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1. Controller Type ke TI Tp P only Tp kpO PI 0 9 t k O 3 30 PID 1 2 tp kp 20 0 50 Ciancone Method Ciancone and Marlin created an open loop method of tuning controllers based on a single parameter called fraction dead time Fraction dead times ranges between 0 0 and 1 0 and is calculated from the FODT parameters It represents the fraction of the total time needed for the open loop process step response to reach 63 2 of its final value that is due to dead time Determining PI controller parameters using Ciancone correlations is a three step procedure 1 From the FODT kp Tp and 0 model calculate the fractional dead time as O t gt 0 2 Use the appropriate graph from Marlin Thomas E Process Control Designing Processes and Control Systems for Dynamic Performance McGraw Hill New York 2 edition page 286 to determine the dimensionless tuning values K K T Tp 9 Calculate the dimensional controller tuning values from the dimensionless tuning values and the FODT parameters 94 3 3 22 Jorn 3 23 Fine Tuning The values for controller tuning constants determined by correlation methods are just swags to be applied to the physical system initially and improved based on empirical performance during fine tuning See Figure 3 30 for the well tuned PI controlled process Well Tuned PI Controller 1 5 y and r i 10 20 30 40 50 60 70 80
2. Step 4 Press STOP to end the program at end of experiment Step 2 a 2 c 3 a iii 3 a vi Press Run Pump to run pump and vice versa Step 1 e This button indicates which tank s level is being controlled Toggle the button fo switch between tank and nk2 Step 3 a v Step 3 b Use this scroll bar to view response for previous tuning parameters Step 3 a iv Step 3 a vi Step 3 c i To record data in excel sheet press this button LED in green Step 3 a v Step 3 b Use this scroll bar to view manipulated variable pump input for previous tuning parameters indicates writing to the file Step 3 a i 3 b i Enter PID tuning parameters here Figure 3 34 Detailed Explanation of Step by Step Procedure for Tuning 103 3 Generate empirical data See Figure 3 34 for step by step explanation a For initial PI parameters i Enter the instructor specified initial PI parameters SWAGs calculated from the theoretical settings in the PID parameters input box Note 1 enter the integral time and derivative time in minutes 2 Make sure tp 0 for PI control ii Enter the set point of 3 cm iii Press Run pump to start the pump iv Once the steady state liquid level is reached on tank2 See tank2 level graph click write data button and then change the set point to the value given to your group v Note the initial pump voltage change and observe the pump voltage response along wi
3. 153 Experimental Data a with pump start up effect b without pump start up effects a aut Pak A raha te ed Std Fal ental oes 154 Modified Pump Vl Front Panel s cc eccgiec scuisvern tn eacdse ea eteaowatiaciaias 155 a Front Panel of Old LABPID VI Program b Data File Recorded by Old PAB PET Pe Oi soci a ene e dase E enue ecae oreo 158 a Modified LabPID1 VI Front Panel b Data Filed Recorded by New LaBPID NV nsiro anin Maret aan neon RISTO D eT nye MUS NseeT e TNO a 161 xvii CPI DAC DIN FODT LabVIEW LED PI PID PVC RCA SISO UPM LIST OF ACRONYMS Chemical Process Industries Data Acquisition Card Deutsches Institut fiir Normung First Order plus Dead Time Laboratory Virtual Instrumentation Engineering Workbench Light Emitting Diode Proportional Integral Proportional Integral Derivative Poly Vinyl Chloride Radio Corporation of America Single Input Single Output Universal Power Module xviii DEVELOPING IMPLEMENTING AND ASSESSING COUPLED TANK EXPERIMENTS IN AN UNDERGRADUATE CHEMICAL ENGINEERING CURRICULUM Narendra Kumar Inampudi Dr Patrick J Pinhero Thesis Supervisor ABSTRACT Five experimental modules that fit into the Undergraduate Chemical Engineering Curriculum were developed using the existing Coupled Tank Apparatus Students of different educational levels get an opportunity to develop practical skills like modeling simulating and model validating as well as
4. 0 4763 2 Co 18 36 3 1415 s V6346 2 981 Co 0 9235 The experimental data verify that resistance flow is proportional to the square root of the tank level because the slope of the regressed line is very close to 2 considering experimental error as predicted by Equation 4 3 and shown in Figure 4 3 118 4 3 Experiment 2 Modeling Liquid Level in a Cylindrical Tank 4 3 1 Pre lab Tasks 1 as f L V Material balance on the tank lage of B e a _ l rate of mass l rate of mass 4 5 of mass in tank lentering in tank leaving out of tank In the following equations M mass of water V Volume of water p density of water F Flow into cylindrical tank F Flow out from the cylindrical tank Ar cross sectional area of the tank A cross sectional area of the outlet orifice K pump flow constant V velocity of water at outlet orifice g accelaration due to gravity dM_ W o oe i a Ca o dL Ara tiio Fi KVpump gives dL T at KVpump Aoo dL K ae V C 2g aE f L V 4 7 Dry D Note that Ar 1 and A T 119 2 Steady state pump voltage V as a function of steady state liquid level Ls At steady state the change in height with time is zero so Equation 4 7 is equal to zero A K C297 Vb a T where L is height at steady state and V is pump voltage at steady state JL 4 8 2940C k 3 Deviation variables and linearized model at steady state
5. 178 APPENDIX 2 BLOCK DIAGRAMS OF LABVIEW PROGRAMS 1 Block Diagram of Pump VI ae g Sa li from DEVIF some time apo yj SS war lavefoty Chart E jr m error out k 0ev2jao0 fe jim en MgO y i chan 1Sanp e The Green circles are the inputs controls red color circles are safety interlock system and the black one is the indicator 179 2 Block Diagram of LabPID1 VI pied fromDemo PID with MIO board RICH2 04 23 07 vy Write to Data Files tead Tank 1 7 n 23 5 anki Cal Factor jj DATA tead Tank 2 at 5 Pump Vokage ank2 Cal Factor hap rive output setpoint level cr T magi B p a Pump voage Graph TD paranetel Ge PID parameters Hidden Autotune control Limit Action ROGRAM STI ANK LEVEL LII e The Green circles are the inputs controls red color circles are safety interlock system and the black one is the indicator 180
6. After evaluating the experimental apparatus and computer programs during summer 2008 a one page procedural handout was prepared for running the modeling experiments Fall 2008 ChE 4370 students were the first to do the process modeling experiments on the Coupled tank system using this handout They performed the upper tank level modeling experiment experiment 2 twice Incoherent pressure sensor voltage readings necessitated the second experimental trial i First Trial of Experiment 2 For the first trial students performed the experiment without calibrating the pressure sensors At that point student handouts were rewritten to be more self contained A theory section on modeling was added to the procedures for guiding the students through the experiment However sensor calibration was not included in those procedures At that time calibration was performed by the Teaching Assistant four 4 days before the experiment was run rather than having the students doing it during the 151 lab Even with calibrated pressure sensors students got inconsistent readings for the pressure sensor voltage and were in a total confusion about how to do data analysis for the experiment Students were also confused by the Pump VI front panel The section circled in Figure 5 1 was the cause of this confusion They thought the data collected and displayed were for tank volumes instead of pressure sensor voltages Students in Fall 2008 were conf
7. Decreases Increases Increases Eliminated Increasing tp Small Decrease Decreases Decreases No effect 97 Proportional gain k An increase in absolute value of controller gain ke will speed up the response but at the expense of system stability Integral Gain ti An increase in integral time t1 tends to slow down the response and decrease the overshoot while the lower Ty speeds up the response and increases overshoot Too low of a value for t can lead to instability Derivative time tp An increase in derivative time helps system stability However this control action is very sensitive to measurement noise Usually only PI control is used for loops where there is measurement or output noise Three Laws of Feedback Controller Tuning 1 Control performance must be defined with respect to all important plant operating goals The desired behavior of the controlled variable and the manipulated variable must be defined for expected disturbances model errors and noisy measurements 2 The dynamic behavior of both the controlled variable and the manipulated variable must be observed when analyzing the performance of feedback control systems Complete diagnosis is not possible without information on both variables 3 When tuning a feedback controller where you start is not as important as where you finish The values for controller tuning constants determined by correlation 98 methods are just sw
8. Observe the pressure sensor voltage reading in the Tank1 display box If it is not 0 V manually adjust offset potentiometer screw for Tank 1 on the calibration and signal conditioning circuit board See Figure 3 17 using the potentiometer adjustment tool flat head screw driver to obtain 0 V Turn the offset potentiometer screw clockwise to increase the voltage reading and vice versa Cover the tank outlet with your finger Using the quick connect at Out1 apply a voltage to the pump and fill the tank to 25 cm Then turn off the pump Apply 0 V to the pump Observe the voltage reading in the tank display box If it is not 4 10 V 0 03 is okay at 25 cm manually adjust gain potentiometer screw for tank to obtain 63 4 10V Turn the gain potentiometer screw clockwise to increase the voltage reading and vice versa Offset screw tank2 Gain screw tank2 Offset screw tank Gain screw tank Figure 3 17 Calibration and Signal Conditioning Circuit Board f Drain the tank g Check to see that the reading returns to 0V Readings may take 30 seconds or so to stabilize If not repeat 4b 4f until you get OV at Ocm and 4 10V at 25cm of level This may take several trials 5 Calibrate lower tank s pressure sensor a Repeat the same procedure described from 4a 4g for tank2 by bringing tank2 using quick connect Out2 Make sure you disconnect Out1 while calibrating tank2 64 Press this butt
9. Eventually a new experiment illustrating the effect of adding the feed forward mechanism could be added to the existing modules e Connecting LabVIEW to the internet would be a notable project Then these experiments could be made available to distance education students providing access to the laboratory experiments even without requiring physical presence 5 6 Miscellaneous The following are the specifications for parts of the experimental apparatus that will eventually require replacement The orifices and o rings are supplied by McMaster Carr Orifice e Nylon Hex Head Cap Screw e 3 8 16 thread 1 2 length e off white fully threaded e Vendor name McMaster Carr e Catalog code 91244A620 e Price USD 6 09 per 25 e The orifices can be machined according to the desired orifice diameter 168 O ring e Type o ring e C S shape round e ID 3 8 e OD 9 16 e Width 3 32 e Material EPDM Ethylene Propylene e Durometer Hard e Color Black e Vendor name McMaster Carr e Catalog code AS568A Dash No 110 e Price USD 3 57 per 25 Pressure sensor Pressure sensor is manufactured by Honeywell S amp C and supplied by Newark Electronics e Operating Pressure Max lpsi e Sensor Output Voltage e Port Size 0 04 e Port Style Straight e Pressure Measure Type Differential e Sensor Terminals Through Hole 169 Manufacturer name Honeywell S amp C Vendor name
10. Figure 3 19 Coupled Tank Apparatus The resistance of this discharge can be varied by replacing the orifice inserts of different diameters into a threaded hole at the bottom of the tank For this experiment use only the medium inserts of diameter 0 476cm for both tanks A drain tap is also provided in the apparatus to introduce disturbance flow into either tank or tank2 By opening the drain tap liquid from tank1 flows directly to the reservoir The pump propels water vertically 69 to two quick connect orifices Out1 and Out2 which are usually closed The system is equipped with different diameters for these two orifices for configurability Teflon Tubing of 1 4 I D with compatible couplings is provided to enable the pump to feed one tank or both tanks The water level in each tank is measured by a pressure transducer located at the bottom of each tank Theory PID Controller Algorithm The Proportional Integral derivative PID controller is the mostly commonly used feedback algorithm in control systems Due to robustness and simplicity in operation about 95 of closed loop industrial processes use PID controllers A PID controller attempts to reduce the error which is calculated as the difference between the controlled variable s set point and its measured value A PID controller takes corrective action on the process input according to the algorithm shown in Figure 3 20 to keep the error to a minimum l The PID contr
11. Figure 3 29 Step Response Characteristics of Underdamped Second Order Processes Decay ratio Decay ratio is defined as the ratio of the sizes of successive peaks 92 Calculation of Initial Tuning Parameters There are three general methods for calculating PID tuning parameters Classic closed loop methods force the closed loop system to the edge of stability by inducing sustained oscillation in the output The closed loop Ziegler Nichols method and Tyres Luyben method are classic examples The direct synthesis method P derive both a controller and its parameters from the transfer functions of a known process model and a defined closed loop output response Open loop methods such as the open loop Ziegler Nichols l method the Cohen Coon method l and the Ciancone Marlin method are based on the parameters of a first order plus dead time FODT process model The open loop Ziegler Nichols and Ciancone methods will be used to determine initial estimates swags of controller tuning parameters in this experiment Open Loop Methods Ziegler Nichols Method Ziegler Nichols developed a tuning method based on a FODT model that produces approximate quarter wave damping 6 Given a first order plus dead time FODT process model whose transfer function is Kye 9s 3 21 TpS 1 G s Fr use formulae given in Table 3 2 to calculate Ziegler Nichols swags 93 Table 3 2 Ziegler Nichols Open Loop Tuning Parameters
12. Narendra K Inampudi iii TABLE OF CONTENTS ACKNOWLEDGEMENTS perni ne tices E EEE speast ee ant EE Nouaseca waynes ii EISTOFTABEES seit eae a i O E AOE E lc cata E A a iA viii LISFOFFIGURES so as ce A E T E e ea act aa tn cia adets xi LIST OF AGRON YIMS iseni a A RN xviii ABSTRACT aee n a aa le Fen E A E A a XIX CHAPTERS 1 INTRODUCTION pde onea ae a sain E a aiee edema deck E A E inet 1 1 1 Importance of Process Dynamics and Control 0 0 cee eeceeseeeeceeeceeeneeeneeereeeeeeaees 1 1 2 Common Laboratory Experiments Taught in Various Universities 064 3 13 Motivations ec Sa Fa hari ae Sal a aa odd Pa ala eae Ss 5 14 OBJECTIVES Zeina a a E A a E A AEA AA Ea i 5 1 5 Th sis Organization asninn nne ena a a a a aaia 6 VG REPSPERCES a 24 ccc sod vsevaksSaheees cane Picea ti vate aaa n a decals a a eRe aaa Nselane 9 2 MATERIALS AND METHODS sciscd aiisreeiecvisveiiataehdatar E E N RRE 11 2 1 Coupled Tank Apparatus Description ccccceccceeseeeseeeeeceeeeeeeeeeseecnseeneenaees 11 2 2 Component Description cgassesh cased ssbatactcet seas at guaster yeas alee Coane ved ea ozau ateciatos Boasts 12 2 3 Coupled Tank Model Parameters i lt 3s cssteesusesectssstetatsdendoa ga thtvcdvacdaGesteeedaats 17 2 4 Electrical Component Connecnonss cncsictsa east arischcteais st oieeuielsanauteansctuteaveat ese 18 2 Aid Cable NOmenC lature s2iynsaxtasaestacvariatentsnaaedelanetans iaanede ern iati aR tainen 19
13. and not too oscillatory Inappropriate values leads to bad control unstable sluggish and oscillatory Adjust the PID tuning parameters as necessary so that the response to a set point change is reasonable Lab Procedure Precautions and Other Notes e Make sure that the reservoir s distilled water level is at least three fourths full e A watchdog is programmed into LabPID1 vi so that the tanks do not overflow If the liquid level in either of the tanks reaches 25cm the pump is turned off and the pump continues to remains idle until the tank s voltage drops below 4 3 V e Do not panic the pump can be noisy If it starts smoking that s another matter Shut off the pump by clicking Stop on the LabPID1 VI program 1 Start up of experiment program a Familiarize yourself with the apparatus See Figure 3 19 b Double click the LabPID1 VI icon on the desktop It opens the LabPID1 VI program in LabVIEW Familiarize yourself with the icons controls and indicators and what they do on the screen See Figure 3 24 81 2 c d e Click the white arrow button on the top left of the screen to start the program A window pops up on the screen asking user to define an output file Assign a file name and save it in Microsoft Excel spreadsheet format e g yourname xls The output file records PID parameters and tank levels set point and pump voltage as a function of time Use Control Tank Toggle to switch to tank
14. gain relating the pump voltage to the inlet flow rate Orifice coefficient i Start the program ii Set Pump Voltage to 1V in pump voltage input box iii Wait until the liquid level reaches steady state and remains there for 1 2 minutes iv Note the steady state liquid level and the steady state pressure sensor voltage in a notebook v Repeat steps 5 a ii to 5 a iv for 5 6 different pump voltage values equally spaced between 1 V and 1 65V Data Analysis 1 Find the gain relating the pump voltage to the inlet flow rate 2 Find the gain relating the tank s liquid level to the pressure sensor voltage 3 Using the appropriate plot find the orifice coefficient 40 3 3 Experiment 2 Modeling Liquid Level in a Cylindrical Tank Objective Formulate and validate a dynamic model for the liquid level in a cylindrical tank Tasks e Derive a dynamic model for the liquid level in a cylindrical tank e Obtain the necessary experimental data to validate the dynamic model e Solve the nonlinear dynamic model and its linearized approximation for laboratory conditions e Compare the theoretical model its linearized approximation and the empirical data obtained in the laboratory Coupled Tank Apparatus Description B The Quanser coupled tank apparatus is shown in Figure 3 7 next page The apparatus is a bench top model consisting of a pump two cylindrical tanks made of plexiglas and water basin reservoir These two tanks are of v
15. It is extremely useful especially at the time of figuring out how a steady state of level looks like on the screen 164 Comment 4 I don t have any problem getting through this experiment To sum up all the subtle things that students encountered during the lab sessions are addressed in the module write up 5 3 2 Experiment 4 and Experiment 5 These two tuning experiments were tested by 21 senior chemical engineering students in ChE 4370 during the Spring 2009 semester Students worked in a group of two and were asked to comments on the laboratory sessions and the module handouts Their comments are as follows Comment 1 The lab module handouts were very clear and concise We had problems with apparatus 4 During our experiment the set point of tank2 was set at 3 cm and the software reads 3 cm but there was no water in the tank We had to fiddle around with apparatus with settings and we ended up changing the offset on the calibration and signal circuiting board Sometimes even the removal of air pockets also does not eliminate the offset The solution to this problem is to adjust the offset to zero by turning the potentiometer screws on the calibration board Comment 2 The apparatus seemed to be in good working order and was properly calibrated No issues occurred The handout was very detailed and helpful for the experiment and we especially liked Table 3 1 effect of tuning parameters on response to a step
16. K 17 9 cm s V b Tank diameter D 4 445 cm c Outlet orifice diameter Do 0 4762 cm d Gain relating water level to sensor voltage 6 0 6 4 cm V e Acceleration due to gravity g 981 cm s 2 Find the steady state pump voltage Vs as a function of the steady state liquid level Zs 3 Define deviation variables and linearize the model about steady state 4 Determine the transfer function for this open loop process What type of process model does this transfer function represent What are the process model parameters LabVIEW Pump VI Program Explanation The Pump VI program is a LabVIEW routine that operates the open loop tank level process and Figure 3 9 shows the controls and indicators on the Pump VI front panel The PUMP VOLTAGE vertical slider and the input box below it are used to set the pump voltage It is advised to type a number into the input box instead of moving the slider when creating a step change The data display boxes in the center of the screen show the time in milliseconds and the tank1 tank2 pressure sensor output voltages and the pump 46 File Edit Yiew Project Operate Tools Window Help da n 13pt Application Font w FARA STOP m C 5 Taki ZY 217899 mam 4 Time millisec j Tank2 ZW DATA 3 is Pump B Tank pressure 0 01 2 2 sensor Voltage V 2 3 nl JE Tank 2 Pressure sensor 0 08 TANK 1 imr TANK2 H 2 naa Vokage W LMT aeron MIT T A WRITE DATA j
17. Note If you had to calibrate the sensor s again make sure there are no air bubbles over in the sensor before you start recording data If there are bubbles repeat step 3b Click the WRITE DATA button Make a positive step change to 1 25 1 5 Volts in the pump voltage by entering a number into the PUMP VOLTAGE input box and pressing enter Do not make the step change so large that the Safety Interlock System s watchdog program kicks off Wait for the tank2 liquid level to reestablish steady state 66 i Once steady state is established step change the pump voltage to steady state value from 6 g j Click the WRITING DATA to stop recording data k Repeat steps 6e 6j three more times for same pump voltage 7 Press STOP button to stop the program Data Analysis 1 Find the sensitivities for pressure sensor voltages to tank levels from the calibration data in steps 6 a and 6 b 2 Solve the linearized approximation model using MATLAB for the step change you performed in the laboratory 3 Determine a First order plus dead time FODT model from the empirical data 4 Graphically compare the linearized approximation the FODT model and the lab data 67 3 5 Experiment 4 Tuning a PI Controller for Level Control of a Cylindrical Tank Objective To gain hands on experience in tuning a PI controller for level control of cylindrical tank Pre lab Tasks e Calculate level con
