification test monitoring for the Jacobsen Skogestad high purity distillation column setpoint r 0 1 0 1 tracking test with MPC MPC tuning set MPC Setpoint Tracking Test Setpoint Weighted MFD
47. or designing a modified zippered power spectrum as shown in Figure 42a The input magnitude is set to u 14 14 The high magnitude helps in reducing the uncertainty norm bound by applying a higher signal to noise ratio as indicated by the following equation n la N 21 where n is the number of model parameters and N is the data length The nature of the distil lation process requires information at the lower frequencies for accurate gain directionality of steady state while the closed loop dynamics requires information at the higher frequen cies Considering such characteristics we can decide on design parameters TH 67 TE m 15 2 and B 3 that lead to a much shorter bandwidth i e a sequence length N 316 The higher correlated harmonics increase the corresponding output span in the 1 1 direction see Figure 43 which ultimately enhances the low gain directionality Spectral analysis is applied to compute nonparametric frequency responses P using a Hamming window with 128 lags An uncertainty description bound is estimated to define a set of models as shown in Figure 45 As a consequence robust loopshaping can be applied In this experiment robust stability is satisfied over all frequencies as shown in Fig ure 46 Robust stability and performance conditions from robust loopshaping can be used 45 to assess control adequacy of the models estimated from the data and hence can influence the dec
48. ot Figure 38 Plotting options on the Robust Loopshaping GUI LOOP SHAPING computes robust loop bounds taking advantage of u analysis i e 6 S and 6 A SAVE stores all the information from the GUI into a file LOAD opens a file and uploads it onto the GUI CLEAR empties all the information on the GUI toWorkspace exports all the information to the Matlab workspace 8 2 7 Sensitivity Function Specification With computed robust loop bounds the user can optionally specify a nominal model that can meet robustness conditions The specified nominal model and computed loop bounds are used a guideline for controller tuning in control relevant curvefitting 38 IIS IHG I Figure 39 Plotting window on the Robust Loopshaping GUI Close Figures Robust Statbility Mu Analysis Test LOOP SHAPING SAVE LOAD CLEAR PRINT Figure 40 Action buttons on the Robust Loopshaping GUI 9 Illustrative Examples of CR IDENT CR IDENT includes two built in illustrative example cases to help the user with appro priate parameter specification on the GUIs In this section we demonstrate step by step procedures for using CR IDENT on two example cases a modified version of the Shell Heavy Oil Fractionator Problem Prett and Garcia 1988 and Jacobsen Skogestad distilla tion column Jacobsen and Skogestad 1994 The results and discussion for the Jacobsen Skogestad distillation column are
49. presented later in this section 39 Sensitivity Function Specification HOw Design CII Sew Design NUM DEN Figure 41 Nominal model specification on the Robust Loopshaping GUI 9 1 Illustration with Shell Heavy Oil Fractionator Problem 1 Open the Multivariable Input Signal Design GUI 2 Hit Heavy Oil Fractionator button and it brings the preset parameters on the GUI The user may change some design options or multisine signal type 3 Choose Time Series Power Spectral Density and Auto Cross Correlation 4 Hit Analyze Plot button 5 Put test01 on the edit box above the toWorkspace button 6 Hit toWorkspace button 7 Go to the Matlab command window Run run_shell_idtest and follow the instruc tions from the program such that Enter Multisine Input Data Structure e g contains u testO0l Please make input signals as us i i channel index Please enter a number of cycles for running nc 3 21 Please enter a name for saving Input Output data to a structure idtest0l idtest01l u 7000x2 double y 7000x2 double Ts 4 Ns 350 ns 10 ncycles 21 with vard 1 0 for the noise option on the popup menu selection Lowering the value of vard will require less input signal cycles for successful estimation The user may change noise realization inside the script program of run_shell_idtest m 8 Open the Frequen