18. Pressure sensor Lower tank tank2 Disturbance or drain tap Calibration and Signa Conditioning Circuit Board Water basin reservoir Figure 3 1 Coupled Tank Apparatus For this experiment use only medium inserts of diameter 0 476cm for both tanks A drain tap is also provided in the apparatus to introduce disturbance flow into either tankl or tank2 By opening the drain tap liquid from tank1 flows directly to the reservoir The pump propels water vertically to two quick connect orifices Out and Out2 which are usually closed The system is equipped with different diameters for these two orifices for configurability Teflon Tubing of 1 4 I D with compatible couplings is provided to enable the pump to feed one tank or both tanks The water level in each tank is measured by a pressure transducer located at the bottom of each tank 31 Theory The overall material balance on the cylindrical tank is rate of mass rate of mass te of aera l E l lentering the system leaving the system of mass in system dM dV _ 7 ade fa eC Pio M mass p density V Volume F input flow rate F output flow rate A schematic of the cylindrical tank system is shown in Figure 3 2 In this experiment liquid is pumped from a reservoir into a cylindrical tank at a flow rate F volume time The input flow rate is proportional to the pump voltage 1 e IM es 3 2 where K volume time Volt is a constant and Vpump
19. X L L andu V V dX a EE x4 lt i U dt 4 By defintion of steady state f L V 0 So dX g Ao 1 K aN n A a E dt a rE Ar letc 2 C and etc he Ar and Cz Ae Y xX dY dX sY s c Y s cU s 120 s c1 Y s c2U s Y s c U s s c Y s _ 2 4 9 U s 1 ce s 1 This is first order system with gain c2 c1 and time constant 1 c1 4 3 2 Experiment 2 Results Carrying out the experimental procedures described in Section 3 3 produces a graph similar to Figure 4 4 The curves show how the tank level changes when there is a step change in input pump voltage from 0 7 V to 1 25 V for different trials This graph yields the parameters for first order plus dead time FODT model for the particular process The final height of upper tank is not same for each apparatus for same step change in pump voltage because the flow rate is not same for a particular pump voltage across all the apparatuses All the graphs in this subsection are for step changes in input pump voltage from 0 7 volts to 1 25 volts and only for the upper tank in each apparatus Doing a step change from one steady state level to another eliminates dead time and start up effects in each apparatus The plots are ten repeated experimental procedures The red curves indicate the 95 confidence interval C I and the black line indicates the mean for the upper tank liquid level as a function of time The yellow curv
20. amplification gain When carrying a label showing 5 at both ends the cable has that particular amplification gain a b Figure 2 8 From Analog Sensors Cable b To Analog to Digital Cable Figure 2 8 a shows From Analog Sensors cable which is 6 pin mini DIN to 6 pin mini DIN This cable carries analog signals from one or two pressure sensors to the UPM where the signals can be either monitored and or used by an analog controller The cable also carries a 12 V DC line from the UPM in order to power a sensor and or signal conditioning board Figure 2 8 b shows To Analog to Digital cable which is 5 pin DIN to 4 x RCA This cable carries the analog signals taken from the pressure sensors unchanged from the UPM to Digital To Analog input channels on the data acquisition terminal board 20 2 4 2 Coupled Tank Wiring Summary Table 2 3 describes the electrical connections necessary to run the coupled water tank system The cable numbers are labeled in Figure 2 5 a Table 2 3 Coupled Tank Apparatus Wiring Summary Cable From To Signal 1 DAC 0 UPM From D A Control signal to UPM 2 UPM To Load Coupled Tank s Power leads to gear pump F a Terminal Board Tank 1 and tank 2 level 3 CEMS TODE iio ADCHO feedback signals to the DAQ S2 to ADC 1 board through UPM Coupled tank s ey i 4 UPM S1 amp S2 Liquid level feedback signal to Pressure Sensors the UPM 5 Power supply outle
21. needs larger gain k Figure 3 23 gives examples of improperly tuned responses Figure 3 23 a has a sluggish response due to too little integral action To speed up the response lower ty Proportional gain is not raised to speed up the response because the initial change manipulate variable is within 70 150 of final steady state value Figure 3 23 b has a sluggish response due to too little proportional gain k To speed up the response increase k When fine tuning a PI controller adjust the proportional gain ke first and then adjust the integral time ty 77 Effect of Tuning Parameters on Output Response to a Setpoint Step Change The above discussion involved only a PI controller Tuning a PID controller requires knowledge of the effects of all three tuning parameters A general guide follows Table 3 1 Effect of Controller Tuning Parameters on Higher Order Processes Parameter Rise Time Overshoot Settling Time Offset Increasing ke Decreases Increases No effect Decreases Decreasing t Decreases Increases Increases Eliminated Increasing tp Small Decrease Decreases Decreases No effect Proportional gain k An increase in absolute value of controller gain ke will speed up the response but at the expense of system stability Integral Gain ti An increase in integral time tr tends to slow down the response and decrease the overshoot while the lower t speeds up the response
22. snappy and not too oscillatory Inappropriate values leads to bad control unstable sluggish and oscillatory Adjust the PID tuning parameters as necessary so that the response to a set point change is reasonable 26 2 8 Calibration Procedure for the Pressure Sensors Make sure that the tanks to be calibrated are empty before starting the calibration If not empty it using the disturbance tap black flap near the bottom of tank2 for tank and removing the plug finger for tank2 Water can be pumped only to the tank by using the quick connect at Out1 Use a finger to plug the tank1 orifice Observe the tank voltage on the Pump VI front panel If it is off from 0 V at zero cm manually adjust offset potentiometer screw for tank1 on the calibration and signal conditioning circuit board using the potentiometer adjustment tool flat head screw driver to obtain 0 V Turning the screw clockwise will decrease the voltage and vice versa Now fill tank to 25 cm and observe the voltage reading for tank1 If it is off from 4 10 V adjust the gain potentiometer screw for tank1 to obtain 4 10 V Turning the gain potentiometer screw clockwise will increase the voltage and vice versa Now drain water from the tank using the using disturbance tap Check whether the offset is back to 0 V or not If not repeat steps 4 7 until you get the offset for the tank as OV OV offset is usually achieved by 2 3 rep
23. vii Table 1 1 1 2 2 1 4 1 LIST OF TABLES Page Process Control Textb0Gks cscuw aches asiionwilue clog ian bitaiitieuiant 4 Common Chemical Process Dynamics and Control Course Topics 6 4 Calibration and Signal Conditioning Circuit Board Components 04 17 Coupled Tank System Model Parameters ceccccescceeceeeeeseeeeeeeteeeeeeensees 17 Coupled Tank Apparatus Wiring Summary eceeeeeeseeeeeeeceeceseeeeeeeeeeaees 21 Effect of Controller Tuning Parameters on Higher Order Processes 78 Ziegler Nichols Open Loop Tuning Parameters ccceseeseereeeeeeeeceeeeneeeaee 94 Effect of Controller Tuning Parameters on Higher Order Processes 97 Experimental Data Relating Pump Voltage and Flow Rate for Apparatus occ oF Lis Seater e E A ea teed une ane vetoed aha 111 Experimental Data Relating Pump Voltage and Flow Rate for Apparatus 2 IRE Te E REEE E EEE AA E EE A 111 viii 4 5 4 6 4 8 4 10 4 11 4 12 4 13 Experimental Data Relating Pump Voltage and Flow Rate for Apparatis 3 nsien e A E E R yee E A EN E ES Experimental Data Relating Pump Voltage and Flow Rate for PRADA AUS Os acne ae Sih a e Ta A E R R ata i R E Pump Flow Constants for the Different Apparatus cccceeseeeeeeereeeteees Experimental Data Relating Pump Voltage and Flow Rate Apparatus 2 Experimental Data Relating Pump Voltage and Flow Rate Appar
24. 40 0 77 0 081 0 436 Apparatus 3 0 115 1 45 0 75 0 067 0 489 Apparatus 4 0 116 1 45 0 75 0 087 0 409 4 6 2 Data Analysis Following tuning rules stated in section 3 6 the results for this experiment were obtained The output response from Ziegler Nichols parameters applied to the PI level controller yields an oscillatory response Using tuning rules the PI controller is detuned for the desired response The initial guesses Ziegler Nichols parameters were k 0 391 145 and t 0 193 and the fine tuned parameters were ke 0 06 and t 0 325 Figure 4 21 shows the simulink model for the experiment initial guesses Figure 4 22 depicts the output response for PI control using Ziegler Nichols and the final tuning parameters for a set point change from 3 cm to 13cm Figure 4 23 depicts the input response to the set point change from 3 to 13 cm for the same process To aid in analysis Simulink simulation data is also added to the plot Students used a different initial guess different from the values given in Table 4 15 Clock Time u pii Manipulated Input 1 Setpoint Stope 21 591 x al A 7 pii p FID aaa 34 51 Step PID Controller Saturation Transport Output Variable Delay Process Figure 4 21 Simulink Model for Experiment 5 Apparatus 3 Table 4 17 Block Parameters for Simulink Model Experiment 5 Block Parame
25. 40 13 49 11 86 0 75 11 56 11 59 11 56 11 72 11 53 11 56 11 59 13 81 1 00 8 82 8 87 8 69 8 60 8 62 8 94 8 76 18 27 1 25 6 97 7 19 6 97 7 22 6 97 7 22 7 09 22 57 1 50 5 97 6 12 5 94 5 90 5 94 5 94 5 97 26 81 4 2 3 Calibration of Pressure Sensor Voltage to Tank Liquid Level Table 4 8 shows the experimental data relating pressure sensor voltage tank voltage to liquid level in the tank1 apparatuses The data for tank1 is acquired in step 4 h of the lab procedure in experiment 1 Table 4 8 Pressure Sensor Calibration Data Tank1 Pressure Sensor Voltage V Liquid level Apparatus 1 Apparatus 2 Apparatus 3 Apparatus 4 0 0 03 0 03 0 00 0 03 5 0 84 0 75 0 83 0 82 10 1 66 1 56 1 64 1 65 15 2 50 2 36 2 48 2 48 20 3 30 3 14 3 31 3 29 25 4 07 3 89 4 10 4 12 Each apparatus has similar readings for both tanks A calibration chart is drawn with Tank Sensor Voltage as independent variable and Liquid Level as dependent 115 variable This gives an equation of the form y mx c where the slope m gives the gain value 30 J Appl Tank level 6 091 pressure sensor voltage 0 027 App2 Tank level 6 346 pressure sensor voltage 0 155 App3 Tank level 6 080 pressure sensor voltage 0 025 25 4 App4 Tank Level 6 099 pressure sensor voltage 0 095 20 Apparatus 1 B45 pp E E Apparatus 2 O a A Apparatus 3 10 E X Apparatus 4 5 0 Voltage
26. 51 12 79 1 00 8 94 8 69 8 91 8 66 8 88 8 93 8 84 18 11 1 25 7 06 7 00 7 10 7 09 6 97 7 13 7 06 22 67 1 50 6 03 5 90 5 85 5 75 5 78 5 90 5 87 27 26 Table 4 4 Experimental Data Relating Pump Voltage and Flow Rate for Apparatus 4 Time in seconds pump g A 3 g n Flowrate voltage Trial Trial Trial Trail Trial Trial Avera mis vV 1 2 3 4 5 6 0 50 18 75 18 97 19 15 18 66 18 34 18 66 18 76 8 53 0 65 13 43 13 85 13 66 13 47 13 62 13 91 13 66 11 72 0 75 11 53 11 38 11 47 11 56 11 50 11 47 11 49 13 93 1 00 8 63 8 43 8 59 8 53 8 62 8 63 8 57 18 67 1 25 6 85 7 03 6 87 7 09 6 78 6 94 6 93 23 10 1 50 5 94 5 88 5 82 5 88 5 78 5 79 5 85 27 36 112 The data from Table 4 2 is plotted in Figure 4 1 30 00 Flow rate 18 04 pump voltage 25 00 20 00 15 00 Flow rate ml s 10 00 5 00 0 00 0 0 5 1 1 5 2 pump voltage V Figure 4 1 Pump Voltage and Flow Rate Calibration for Apparatus 2 Trial 1 Pump flow constant K across apparatus K varies slightly across the apparatus and is determined by the procedure described in section 4 2 2 The K values are tabulated in Table 4 5 Table 4 5 Pump Flow Constants for the Different Apparatus Apparatus K cm s V Apparatus 1 17 40 Apparatus 2 17 99 Apparatus 3 17 76 Apparatus 4 18 33 average of three trials 113 Pump flow constant K with time on
27. AEE Eana 4 5 2 Data ANalySiS onneni e E a a e E E aa 4 6 Experiment 5 Tuning a PI Controller for Level Control of Second Tank 1 Coupled Tank Syst me a a a a a a 4 6 1 PreLab Tasks anana a a A aaa i a NITATE 4 62 NIAAA MANY SIS 259 sas r E T ER R E E E E P a A EAA EA EARE E E EEA E E E E A AEE STUDENT FEEDBACK AND FUTURE WORK esssesssseesssssesssseerssseerrsseerssse Daly Progression Of projecties ino aE E E R A aT 5 1 1 Experiments 2 and 3 Modeling Liquid Levels in the Tanks 5 1 2 Experiments 4 and 5 Controlling Liquid Level in the Tank 5 1 3 Experiment 1 Orifice Coefficient Determination ceceseeteeneeeeees O Orero a AEE E EE E E osbe eee ieee ee 5 3 Student feedback on Laboratory Modules ccccscecsseceseceeeeeeeeeeeeceeeeeeeeees vi 5 3 1 Experiment 2 and Experiment 3 gt s 3 cccccssadveecccasnesantude Ghadecueccsunaseecadetienss 164 5 3 2 Experiment 4 and Experiment ccccsccsacieves tacceasssouvescctaasnd lar deavte vada taaas 165 5 3 3 eX POP MGI asa ois teat cheese gaits ea tatu i ea att 166 5 4 Recommendations sssrinin irine e EEE E E A E A ARA 167 SARUTE WOK osie A A E eae E a e ee 167 5 6 IWS CCMA OS i ninna a a a a a a a a a a 168 APPENDIX APPENDIX 1 MATLAB Code for Experiment 2 ssssoeseesseeeneeseosseesresresseesresessresee 171 APPENDIX 2 Block Diagrams of LabVIEW Programs sessesseseesseseesesseseesessesessse 179
28. Newark electronics Newark part number 16F3194 Manufacturer part no 24PCAFA6D Price 21 08 per piece 170 APPENDIX 1 MATLAB CODE FOR EXPERIMENT 2 The following is the MATLAB code for Figure 4 4 Similar code was written for Figure 4 5 to Figure 4 7 Using the almost the same program Figure 4 10 through Figure 4 13 and Figure 5 3 were plotted load C MATLAB 7 work Mfiles a lel txt t alel 1 time column in data file B alel 2 tank1 voltage C alel 3 tank2 voltage D alel 4 pump voltage n 1 m 2 Max 10 total number of trials for the experiment calibl 6 091 calibration factor for level in the tank to pressure sensor voltage reft 110 Usually the time between each data point is 99 101 millisecond So 110 seconds is taken as reference to split the trials datahead 1 1 while m lt Max splitting the entire data into 10 different trials if t n 1 t n gt reft datahead m n 1 m m l 171 end n ntl end m l datahead Max length t finding the length of datasets while m lt Max finding the dataset from t 0 time of step input to time at steady state head datahead m while head lt rear if D head 0 7 amp amp D head 1 1 25 Step change is made from 0 7 to 1 25 Step change is point were a change in input voltage is observed datastart m head 1 end head head 1 end m m l end m l c 1 while c lt length newsetwo 1 se
29. Pump Voltage Y 0 bo Tl 5 Time Figure 3 9 Pump VI Front Panel voltage in Volts Tank pressure sensor voltages and the pump voltage are also displayed in the waveform chart on the right of the screen Write data glows to indicate when the program is writing data to the user defined file tankl and or tank2 limit LED glow when the tank voltages are in the range 4 3 to 4 5 V indicating the danger of tank overflow At this point the Safety Interlock System s watchdog routine shuts off the pump and the pump continues to remain idle until the voltage range is again with the acceptable range less than 4 3 Volts Important Note The measured variables in tankl amp tank2 are pressure sensor voltages and not the tank volumes or liquid levels Lab Procedures Precautions and Other Notes e Make sure that the reservoir s distilled water level is at least three fourths full 47 e A watchdog is programmed into pump vi so that the tanks do not overflow If the liquid level in either of the tanks reaches 25cm the pump is turned off and the pump continues to remain idle until the tank s voltage drops below 4 3 V in tanks e Do not panic the pump can be noisy If it starts smoking that s another matter Shut off the pump by clicking Stop button on the Pump VI e Avoid parallax error while measuring the tank level take measurements with an eye line directly perpendicular to the level 1 Familiarize yourself wi
30. The Run pump button is used to run the pump Control Tank Toggle button is used to switch level control between tank and tank2 Write data glows when the program is writing data to the user defined file 79 In addition to the initialization controls described above the PID tuning parameters are entered and displayed here The STOP button is used to stop the program Figure 3 24 LabPID1 VI Front Panel The dynamic response of the output variables are shown in the center of the screen The Limit action LED along with either the tank 1 Limit or tank2 Limit LED glows when the tank voltages are in the range 4 3 to 4 5 V In this voltage range the safety interlock system takes control to avoid overflow The levels of tank and tank2 along with the set point are displayed numerically in cm They are also plotted on a waveform chart below their numerical display The dynamic response of the input variable is shown on the right of the screen The pump voltage is displayed on a vertical indicator and is plotted on the waveform chart below the vertical indicator The horizontal scroll bar below the waveform charts enables the user to view earlier responses Use the horizontal scroll bar to note how the input and output variables 80 respond to a step change for various tuning constants and based on these responses tune the process Appropriate values for the PID parameters lead to good control stable snappy
31. To Worbspaced a Scope Step Figure 4 15 Simulink Model for Experiment 3 Apparatus 1 Block Parameters Step Block Parameters Transfer Fen Step Transfer Fen Output a step Matrix expression for numerator vector expression for denominator Output width equals the number of rows in the numerator Coefficients are for descending powers of Parameters s Step time Parameters Numerator Initial value 7 6695 Denominator 56 4001 15 0861 1 Absolute tolerance fauto Sample time jo V Interpret vector parameters as 1 D MV Enable zero crossing detection Cancel Help Ay Cancel Help Apply Figure 4 16 Block Parameters for Simulink Model Apparatus 1 and Experiment 3 138 Experimental data FODT approximation Simulink approxiamtion Tank level cm 2 0 50 100 160 200 250 Time Sec Figure 4 17 Comparison of Experiment 3 Data Simulink and FODT Approximations for Tank2 Apparatus 1 The FODT approximation Simulink approximation and empirical data are all plotted in Figure 4 17 for comparison The experimental and Simulink linearized model approximation deviates from the process because of the accuracy limits of linearization A linearization is only approximate near the point it is linearized about and that was its initial steady state FODT approximation closely follows the experimental data because the FODT parameters are taken from experimental
32. and increases overshoot Too low of a value for t can lead to instability Derivative time tp An increase in derivative time helps system stability However this control action is very sensitive to measurement noise Usually only PI control is used for loops where there is measurement or output noise 78 Three Laws of Feedback Controller Tuning 1 Control performance must be defined with respect to all important plant operating goals The desired behavior of the controlled variable and the manipulated variable must be defined for expected disturbances model errors and noisy measurements 2 The dynamic behavior of both the controlled variable and the manipulated variable must be observed when analyzing the performance of feedback control systems Complete diagnosis is not possible without information on both variables 3 When tuning a feedback controller where you start is not as important as where you finish The values for controller tuning constants determined by correlation methods are just swags to be applied to the physical system initially and improved based on empirical performance during fine tuning After completing this experiment you will have hands on experience with laws two and three and a better understanding of the issues involved in law one LabPID1 VI Program Explanation The front panel of LabPID1 VI is shown in Figure 3 24 On the left side of the screen the set point for the liquid level is entered
33. data to write data into the file Step 5 g Click Writing Data to stop recording to file Step 5 c Enter a voltage value between 0 5 0 75Volts here to get initial steady state value Step 5 e Enter a voltage value between 1 and 1 5Volts Step 5 f Step change pump voltage back to 0 5 0 75 Volts of step 5 b Figure 3 12 Step by Step Procedure for Experiment 2 52 f g h Once steady state is established step change the pump voltage to its original steady state value from step 5c Click the WRITING DATA to stop recording data Repeat steps 5c 5g three more times for same pump voltages 6 Press STOP button to stop the program Data Analysis 1 2 3 4 5 Compute the gain relating the tank voltage to the tank level using the calibration data from step 5 b Solve the nonlinear model using MATLAB for the step changes in pump voltage you performed in the lab Solve the linearized approximation of the nonlinear model using MATLAB for the step changed you performed in the lab Graphically compare the nonlinear model its linearized approximation and the lab data Determine the transfer function relating the output variable liquid level to the input variable pump voltage as first order plus dead time model Give the confidence interval for each of the model parameters 6 53 3 4 Experiment 3 Modeling Liquid Level in a Coupled Tank System Object
34. data itself 139 4 5 Experiment 4 Tuning a PI controller for Level Control of Cylindrical Tank 4 5 1 Pre Lab tasks 1 Calculations similar to the one described in section 4 3 2 yield the FODT parameters for the upper tank process of each apparatus Summary of results for all the apparatus are tabulated in Table 4 11 Table 4 11 Upper Tank Model Parameters for Experiment 4 Tank1 cm Volt Apparatus 1 16 909 Apparatus 2 15 727 Apparatus 3 15 727 Apparatus 4 16 909 Table 4 12 Ciancone PI Tuning Parameters for Tank1 Experiment 4 Tank 0 0 Tp KeKy Ti Tpt 8 ke TI Volt em min Apparatus 1 0 1 5 0 74 0 089 0 170 Apparatus 2 0 1 5 0 74 0 095 0 154 Apparatus 3 0 1 5 0 74 0 095 0 148 Apparatus 4 0 1 5 0 74 0 089 0 167 140 4 5 2 Data Analysis Table 4 12 gives the Ciancone parameters for upper tank level control for all the apparatus Following tuning rules stated in section 3 5 the results for this experiment were obtained The desired output response for a fine tuned process is almost achieved with the Ciancone parameters These parameters were slightly conservative So the proportional gain is slightly increased and integral time is slightly decreased to complete fine tuning Initial estimates were k 0 095 and t 0 148 and the final tuning parameters were k 0 1 and t 0 15 for apparatus 3 Figure 4 18 shows the Simulink model for the experiment a
35. ed New York McGraw Hill 1991 3 These experiments are done by students following Chapter 3 3 and 3 4 in this thesis 149 CHAPTER 5 STUDENT FEEDBACK AND FUTURE WORK 5 1 Progression of the Project This project was started in May 2008 to sort out and fix issues with the existing Process Control Lab This section narrates in chronological order and with respect to the individual experiments how the project progressed to create a more practical and streamlined laboratory experience for the students Summer 2008 Time was taken to understand the coupled tank apparatus learn LabVIEW basics and to comprehend the LabVIEW code for the existing programs The Process Control Lab has four matching bench top experiments designated Apparatus 1 Apparatus 2 Apparatus 3 and Apparatus 4 respectively Each includes the Quanser coupled tank apparatus and a computer running LabVIEW Apparatus 4 was running an evaluation copy of LabVIEW and therefore a licensed version of LabVIEW was installed 150 5 1 1 Experiments 2 and 3 Modeling Liquid Levels in the Tanks Spring 2008 According to Dr Myers the four experiments were not setup and available in a high bay area until very late in the semester due to space issues related to construction Students were able to run the experiments using the literature available from Quanser and hands on instruction from Dr Myers However the data were unusable for model validation Fall 2008
36. feed one tank or both tanks The water level in each tank is measured by a pressure transducer located at the bottom of each tank 3 4 Theory What is modeling and what is a mathematical model e The process of deriving the set of equations algebraic and or differential that can be used to describe the response of the system to one or more inputs is called modeling e The equations which describe the system behavior are called the mathematical models of the system What are reasons for modeling e Improve or understand the chemical process operation is the overall objective for developing a dynamic process model e These models are often used to simulate the process behavior in operator training in process design in safety system analysis and in process control How is a system modeled e The basis for modeling actually depends on the system However almost all systems important to chemical engineers can be modeled with both overall and component mass balances energy balances and momentum balances Modeling a 43 simple situation like the liquid surge vessel requires only an overall material balance on the system Overall material balances are sufficient to describe a system only if the roles of temperature individual component compositions and pressure are not important However if there is an energy change in the system like a temperature changes an energy balance must be considered in modeling An e
37. in process design in safety system analysis and in process control How a system is modeled e The basis for modeling actually depends on the system However almost all systems important to chemical engineers can be modeled with both overall and component mass balances energy balances and momentum balances Modeling a simple situation like the liquid surge vessel requires only an overall material 56 balance on the system Overall material balances are sufficient to describe a system only if the roles of temperature individual component compositions and pressure are not important However if there is an energy change in the system like a temperature changes an energy balance must also be considered in modeling An example of this situation is modeling of a heated mixing tank The basis for modeling a tank s dynamic liquid level is an overall material balance It has the form 3 11 ee of pee _ l rate of mass l rate of mass of mass in system f lentering the system leaving the system A more in depth explanation about modeling can be found in Chapter 2 of B Wayne Bequette Process Control Modeling Design and Simulation Prentice Hall 2003 Reservoir Figure 3 14 Schematic of Coupled tank system 57 Suppose two identical cylindrical tanks are arranged in series as shown schematically in Figure 3 14 The input flow rate is proportional to the pump voltage i e F KVpump 3 12 where K volume tim
38. is the pump voltage Reservoir Figure 3 2 Schematic of Cylindrical Tank 32 The liquid exits the tank by gravity discharge through a small orifice with cross sectional area Ao The tank s output velocity v length time is given by C orifice coefficient or discharge coefficient 2 P P is nothing but head and is given by pgL and 1 Z a is almost equal to 1 Thus vo Co 2gL 3 4 where g is the acceleration due to gravity and Z is the tank s liquid level Volumetric output flow rate is F AoV 3 5 F C A J2gL At steady state F Fy Ki SCA 20L 3 6 Pre Lab tasks e Prepare a spreadsheet that defines the experimental data necessary to define the gain relating the pump voltage to the inlet volumetric flow rate 33 e Prepare a spreadsheet that defines the experimental data necessary to calibrate the pressure sensor to the tank s liquid level e Use Equation 3 5 and show how orifice coefficient can be graphically determined from the experimental data LabVIEW Pump VI Program Explanation The Pump VI program is a LabVIEW routine that operates the open loop tank level process and Figure 3 3 shows the controls and indicators on the Pump VI front panel The PUMP VOLTAGE vertical slider and the input box below it are used to set the pump voltage It is suggested to type a number into the input box instead of moving Eile Edit Yiew Project Operate Tools Window Hel
39. real time process control and Proportional Integral PI controller tuning in a laboratory setting These experimental modules are self contained and each module can be used individually or in combination These experiments developed were tested by engineering graduates and undergraduates and are ready for use in teaching Discussions for the experimental results as well as problems encountered during the lab sessions are included so that the lab instructor can get the maximum use from this work Finally an outline of the project and recommendations for future work were added so that one can expand on this work starting from a firm foundation Xxix CHAPTER 1 INTRODUCTION 1 1 Importance of Process Dynamics and Control Chemical processes in industries are becoming more complicated and are eventually designed with intricate control systems in modern times Controlling these processes requires a chemical engineer who has comprehensive knowledge of the basic principles and the advanced techniques in process control design Inadequate understanding of the concepts by the students who in turn get hired into operator control engineer process engineer and managerial positions may result in fatal loss of life and property Today s control systems include more diagnostic sensors and automation delivering increasing volumes of data However the gains accrued from closer process control and management can often be offset by losses due to time s
40. tank to the pump voltage What kind of process mode does this transfer function represent What are the model parameters LabVIEW Pump VI Program Explanation The Pump VI program is a LabVIEW routine that operates the open loop tank level process and Figure 3 15 shows the controls and indicators on the Pump VI front panel The PUMP VOLTAGE vertical slider and the input box below it are used to set 59 File Edit View Project Operate Tools Window Help SY E n 13pt Application Font w ESEAS e 25 Tank ZR E 217899 hre 4 Time millisec Tank 2 iw DATA Pump iw g Tanki pressure lo oi E 2 sensor Voltage Y i 2 1 a Tz Pressure sensor 10 08 TANK 1 umm TANK2 Ed i ge V z UMIT action UMIT WRITE DATA Jo Pump Voltage 0 Figure 3 15 Pump VI Front Panel the pump voltage It is advised to type a number into the input box instead of moving the slider when creating a step change The data display boxes in the center of the screen show the time in milliseconds and tank1 tank2 pressure sensor output voltages and the pump voltage in Volts Tank pressure sensor voltages and the pump voltage are also displayed in the waveform chart on the right of the screen Write data glows to indicate when the program is writing data to the user defined file The tank and or tank2 limit LED glow when the tank voltages are in the range 4 3 to 4 5 V indicating the danger of tank overflow At this point the Safety Interlock Sys
41. the coupled tank system 3 A watchdog subroutine was written into LabPID1 VI program to perform the Safety Interlock System function of a control system which takes corrective action when unacceptable operating conditions are approached For this experiment the watchdog subroutine acts to avoid tank overflow As written the subroutine abruptly halted the program and aborted the experiment Instead the watchdog subroutine should idle the pump when overflow conditions are 158 approached and then resume normal control actions when acceptable operating conditions resume Tuning a controller is a trial and error process of changing the values of the controller s tuning parameters based on the dynamic responses of the manipulated input and the measured output As written the LabPID1 VI screen provided no way for the students to view the dynamic responses for previously chosen tuning parameter values Properly tuning a controller requires knowledge of both the manipulated input and the measured output as the system moves from one steady state to another As shown in Figure 5 5 b only the dynamic values for the pressure sensor voltages which indicate the path of the measured output tank liquid level are displayed and recorded The dynamic values for the pump input voltage which indicate the path of the manipulated input inlet flow rate must also be displayed and recorded LabPID VI only recorded dynamic data in tab delimited column
42. the pump start up effects were ameliorated Furthermore when comparing the experimental data with a Simulink simulation of the process model validation was not possible The output responses showed a much larger gain that predicted by either the model equations or the Simulink simulation The cause of this discrepancy must be either bugs in the Pump VI program or incorrect modeling Pump VI was thoroughly checked and found to be in good order That meant that incorrect modeling was the root cause Checking the models for accuracy lead to the conclusion that the models were mathematically correct At that point each of the model parameters was investigated Eventually it was determined that pump flow constant supplied by the manufacturer was wrong A simple experiment 156 involving a timer and graduated cylinder showed this value to be in the range of 17 4 to 18 4 cm s V where as the Quanser user manual gave the value 3 3 cm s V Incorporating this new pump flow constant into the model produced experimental results that compared well with both the nonlinear model produced by integration within MATLAB and the linearized model produced using Simulink Model validation is now achievable Considering the limitations of experimental error in the lab and model linearization for use within Simulink these experiments provide a valuable learning experience for developing skills in process modeling 5 1 2 Experiments 4 amp 5 Controllin
43. 0 193 Experimental Data Fine Tuned parameters Ke 0 06 taui 0 325 Simulink Model Initial Estimates Ziegler Nichols parameters Kc 0 391 taui 0 193 Simulink Model Fine Tuned parameters Kce 0 06 taui 0 325 pump voltage u V Figure 4 23 Comparison of Input Response between Experimental Data and Simulink Approximation for Ziegler Nichols and Fine Tuned PI Tuning Parameters for Setpoint Change from 3 to 13 Cm in Tank2 Apparatus 3 In the Simulink model a saturation block is added to the model because it was observed that the pump behaved like on off controller initially This means the Ziegler Nichols parameters are too aggressive for the system and the safety interlock system came into action The Simulink data for input response is off from the experimental data for the Ziegler Nichols parameters The safety interlock system injected more oscillation than it is predicted by adding a saturation block in the Simulink model to account for the effect of the safety interlock system The fined tuned output response obeys the given tuning rules no more than 10 overshoot and an initial input response is within 70 150 of its steady change For this experiment the students have input response within 50 200 of its steady state 148 4 7 References 1 B W Bequette Process Control Modeling Design and Simulation Prentice Hall 2003 2 D R Coughanowr Process Systems Analysis and Control 2nd
44. 1 This will bring tank1 online for level control Remove the air pockets a Press Run pump and then enter a random set point lt 10 cm and watch for any air bubbles over in the pressure sensor for the tank your tuning Air pocket in sensor Poke gently with poking rod to eliminate it Figure 3 25 Removal of Air Pockets in Pressure Sensor 82 b Air pockets will form in the sensors most of the time Whether or not you see bubbles poke the rod into tank1 sensor cavity as shown in Figure 3 25 to remove them Caution 1 Be gentle with the sensor while removing bubbles A violent stroke on the sensor could ruin it 2 Don t get confused with the bubbles formed and floating at the top of tank for bubbles over in sensor c Once air pockets are removed click Run Pump to stop pump 3 Generate empirical data See Figure 3 26 a For initial Ciancone PI parameters i Enter the initial Ciancone PI parameters SWAGs calculated from the theoretical settings in the PID parameters input box Note 1 Enter the integral time and derivative time in minutes 2 Make sure tp 0 for PI control ii Enter the set point of 3 cm iii Press Run pump to start the pump iv Once the steady state liquid level is reached on tank1 See tank1 level in waveform chart on screen click write data button and then change the set point to the value given to your group v Note the initial pump voltage change and o
45. 12 Experiment 3 Data Tank2 Apparatus 2 135 Height cm 100 Time Sec Figure 4 13 Experiment 3 Data Tank2 Apparatus 3 Height cm Time Sec Figure 4 14 Experiment 3 Data Tank2 Apparatus 4 136 4 4 3 Data Analysis 1 Calibration Data Results will be similar to the one documented in section 4 3 3 2 For the second order process Lj and Lz are the initial steady state value before step change in tank and tank2 respectively for apparatus 1 L1 and Lzs are 3 75 and 2 58 cm respectively Actually Li and Lz should be equal but because of the allowable calibration limits of 0 1 around 0 V after calibration there will be differences in heights gain k kk 4 7748 L 4 7748 V2 58 7 6695 Tt natural period 4 2582 L JLo 7 5100s V aa 1 0044 Vlas VLes Damping factor The Transfer function of the second order system isl Y s k X s T2s2 2ts 1 7 6695 T ti FS eA RA A aA AAA ESA a a ransfer function 7 5100 2s2 2 1 0044 7 5100 xs 1 2 7 6695 56 4001s2 15 0861s5 1 137 3 Comparison of Experimental Data and Simulink Linear Approximation Experimental Data is obtained by following the lab procedure in section 3 4 The Simulink approximation is obtained from the model shown in Figure 4 15 and block parameters in Figure 4 16 Cae Clock To Wtorep ace To Workspace 7 6695 56 4001s 415 08615 4 Transfer Fen
46. 2 4 2 Coupled Tank Wiring Summary ccceeccessceeseeceeceseeeeeeeeseeenaeenteeeees 21 2 9 CONE SULTON oaned a a a tage ARR aaa eae 21 2 6 Pumped F Mii a3 testsh ia tat oe n wate aa iat ees oh ula eda ala EEA 23 2 7 Data Acquisition and Software ccccccssccssecssecsesecseeceescecssecesecseceeeaeecsaeceeesaees 24 2 7 1 LabVIEW Pump VI Software Explanation cccecscecsseceteceeteceteeeeees 24 2 7 2 LabPID1 VI Program Explanation 25 24 ess sis y esc steeasses axeagetonasae a ieeapess 25 2 8 Calibration Procedure for Pressure Sensors ssssseesessesessrseesesseseesessersessesee Zi 2O HIRE TOLCTIC Eana tt codlest s amp A a Sau ay sandals aaah E 28 LABORATORY TEACHING MODULES cecececcessssseseceeeecneeeeceeeeeceaeeaeeaeeaeeaes 29 3T MARCO GING TO Misses Sc Si acest e Faas ae an oat Dc laa a og loans 29 3 2 Experiment 1 Orifice Coefficient Determination ce eeceseeneeeeeeeeeeteeeeeeaee 30 3 3 Experiment 2 Modeling Liquid Level in a Cylindrical Tank ee 41 3 4 Experiment 3 Modeling Liquid Level in a Coupled Tank System 54 3 5 Experiment 4 Tuning a PI Controller for Level Control of a Cylindrical Tank 68 3 6 Experiment 5 Tuning a PI Controller for Level Control of Second Tank in Coupled Tank System esses atee odeccas vances cea cbadeausyencac cis aantety meee bemeaneee 86 3 7 Correcting Pump VI Start up Issues ecccecceeeceeeceeseeceeeceseeee
47. 2003 127 4 4 Experiment 3 Modeling the Liquid Level in the Second tank of a Coupled Tank System 4 4 1 Pre Lab Tasks 1 Material balance on the lower tank g of aes 7 l rate of mass l rate of mass of mass in tank lentering in tank leaving out of tank Ap Pa Te ee dL Ar dt C o o01901 Co A020902 Dr where Ar Ar Ar 1 7 2 Dade Do2 Ann m amp Aon Vor Coy 2gly amp Do2 Coy 29 L2 f Lz L1 2 as oy L2 4y 2g Eo 4 10 Ar cand J 2560 22 a I 0 4697 L 0 4697 L f Lo L4 2 At steady state the change in height with time is zero so Equation 4 10 is equal to Zero 128 dL dt Co 29 2 as Co 29 las Lis Los 3 Define the deviation variables as Let X L Los and U Li Lis dX or or flas las 5 a x l U By defintion of steady state f L2 L1 0 So E k E EN F fa c 1 0 2348 e a aL 2 Ar Lo Lo tan k BG ge eee Y xX X IX Wa ae Ge ae O 129 Y s _ u s sta Q ro a _ k u s 1 s 1 Tts 1 _ 0 2348 Vlas vias _ bos 4 11 o 0 2348 Lz Lis 1 t3 ___ 4 2582 L 4 12 0 2348 L Los Y s _ fe ky 4 13 UC 4 2582 Lp s 1 T2s 1 upper tank lower tank 5 L2 s _ k k2 V s T1T2S2 T44 T2 S 1 This is a second order system with gain k k3 natural period T T2 T VT Tz and damping factor As shown in sect
48. 90 100 time time Figure 3 30 Well Behaved Process Controller Fine Tuning of a PI Controller Use the previously determined control parameter initial guesses and fine tune the PI controller using the rules that follows l 95 Three important features relating to the manipulated variable are notable from the well behaved process in Figure 3 30 l The manipulated variable changes immediately when the set point is changed This change is due to the proportional mode is equal to kc AE t Kc R t This initial change is typically restricted to 70 to 150 percent of the change at the final steady state There is a delay between the time the manipulated variable changes and the time when the controlled variable responds This delay is due to process dead time and no controller can reduce this delay to less than the process dead time During the delay time the manipulated variable increases linearly This is due to the integral mode During this period the error is constant so the proportional term does not change but the integral term increases linearly with slope equal o EO TI t After the controlled variable begins its transient response the proportional term decreases while the integral term continues to increase At steady state the end of the transient response the proportional term is zero because the error is zero and the integral term has adjusted the manipulated variable to a value that reduces the
49. DEVELOPING IMPLEMENTING AND ASSESSING COUPLED TANK EXPERIMENTS IN AN UNDERGRADUATE CHEMICAL ENGINEERING CURRICULUM A Thesis presented to the Faculty of the Graduate School at the University of Missouri In Partial Fulfillment of the Requirements for the Degree Master of Science by NARENDRA KUMAR INAMPUDI Dr Patrick J Pinhero Thesis Advisor JULY 2009 The undersigned appointed by the Dean of the Graduate School have examined the thesis entitled DEVELOPING IMPLEMENTING AND ASSESSING COUPLED TANK EXPERIMENTS IN AN UNDERGRADUATE CHEMICAL ENGINEERING CURRICULUM presented by Narendra Kumar Inampudi a candidate for the degree of Master of Science and hereby certify that in their opinion it is worthy of acceptance Dr Patrick J Pinhero Dr Mary A Myers Dr Matthew Bernards Dr John M Gahl weeeeeee 10 the Chemical Engineering Department University of Missouri ACKNOWLEDGEMENTS I would like to thank my advisor Dr Patrick Pinhero for his support encouragement insightfulness and critical comments throughout this project I wish to express my sincere appreciation to my co advisor Dr Mary Myers for all her time guidance patience encouragement kindness and help with developing the experiments unconditional support and reviews especially with editing the thesis I thank Dr Matthew Bernards for his comments on this work and for serving as a thesis committee memb
50. Pressure sensor Lower tank tank2 Disturbance or drain tap Calibration amp Signal Conditioning Circuit Board Water basin reservoir Figure 3 13 Coupled Tank Apparatus the tank For this experiment use only the medium inserts of diameter 0 476cm for both tanks A drain tap is also provided in the apparatus to introduce disturbance flow into either tank or tank2 By opening the drain tap liquid from tank1 flows directly to the reservoir The pump propels water vertically to two quick connect orifices Outl and Out2 which are usually closed The system is equipped with different diameters for 55 these two orifices for configurability Teflon Tubing of 1 4 I D with compatible couplings is provided to enable the pump to feed one tank or both tanks The water level in each tank is measured by a pressure transducer located at the bottom of each tank 3 4 Theory What is modeling and what is a mathematical model e The process of deriving the set of equations algebraic and or differential that describe the response of the system to one or more inputs is called modeling e The equations which describe the system behavior are called the mathematical models of the system What are reasons for modeling e Improve or understand chemical process operation is the overall objective for developing a dynamic process model e These models are often used to simulate the process behavior in operator training
51. Trial Trail Trial Trial Average mis 1 2 3 4 5 6 0 50 20 88 20 47 20 22 20 18 20 19 20 34 20 38 7 85 0 65 14 56 14 53 15 12 14 62 14 41 14 28 14 59 10 97 0 75 12 28 12 81 12 69 12 78 12 78 12 87 12 70 12 60 1 00 9 37 9 28 9 31 9 22 9 15 9 03 9 23 17 34 1 25 7 25 7 43 7 25 7 19 7 25 7 25 7 27 22 01 1 50 5 91 6 03 5 91 6 18 6 03 6 04 6 02 26 59 Table 4 2 Experimental Data Relating Pump Voltage and Flow Rate for Apparatus 2 Trial 1 Time in seconds pump voltage Trial Trial Trial Trail Trial Trial orase pan y 1 3 4 5 6 verag 0 50 18 40 19 22 17 97 18 16 18 12 17 81 18 28 8 75 0 65 13 38 13 34 13 53 14 03 13 50 13 56 13 56 11 80 0 75 1138 11 37 11 72 11 63 11 65 11 40 11 53 13 88 100 869 856 863 869 871 8 56 8 64 18 52 125 718 709 7 00 707 703 705 7 07 22 63 150 5 87 5 94 612 600 612 606 6 02 26 59 111 Table 4 3 Experimental Data Relating Pump Voltage and Flow Rate for Apparatus 3 Time in seconds Pome 7 g g Flowrate voltage Trial Trial Trial Trail Trial Trial versie ais vV 1 2 3 4 5 6 0 50 22 16 22 34 21 59 21 97 21 82 21 53 21 90 7 31 0 65 14 72 14 71 15 06 14 91 15 78 15 81 15 17 10 55 0 75 12 40 12 50 12 62 12 60 12 31 12 63 12