50. rett and Garc a 1988 and Jacobsen Skogestad high purity distillation columns Jacobsen and Skogestad 1994 These examples can be accessed directly from the GUI A variety of multisine input signal designs supported by the toolbox is demonstrated and the data arising from these designs are used to obtain models which are evaluated through the closed loop Model Predictive Control application This document is organized as fol lows Section 2 describes the installation of the CR IDENT release and Section 3 shows how to get started with the CR IDENT Section 4 explains the Multivariable Input Signal Design GUI and Section 5 introduces examples of Matlab Simulink for the open loop ex periment simulation Sections 6 and 7 present the Frequency Response Estimation GUI and Control Relevant Curvefitting GUI respectively Section 8 presents the Robust Loop shaping GUI that involves uncertainty estimation performance weight specification and L analysis The illustrative example cases are given with step by step procedures and dis cussed in Section 9 Section 9 3 presents an illustrative example that follows the identi fication test monitoring procedure taking advantage of interactive and iterative usage for control relevant modeling targeted on Model Predictive Control application Finally Sec tion 10 presents remarks and conclusions 2 Installing CR IDENT and System Requirements The directory structure for the CR IDENT toolbox is shown in Figure 2
51. rrently it cannot contain the uncertainty description and other information from the GUI toWorkspace puts the current data information into the Matlab workspace in struct format with a given variable name 25 CLEAR empties all the information and data on the GUI Close Figures closes all the Matlab figures 6 4 Examples By the use of the Input Signal Design GUI two examples of open loop testing experiment are performed in Matlab Simulink Their Simulink MDL files are available in the exam ple directory The input output dataset are uploaded for frequency response estimation by hitting the buttons in Figure 22 i Example Cases A Modified Shell Heavy Oil Fractionator Jacobsen Skogestad Distillation Column Figure 22 Example cases on the Frequency Estimation GUI A Modified Shell Heavy Oil Fractionator provides the two cases using phase shifted and standard zippered multisine input designs In addition the model is slightly modified from the Shell Heavy Oil Fractionator with longer time delays in transfer functions Jacobsen Skogestad Distillation Column provides the three cases using phase shifted standard zippered and modified zippered multisine input designs In particular the modi fied zippered spectrum is considered for the directional adjustment to enhance the low gain directionality in the outputs meaningful for such a highly interactive systems 7 Control Relevant Param
52. rs numerical oscillations in y and overshoot in y A synergistic effect of using the directional input signal design and weighted curvefitting clearly results in the accurate estimate of the low singular values Figure 49 In spite of the large number of testing cycles the unweighted curvefitted model does not show a reasonable estimate of the low singular values This is clear evidence that the weighted curvefitting is effectively able to efficiently capture the low gain directional information which is designed to be emphasized by the use of a modified zippered spectrum The performance weight and tuning parameters can provide flexibility to adjust the robust loop bounds during the iterative procedure between the curvefitting and loopshaping The success of control relevant and robust models can be guaranteed when a sufficient number of testing cycles are tested so that the uncertainty norm bound is reduced to a suitable level A control relevant model satisfying robustness conditions is obtained after 14 cycles at which time experimental testing is halted At each cycle interval the identification test monitoring framework evaluates updated robust loopshaping bounds and whether these are applicable for weighted curvefitting if so we can halt identification testing Figures 51 to 52 show the intermediate identification test monitoring analysis at 5 and 10 cycles respectively Their Small Gain conditions 46 Input PSD