52. V Figure 4 2 Calibration Chart Pressure Sensor Voltage Versus Level in the Tank1 Although typical gain values range from 6 1 6 4 it need not be in this range because the gain values depend on how the potentiometer screws are adjusted Moreover it doesn t need to be regressed the origin because sometimes there will be slight offset from zero at zero level in the tank 116 4 2 4 Orifice Coefficient Following the procedure described in step 5 in lab procedure of section 3 2 produces the data tabulated in Table 4 9 and plotted in Figure 4 3 Table 4 9 Experimental Data log Vpump vs log Vsensor Apparatus 2 Vpump Vsensor log Vpump Log Vsensor 1 10 1 16 0 04 0 06 1 25 1 57 0 10 0 20 1 40 2 03 0 15 0 31 1 55 2 50 0 19 0 40 1 70 3 02 0 23 0 48 1 85 3 63 0 27 0 56 0 60 log V gensor 2 183 l0g V pump 0 019 0 50 0 40 log V sensor 2 Ww oO 2 N 0 05 i i 0 15 0 30 log V pump Figure 4 3 Log Vpump vs Log Vsensor for Apparatus 2 117 The intercept of Figure 4 3 yields the value of orifice coefficient as shown below and described in section 4 2 1 Note that zn for Equation 4 4 comes from Figure 4 2 and is the slope of the line between pressure sensor voltage and tank level for apparatus 2 for this example calculation K slob 0 019 B 17 99 10 cm 17 99 1 02 18 36 B SW CoAo 2g 18 36 V6 346
53. a glows when the program is writing data to the user defined file i i fe eageea Amo wee B Tural not be conhd wth Ld Psat FESS ADAG AD mre weron 89 nartaberaw Figure 2 12 LabPID1 VI Front Panel 25 In addition to the initialization controls described above the PID tuning parameters are entered and displayed here The STOP button is used to stop the program The dynamic response of the output variables are shown in the center of the screen The Limit action LED along with either the tank Limit or tank2 Limit LED glows when the tank voltages are in the range 4 3 to 4 5 V In this voltage range the Safety Interlock System takes control to avoid overflow The levels of tank and tank2 along with the set point are displayed numerically in cm They are also plotted on a waveform chart below their numerical display The dynamic response of the input variable is shown on the right of the screen The pump voltage is displayed on a vertical indicator and is plotted on the waveform chart below the vertical indicator The horizontal scroll bar below the waveform charts enables the user to view earlier responses Use the horizontal scroll bar to note how the input and output variables respond to a step change for various tuning constants and based on these responses tune the process Appropriate values for the Proportional Integral Derivative PID parameters lead to good control stable
54. a model s differential equations using MATLAB using Simulink to simulate a system comparing experimental results with approximations and understanding the limits of accuracy e Experiments 4 and 5 supply hands on experience in fine tuning a PI controller for level control 163 5 3 Student Feedback on Laboratory Modules 5 3 1 Experiment 2 and Experiment 3 To access the usability of the module handouts seven undergraduate juniors in chemical engineering and three masters students in electrical engineering performed the experiments with little or no supervision None of the students had taken the ChE Process Control course prior to performing the experiment They were all able to get through the experiments with little or no difficulty Their reviews of the modules were taken into consideration when the modules were modified and all of their concerns were addressed Some of their comments and the actions to address their concerns follow Comment 1 It will be a nice idea to have figure for calibration and signal circuiting board This was addressed by creating Figure 3 11 and annotating it appropriately Comment 2 T have difficulty in figuring out where the pressure sensor is at the time of removal of air pockets This was taken into account and Figure 3 10 is included at the removal of air pockets procedure explanation Comment 3 I like the figure explaining step by step procedure with screenshot
55. ab delimited output file written by LabPID1 VI addressed issues five and six described above as shown in Figure 5 6 b Lab module handouts were written to address issues seven eight and nine A procedure for addressing the issues with starting the LabVIEW program is provided in section 3 7 160 Ee Gt Yew Bret peate ods indon He SE elm e tee Eo S Ble Eat Yew pet Format Tos Data Window Hep JGUZAIPA IH ABB Joo Br Niwee F 0 2 Se Oe eS Ss Pump Integral Derivativ Time TANK TANK SetPoint Voltage time e aaa seconds Aem 2em cm V Ke min time min Sal is T 3 3 0813 5 ea baad 347 3 3 OSS 03 07 pai 347 3B 3 0 3 07 epe a 3 31531 3 0e 03 C 3 3 3 ou O wm i 34S 3453 3 0883 03 07 Z 347 3 3 O 3 PID parameters Za 755 347 3138 3 08 8 03 O07 o immi um am 3 A a eet ui aum 3 3 oa 03 O7 Teer FETTET 347 303 3 OBLE 3 07 Aut am aB 3 BSCS ANT UEN 2 naw n2 n7 n a b Figure 5 6 a Modified LabPID1 VI front panel b data filed recorded by new LabPID VI FODT parameters calculated without accounting for pump startup effects were given to the students for determining initial swags for controller tuning parameter via open loop methods for both experiments 4 and 5 Since these FODT parameters were about 300 off due to pump startup effects the initial swags the students calculated for experiments 4 and 5 were also way off When tuning a contro
56. ages and the pump voltage are also File Edit View Project Operate Tools Window Help gt E m 13pt Application Font IESE EJ STOP PUMP VOLTAGE ae s Tank 1 Iw TRG a Time millisec 217899 Tank2 2 DATA 2 Pur 3 Tanki pressure n 0i aL g 2 sensor Voltage W jo ne iy o B ies z maske sensor 10 08 T ANK 4 umr TANK2 t piis Yoltag ACTION LIMIT WRITE DATA 6 Pump Voltage V fo 8 bo reer Time Figure 2 11 Pump VI Front Panel 24 displayed in the waveform chart on the right of the screen Write data glows to indicate when the program is writing data to the user defined file The tank and or tank2 limit Light Emitting Diode LED glow when the tank voltages are in the range 4 3 to 4 5 V indicating the danger of tank overflow At this point the Safety Interlock System s watchdog routine shuts off the pump and the pump continues to remain idle until the voltage range is again within the acceptable range less than 4 3 Volts Important Note The measured variables in tank amp tank2 are pressure sensor voltages and not the tank volumes or liquid levels 2 7 2 LabPID1 VI Program Explanation The front panel of LabPID1 VI is shown in Figure 2 12 On the left side of the screen the set point for the liquid level is entered The Run pump button is used to run the pump Control Tank Toggle button is used to switch level control between tank and tank2 Write dat
57. ags to be applied to the physical system initially and improved based on empirical performance during fine tuning After completing this experiment you will have hands on experience with laws two and three and a better understanding of the issues involved in law one LabPID1 VI Program Explanation The front panel of LabPID1 VI is shown in Figure 3 32 On the left side of the screen the set point for the liquid level is entered The Run pump button is used to run the pump Control Tank Toggle button is used to switch level control between tank and tank2 Write data glows when the program is writing data to the user defined file In addition to the initialization controls described above the PID tuning parameters are entered and displayed here The STOP button is used to stop the program Figure 3 32 LabPID1 VI Front Panel 99 The dynamic response of the output variables are shown in the center of the screen The Limit action LED along with either the tank Limit or tank2 Limit LED glows when the tank voltages are in the range 4 3 to 4 5 V In this voltage range the Safety Interlock System takes control to avoid overflow The levels of tank and tank2 along with the set point are displayed numerically in cm They are also plotted on a waveform chart below their numerical display The dynamic response of the input variable is shown on the right of the screen The pump voltage is displayed on a vertical ind
58. ameter 0 4762 cm Dio Large Outflow orifice diameter 0 5556 cm Dwo Diameter of orifice without any insert 0 7560 cm g Acceleration due to gravity 981 cm s 2 4 Electrical Components and Connections Electrical connections must be made between the three major components The Universal Power Module Quanser UPM 2405 which serves as a power amplifier the Quanser Q8 terminal board Data Acquisition and Control DAC Board and the Coupled Tank Apparatus Figure 2 5 shows the Hardware required for the Coupled Tank system and Figure 2 6 shows the Coupled tank connections a b Figure 2 5 a Universal Power Module UPM 2405 b Q8 Terminal Board Connections 18 Figure 2 6 Coupled Tank Connections 2 4 1 Cable Nomenclature Figure 2 7 and Figure 2 8 depicts the cables used in wiring the Coupled Tank system a b Figure 2 7 a From Digital To Analog Cable b To Load Cable of Gain 5 Figure 2 7 a shows From Digital To Analog cable which is 5 pin Deutsches Institut f r Normung DIN connector to Radio Corporation of America RCA adapter This cable connects an analog output of the data acquisition terminal board to the power module for proper power amplification Figure 2 7 b shows To Load cable which is a 4 pin DIN to 6 pin DIN connector This cable connects the output of the power module 19 after amplification to the gear pump One end of this cable contains a resistor that sets the
59. ange from one level to another level eliminates start up effects in these apparatuses The graphs are 132 plotted by repeating the experimental procedures 10 times Red color line indicates the 95 confidence interval C I and the black color one is mean for the entire set of values Data set in yellow color is actual data collected on the apparatus The MATLAB code similar to generate these graphs is attached in Appendix 1 Height crn Time Sec Figure 4 10 Experiment 3 Data Tank2 Apparatus 1 133 0 4 L L 1 1 1 1 1 1 4 L 1 1 1 1 1 1 1 L L 1 1 1 o 1 2 3 a 5 6 7 8 9 10 12 13 14 15 16 17 18 19 2 21 2 B 24 235 Time Sec Figure 4 11 Enhanced View in Initial Stages of Experiment 3 Data for Apparatus 1 Sample Calculation for Process gain K Process Time Constant t and Process Dead Time g First order dead time process is represented by E Kp e 9s ae TS 1 ue Process gain Ky change in output variable change in input variable 13 0 2 58 1 35 8 from Figure 4 10 18 9454 cm V From Figure 4 11 dead time is 3 8 sec Time to approach 63 2 of the new steady state is 0 632 13 2 58 2 58 9 16 cm 134 In Figure 4 10 the value for a height of 9 15 cm is Tp 33 6 seconds 18 9454e 73 85 Transfer function G s TT represents the FODT model of the process pictured in Figure 4 10 Height cm 200 250 Time Sec Figure 4
60. asvseeanieans Gea vewdiese Sia 117 Experiment 2 data for Apparatus 1 ccccceccccceseceseeeeseeeseeceeeceneeneeeeeseeeaeens 122 Experiment 2 data for Apparatus 2 ccccccccccceseceseceeseeeseeceseceteeeeeeesseeeaeens 123 xiv 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 Experiment 2 Data for Apparatus 3 ccccccccceeseceseceeeceeseeceseceeeeeeeeeseeeaeees 123 Experiment 2 Data for Apparatus 4 ceccccccceseceseceeseeeseecesecneeneeeenseeeaeens 124 Calibration Chart Pressure Sensor Voltage vs Level in the tank Apparatus DS tan od et ise Pa hid ant ae a Sed aud Soa atlas Falah cata 126 Comparison of Experimental Data with Simulink Non Linear and Linear Approximations for Apparatus oo cei eeceseeceeeeceseceseceesseeeeeeeeeaecnaeeneeees 127 Experiment 3 Data Tank2 Apparatus 1 ooo cc ceccceceeeseeeseeceeceeeeeeeeeeseeeaeens 133 Enhanced View in Initial Stages Experiment 3 Data for Apparatus 1 134 Experiment 3 Data Tank2 Apparatus 2 00 cccceccceceeesceesseceeceeeceeeeeeseeeaeens 135 Experiment 3 Data Tank2 Apparatus 3 0 ccccecceesceesceeseeceseceeeeeeeeeeseeesaeens 136 Experiment 3 Data Tank2 Apparatus 4 0 ccccecceecceeceeseeeeeceeeeeeeeeeseeeaeens 136 Simulink Model for Experiment 3 Apparatus 1 cccccccecceseeeeceeeteeenteees 138 Block Parameters for Simulink Model Apparatus 1 Experiment 3 138 Comparison of Exper
61. ate Coupled and Input Coupled SISO System 2 6 Pumped Fluid Distilled water is the pumped fluid The reservoir water is taken from the Barnstead NANOpure Diamond Life Science UV UF ultrapure water system which has a resistivity of 18 mQ cm located in Dr Pinhero s laboratories Distilled water is recommended to fill the water in the reservoir to avoid deposits on and staining on plexiglas tubes and other equipment 23 2 7 Data Acquisition and Control Software The LabVIEW programs Pump VI and LabPID1 VI are for control of pump speed and to acquire voltage data from the pressure transducers in either tank and or tank2 LabVIEW is installed on Dell workstation running the Windows XP operating system Pump VI has NIDAQm x device drivers 8 0 0f0 and LabPID1 VI has Traditional Data Acquisition software 7 4 1f4 for data acquisition 2 7 1 LabVIEW Pump VI Program Explanation The Pump VI program is a LabVIEW routine that operates the open loop tank level process and Figure 2 11 shows the controls and indicators on the Pump VI front panel The PUMP VOLTAGE vertical slider and the input box below it are used to set the pump voltage It is advised to type a number into the input box instead of moving the slider when creating a step change The data display boxes in the center of the screen show the time in milliseconds and tank1 tank2 pressure sensor output voltages and the pump voltage in Volts Tank pressure sensor volt
62. atus 2 Mittal erea an nen Re an a an dda A A ES Pressure Sensor Calibration Data Tank oo ceeeeessssssssssssssnsssssnsnsssnseees Experimental Data log Vpump VS log Vsensor APParatus 2 oie eee cree Calibration Chart Readings for Tank ccceccccceseceseceeeeeeseecseeceseeneeeeeseees Upper Tank Model Parameters for Experiment 4 00 0 0 eeceecceesseeeteeeteeeeees Ciancone PI Tuning Parameters for Tank1 Experiment 4 eee Block Parameters for Simulink Model Experiment 4 Apparatus 3 4 14 4 15 4 16 4 17 Tank2 Model Parameters for Experiment 5 0 cccceccceesseeeteceeeeeeeeeeeeeeeseees 144 Second Tank Ziegler Nichols PI Tuning Parameters for FODT Model 145 Ciancone PI Tuning Parameters for Tank2 Experiment 5 0 ee eeeeeeeeees 145 Block Parameters for Simulink Model Experiment 5 0 ccecceesceeseenees 146 LIST OF FIGURES Figure 2 1 Coupled Tank Apparatus cxevets scsi eats oag easel toed hurled Sauas farses 2 2 Coupled Tank Plant a Front View and b Back View c eeee 2 3 Calibration and Signal Conditioning Circuit Board cc ceeeeeeeeeeeeeeee 2 4 a Base of Coupled Tank Apparatus b Quick connects Out1 and OUT OU AB Sn e i E E a ccna aicevaees 2 5 a Universal Power Module UPM 2405 b Q8 Terminal Board Connections renmen a a E a a a a RGT 2 6 Coupled tank Connections ssssssssssseeseeseesseesreseessessesetsseessessrssressees
63. bserve the pump voltage response along with tank level response as the system reaches the new steady state 83 vi Once the new steady state is reached click write data to stop recording and run pump to stop the pump Step 2 a Step 3 a ii Step 3 a iv Enter set point here Step 1 c Press this button to start the program button will be white color arrow when program is not running and black arrow when running Step 4 Press STOP to end the program at end of experiment Step 2 a 2 c 3 a ili 3 a vi Press Run Pump to run pump and vice versa Step 1 e This button indicates which tank s level is being controlled Toggle the button fo switch between tank and j4nk2 Step 3 a v Step 3 b Use this scroll bar to view response for previous tuning Step 3 a iv Step 3 a vi Step 3 c i To record data in excel sheet press parameters l this button LED in green Step 3 a v Step 3 b Use this indicates writing to the file scroll bar to view manipulated variable pump input for previous tuning parameters Step 3 a i 3 b i Enter PID tuning parameters here Figure 3 26 Detailed Explanation of Step by Step Procedure for Tuning 84 b Fine Tuning i Use scroll bars below tank level and voltage vs time plots to view response for previous tuning parameters ii Adjust the k and t for best closed loop response Use a trial and error method based on PI controller tunin
64. cceaysceteciaste congyaadectesnssintesec auisstiactnedetweadaadovaaantice 80 Removal of Air Pockets in Pressure Sensor seceeseeceeseceeceseeneeeseeseeeaeenaes 82 Detailed Explanation of Step by Step Procedure for Tuning eee eeeeeee 84 Coupled Tank Apparatus s scssacseercicss cca sxtsstsabacss otia anoa SAET ASERRE 88 xiii 3 28 3 29 3 30 3 31 3 32 3 33 3 34 3 35 4 1 4 5 PID Controller Block Diagram in a Feedback Loop eeeceeseeceeeeeeteeeeeenee 90 Step Response Characteristics of Underdamped Second Order Processes 92 Well Behaved Process Controller oo cccccessssssssssssssssssssssssnsssssnsssssssssssssnsnsees 95 Improperly Tuned Controllers a sluggish response due to too little integral action needs smaller tr integral time b sluggish response due to too little proportional action needs larger gain Ke eceeeseeeteeneeereeeeees 97 EabPIDI VI Front Paneli reesen a e e E e Aahe 99 Removal of Air Pockets in Pressure Sensor secessceeseeeeeeeecesecneeeneeeeeeerees 102 Detailed Explanation of Step by Step Procedure For Tuning 103 Issues with the LabVIEW Program Start Up ceccecsseesseesteceeeeeeeeeeeeeeeaeees 106 Pump Voltage and Flow Rate Calibration for Apparatus 2 Trial 1 113 Calibration chart Pressure Sensor Voltage versus Level in the Tank1 116 Log Vpump VS Log Vsensor for AP Paras vs sash sacine
65. change in set point 165 Comment 3 While completing the lab all the equipment worked properly and efficiently The Lab module handout is very clear and concise Comment 4 Overall lab was very practical and lab module handout was helpful Comment 5 Curious about how the air pockets affect the pressure sensor readings This is addressed in page 153 Comment 6 The lab handout was easy to follow and explained everything very well so there are no additional recommendations for it particular Comment 7 As noted in the lab there are some start up issues that cause the system to overshoot the set point and reach the maximum tank level This is probably to do with background setting not being reset as a complete reset of the program solves the problem The Lab Module handout was very helpful Not only did it contain step by step instructions along with corresponding photos and screenshots but also contained the theory behind the lab This was particularly helpful in understanding why the system behave the way it did when the setting was changed 5 3 3 Experiment 1 This experiment was not tested by students as most sections were taken from experiment 2 which was tested earlier by students and should be sufficient for the freshmen to go through this experiment 166 5 4 Recommendations Having performed experiments 2 3 4 5 in the Chemical Engineering Process Control course for two semesters t
66. chdog software interlock is programmed into pump vi so that the tanks do not overflow If the liquid level in either of the tanks reaches 25cm the pump is turned off and the pump continues to remain idle until the tank s voltage drops below 4 3 V e Do not panic the pump can be noisy If it starts smoking that s another matter you can shut off the pump by clicking Stop button in the program e Avoid parallax error while measuring the tank level take measurements with an eye line directly perpendicular to the level 35 1 Familiarize yourself with the apparatus and how it relates to the schematic 2 3 a See Figure 3 1 and Figure 3 2 Start the pump vi program and Open a data file a Double click the Pump VI icon on the desktop It opens the pump vi program in LabVIEW Familiarize yourself with the icons controls and indicators on the screen shown in Figure 3 3 b Click the white color arrow button on the top left of the screen to start the program A window pops up on the screen asking to define an output file c Assign a file name and save it in Microsoft excel spreadsheet format for example yourname xls Removal of air pockets a Run the pump by giving a random pump voltage between 0 5 1 Volts in the voltage input box below the PUMP VOLTAGE vertical slider and watch for any air bubbles over in the pressure sensor located at the bottom of the top tank b Air pockets will almost always
67. d the students produced consistent coherent data for further analysis However due to time constraints they did not compare the experimental results with a Simulink simulation of the process The pump start up issue with Apparatus 4 was not addressed directly During this second trial of experiment 2 a student broke the upper tank orifice by over tightening the insert while calibrating the pressure sensor This rendered Apparatus 4 unavailable for rest of the semester While this allowed postponing addressing the pump problem it necessitated a more equipment friendly calibration procedure 155 Spring 2009 Handouts for experiment 2 and experiment 3 were rewritten to address all of the issues encounters to date The pump start up issues was addressed by making the step change in pump voltage from one steady state to other steady state instead of from the pump s rest state to a new steady state With this change no pump start up anomaly was observed as one can see in Figure 5 3 b Several graduate students volunteered to perform the experiments and evaluate the handouts All of their comments were edited into the final edited version of the handouts shown in sections 3 2 and 3 3 Unfortunately the handouts were not finished in time for the Spring 2009 ChE 4370 students to perform these experiments The data produced by the graduate students surfaced another issue The FODT parameters were off by approximately 300 even after
68. dead time as O t gt 0 74 2 Use the appropriate graph from Marlin Thomas E Process Control Designing Processes and Control Systems for Dynamic Performance McGraw Hill New York 2 edition page 286 to determine the dimensionless tuning values K Kp 77 Tp 0 3 Calculate the dimensional controller tuning values from the dimensionless tuning values and the FODT parameters KK ke a 3 17 p T 6 T Ty an p 3 18 Fine Tuning The values for controller tuning constants determined by correlation methods are just swags to be applied to the physical system initially and improved based on empirical performance during fine tuning See Figure 3 22 for the well tuned PI controlled process Fine Tuning of a PI Controller Use the previously determined control parameter initial guesses and fine tune the PI controller using the rules that follow Three important features relating to the manipulated variable are notable from the well behaved process in Figure 3 22 75 Well Tuned PI Controller 1 5 T T T T T T T T T y andr Figure 3 22 Well Behaved Process Controller 1 The manipulated variable changes immediately when the set point is changed This change is due to the proportional mode and is equal to kceAE t kc R t This initial change is typically restricted to 70 to 150 percent of the change at the final steady state 2 There is a delay between the time the
69. douts and their comments are listed in section 5 3 2 The experimental results compared favorably with the Simulink simulation Hence the students got to experience essence of tuning 5 1 35 Experiment 1 Discrepancies between the experimental results for experiments 2 and 3 and their Simulink approximations lead to the development of a new experiment As described in the Spring 2009 subsection of section 5 1 1 experiments were performed to prove that the pump flow constant K documented by manufacturer was only 17 18 of the true 162 value As a consequence of the root cause analysis and verification a simple experiment was designed that could be used in a freshmen class for a variety of engineering disciplines The experiment to determine orifice coefficient comprises several learning experiences for basic engineering skills These learning experiences include design of experiment data acquisition using LabVIEW programs calibration of sensors The handout module for this experiment is given in section 3 1 It has not yet been tested by students 5 2 Outcomes e Experiment 1 provides students with the opportunity to get a feel for laboratory calibrate sensor instrumentation experience graphical user interface programs for data acquisition and develop critical thinking e Experiments 2 and 3 offer students foundational learning experiences in formulating a dynamic model from material balances validating system models solving
70. e Volt is a constant and Vpump is the pump voltage The liquid exits the tank by gravity discharge through a small orifice The outlet velocity length time of each tank small orifices is given by 3 13 C orifice coefficient or discharge coefficient 2 P P is nothing but head and is given by pgL and 1 be a is almost equal to 1 Thus Vvo Coy 2gL 3 14 where g is the acceleration due to gravity and Z is the tank s liquid level Pre lab Procedures 1 Assuming constant density find the nonlinear model relating the liquid level in the second tank to the liquid level in the first tank That means find B f L2 L1 Use the parameters 58 a Pump flow constant K 17 90 cm s V b Tank diameter D 4 445 cm c Outlet orifice diameter Doi Doz 0 4762cm d Gain relating water level to sensor voltage 6 0 6 4 cm V e Acceleration due to gravity g 981 cm s 2 Determine the upper tank s steady state level as a function of the lower tank s steady state level 3 Define deviation variables and linearize the model around steady state to determine the transfer function relating the lower tank s liquid level to the upper tank s liquid level 4 Draw a block diagram for the open loop two tank process Include all appropriate transfer functions and label all information signal streams 5 Use this block diagram to find the transfer function relating the flow out of the second
71. e best possible manner within the Process Dynamics and Control course e To practically demonstrate fundamental concepts like modeling and simulating a process system and validating a dynamic model e To introduce and provide hands on experience with Laboratory Virtual Instrumentation Engineering Workbench LabVIEW graphical user interface control programs e To provide hands on experience in tuning the Proportional Integral PI controller for the apparatus e To modify the existing experiments and their LabVIEW code for self containment and robustness e To develop a new laboratory which uses the same existing equipment Integrating a laboratory experience into Process Control course allows students to model a chemical process using differential equations which helps them better understand the chemical process and then simulate the process in Simulink simulation software from the MathWorks Finally comparing the Simulink prediction of process with the experimental results and analyzing the reasons for any discrepancies in the results allows for validating the model Other labs provide the students with actual hands on experience in tuning a PI controller for the same process using the tuning rules taught in the class at later stage in semester 1 5 Thesis Organization Chapter 1 e Introduction e Motivation and e Objectives Chapter 2 e Apparatus Description e Software Description e Pressure Sensor Cal
72. e flap should be horizontal to the ground For draining the fluid flap should be in line with the drain pipe or vertical to the ground Flow Splitter Component 16 This divides the flow between Outl and Out2 so that different configurations Single Input Single Output SISO State Coupled SISO and State Coupled and input Coupled SISO configurations are possible Pressure Sensor Component 17 A pressure sensor is located at the bottom of each tank to measure the head in that tank The sensor output voltage increases proportional to the applied pressure The output measurement is processed through signal conditioning board component 18 and made available as 0 5V DC signal Sensitivity of the measurement is to be determined and is usually in the range of 6 0 6 4 cm s V for both pressure sensors Calibration of each pressure sensor s offset and gain potentiometers are required to keep level measurements consistent with the liquid used in the experiment Calibration and Signal Conditioning Circuit Board Component 18 To calibrate the pressure sensors the bottom of the Coupled Water tank apparatus houses a signal conditioning circuit board identified by component 18 Table 2 1 provides a list of different signal potentiometers to be tuned during sensor calibration 16 Table 2 1 Calibration and Signal Conditioning Circuit Board Components ID Description ID Description 23 Tank1 Sensor Offse
73. eats of steps 4 7 If yes check whether the voltage is 4 10 V at 25 cm of water level 27 2 9 10 11 12 13 Double check whether voltage is reading 0 V when tank1 is empty and 4 10 V at 25 cm water level Tank2 is brought online for calibration by using quick connect at Out2 and disconnecting quick connect on Out1 Plug orifice of tank2 with a finger Follow steps 4 9 to calibrate the offset and gain potentiometers for tank2 Now the apparatus is ready for experimentation Reference Coupled Water Tanks User Manual Document Number 557 Revision 03 Quanser 28 3 1 CHAPTER 3 LABORATORY TEACHING MODULES Introduction Five experiments were designed to introduce and provide hands on experience with the concepts of modeling simulation model validation feed back control and PI controller tuning Different educational levels of undergraduate chemical engineering students can gain practical skills using these experimental modules These five skills are some of the most important practical tools to graduates seeking positions in the process industry These modules offer useful exercises in the following Instrument calibration Finding orifice coefficient flow constant for gravity discharge Formulation and validation of a dynamic model for liquid level in a cylindrical tank Formulation and validation of a dynamic model for liquid level in the second tank of a coupled
74. eeeeeeenseeesaeenes 106 3 8 Referentes asedcrs Sia iiignd dupe an eo Ate Aa pane e ae ieee 107 gt RESULTS AND DISCUSSION Serei n AT tienea rac edna tees 109 Mes VVC UAC LOIN s nese Pac a ence ci ig salad Saas ARE E oa osname anaes 109 4 2 Experiment 1 Orifice Coefficient Determination ccc ceeeeceeeeeeeeceeeneeenee 109 4 2 1 PreLab Pasks iarna a pepe en b wae 109 4 2 2 Calibration of Pump Voltage to Flow Rate cccecccescceeseeereeeteeeeseeees 111 4 2 3 Calibration of Pressure Sensor Voltage to Tank Liquid Level 115 A DAS Orifice C OS LICIOME iin ina a iaa i n a a 117 4 3 Experiment 2 Modeling Liquid Level in a Cylindrical Tank 0 eee 119 4 3 15 Pre ab Tasks sig ssjacguks sents a prance ead wd hea ae amass 119 4 3 2 Experiment 2 RESUS ccsstsites hc tueas en lecbtbah sears secant Bi ateananrewanteadeanmowy tats 4 3 3 Data Analys inane dria ee r As ev detghie Avs eatin Aida Rie gees 4 4 Experiment 3 Modeling the Liquid Level in the Second Tank of a Coupled Fank System aa areteadsetaticsna sin el o beste bars eeadeladissvacais eibekd odgasatnadded asian mentees A MS SPC MA VAS KG ocx asaictyoo eh a a aclu a ye a ahetea cae 4 4 2 Experiment 3 Results seis sitacdeciseseaisbadncte cs nasenidincdl bine eaneeassetialas 443 Data Analysis isian hat 58 oe greed Sees Pea at E a gat tea 4 5 Experiment 4 Tuning a PI Controller for Liquid Level of a Cylindrical 45 1 PreEab Tasks herh e aai a E aae E
75. eesceseenseenees 49 Calibration and Signal Conditioning Circuit Board 0 0 0 ee eeseeseereeeeeeeeeeees 50 Step by Step Procedure for Experiment 2 ccccceccceeseeeseeeseceteceteeeeeeeeseees 52 Coupled Tank Apparatus ax ccacstusiess agents aieadeaccteaenssanede tua ease at aeaes 55 Schematic of Coupled tank System vcssss cacessassessccssvssedastevsstantanssadareessassaacens 57 xii 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 3 26 3 27 Puri Wl Front Panelo aseene a sc ade ges a a tude Seater vs ideas 60 Removal of Air Pockets in Pressure Sensor csceeseeeeeeeceteceseeneeeeeeeeeeseenaes 62 Calibration and Signal Conditioning Circuit Board 0 0 0 0 ee eeeeeceeneeeeeeeeeeees 64 Step by Step Procedure for Experiment 3 3 sy ccucscesvend andes SSatesuneuces 65 Coupled Tank Apparatus s ciisvcu2 cceacoie bongStacdewaidl aaa eed Gai ete Stnas erase eauaee 69 PID Controller Block Diagram in a Feedback Loop ce eeeeeeeceeeeeeteeeeeenee 71 Step Response Characteristics of Underdamped Second Order Processes 73 Well Behaved Process Controller sa sactscssaieessaotucdesadeaeancenactsees tateenaes eats 76 Improperly Tuned Controllers a sluggish response due to too little integral action needs smaller tr integral time b sluggish response due to too little proportional action needs larger gain Ke eeeseseeeteeneeereeeeees 77 LabPID 1 Vi Front Patel osc s
76. eese 2 7 a From Digital To Analog Cable b To Load Cable of Gain 5 2 8 a From Analog Sensors Cable b To Analog to Digital Cable 2 9 a SISO Configuration b State Coupled SISO Configuration 2 10 State Coupled and Input Coupled SISO System ssennseseeeseeseeseesseesee ee 2 11 Purp VI Front Patel y cisccs ssccpunhicsdienedscasetevahsesarous meonanducsoawueteveteadbaraantaetite x1 2 12 3 1 3 7 3 8 3 10 3 11 3 12 3 13 3 14 BaP HDL VI Ftont Paine tinnarona tie las e a a a tla tunis yates 25 Coupled Tank Apparatus nvcichasaaresupadeansguas teeaeneteadasnes onceencctmsarnyeae eseanstusecnendcees 31 Schematic of Cylindrical Tank vi 022 ccihscenzasdesaaashdesaatens ease Naadoas aden ictenm 32 Pump VI Front Pane lice wncsseisantinus eia A oad Seal E T catenin tas 34 Removal of Air Pockets in Pressure Sensor s sssseseesesseseesseseesesseseesesseeeesee 37 Calibration and Signal Conditioning Circuit Board s ssssessesessesseesesseseesessee 38 Step by Step Procedure for Experiment 1 o cc ee ceccceceseeesseceteceeeeeeeeeeeeenaeenes 39 Coupled Tank Apparatus eco loah ucts as end sa et ancecays saree ba Socuaweaeeow sa ep baaceas case aeeeens 42 Schematic of Cylindrical Qiks sac coccnt a useueres bass archicad sobs cos a Marcia tia 45 Pump VI Front Panel 655 20 ceehas ene Adal e ee ates 47 Removal of Air Pockets in Pressure Sensor ccssceseeseeseseceecc
77. eplacing the orifice inserts of different diameters into a threaded hole at the bottom of the tank A drain tap is also provided in the apparatus to introduce disturbance flow into either tank1 or tank2 By opening the drain tap liquid from tank1 flows directly to the reservoir The pump propels water vertically to two quick connect orifices Out1 and Out2 which are usually closed The system is equipped with different diameters for these two orifices for configurability Teflon Tubing of 1 4 I D with compatible couplings is provided to enable the pump to feed one tank or both tanks The water level in each tank is measured by a pressure sensor located at the bottom of each tank 2 2 Component Description Overall frame Component 1 The overall frame is made of plexiglas and dimensions for overall frame height width and depth are 0 915 m 0 305 m and 0 305 m respectively 12 a b Figure 2 2 Coupled Tank Plant a Front View and b Back View Figure 2 3 Calibration and Signal Conditioning Circuit Board 13 a b Figure 2 4 a Base of Coupled Tank Apparatus b Quick connects Out1 and Out2 Couplings Water Tanks Component 2 amp 3 The water tanks are made of plexiglas and have a uniform cross sectional area of 0 045 m each Water Basin Component 4 The water reservoir is an ordinary poly vinyl chloride PVC basin and is filled with 18 MQ distilled water from a Barnstead NANOpu
78. er I thank Dr John Gahl for his unwavering faith in believing my ability to complete this work and for serving as committee member I would like to express my gratitude to Department of Chemical Engineering University of Missouri for its financial support all through my graduate studies I thank Richard Oberto for his immense help and whose expertise in LabVIEW knowledge about Lab equipments both in Process Control Laboratory and Unit Operations Lab was a treasure My special thanks were reserved to my sisterly friend Gayatri Kallepalle for all her unconditional help patience especially at the crunch time with MATLAB and with testing the experiments and acting as a catalyst for my research work whenever needed ii My whole hearted thanks to Rita Preckshot for all her patience kindness friendly attitude towards me and for her valuable input she gave to make my life at Mizzou a comfortable one I thank the Fall 2008 and Spring 2009 students of ChE 4370 for their critical reviews and feedback on the experiments I would like to extend my thanks to Arun Vasireddy Bryan Sawyer roommates friends Dr Pinhero s research group and colleagues ETS technicians Rex Brian and their colleagues and all those invisible hands which helped me in completing this thesis Finally last but not the least I express my thanks to my grandparents parents uncle and my extended family for all their love and support throughout my life
79. erstanding see Figure 3 11 Drain the tank Check to see that the reading returns to OV readings may take 30 seconds or so to stabilize If not repeat 4b 4f until you get OV at 0 cm and 4 10V at 25cm of level This may take several trials 5 Generate the empirical data a b c d e See detailed step by step procedure shown in Figure 3 12 Record the pressure sensor voltage readings for tank1 liquid levels of 0 5 10 15 20 25 cm in a notebook Set the pump voltage usually around 0 7 Volts so that the steady state liquid level in tank1 is around 3 cm Note the pump voltage at steady state Note If you had to calibrate the sensor again make sure there are no air bubbles over the sensor before you start recording data If there are bubbles repeat step 3b Click the WRITE DATA button Make a positive step change between to 1 5 Volts in the pump voltage by entering a number into the PUMP VOLTAGE input box and pressing enter Do not make the step change so large that the Safety Interlock System s watchdog program kicks off Wait for the liquid level to reestablish steady state 51 Press this button to start the program Button will be white arrow when program is not running and will be in Step 5 e This is how steady state looks Observe for the black color when program is running insta AEN These LED s glow when Safety Interlock System is in action Step 5 d Click Write
80. es are the actual data collected on the apparatus The MATLAB code for the graphs is attached in Appendix 1 121 Height crn 40 Time Sec Figure 4 4 Experiment 2 Data for Apparatus 1 Graphs analogous to Figure 4 4 for apparatus 2 apparatus 3 and apparatus 4 are plotted in Figure 4 5 through Figure 4 7 respectively The final steady state level is not same for the same step change because there is a slight difference in pump flow constant K across the apparatus The spread among the trials may be attributed to pressure sensor hysteresis which did allow the return to the original voltage level 122 Height cm Time Sec Figure 4 5 Experiment 2 Data for Apparatus 2 Height cm a wR po g I A ae 3 j 5 25 10 20 30 40 50 60 70 80 Time Sec Figure 4 6 Experiment 2 Data for Apparatus 3 123 Height crn 0 20 40 0 80 100 120 Figure 4 7 Experiment 2 Data for Apparatus 4 Sample Calculation for Process gain K Process Time Constant tp and Process with Dead Time 0 The process gain is computed as the steady state change in the output variable divided by the change in manipulated variable Figure 4 4 is used for calculations Initial height in the tank 1 45 cm Final height reached in the tank 10 75 cm Initial input pump voltage 0 7 V Final input pump voltage 1 25 V Process gain K change in liquid le
81. f different diameters into a threaded hole at the bottom of the tank For this experiment use only the medium inserts of diameter 0 476cm for both tanks A drain tap is also provided in the apparatus to introduce disturbance flow into either tank or tank2 By opening the drain 87 Quick Connects Out1 and Out2 ressure Sensor Lower tank tank2 Disturbance or drain tap Calibration and Signa Conditioning Circuit Board Water basin reservoir Figure 3 27 Coupled Tank Apparatus tap liquid from tank flows directly to the reservoir The pump propels water vertically to two quick connect orifices Out1 and Out2 which are usually closed The system is equipped with different diameters for these two orifices for configurability Teflon Tubing of 1 4 I D with compatible couplings is provided to enable the pump to feed one tank or both tanks The water level in each tank is measured by the pressure transducer located at a bottom of each tank 88 Theory PID Controller Algorithm The Proportional Integral derivative PID controller is the mostly commonly used feedback algorithm in control systems Due to robustness and simplicity in operation about 95 of closed loop industrial processes use PID controllers A PID controller attempts to reduce the error which is calculated as the difference between the controlled variable s set point and its measured value A PID controller takes corrective action on the process in
82. form in the sensor whether or not you see bubbles poke the rod into sensor as shown in Figure 3 4 Cautions 1 Be gentle with the sensor while removing bubbles A violent stroke on the sensor could ruin it 2 Don t get confused with the bubbles formed and floating at the top of tank for bubbles in sensor 36 c Once air pockets are removed proceed to calibration of the tank pressure sensor Step 4 ir pocket in sensor Poke gent with poking rod to eliminate it Figure 3 4 Removal of Air Pockets in Pressure Sensor 4 Calibrate the upper tank s pressure sensor a Make sure that tank is empty by setting 0 V in PUMP VOLTAGE input box before starting the calibration If not empty it by using the disturbance tap black flap near the bottom of tank2 b Observe the pressure sensor voltage reading in the tank display box If it is not 0 V first manually adjust offset potentiometer screw for tank on the calibration and signal conditioning circuit board See Figure 3 5 using the potentiometer adjustment tool flat head screw driver to obtain 0 Volts Turn the offset potentiometer screw clockwise to increase the voltage reading and vice versa c Cover the tank outlet with your finger 37 d Using the quick connect at Outl apply a voltage to the pump and fill the tank to 25 cm Then turn off the pump Apply 0 voltage to the pump Offset screw tank2 Gain screw tank2 Offset screw tank1 Ga
83. g Liquid Levels in the Tank Spring 2008 The LabVIEW program LabPID1 VI was written to perform data acquisition and PID level control for the coupled tanks apparatus Figure 5 5 a shows the front panel screen displayed by LabPID1 VI and Figure 5 5 b shows the tab delimited data file recorded by LabPID1 VI This program as it existed during the Spring 2008 semester was totally unsuitable for executing the tasks it was written to perform The particular issues with the LabPID1 VI program are enumerated as follows 1 Input boxes for entering the tuning parameters the button for switching between tanks for level control as well as the slider and input box for establishing and or changing the set point seem randomly placed around the screen as shown in Figure 5 5 a This was quite confusing for students The front panel must be 157 reorganized to help students most of who have never seen the panel of a control system understand the basic elements of a control system Microsoft Excel Ciancone 111308 xls Ble Edt Yew rset Format Tous Data Window Heb DEURA EIA aA JI feror fo fpa oo a b Figure 5 5 a Front Panel of Old LabPID VI Program b Data File Recorded by Old LabPID VI Program 2 Although there was a button for switching level control between tank 1 and tank 2 the control function within LabPID VI did not work for the lower tank in
84. g and parametric effect topics in the theory section Parametric effects are listed in Table 3 1 for assistance The allowable percent overshoot is 10 iii Repeat steps 3 a i to 3 a vi without recording data until you get desired closed loop response for both the output and input variables Use scroll bars below tank level and voltage vs time plots to view response for previous parameters iv Once desired response is attained go 3 c c Final PI parameters i Repeat steps 3 a 1 to 3 a vi with final tuning parameters Make sure you record data this time 4 Press STOP button at the end of the experiment Data Analysis 1 Graphically compare the empirical set point responses of tank1 for both sets initial Ciancone and fine tuned of PI tuning parameters 85 2 Compare each of the empirical closed loop responses both its input and output with its SIMULINK equivalent Discuss any discrepancies Why might there be any discrepancies 3 6 Experiment 5 Tuning a PI Controller for Level Control of the Second Tank in Coupled Tank System Objective To gain hands on experience in tuning a PI controller for level control of the second tank in a coupled tank system Pre lab Tasks 1 Calculate level control tuning parameters using the open loop Ziegler Nichols method for a PI control algorithm Use Table 3 2 2 Calculate level control tuning parameters using the Ciancone method for a PI control algorithm and a set