53. set pa rameters on the GUI The user may change some design options or multisine signal type 3 Choose Time Series Power Spectral Density and Auto Cross Correlation 4 Hit Analyze Plot button 5 Put test02 on the edit box above the toWorkspace button 6 Hit toWorkspace button 7 Go to the Matlab command window Run run _jacobsen _skogestad_idtest and follow the instructions from the program such that Enter Multisine Input Data Structure e g contains u test02 Defining the Full Order High Purity Column MULTIVARIABLE IDENTIFICATION OF THE HIGH PURITY DISTILLATION COLUMN The 82 state high purity column is described as y t P_LV s u t P_F s d t where dyD laL VCE A l3 u t d t dF dxB lav Enter the variance of noise added to Output 1 0 no noise 4 7e 005 Enter the variance of noise added to Output 2 0 no noise 8 7e 005 Please make input signals as us i i channel index Please enter a number of cycles for running nc 3 6 Please enter a name for saving Input Output data to a structure idtest02 42 10 11 12 13 14 15 16 17 18 19 20 21 idtest02 u 4580x2 double y 4580x2 double TS 8 Ns 916 ns 78 ncycles 6 Inside the script program run jacobsen_skogestad_idtest m the user may change noise realization Open the Frequency Response Estimation GUI
54. shaping GUI The Robust Loopshaping GUI supports data formats from the Frequency Response Esti mation GUI and the Control Relevant Parameter Estimation GUI Specifically the Robust Loopshaping GUI needs input and output data frequency responses or a parametric model to evaluate robustness conditions In addition the data structure from the Robust Loop shaping GUI can work with the Control Relevant Parameter Estimation GUI supporting iterative procedure during identification test monitoring 34 8 2 Getting Started with Robust Loopshaping 8 2 1 Loading DATA A dataset from Frequency Response Estimation GUI and Control Relevant Parameter Es timation GUI is loaded using the block in Figure 32 The user can load the data from the Matlab workspace or a mat file From the workspace the user enters a data structure name on the edit box and hit the LOAD DATA button If the entered data is not available on the workspace an error mes sage will appear From a mat file the user just hits the LOAD DATA button with the empty edit box Then it prompts the file open window for selecting a data file Loading Data Structure 1 Enter a data structure name or click on LOAD DATA button for Mat File rscrloopO3ff LOAD DATA rscrloop03ff is loaded 1 Process contains 2 output s and 2 input s Data has ns 27 Ns 316 and 34 cycles Output constains noise signal at 2 1814 3 0203 dB Figure 32 Loa
55. stencies in dynamic models for ill conditioned plants application to low order models of distillation columns Ind Eng Chem Res 33 631 640 Lee H 2006 A plant friendly multivariable system identification framework based on identification test monitoring PhD thesis Dept of Chemical Engineering Arizona State University Tempe AZ U S A Lee H and D E Rivera 2004 A control relevant plant friendly system identification methodology using shifted and zippered input signals In 2004 AIChE Annual Meeting Austin TX paper 414r Lee H and D E Rivera 2005a Control relevant curvefitting for plant friendly multi variable system identification In 2005 American Control Conference Portland OR pp 1431 1436 Lee H and D E Rivera 2005 An integrated methodology for plant friendly input signal design and control relevant estimation of highly interactive processes In Annual AIChE 2005 Meeting Cincinnati OH paper 520b Lee H D E Rivera and H D Mittelmann 2003a A novel approach to plant friendly multivariable identification of highly interactive systems In Annual AIChE 2003 Meeting San Francisco CA paper 436a Lee H D E Rivera and H Mittelmann 2003 Constrained minimum crest factor mul tisine signals for plant friendly identification of highly interactive systems In 3th IFAC Symp on System Identification Rotterdam pp 947 952 56 Ljung L and T Glad 1994 Modeling of Dynamic