85. hey have been streamlined for optimal use of lab time This is essential if they are to be used in the new undergraduate laboratory Furthermore a better understanding where these learning experiences fit into the Chemical Engineering curriculum has been gained Experiment 1 can be added to a freshman level course of almost any engineering discipline Experiment 2 could easily be integrated into ChE 2225 the sophomore year material and energy balance course Experiment 3 is most appropriate for integration into ChE 4370 the senior year process control course because knowledge of Laplace transforms is necessary to solve the pre lab tasks Experiments 4 and 5 are only appropriate to ChE 4370 However Experiments 4 and 5 could be combined into a single hands on 2 hour lab experience in controller tuning 5 5 Future Work e The Pump VI and LabPIDI VI programs are not written in same version of LabVIEW This causes start up issues related to drive conflicts This can be eliminated by having the two LabVIEW programs written in the same version of LabVIEW Pump VI is already in the new version of LabVIEW so rewriting the LabPID1 VI in new version is the logical choice to solve these startup issues This needs to be done 167 e The existing LabPID1 VI uses a feedback control mechanism to maintain a tank s liquid level A new LabVIEW program using a feed forward mechanism in combination with the feedback mechanism could be written and tested
86. ibration Procedure Chapter 3 e Orifice Coefficient Determination e Experimental Module for Modeling the Liquid Level in a Cylindrical Tank e Experimental Module for Modeling the Liquid Level in the Second Tank of a Coupled Tank System e Experimental Module for Tuning a PI Controller for Level Control of a Cylindrical Tank e Experimental Module for Tuning a PI Controller for Level Control of the Second Tank in a Coupled Tank System e Correcting Pump VI Startup Issues Chapter 4 Results and discussions for e Experimental module for Orifice Coefficient Determination e Experimental Module for Modeling the Liquid Level in a Cylindrical Tank e Experimental Module for Modeling the Liquid Level in the Second Tank of a Coupled Tank System e Experimental Module for Tuning a PI Controller for Level Control of a Cylindrical Tank e Experimental Module for Tuning a PI Controller for Level Control of the Second Tank in a Coupled Tank System Chapter 5 e Project Progression e Outcomes e Student Feedback e Recommendations e Future Work e Miscellaneous Appendix e MATLAB Code for Experiment 2 Results e LabVIEW Block Diagrams for Pump VI and LabPID1 VI 1 6 10 11 12 13 14 15 16 References M A Larson O A Heng Process Dynamics Experiment Journal of Chemical Education 1962 39 29 31 Intelligent Manufacturing Systems Report IMS 99002 View point The Gree
87. icator and is plotted on the waveform chart below the vertical indicator The horizontal scroll bar below the waveform charts enables the user to view earlier responses Use the horizontal scroll bar to note how the input and output variables respond to a step change for various tuning constants and based on these responses tune the process Appropriate values for the PID parameters lead to good control stable snappy and not too oscillatory Inappropriate values leads to bad control unstable sluggish and oscillatory Adjust the PID tuning parameters as necessary so that the response to a set point change is reasonable Lab Procedure Precautions and Other Notes e Make sure that the reservoir s distilled water level is at least three fourths full 100 A watchdog is programmed into LabPID1 VI so that the tanks do not overflow If the liquid level in either of the tanks reaches 25cm the pump is turned off and pump continues to remains idle until the tanks voltage drops below 4 3 V Do not panic the pump can be noisy If it starts smoking that is another matter Shut off the pump by clicking Stop on the LabPID1 VI program 1 Start up of experiment program 2 a b c d e Familiarize yourself with the apparatus See Figure 3 27 Double click the LabPID VI icon on the desktop It opens the LabPID VI program in LabVIEW Familiarize yourself with the icons controls and indicators and what they do on the
88. ichamp Process Dynamics and Control New York Wiley 1989 17 C A Smith and A B Corripio Principles and Practice of Automatic Process Control 2nd Ed New York Wiley 1997 18 G Stephanopoulos Chemical Process Control Englewood Cliffs NJ Prentice Hall 1984 19 J D Griffith The Teaching of Undergraduate Process Control Chemical Engineering Education Projects Committee American Institute of Chemical Engineers Nov 1993 10 CHAPTER 2 MATERIALS AND METHODS 2 1 Coupled Tank Apparatus Description The Quanser coupled tank apparatus is shown in the Figure 2 1 The apparatus is a bench top model consisting of a pump two cylindrical tanks made of plexiglas and Quick Connects Outl and Out2 ressure sensor Lower tank tank2 Disturbance or drain tap Calibration and Signa Conditioning Circuit Board Water basin reservoir Figure 2 1 Coupled Tank Apparatus 11 water basin reservoir These two tanks are of volume 133 35cm each and are mounted on a platform with a metering scale behind each tank indicating the approximate liquid level in tank The two tanks are vertically mounted on a platform and positioned in such a manner that outflow from the top tank tank1 serves as inflow for the lower tank tank2 Outflow from the lower tank goes directly into a reservoir From each tank fluid exits by gravity discharge through a small orifice The resistance of this discharge can be varied by r
89. ies This suggests that a mere academic understanding of control principles will not suffice in industry Students require a hands on practical experience in the laboratory before they step into industry 1 2 Common Laboratory Experiments Taught in Various Universities Some of the common laboratory experiments taught in university process control courses are as follows e Pressure and level controll e Temperature and level control in a heated tank e Air temperature control e Temperature and level control in a liquid tank e Control of a batch reactor e Control of empty and packed bed tubular reactor e Control of a heated bar temperature e Double pipe heat exchanger e Temperature control in an air bath e Water flow control under oscillatory load disturbances e Single tank pH controll e Interacting water tank controll e Temperature control with variable measurement time delay l e Integrating tank level controll e Cascade control of temperature in a water tank 3 e Dye concentration control with load disturbances e Four tank water level controll e Temperature and level control in a water tank e Multitank pH control Numerous textbooks are available for teaching the process dynamics and control course and the popular ones are listed in Table 1 1 The common topics covered in these courses are listed in Table 1 2 Table 1 1 Process Control Textbooks lt
90. igure 4 8 Calibration Chart Pressure Sensor Voltage vs Level in the Tank Apparatus 1 Although typical gain values range from 6 1 6 4 it need not be in this range because the gain values depend on how the potentiometer screws are adjusted Moreover it doesn t need to be regressed through the origin because sometimes there will be slight offset from zero at zero level in the tank 126 2 Comparison with experimental data 10 experimental data nonlinear approximation 4 linear aapproximation Tank Level cm D 40 Time sec Figure 4 9 Comparison of experimental data with Simulink non linear and linear approximations for apparatus 1 Figure 4 9 shows the comparison of experimental data with Simulink non linear and linear approximations for apparatus 1 The reason for deviation of experimental data from non linear approximation might be attributed to the sensor voltage not being at zero at start of the experiment This offset is not adjusted if it is within 0 1 V of zero The linear approximation is way off even from the non linear approximation because the step change is almost 80 of initial steady state about which the model is linearized Linear approximation holds good only for small input changes from the point about which the model is linearized This is shown in the exercise problem 2 8 B W Bequette Process Control Modeling Design and Simulation Prentice Hall
91. iment 3 data Simulink and FODT Approximations for Tank2 Apparatus 1 0 0 ce eeceeeeseeeeeeeeceaeceseeeeeeeeaees 139 XV 4 18 4 19 4 20 4 21 4 22 4 23 Simulink Model for Experiment 4 Apparatus 3 0 cccccccccceeseeeseeeteeeeseeees 142 Comparison of Tank Level Response between Experimental Data and Simulink Simulation for Set Point Change in Tank Ciancone Method and Fine Tuned PI Control Parameters ecececeeeceeeseseeecesescececececeseceeece 143 Input Voltage Response between Experimental Data and Simulink Simulation for Set Point Change in Tank1 Ciancone Method and Fine Tuned PI Control Parameters ccceccce ccc cccccccccecececececececececececeeeeees 143 Simulink Model for Experiment 5 Apparatus 3 cccccccscceseceeeeeteeeeseeees 146 Comparison of Output Response between Experimental Data and Simulink Approximation for Ziegler Nichols and Fined Tuned PI Tuning Parameters for Set Point Change from 3 to 13 Cm in Tank2 ANPP ATAtUS 3 sisser iiipin siari te deaf gent ch eas a aeara aTa eian 147 Comparison of Input Response between Experimental Data and Simulink Approximation for Ziegler Nichols and Fined Tuned PI Tuning Parameters for Set Point Change From 3 to 13 Cm in Tank2 Apparatus 3 148 xvi 5 1 5 5 5 6 Screenshot of How the Pump VI Front Panel Looked in Spring 2008 152 Dynamic Change in Pressure Sensor Reading for No Pump Voltage
92. in screw tank1 Figure 3 5 Calibration and Signal Conditioning Circuit Board e g h Observe the voltage reading in the tank1 display box If it is not 4 10 V 0 03 of this value is okay at 25 cm manually adjust gain potentiometer screw for tank1 to obtain 4 10V Turn the gain potentiometer screw clockwise to increase the voltage reading and vice versa Caution Make sure to adjust the correct potentiometer screw For better understanding see Figure 3 5 Drain the tank Check to see that the reading returns to OV readings may take 30 seconds or so to stabilize If not repeat 4b 4f until you get OV at 0 cm and 4 10V at 25cm of level This may take several trials Record the voltage sensor readings for the tank levels of 0 5 10 15 20 25 cm in a notebook 38 Step 5 a i Press this button to start the eons Step 5 a iii This is how steady program Button will be a white arrow state looks Observe for the when program is not running and will Pa tank1 liquid steady state be black in color when program is running Renny oP These LED s glow when Safety Interlock System is in action Step 5 a iv Record these values in a notebook Step 5 a ii Enter pump voltage here in volts from 0 5 V to 1 5 V Figure 3 6 Step by Step Procedure for Experiment 1 39 5 Get the empirical data Pump Flow constant K a Using a timer and graduated cylinder obtain the data necessary to determine the
93. ion 4 3 1 the top tank process gain is computed as follows for apparatus 1 130 K a A K 2L1 1 EG At J 9CoAo1 e V9 e4os 17 4 V2 L e a V981n 0 9235 L55 4 7748 L 2Lis Ay 2 Dr yV a A e g C Ao1 g Oo o1 2 4 4450 1 L saz 04783 0 9235 V 15 4 2582 L From Equation 4 13 s _ Je kz U s 4 2582 Lzs s 1 T2st1 T2 4 25824 Los For a second order system gain k k 4 7748 L 28 4 7748 L gt Lis 131 T 4 2582 L 4 2582 L5 T 4 2582 _ 4 Lis Lo fe 4 2582 Lis 4 2582 L2 2 4 2502 eee Ji pu 25 hus vias 4 4 2 Experiment 3 Results Carrying out the experimental procedures described in section 3 4 yields graphs plotted in Figure 4 10 through Figure 4 14 for each of the four apparatus respectively These are the empirical models for the particular process The curves show how the lower tank level changes when there is a step change in input pump voltage from 0 8 V to 1 35 V for different trials The final height in the lower tanks is not same for all the apparatus for same step change in pump voltage because the flow rate is not same for a particular pump voltage across the apparatuses as each one have a different pump flow constant All the graphs in this section are for step changes in input pump voltage from 0 8 volts to 1 35 volts and only for tank2 in all apparatuses Doing a set ch
94. ive Formulate and validate a dynamic model for the liquid level in the second tank of a coupled tank system Tasks e Derive a linearized dynamic model for the liquid level in the second tank of the coupled water tank apparatus e Obtain the necessary experimental data to validate the linearized dynamic model e Derive a first order plus dead time FODT model from the laboratory data e Compare the linearized model FODT model and the empirical data obtained in the laboratory Coupled Tank Apparatus Description The Quanser coupled tank apparatus is shown in Figure 3 13 next page The apparatus is a bench top model consisting of a pump two cylindrical tanks made of Plexiglas and water basin reservoir These two tanks are of volume 133 35cm each and are mounted on a platform with a metering scale behind each tank indicating the approximate liquid level in cm in the tank The two tanks are vertically mounted on platform and positioned in such a manner that outflow from the top tank tank1 is used 54 as inflow for the lower tank tank2 if second tank is used for experiment Outflow from the lower tank goes directly into a reservoir From each tank fluid exits by gravity discharge through a small orifice The resistance of this discharge can be varied by replacing the orifice inserts of different diameters into a threaded hole at the bottom of metering scale in cm Quick connect Out1 Upper tank tank1
95. king user to define an output file 61 c Assign a file name save it in Microsoft excel spreadsheet format for example yourname xls 3 Removal of air pockets ir pocket in sensor Poke gent with poking rod to eliminate it Figure 3 16 Removal of Air Pockets in Pressure Sensor a Run the pump by giving a random pump voltage between 0 5 1 and watch out for air bubbles over in the pressure sensors located at the bottom of each tank for both tank1 and tank2 b Air pockets will form in the sensors most of the time whether or not you see bubbles poke the rod into sensors of both tank and tank2 as shown in Figure 3 16 Caution 1 Be gentle with the sensor while removing bubbles A violent stroke on the sensor could ruin it 62 c 2 Don t get confused with the bubbles formed and floating at the top of tank for bubbles in sensor Once air pockets are removed stop pump by setting 0 V as the pump input and observe for the tankl and tank2 voltages on Pump VI front panel If the tank voltage value is within 0 1 Volts of 0 V for both tanks when they are empty proceed to generate empirical data Step 6 Otherwise head to calibration of the both tanks pressure sensors Step 4 and 5 4 Calibrate the upper tank s pressure sensor a b c d e Make sure that tankl is empty before starting the calibration If not empty it using the disturbance tap black flap near the bottom of tank2
96. ller the starting tuning parameter values are almost immaterial compared to the ending tuning parameter values but choosing the most appropriate swags certainly expedites the tuning process Fall 2008 ChE 4370 students were provided with a significant learning experience in the Process Control Lab With their inappropriate swags students got a feel for tuning because they were provided a considerable hands on opportunity for developing skills in controller tuning 161 Spring 09 Lab Module Handouts for experiments 4 and 5 were modified based on all of the lessons learned to date These self contained modules provide the information necessary to perform these experiments Specifications for pre lab preparation laboratory operation post lab data analysis and references are all included The final version of theses handouts modules are provided in sections 3 5 and 3 6 Seniors taking ChE 4370 used these handouts to perform experiments 4 and 5 FODT parameters calculated taking into account the pump start up effects were given to the students for determining initial swags using open loop methods This time the students found much more appropriate values for the initial PI controller tuning parameters As a consequence level control performance was much better The burden of tuning the controller from unacceptable performance was lifted The lab experience involved fine tuning instead of retuning These students were asked to assess the han
97. manipulated variable changes and the time when the controlled variable responds This delay is due to process dead time and no controller can reduce this delay to less than the process dead time 3 During the delay time the manipulated variable increases linearly This is due to the integral mode During this period the error is constant so the proportional term does not change but the integral term increases linearly with slope equal to ke E t TI After the controlled variable begins its transient response the proportional term decreases while the integral term continues to increase At steady state the end of the 76 transient response the proportional term is zero because the error is zero and the integral term has adjusted the manipulated variable to a value that reduces the offset to zero These three features are very useful for recognizing maladjusted tuning parameters when fine tuning Improperly Tuned PI Controller Improperly Tuned PI Controller T T T T T r r r r T yandr in yandr on 1 1 f 1 f 1 f 1 1 f 1 1 1 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 time time 1 1 1 1 1 1 fi 1 L 0 10 20 30 40 50 60 70 80 90 100 time a b Figure 3 23 Improperly Tuned Controllers a sluggish response due to too little integral action needs smaller t1 integral time b sluggish response due to too little proportional action
98. n Imperative for Process Industries Improve performance while reducing carbon emissions Online Industry week April 17 2008 B Joseph C M Ying D Srinivasgupta A laboratory to supplement courses in process control Journal of chemical engineering Education 2002 36 1 p 20 25 S Ang R D Braatz Experimental projects for the process control laboratory Journal of chemical engineering Education 2002 36 3 p 182 187 B W Bequette B A Ogunnaike Chemical Process Control Education and Practice IEEE April 2001 p10 17 B W Bequette Process Control Modeling Design and Simulation Prentice Hall 2003 D R Coughanowr Process Systems Analysis and Control 2nd Ed New York McGraw Hill 1991 D R Coughanowr and L B Koppel Process Systems Analysis and Control New York McGraw Hill 1965 K T Erickson and J L Hedrick Plant wide Process Control New York Wiley 1999 W L Luyben Process Modeling Simulation and Control for Chemical Engineers 2nd Ed New York McGraw Hill 1990 M L Luyben and W L Luyben Essentials of Process Control New York McGraw Hill 1997 T E Marlin Process Control Designing Processes and Control Systems for Dynamic Performance 2nd Ed New York McGraw Hill 2000 B A Ogunnaike and W H Ray Process Dynamics Modeling and Control New York Oxford 1994 J B Riggs Chemical Process Control Lubbock TX Ferret 1999 D E Seborg T F Edgar and D A Mell
99. n aa rrr o Bequette Marlin Coughanowr Ogunnaike and Ray Coughanowr and Koppel Riggs Erickson and Hedrick Seborg Edgar and Mellichamp Luyben Smith and Corripio 1 k Tashamanddaiwhenane e Sienhinan ailad e l Luyben and Luyben Stephanopoulos Table 1 2 Common Chemical Process Dynamics and Control Course Topics Topics Lecture time Process Dynamics and Modeling 28 1 Feedback Control and tuning 22 1 Stability and Frequency Response Analysis 14 3 Computer Simulation 8 9 Advanced Control Techniques 8 4 Control System Hardware 7 7 Computer Control Systems 4 8 Other 5 7 13 Motivation The previous sections underline the importance of a competent control course in the undergraduate chemical engineering program This project was prompted by resources in the Department of Chemical Engineering at University of Missouri and motivation to improve the laboratory experiments in the control class The focus is on developing a practical robust and portable laboratory with flexibility for future development and eventually adding online access Providing an online controls course would make the MU Chemical Engineering Curriculum much more flexible in addressing issues related to unlimited open schedule access and extension learning 1 4 Objectives e To use the existing coupled water tank apparatus in Department of Chemical Engineering University of Missouri in th
100. nd block parameters are tabulated in Table 4 13 Figure 4 19 depicts the output tank1 level response to a set point change from 3 cm to 15 cm for PI level controller for initial and final tuning parameters and Figure 4 20 depicts the input response to the set point change from 3 to 15 cm for the same process and controller parameters To aid in analysis Simulink simulation data are also added in Figure 4 19 and Figure 4 20 Note The PID algorithm used in PID controller in Simulink is 1 ft d u t k lew i e a do Tp ae So Proportional parameter ke 0 095 for initial guess Integral parameter k t 0 095 0 148 60 0 0106 s Derivative parameter tp kctp 0 for this experiment It is important to make sure that units are consistent for all the block parameters 141 Clock Time ui pit Manipulated Input Setpoint Step PID Controllert Process Figure 4 18 Simulink Model for Experiment 4 Apparatus 3 Scope ywipif Output Variable Table 4 13 Block Parameters for Simulink Model Experiment 4 Apparatus 3 Derivative time Tp Block Parameter Step pions pine parameters tuned Step 0 0 Initial Value 0 0 Final Value 12 12 Sample 0 0 Ciancone Fine Block Parameter PID controller Parameters tuned Proportional Gain k 0 095 0 100 Integral time qty 0 0106 0 0144 0 0 142 16 14 Set point 15 cm Experimental Data Initial Es
101. nk V 0 9235 A01 Atank sqrt 2 g L 0 5 The above two MATLAB files should in the same folder as this one Tank1 Simulation Separate m file Function File for Non Linear Model function Xaot tank I nlin t L Parameters K 17 8 g 981 Doi 0 47625 Drank 4 445 175 Ank pi 4 Dtank 2 Agi pi 4 Dol 2 Step change in Pump Voltage Vo 0 7 delV 0 55 V V0 delV Nonlinear State Equation Xdot 7 K Atank V pm Ao1 Atank sqrt 2 g L 0 5 Function File for Linear Model function Xaot tank11 t L Parameters Lo 1 45 K 17 4 g 981 Doi 0 47625 Dunk 4 445 Atank pi 4 Dtank 2 176 Aoi pi 4 Dol 2 Step change in Pump Voltage Deviation Variables Vo 0 7 delV 0 55 V delV Linear State Equation Xdot K Atank V A01 Atank sqrt g 2 L0 L Tank 1 Simulation Main Calling Program and Output Get numerical integration for the nonlinear process tspann 0 100 LnlinO 1 45 tnlin Lnlin ode45 tank1n tspann LnlinO Get numerical integration for the linear process tspanl 0 100 LlinO 1 45 tlin Llin ode45 tank11 tspanl Llin0 177 figure 1 plot tnlin Lnlin tlin Llin title Tank 1 Simulation Comparison for Apparatus 1 xlabel Time sec ylabel Tank Level cm legend nonlinear linear
102. ocess output diverges with or without 90 oscillation Adjusting the control parameters to get the desired output response is called tuning The desired behavior of the process output differs depending on the application For some processes overshoot is allowed For other processes overshoot is not tolerable For example in the process of manufacturing plastic gloves the positioning of a double plastic film is necessary If an overshoot occurs the plastic films wrinkle unacceptably 1 Except in applications where oscillations cannot be tolerated processes are usually tuned to respond as second order under damped system with a damping factor between 0 4 and 0 8 l This gives a sufficiently fast response Smaller values for the damping factor yield excess overshoot and larger values yield sluggish slow response Second Order Underdamped Response Definitions Overshoot Overshoot is the distance between the first peak and the new steady state Rise time It is the amount of time it takes to first reach the new steady state value 4 Settling time The time it takes the process to nearly attain its steady state value usually within 2 or 5 of its final value 91 Offset The error discrepancy between the setpoint and the process output at steady state is called offset Time to first peak Bits 40 5s 1 overshoot ratio X Z decay ratio Y X rise time period of oscillation unit step response
103. offset to zero These three features are very useful for recognizing maladjusted tuning parameters when fine tuning 96 Improperly Tuned PI Controller Improperly Tuned PI Controller T T T T T r r r r T yandr o n y andr f 1 1 1 f 1 f 1 fi 1 1 f 1 f 1 1 1 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 time time 1 1 1 1 1 1 L 1 1 a 10 20 30 40 50 60 70 80 90 100 time time a b Figure 3 31 Improperly Tuned Controllers a sluggish response due to too little integral action needs smaller tr integral time b sluggish response due to too little proportional action needs larger gain k Figure 3 31 gives examples of improperly tuned responses Figure 3 31 a has a sluggish response due to too little integral action To speed up the response lower ty Proportional gain is not raised to speed up the response because the initial change manipulate variable is within 70 150 of final steady state value Figure 3 31 b has a sluggish response due to too little proportional gain k To speed up the response increase k When fine tuning a PI controller adjust the proportional gain ke first and then adjust the integral time tr Table 3 3 Effect of Controller Tuning Parameters on Higher Order Processes Parameter Rise Time Overshoot Settling Time Offset Increasing k Decreases Increases No effect Decreases Decreasing t
104. oller Proceedings of 3 European Control Conference 1995 8 B W Bequette Process Control Modeling Design and Simulation Prentice Hall 2003 page 172 9 Basilio J C and S R Matos Design Of PI and PID Controllers with Transient Performance Specification IEEE Transactions on Education Vol 45 No 4 November 2002 10 Seborg D E Edgar T F and D A Mellichamp Process Dynamics and Control 2nd Edition page 117 11 Ziegler J G and N B Nichols Optimum Settings for Automatic Controllers Trans ASME 64 759 768 1942 12 Luyben M L and W L Luyben Essentials of Process Control McGraw Hill New York 1997 13 Cohen G H and G A Coon Theoretical Considerations of Retarded Control Trans ASME 75 827 1953 14 R Ciancone and T Marlin Tune controllers to meet plant objectives Control 5 50 57 1992 15 Marlin Thomas E Process Control Designing Processes and Control Systems for Dynamic Performance McGraw Hill New York 2 edition 107 16 B W Bequette Process Control Modeling Design and Simulation page 202 Prentice Hall 2003 108 CHAPTER 4 RESULTS AND DISCUSSIONS 4 1 Introduction This chapter has five subsections Each subsection has pre lab tasks experimental results data analysis solutions and discussion of the results for each of the five experiments in the Chapter 3 4 2 Experiment 1 Orifice Coefficient Determination 4 2 1 Pre Lab Ta
105. oller algorithm has three components proportional integral and derivative A proportional only controller reacts to and accounts for the current error However a P only controller cannot drive the steady error to zero A PI controller reacts to and accounts for the current error as well as its history A PI controller drives the steady state error to zero However the integral component adds to instability if k is improperly tuned A PID controller reacts to and compensates for the current error its 70 history and its future direction I The derivative component adds to stability and speed of the response if properly tuned P k e t Scene Process Figure 3 20 PID Controller Block Diagram in a Feedback Loop The weighted sum of these three actions is used in a PID controller to take corrective action The corrective action taken by a PID controller algorithm is computed as follows 1 ft de t u t k ew e a da Tp 2 3 15 Ti Jo dt where k is proportional gain t is integral time and Tp is derivative time For PI control there is no derivative term so kofe u t k e t e a do 3 16 1 Jo where ke is proportional gain t is integral time Tuning 71 If PID controller parameters ke Tr Tp are chosen incorrectly then the controlled output can become unstable i e the process output diverges with or without oscillation Adjusting the control parameters to get the desired output respon
106. olume 133 35cm each and are mounted on a platform with a metering scale behind each tank indicating the approximate liquid level in cm in the tank The two tanks are vertically mounted on platform and positioned in such a manner that outflow from the top tank tank1 is used as inflow for the lower tank tank2 if the second tank is used for the experiment 41 Outflow from the lower tank goes directly into a reservoir From each tank fluid exits by gravity discharge through a small orifice The resistance of this discharge can be varied by replacing the orifice inserts of different diameters into a threaded hole at the bottom of the tank For this experiment use only the medium inserts of diameter 0 476cm for both tanks metering scale in cm Quick connect Out1 Upper tank tank1 Pressure sensor Lower tank tank2 Disturbance or drain tap Calibration amp Signal Conditioning Circuit Board Water basin reservoir Figure 3 7 Coupled Tank Apparatus A drain tap is also provided in the apparatus to introduce disturbance flow into either tankl or tank2 By opening the drain tap liquid from tank1 flows directly to the reservoir The pump propels water vertically to two quick connect orifices Out1 and Out2 which are usually closed The system is equipped with different diameters for 42 these two orifices for configurability Teflon Tubing of 1 4 I D with compatible couplings is provided to enable the pump to
107. on to start the program Button will be white arrow when program is not running and will be in black color when program is running Step 6 h This is how steady state looks Observe for the tank2 liquid level These LED s glow when Step 6 f Click Write data to write Safety Interlock System is data into the file in action Step 6 j Click Writing Data to stop recording to file Step 6 e Enter a voltage value between 0 5 0 75Volts here to get initial steady state value Step 6 g Enter a voltage value between 1 and 1 5Volts Step 6 i Step change pump voltage back to zero Figure 3 18 Step by Step Procedure for Experiment 3 65 6 Generate the empirical data a b c d e g h Record the pressure sensor voltage readings for tankl liquid levels of 0 5 10 15 20 25 cm in notebook While doing this step hold the tank level by blocking orifice insert with finger Make sure you connect Outl and disconnect Out2 Repeat 6 a for tank2 Make sure you connect Out2 and disconnect Out1 this time Before starting the experiment plug in only Outl using quick connect Make sure Out2 is disconnected before you start taking data See Figure 3 18 for step by step procedure Set the pump voltage so that the steady state liquid level in tank2 is around 3 cm Note the pump voltage will be usually around 0 8 V and liquid level in tank at steady state
108. p gt n 13pt Application Font w IESE EJ STOP VOLTAGE Tank 1 Iw WRITE Time milisec 217899 Tonk A DATA Pui a Tanki pressure r sensor Yokage Yy jo 0i Tank 2 Pressure sensor 0 08 TANK 1 umr TANK2 Ape epee ty LIMIT getioy LIMIT WRITE DATA 6 Pump Voltage lo 8 olo nus n amorum Amplitude bo say fear er 1 o 100 Ene Figure 3 3 Pump VI Front Panel the slider when creating a step change The data display boxes in the center of the screen show the time in milliseconds and the tank1 tank2 pressure sensor output voltages and the pump voltage in Volts Tank pressure sensor voltages and the pump voltage are also 34 displayed in the waveform chart on the right of the screen Write data glows to indicate when the program is writing data to the user defined file Tank1 and or tank2 limit LED glow when the tank voltages are in the range 4 3 to 4 5 V indicating the danger of tank overflow At this point the Safety Interlock System s watchdog routine shuts off the pump and the pump continues to remain idle until the voltage range is again with the acceptable range less than 4 3 Volts Important Note The measured variables in tankl amp tank2 are pressure sensor voltages and not the tank volumes or liquid levels Lab Procedures Precautions and Other Notes e Make sure that the reservoir s distilled water level is at least three fourths full e A wat
109. p VI Start up Issues The two LabVIEW programs Pump VI and LabPID1 VI are written in different versions This can cause device driver conflict issues To counter this problem AOE af aef TRT ei ieee eve Hs FO BPALABA Eroan SX em Figure 3 35 Issues with the LabVIEW Program Start Up 1 Click Measurement and automation icon on the desktop or access it from the programs in the windows menu 2 Expand NI DAQmx devices in the expanded devices and interfaces 3 Right click on NI DAQmx devices and then do self test and reset the device 4 The screen display shows now the device has successfully tested for self test and device has been reset successfully for reset 106 3 8 References 1 Coupled Water Tanks User Manual Document Number 557 Revision 03 Quanser 2 CJ Geankoplis Transport Processes and Separation Process Principles Prentice Hall 2003 3 B W Bequette Process Control Modeling Design and Simulation Prentice Hall 2003 4 Donald R Coughnowr Process Systems Analysis and Control 2 edition McGraw Hill International editions 1991 5 Flow through Orifices Perry Chemical Engineering Handbook 8 Edition Page 6 22 6 Streiner D L Maintaining Standards Difference between the Standard Deviation and Standard Error and when to use each Can J Psychiatry Vol 41 October 1996 7 Astrom K J and Hagglund T H New tuning methods for PID contr
110. pent in dealing with the unexpected events in the process Human operators engineers continue to face the responsibility for making important and complex decisions frequently within a very limited timeframe Incidents such as Three Mile Island Bhopal and Chernobyl provide chilling examples of faults that turned into disasters partly due to improper control actions taken by the operators 7 Almost every chemical process industry CPI employs one or more process control strategies for one or multiple reasons like safety and reliability of the process maintaining the constant desired purity of product maximizing the profitability of the process and environmental issues Some of the most common chemical process industries using process control are e Hydrocarbon fuels e Chemical products e Pulp and paper products e Agrochemicals e Man made fibers e Food Industry The importance of process control has increased in the process industries over the past 30 years driven by global competition rapidly changing economic conditions more stringent environmental and safety regulations and the need for more flexible yet more complex processes to manufacture high value added products A modern undergraduate course in chemical process control should reflect the diverse milieu of process control theory and applications and encompass process dynamics computer simulation measurement and control hardware feedback control and advanced control strateg
111. point change Use the appropriate graph from Marlin Thomas E Process Control Designing Processes and Control Systems for Dynamic Performance McGraw Hill New York 2 edition page 286 86 Note e The model parameters will vary slightly among the apparatus because they have different pump flow constants Use values of process gain time constant and dead time corresponding to the apparatus on which you do the tuning experiment to calculate the tuning parameters e For calculating t 8 Kp use the output tank level response for step change in pump voltage graph obtained in experiment 3 assuming a pseudo first order process for the second tank Coupled Tank Apparatus Description uy The Quanser coupled tank apparatus is shown in Figure 3 27 The apparatus is a bench top model consisting of a pump two cylindrical tanks made of Plexiglas and water basin reservoir These two tanks are of volume 133 35cm each and are mounted on a platform with a metering scale behind each tank indicating the approximate liquid level in tank The two tanks are vertically mounted on platform and positioned in such a manner that outflow from the top tank tank1 serves as inflow for the lower tank tank2 if second tank is used for experiment Outflow from lower tank goes directly into reservoir From each tank fluid exits by gravity discharge through a small orifice The resistance of this discharge can be varied by replacing the orifice inserts o
112. put according to the algorithm shown in Figure 3 28 to keep the error to a minimum l The PID controller algorithm has three components proportional integral and derivative A proportional only controller reacts to and accounts for the current error However a P only controller cannot drive the steady error to zero A PI controller reacts to and accounts for the current error as well as its history A PI controller drives the steady state error to zero However the integral component adds to instability if k is improperly tuned A PID controller reacts to and compensates for the current error its history and its future direction The derivative component adds to stability and speed of the response if properly tuned 89 P k e t Setpoint Output Process Figure 3 28 PID Controller Block Diagram in a Feedback Loop The weighted sum of these three actions is used in a PID controller to take corrective action The corrective action taken by a PID controller algorithm is computed as follows 1 ft de t u t ke lew e a do Tp 3 19 Ti Jo dt where k is proportional gain ty is integral time and Tp is derivative time For PI control there is no derivative term so ke f u t ke t e a do 3 20 I Yo where ke is proportional gain t is integral time Tuning If PID controller parameters ke T Tp are chosen incorrectly then the controlled output can become unstable i e the pr
113. re Diamond Life Science UV UF ultrapure water system 14 Pump Component 5 The coupled water tank pump is a gear pump with a 12 Volt Direct Current DC motor and heat radiating fins The parts of the pump that come into contact with the pumped fluid are two molded Delrin gears in a Delrin pump body a stainless steel shaft a Teflon diaphragm and a Buna N seal It is also equipped with 3 16 ID hose fittings Rubber Tubing Component 6 The Tubing is made of Teflon with 1 4 ID Quick Connect Inlet Orifice Outl amp Out2 Component 7 amp 8 These quick connect inlet orifices are used to bring online only tank1 or only tank2 or both with various configurations Quick Connects Outl and Out2 Couplings Component 9 amp 10 These are the couplings that connect quick connect inlet orifice and the hose that run either to tank or tank2 Outlet inserts Component 11 12 13 14 Outflow from the tanks can be varied by using the different outlet inserts provided by the manufacturer The four different inserts provided are small medium and large outlet inserts with diameters of 0 3175 cm 0 4762 cm and 0 5556 cm respectively as well as a plug 15 Disturbance Tap Component 15 The disturbance tap which is operated manually serves as a drain valve in case of emergency when the LabVIEW program is not taking control limit action for level control of tankl To close the tap th
114. re than 10 overshoot and an initial input response is within 70 150 of its steady change For this experiment the students have input response within 50 200 of its steady state 4 6 Experiment 5 Tuning a PI Controller for level control of the Second Tank in a Coupled Tank System 4 6 1 Pre Lab Tasks Calculations similar to the one described in section 4 4 2 yield the FODT parameters for the lower tank process of each apparatus Summary of results for all the apparatus are tabulated in Table 4 14 Table 4 14 Tank2 Model Parameters for Experiment 5 Process Gain Kp Time constant tp Dead time 9 Tank2 cm Volt s s Apparatus 1 18 945 33 6 3 8 Apparatus 2 17 182 29 5 4 5 Apparatus 3 21 691 34 6 4 5 Apparatus 4 16 618 28 9 3 8 144 Open loop methods use the values in the Table 4 14 to generate PI tuning parameters Ziegler Nichols and Ciancone parameters are listed in Table 4 15 and Table 4 16 respectively Table 4 15 Second Tank Ziegler Nichols PI tuning parameters for FODT model Ziegler Nichols PI Tuning Parameters Tank2 K TI V cm min Apparatus 1 0 420 0 209 Apparatus 2 0 343 0 248 Apparatus 3 0 319 0 248 Apparatus 4 0 412 0 209 Table 4 16 Ciancone PI Tuning Parameters for Tank2 Experiment 5 Tank2 0 0 1 K K T T 0 ke Volt cm min Apparatus 1 0 102 1 50 0 74 0 079 0 461 Apparatus 2 0 132 1
115. rocedure for removal of air pockets was developed The teaching assistant performed the procedure for removing the air pockets before calibrating the sensors Then a series of 10 trials for both experiment 2 and experiment 3 was performed to make 153 sure students would get consistent readings Consistent readings were observed for Apparatus 1 Apparatus 2 and Apparatus 3 However Apparatus 4 has some pump start up issues as shown in Figure 5 3 a One problem solved another problem noted Experiment 1 Apparatus 4 Shas Veale as paretara N pe eee H Height cm a b Figure 5 3 Experimental Data a with pump start up effect b without pump start up effects To address the confusion associated with the Pump VI front panel the LabVIEW program was modified The resulting alteration to the Pump VI front panel is shown in Figure 5 4 154 Modified section of Pump VI front panel STOP Pune VOLTAGE 5 Taki ZR WRITE 4 Tank2 ad DATA aE Pump ad Tanki pressure sensor Voltage y 0 01 Tank 2 Pressure sensor Voltage y 0 08 Pump Voltage 0 TANKI pmr TANK 2 LIMIT ic b Figure 5 4 Modified Pump VI Front Panel iii Second Trial of Experiment 2 The experimental procedure was modified so that removing the deleterious air pockets preceded calibrating the pressure sensors Both of these steps occurred right before collecting the data During this lab perio
116. rrset c std newsetwo c sqrt Max 1 finding standard deviation meanset c mean newsetwo c finding mean ciover meanset 1 96 serrset finding the 95 Confidence interval cidown meanset 1 96 serrset finding the 95 Confidence interval ee aa end figure 1 m l 172 tnew 0 0 1 74 29 while m lt Max plot tnew newsetwo m y m m l hold on end title Experiment 2 data Apparatus 1 xlabel Time Sec ylabel Height cm hold on plot tnew meanset k tnew ciover r thnew cidown r grid minor hold off Experiment 2 MATLAB Code for Solving Differential Equations for Linear and Non Linear Approximations Linear Approximation Should be in a separate file function xdot tank11 t L Parameters Lo 1 45 K 17 8 g 981 173 Do1 0 47625 Diank 4 445 Atank pi 4 Dtank 2 Aoi pi 4 Do12 Step change in Pump Voltage Deviation Variables Vo 0 7 delV 0 55 V delV Linear State Equation Xdot K Atank V 0 9245 Ao1 Atank sqrt g 2 Lo L For Solving Non Linear Differential Equation This should be in a separate file function Xaot tank1n t L Parameters K 17 4 g 981 Doi 0 47625 Diank 4 445 174 Atank pi 4 Dtank 2 Aoi pi 4 Do1 2 Step change in Pump Voltage Vo 0 7 delV 0 55 V V0 delV Nonlinear State Equation Xdot K Ata
117. s for time tank level tank2 level and set point Students also need pump input voltage readings as noted previously and PID tuning parameter values for post experiment analysis Because of this data omission within LabPID1 VI students were unable to compare the experimental input response with that predicted from Simulink model simulation There were no handouts for documenting the experimental procedures for these experiments Students were in a dilemma about how to run these experiments Experiments are not streamlined for efficient use of the students lab time 159 9 During the trial and error tuning process when overly aggressive tuning parameters are chosen the controller drives the pump in an on off fashion In this circumstance water was spilled on the floor and workbench making the work space a messy safety hazard 10 Due to the fact that Pump VI and LabPID VI were written in different versions of LabVIEW driver conflict issues arose as the LabVIEW programs were started Fall 2008 The first six issues described above were fixed by changing the LabPID1 VI code Changing the control programming within LabPID VI addressed the first four issues Upon implementing the control programming changes the front panel was functionally reorganized as shown in Figure 5 6 a level control for the lower tank was established proper watchdog actions were instituted and views for previous dynamic responses was provided Changing the t
118. screen See Figure 3 32 Click the white arrow button on the top left of the screen to start the program A window pops up on the screen asking to define an output file Assign a file name and save it in Microsoft Excel spreadsheet format e g yourname xls The output file records PID parameters and tank levels set point and pump voltage as a function of time Use Control Tank Toggle to switch to tank2 if it is not the online tank for level control Remove the air pockets a b Run pump for a random set point lt 10 cm and watch for any air bubbles over in the pressure sensor for the both tank1 and tank2 Air pockets will form in the sensors most of the time Whether or not you see bubbles poke the rod into sensor cavity of both tank1 and tank2 as shown in 101 Figure 3 33 to remove them Caution 1 Be gentle with the sensor while removing bubbles A violent stroke on the sensor could ruin it 2 Don t get confused with the bubbles formed and floating at the top of tank for bubbles in sensor Air pocket in sensor Poke gently with poking rod to eliminate it Figure 3 33 Removal of Air Pockets in Pressure Sensor c Once air pockets are removed click Run Pump to stop the pump 102 Step 2 a Step 3 a ii Step 3 a iv Enter set point here Step 1 c Press this button to start the program button will be white color arrow when program is not running and black arrow when running