56. the Matlab Alternatively a frequency re sponse estimator can be obtained as follows Sup yn i 8ne A 10 dd Su uy 0 22 where Su y 0 and Su oy represent power spectra of corresponding signal sequence Lag Window is determined from the number of sinusoids ns and the sequence length Ns Conf Level confidence level is optional for the standard deviation analysis with the frequency response With a selected confidence level the GUI generates shaded areas as sociated with the frequency responses The user can consult the spa command in Matlab for details High Order ARX Analysis utilizes a parametric ARX auto regressive exogenous es timation From a high order ARX model frequency responses are approximated as G a 1 Ayz Ana2 7 Bo By z Bay 2 2 11 where z e for a discrete time model The user can run either single input multiple output SIMO or multiple input multiple output MIMO ARX analysis depending on the order in na nb nk na determines the number of discrete output terms in the ARX model For a 2x2 system na can be given 10 or 10 10 for SIMO and MIMO respectively nb indicates the number of discrete input terms in ARX structure which should be given with respect to each input nk represents the order of discrete input delay in ARX structure which should be given with respect
57. the sensitivity function such that W SI lt 1 14 s Ms Op Vo H a 15 Ss pE Ua where M is the peak sensitivity 0 is the bandwidth and e is given as 0 lt e and 2 W on P H CS Figure 36 is given as W PA lt 1 16 W S Opc Mu 17 i E1 S Whe where M is the maximum gain of CS Op is the controller bandwidth and 1 gt CS at high frequencies The parameters for W and W can be specified on Figure 37 36 My 1w Figure 35 Performance weight W on ICS ja Figure 36 Performance weight W on CS 8 2 5 Transfer Function Plots Robust loopshaping involves a number of transfer functions and the user can plot them on the GUI Select check boxes of transfer functions and hit Refresh Plot button on Figure 38 it will update the figure window as shown in Figure 39 8 2 6 Action Buttons Close Figures closes all the Matlab figures Robust Stability analyzes robust stability on a set of models i e M11 Mu Analysis Test performs U analysis test on a set of models i e u M 37 Performance Weights Wip Weighting C Wu Weighting mb 4 mbe web 0 001 whe A 0 000001 Abc Robust Performance Weighting Figure 37 Performance weight specification on the Robust Loopshaping GUI Transfer Function Plots O Piw Wpiw cS w IH E Wutw cHiw Siwy d F eiw ICi Refresh Pl
58. to each input Order Selection is an option available for SIMO ARX analysis The user should specify ranges of the orders e g 1 10 1 10 1 1 for na nb and nk respectively It also requires a validation dataset with the same data dimension data length can be different as the loaded estimation dataset To load a validation dataset it is the same for loading the estimation dataset by hitting LOAD button Residual Analysis is available with the ARX model and residual data Conf Level confidence level generates the standard deviation analysis with the pa 23 rameter values in the ARX model 6 3 3 Plots With the selected options the user can start analyzing the input output data into frequency responses interactively on the GUI Figure 19 Analysis and Plot Response Amplitudes C Response Phases _ Time Sequences _ Input Power Spectrum _ Output Power Spectrum ESTIMATE Figure 19 Analysis and Plot for frequency response estimation Response Amplitudes generates the frequency response amplitudes for individual trans fer functions Response Phases generates the frequency response phases for individual transfer func tions Time Sequences draws the input and output time sequence over the total length Input Power Spectrum provides an input power spectrum Output Power Spectrum provides an output power spectrum
59. ts for accomplishing system identification see Figure 5 A multisine input u k for the j th channel of a multivariable system with m inputs is defined as m 6 ns uj Es cos OKT 05 y 20 j1 cos kT ji i m6 1 m 9 n5 n4 y Aji cos kT Q5 j 1 m 1 m 9 n5 1 where m is the number of channels ns na are the number of sinusoids per channel m 9 ns Nq N 2 o Oji OF are the phase angles and 5 ji Cji amp ji represents the Fourier coefficients defined by he user ji ji are the snow effect Fourier coefficients and 27i NsT is the frequency grid The snow effect Guillaume et al 1991 refers to sinusoids where both Fourier coefficients and phases are selected by the optimizer which can serve as an aid for achieving plant friendliness Lee et al 2003b The snow effect is not implemented in the current version of CR IDENT instead the user can specify Lf and hf which are Fourier coefficients in the low and high frequency grids Figure 4 shows a general zippered input power spectrum for a three channel MIMO case as implemented in CR IDENT For orthogonal input signals the power spectrum of channels should not be excited at the same frequencies only a single input channel is excited at a specific frequency while the other channels are suppressed To achieve a zippered spectrum we define the Fourier coefficients j for u k as a 0 i m j m 8 1 j m8 n D j a 0