119. se is called tuning The desired behavior of the process output differs depending on the application For some processes overshoot is allowed For other processes overshoot is not tolerable For example in the process of manufacturing plastic gloves the positioning of a double plastic film is necessary If an overshoot occurs the plastic films wrinkle unacceptably 1 Except in applications where oscillations cannot be tolerated processes are usually tuned to respond as second order under damped system with a damping factor between 0 4 and 0 8 l This gives a sufficiently fast response Smaller values for the damping factor yield excess overshoot and larger values yield sluggish slow response Second Order Underdamped Response Definitions Overshoot Overshoot is the distance between the first peak and the new steady state Rise time It is the amount of time it takes to first reach the new steady state value Ef Settling time The time it takes the process to nearly attain its steady state value usually within 2 or 5 of its final value 72 Time to first peak 5 s7 0 5s 1 overshoot ratio X Z decay ratio Y X rise time period of oscillation unit step response Figure 3 21 Step Response Characteristics of Underdamped Second Order Processes Offset The error discrepancy between the setpoint and the process output at steady state is called offset Decay ratio Decay ratio is defined as the ra
120. sks c Determining Orifice Coefficient The orifice coefficient is found from the steady state relation Flow in Flow out Kaine VL 4 1 a Co0404 2g from Equation 3 6 109 The relation between level in the tank and its pressure sensor voltage is determined from calibration of pressure sensor So Equation 4 1 becomes KVpump By Veensor 4 2 In this experiment Vpump is used as the independent variable Applying log on both sides gives K log Vensor 2 loge 2log Vpump 4 3 The graph log Vjump VS log Vsensor is a line with slope 2 and intercept 2 log s f i Aei K Since K is determined by calibrating 2 can be calculated as prrercept 10 2 Combining Equations 4 1 and 4 2 gives By Vensor avL But from the calibration of the pressure sensor L is proportional to Veensor 1 L m Vsensor Therefore L ae CoAoy2gVL and Co can be computed as C 4 4 iB Ag2gvn 110 4 2 2 Calibration of Pump Voltage to Flow Rate The relation between the pump voltage and flow rate is found measuring the volumetric flow rate in a 250 ml graduated cylinder For six pump voltages the time for the liquid to move from 50 ml to 210 ml was recorded The results are tabulated in Table 4 1 through Table 4 4 for all the apparatus Table 4 1 Experimental Data Relating Pump Voltage and Flow Rate for Apparatus 1 Time in seconds pump voltage p Flowrate Trial Trial
121. t UPM power socket UPM power supply 2 5 Configurations A single Coupled tank system can be used to set up different types of experiments as described below Each of these configurations results in a unique control problem Configuration l Single Input Single Output SISO In this system the pump feeds into tank1 and tank2 is not used at all A controller is designed to regulate or track the level in tank1 Different inlet and outlet diameters can be used and tried in tank1 21 Out2 Out Out2 Out D tank1 oo Du tank y D ji paa Doi Do tank2 12 tank2 Pum m Pump i P n AN Vp Vp l lt 5 E lt lt Do Water basin Water basin a b Figure 2 9 a SISO Configuration b State Coupled SISO Configuration Configuration 2 State coupled SISO system In this system the pump feeds into tankl which in turn feeds tank2 A controller is designed to regulate or track the level in tank2 Different inlet and outlet diameters can be used and tried in tank2 Configuration 3 State Coupled and Input Coupled SISO system In this system the pump feeds into tank1 and tank2 using a split flow tank1 also feeds into tank2 A controller is designed to regulate or track the level in tank 2 Different inlet 22 and outlet diameters can be used and tried in tank1 and tank2 tank ri tank2 T Water Basin Figure 2 10 St
122. t Potentiometer 24 Tank1 Sensor Gain Potentiometer 25 Tank2 Sensor Offset Potentiometer 25 Tank2 Sensor Gain Potentiometer 2 3 Coupled Tank Model Parameters Table 2 2 lists and characterizes the main parameters e g mechanical and electrical specifications conversion factors constants associated with the two tank specialty plant Some of these parameters can be used for mathematical modeling of the Coupled Tank system as well as to obtain the water level s Equation Of Motion EOM Table 2 2 Coupled tank system model parameters Symbol Description Value Units K Pump Flow Constant als cm s V apparatus specific Vp max Pump maximum Continuous Voltage 12 V V p_peak Pump Peak Voltage 22 V Douti Out Orifice Diameter 0 4763 cm Doutz Out2 Orifice Diameter 0 4763 cm Li max Tank1 Height i e Water level range 30 cm Du Tank1 Inside diameter 4 4450 cm Ku Tank Water level sensor sensitivity 6 1 cm V Depending upon pressure sensor calibration L2 max Tank2 height i e water level range 30 cm Do Tank2 Inside diameter 4 445 cm K Tank2 Water level sensor sensitivity 6 1 cm V Depending upon pressure sensor calibration 17 Symbol Description Value Units Voias Tank1 and Tank2 Pressure sensor power bias 12 V Prange Tank1 and Tank2 sensor pressure range 0 6 89 KPa Ds Small Outflow Orifice diameter 0 3175 cm Dino Medium Outflow orifice di
123. tank system Fine tuning of a PI controller for level control of a cylindrical tank 29 e Fine tuning of a PI controller for level control of the second tank in the coupled tank system This chapter contains modules for five independent stand alone experiments The modules are written such that each section represents a single self contained experiment Each can be used as a laboratory procedure manual 3 2 Experiment 1 Orifice Coefficient Determination Objective To find the orifice coefficient for a cylindrical tank Coupled Tank Apparatus Description The Quanser coupled tank apparatus is shown in Figure 3 1 The apparatus is a bench top model consisting of a pump two cylindrical tanks made of plexiglas and water basin reservoir These two tanks are of volume 133 35cm each and are mounted on a platform with a metering scale behind each tank indicating the approximate liquid level in tank The two tanks are vertically mounted on platform and positioned in such a manner that outflow from the top tank tank1 serves inflow for the lower tank tank2 if second tank is used for experiment Outflow from lower tank goes directly into a reservoir From each tank fluid exits by gravity discharge through a small orifice The 30 resistance of this discharge can be varied by replacing the orifice inserts of different diameters into a threaded hole at the bottom of the tank lt Quick Connects Out1 and Out2
124. tem s watchdog routine shuts off the pump and the pump continues to remain idle until the voltage range is again within the acceptable range less than 4 3 Volts Important Note The measured variables in tankl amp tank2 are pressure sensor voltages and not the tank volumes or liquid levels 60 Lab Procedures Precautions and Other Notes e Make sure that the reservoir s distilled water level is at least three fourths full e A watchdog software interlock is programmed into pump vi so that the tanks do not overflow If the liquid level in either of the tanks reaches 25cm the pump is turned off and the pump continues to remains idle until the tank s voltage drops below 4 3 V e Do not panic the pump can be noisy If it starts smoking that is another matter Shut off the pump by clicking Stop button on the Pump VI e Avoid parallax error while measuring the tank level take measurements with an eye line directly perpendicular to the level 1 Familiarize yourself with the apparatus and how it relates to the schematic a See Figure 3 13 and Figure 3 14 2 Start the pump vi program and Open a data file a Double click the pump vi icon on the desktop It opens the pump vi program in LabVIEW Familiarize yourself with the icons controls and indicators on the screen shown in Figure 3 15 b Click the white color arrow button on the top left of the screen to start the program A window pops up on the screen as
125. ter Step Ziegler Nichols parameters Fine tuned Step 0 0 Initial Value 0 0 Final Value 10 10 Sample 0 0 146 Block Parameter PID controller Ziegler Nichols parameters Fine tuned Proportional Gain ke 0 391 0 06 Integral time t 0 034 0 003 Derivative time Tp 0 0 Block Parameter Transport Delay Ziegler Nichols parameters Fine tuned Time Delay 4 5 4 5 Input 0 0 Block Parameter Transport Delay Ziegler Nichols parameters Fine tuned Initial buffer size 1024 1204 Pade order for linearization 0 0 Block Parameter Saturation Ziegler Nichols parameters Fine tuned Upper limit 5 Not applicable Lower limit 0 Not applicable Sample time 1 Not applicable Setpoint 13 cm Experimental Data Initial Estimates Ziegler Nichols parameters Ke 0 391 taui 0 193 Simulink Model Initial Estimates Ziegler Nichols parameters Kc 0 391 taui 0 193 20 Simulink Model Fine Tuned parameters Kc 0 06 taui 0 325 Experimental Data Fine Tuned parameters Ke 0 06 taui 0 325 tr tank level y cm Figure 4 22 Comparison of Output Response between Experimental Data and Simulink Approximation for Ziegler Nichols and Fine Tuned PI Tuning Parameters for Setpoint i ll 60 80 100 120 Change from 3 to 13 cm in Tank2 Apparatus 3 147 1 J 140 160 Experimental Data Ziegler Nichols parameters Ke 0 391 taui
126. th tank2 level response as the system reaches the new steady state vi Once the new steady state is reached click write data to stop recording and run pump to stop the pump b Fine Tuning i Use scroll bars below tank level and voltage vs time plots to view response for previous tuning parameters ii Adjust the k and t for best closed loop response Use a trial and error method based on PI controller tuning and parametric effect topics in the theory section Parametric effects are listed in Table 3 3 for assistance The allowable percent overshoot is 10 104 iii Repeat steps 3 a 1 to 3 a vi without recording data until you get desired closed loop response for both the output and input variables Use scroll bars below tank level and voltage vs time plots to view response for previous parameters iv Once desired response is attained go 3 c c Final PI parameters i Repeat steps 3 a i to 3 a vi with final tuning parameters Make sure you record data this time 4 Press STOP button at the end of the experiment Data Analysis 1 Graphically compare the empirical set point responses of tank2 for all three sets initial Ziegler Nichols and Ciancone guesses and fine tuned of PI tuning parameters 2 Compare each of the empirical closed loop responses both its input and output with its SIMULINK equivalent Discuss any discrepancies Why might there be any discrepancies 105 3 7 Correcting Pum
127. th the apparatus and how it relates to the schematic 2 3 a See Figure 3 7 and Figure 3 8 Start the pump vi program and Open a data file a Double click the Pump VI icon on the desktop It opens the pump vi program in LabVIEW Familiarize yourself with the icons controls and indicators on the screen shown in Figure 3 9 b Click the white color arrow button on the top left of the screen to start the program A window pops up on the screen asking to define an output file c Assign a file name and save it in Microsoft excel spreadsheet format for example yourname xls Removal of air pockets a Run the pump by giving a random pump voltage between 0 5 1 Volts and watch for any air bubbles over in the pressure sensor located inside at the bottom of the top tank 48 ir pocket in sensor Poke gent with poking rod to eliminate it al Figure 3 10 Removal of Air Pockets in Pressure Sensor b Air pockets will almost always form in sensor whether or not you see bubbles poke the rod into sensor as shown in Figure 3 10 Caution 1 Be gentle with the sensor while removing bubbles A violent stroke on the sensor could ruin it 2 Don t get confused with the bubbles formed and floating at the top of tank for bubbles in sensor c Once air pockets are removed stop the pump by setting OV as the pump voltage and observe the voltage for the tank1 on Pump VI front panel If the voltage value is within 0 1 Volts of 0 V
128. the same apparatus The pump flow constant K remains almost constant for an individual apparatus over time The test described in section 4 2 2 was performed on three different days Over these three days the values of K on apparatus 2 were 18 04 18 04 and 17 91 cm s V The mean and standard deviation of K are 17 99 cm s V and 0 07 cm s V respectively The standard deviation of 0 07 can be attributed to experimental error and therefore K can be assumed constant with respect to time The data for the trials are tabulated in Table 4 2 Table 4 6 and Table 4 7 Table 4 6 Experimental Data Relating Pump Voltage and Flow Rate Apparatus 2 Trial 2 A Time in seconds voltage Trial Trial Trial Trail Trial Trial Anie A 1 2 3 4 5 6 0 50 18 82 18 34 18 75 18 28 18 38 18 53 18 52 8 64 0 65 13 69 13 53 13 56 13 54 13 50 13 60 13 57 11 79 0 75 11 69 11 59 11 75 11 59 11 68 11 91 11 70 13 67 1 00 8 81 8 97 8 84 8 72 8 78 8 69 8 80 18 18 1 25 7 09 7 00 7 28 7 19 7 00 7 03 7 10 22 54 1 50 6 16 6 00 6 10 5 93 6 07 5 97 6 04 26 50 114 Table 4 7 Experimental Data Relating Pump Voltage and Flow Rate Apparatus 2 Trial 3 pump Time in seconds voltage Trial Trial Trial Trail Trial Trial Average ne Vv 1 2 3 4 5 6 0 50 18 62 18 15 18 57 18 44 18 15 18 41 18 39 8 70 0 65 13 62 13 56 13 41 13 60 13 37 13
129. timates Ciancone parameters Ke 0 095 taui 0 148 12 Simulink Model Fine Tuned Parameters Ke 0 1 taui 0 115 Simulink Model Initial Estimates Ciancone Parameters Ke 0 095 taui 0 148 Experimental Data Fine Tuned Parameters Ke 0 1 taui 0 115 tank level y cm a T ae 6L A 1 J J if 1 1 i L E J 10 0 10 20 30 40 50 60 70 80 90 time s Figure 4 19 Comparison of Tank Level Response between Experimental Data and Simulink Simulation for Setpoint change in Tank1 Ciancone Method and Fine Tuned PI Control Parameters 2 2 T T T T T T T T T Experimental Data Initial Estimates Ciancone parameters Kc 0 095 taui 0 148 Experimental Data Fine Tuned Parameters Kc 0 1 taui 0 115 2b Simulink Model Initial Estimates Ciancone Parameters Ke 0 095 taui 0 148 Simulink Model Fine Tuned Parameters Kc 0 1 taui 0 115 pump voltage u E T 0 8 Figure 4 20 Input Voltage Response Comparison between Experimental Data and Simulink Model for Setpoint Change in Tankl Ciancone Method and Fine Tuned PI Control Parameters 143 The closeness of experimental output response and the Simulink output response indicate that the model parameters given in Table 4 12 are good The slightest deviation between the experimental data and simulink data approximation may be due to sensor hysteresis and non linearity The fined tuned output response obeys the given tuning rules no mo
130. tio of the sizes of successive peaks 73 Calculation of Initial Tuning Parameters There are three general methods for calculating PID tuning parameters Classic closed loop methods force the closed loop system to the edge of stability by inducing sustained oscillation in the output The closed loop Ziegler Nichols method and Tyres Luyben method l are classic examples The direct synthesis method derives both a controller and its parameters from the transfer functions of a known process model and a defined closed loop output response Open loop methods such as the open loop Ziegler Nichols 11 method the Cohen Coon method 13 i and the Ciancone method 14 are based on the parameters of a first order plus dead time FODT process model The open loop Ciancone method will be used to determine initial estimates swags of controller tuning parameters in this experiment Open Loop Methods Ciancone Method Ciancone and Marlin created an open loop method of tuning controllers based on a single parameter called fraction dead time Fraction dead times ranges between 0 0 and 1 0 and is calculated from the FODT parameters It represents the fraction of the total time needed for the open loop process step response to reach 63 2 of its final value that is due to dead time Determining PI controller parameters using Ciancone correlations is a three step procedure 1 From the FODT model kp Tp and 0 calculate the fractional
131. trol tuning parameters using the Ciancone method for a PI control algorithm and a set point change Use the appropriate graph from Marlin Thomas E Process Control Designing Processes and Control Systems for Dynamic Performance McGraw Hill New York 2 edition page 286 Note The model parameters will vary slightly among the apparatus because they have different pump flow constants Use values of process gain time constant and dead time corresponding to the apparatus on which you do tuning experiment to calculate the tuning parameters Coupled Tank Apparatus Description 1 The Quanser coupled tank apparatus is shown in Figure 3 19 The apparatus is a bench top model consisting of a pump two cylindrical tanks made of Plexiglas and water basin reservoir These two tanks are of volume 133 35cm each and are mounted on a 68 platform with a metering scale behind each tank indicating the approximate liquid level in tank The two tanks are vertically mounted on platform and positioned in such a manner that outflow from the top tank tankl serves as inflow for the lower tank tank2 if second tank is used for experiment Outflow from lower tank goes directly into reservoir From each tank fluid exits by gravity discharge through a small orifice a Quick Connects Out1 and Out2 Pressure sensor Lower tank tank2 Disturbance or drain tap Calibration and Signa Conditioning Circuit Board Water basin reservoir
132. used with this section of the Pump VI front panel PUMP vi Front Panel Ele Edt View Project Operate Toos Window Heb Oa WRITE DATA Figure 5 1 Screenshot of How the Pump VI Front Panel looked in Spring 2008 ti Response to the First Trial of Experiment 2 Incoherent pressure sensor voltage readings drew attention to the Pump VI LabVIEW code to the potentiometer calibration screws and to the pressure sensors as the possible root causes of the problem After critically analyzing the LabVIEW code it 152 was removed from the list of probable causes Focus shifted to the potentiometer screws and the pressure sensors for root cause analysis By a series of experiments it was determined that the voltage readings changed dynamically even with no liquid inflow to the tank Figure 5 2 depicts this phenomenon Apparatus 2 Dynamic offset of tank 2 for 6 hours T T T 7 Trail 1 Trail 2 Voltage in V 4 L 1 fi 0 50 100 150 200 250 300 350 400 Time in Minutes Figure 5 2 Dynamic Change in Pressure Sensor Reading for No Pump Voltage Eventually formation of air pockets was observed in the pressure sensors These air pockets would reduce the tank voltage reading because they are less dense than water and would absorb some of the water head pressure as shown in Figure 5 2 Proceeding with the assumption that these air pockets might be the root cause for the incoherent readings a p
133. vel change in pump voltage 10 75 1 45 1 25 0 7 16 909 cm V 124 The process time constant is determined as the time it takes the mean curve to reach 63 2 of the output variable change Tp is time taken for tank level at reach 0 632 10 75 1 45 1 45 cm 7 32cm From Figure 4 4 this time is 13 8 s The process dead time is the amount of time it takes the output variable to react after the manipulated variable is changed Since the manipulated variable is changed at time 0 s and the level starts changing at time 0 s there is no dead time in the upper tank process lt The FODT parameters are K 16 909 cm V ty 13 8 s and 0 0 s for the upper tank of apparatus 1 4 3 3 Data Analysis 1 Calibration Chart Table 4 10 shows pressure sensor voltage tank voltage versus liquid level in the tankl Apparatus 1 This data are acquired in step 5 b in Experiment 2 Each apparatus has similar readings for both tanks Table 4 10 Calibration Chart Readings for Tank Tank Voltage V Liquid level in tank cm 0 85 2 5 3 3 4 09 15 20 25 Pee a 125 A calibration chart is drawn with tank voltage as independent variable and liquid level as dependent variable Plotting these two variables gives an equation of the form y mx c where the slope m gives the gain value as shown in Figure 4 8 tank 1 level 6 115 tank1 pressure sensor voltage 0 169 Tank level cm Voltage V F
134. when the tankl is empty proceed to generate empirical data Step 5 Otherwise proceed with the calibration of the tank pressure sensor Step 4 49 4 Calibrate the upper tank s pressure sensor a Make sure that tank1 is empty before starting the calibration If not empty it by using the disturbance tap black flap near the bottom of tank2 Offset screw tank2 Gain screw tank2 Offset screw tank1 Gain screw tank1 Figure 3 11 Calibration and Signal Conditioning Circuit Board b Observe the pressure sensor voltage reading in the tank display box If it is not 0 V first manually adjust offset potentiometer screw for tank on the calibration and signal conditioning circuit board See Figure 3 11 using the potentiometer adjustment tool flat head screw driver to obtain 0 Volts Turn the offset potentiometer screw clockwise to increase the voltage reading and vice versa c Cover the tank outlet with your finger d Using the quick connect at Out1 apply a voltage to the pump and fill the tank to 25 cm Then turn off the pump Apply 0 voltage to the pump e Observe the voltage reading in the tank display box If it is not 4 10 V 0 03 of this value is okay at 25 cm manually adjust gain potentiometer screw for tank1 50 g to obtain 4 10V Turn the gain potentiometer screw clockwise to increase the voltage reading and vice versa Caution Make sure to adjust the correct potentiometer screw For better und
135. xample of this situation is modeling of a heated mixing tank The basis for modeling a tank s dynamic liquid level is an overall material balance It has the form 3 7 ee of ee rate of mass l rate of mass of mass in system f lentering the system leaving the system A more in depth explanation about modeling can be found in Chapter 2 of B Wayne Bequette Process Control Modeling Design and Simulation Prentice Hall 2003 A schematic of the cylindrical tank system is shown in Figure 3 8 In this experiment liquid is pumped from a reservoir into a cylindrical tank at a flow rate F volume time The input flow rate is proportional to the pump voltage i e F KVpump 3 8 where K volume time Volt is a constant and Vpump is the pump voltage 44 Reservoir Figure 3 8 Schematic of Cylindrical Tank The liquid exits the tank by gravity discharge through a small orifice The tank s outlet velocity length time for small orifices is given by 3 9 C orifice coefficient or discharge coefficient 2 P Pz is nothing but head and is given by pgL and 1 Z a is almost equal to 1 Thus Vvo Coal 2gL 3 10 where g is the acceleration due to gravity and Z is the tank s liquid level 45 Pre lab Procedures 1 Develop the nonlinear model relating the tank s liquid level to the pump voltage i e find z f L V Assume constant density Use the parameters a Pump flow constant

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