60. using the last cycle from the estimation data 6 3 4 Additive Uncertainty Estimation Additive uncertainty estimation is included in the GUI One can assume that each element pi in the plant P is independent but confined to a disk with radius at pj in the Nyquist 24 plane Morari and Zafiriou 1988 Pij Bijl lt Li 12 Therefore a set of models are defined as they reside within the distance For more infor mation for the additive uncertainty description the user can refer to Lee 2006 Additive Uncertainty Estimation Confidence Level 95 0 y Additive Uncertainty Estimation Figure 20 Additive uncertainty estimation on the Frequency Response Estimation GUI 6 3 5 Action Buttons The user can manipulate the estimated frequency responses for further analysis using the action buttons as shown in Figure 21 The estimation data can be in either IDFRD or struct format for further analysis in the CR IDENT Your data msiodata02 is successfully loaded and ready for analysis Enter a Data Hame myfreqest02 Figure 21 Action buttons on the Frequency Response Estimation GUI SAVE stores the estimation data into a mat file LOAD opens a mat data file and uploads it on the GUI Export to IDFRD transforms the frequency response data into an IDFRD object to the Matlab workspace The IDFRD object can be used for the control relevant curvefitting however cu
61. y Response Estimation GUI 6 1 Background in Frequency Response Estimation 6 2 Entry Data Format for Frequency Response Estimation GUI 6 3 Start Estimating Frequency Reponses o 6 34 Loadms DATA sy Le a A 6 ae 6 3 2 Freqeuncy Response Methods 0 3 3 PIOUS a Raa tte ete Mat Hate st oe Dn here oe he 6 3 4 Additive Uncertainty Estimation 630 Action BUONS 2 2 4 4 4 5 ody eh se Bed li Bee Bae 6 4 EXample S Pe are ee ea eR O ea ee a a a dl 7 Control Relevant Parameter Estimation GUI 11 11 13 14 15 16 17 17 18 19 19 19 21 21 22 24 24 25 26 26 7 1 Entry Data Format for Control Relevant Parameter Estimation GUI 7 2 Getting Started with Control Relevant Curvefitting 7 2 1 Loading DATA 7 2 2 Specification for Matrix Fraction Description 7 2 3 Parameter Estimation by Unweighted Curvefitting 7 2 4 Parameter Estimation by Weighted Curvefitting 7 2 5 MPC Evaluation 7 2 6 Action Buttons 7 3 Examples 8 Robust Loopshaping GUI 8 1 Entry Data Format for Robust Loopshaping GUI 8 2 Getting Started with Robust Loopshaping 8 2 1 Loading DATA 8 2 2 Process Source 8 2 3 Uncertainty Estimation e 8 2 4 Performance Weights 254 por Poe e ee ee eee es 8 2 5 Transfer Function Plots
62. zes an input signal type and blocks the choices that are not available with the given input type Users can export the estimated responses in idfrd or struct format These are used in the ensuing modules in support of advanced control system design e g control relevant parameter estimation and robust loopshaping among other uses 20 Components Description y Outputs u Inputs T Sampling Time Ns One cycle sequency length Ns Number of sinusoids in struct Table 2 Components of the experimental data entry structure for Frequency Response Estimation GUI 6 3 Start Estimating Frequency Reponses 6 3 1 Loading DATA An experimental dataset is loaded using the block in Figure 17 The user can load the data from the Matlab workspace or a mat file of either struct or iddata object From the workspace the user enters a data name on the edit block and hit the LOAD DATA button If the entered data is not available on the workspace an error message will appear From a mat file the user hits the LOAD DATA button with the empty edit box Then 1t prompts the file open window for selecting a data file Loading DATA Enter Data Structure Array Name from Workspace or Click LOAD ID DATA for mat Files icob_modzip_frespnos LOAD DATA Input Signal Type Standard Zippered Signals Modified Zippered Signals Figur

user`s manual - Control Systems Engineering Laboratory

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