Design And Implementation Of Controllers For A CSTR Process

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International Journal of Emerging Technology in Computer Science & Electronics(IJETCSE) ISSN: 0976-1353 Volume 23 Issue 1 –JUNE 2016.Design and Implementation of Controllers for aCSTR ProcessEng. Muyizere Darius, Dr. S. SivagamasundariDept. of M.Sc (EI), Annamalai University, Cuddalore.increasing complexity of plant operations together with tougherenvironmental regulations, rigorous safety codes and rapidlychanging economic situations demand the need for moresophisticated process controllers.Model Predictive Control (MPC) is an important advancedcontrol technique which can be used for difficult multivariablecontrol problems. The term MPC describes a class of computercontrol algorithms that control the future behaviour of the plantthrough the use of an explicit process model. At each controlinterval the MPC algorithm computes an open loop sequence ofmanipulated variable adjustments in order to optimize futureplant behaviour. The first input in the optimal sequence isinjected into the plant, and the plant entire optimization isrepeated at subsequent control intervals.The various MPC algorithms only differ amongstthemselves in the model used to represent the process and thenoises and the cost function to be minimized. This type ofcontrol is of an open nature within many works have beendeveloped, being widely received by the academic world and byindustry.Abstract—Continuous Stirred Tank Reactor (CSTR) isthe most important process which plays a significantrole in process and chemical industries. Variousprocess variables like temperature, concentrationhave to be controlled in this Process. The ProportionalIntegral Derivative (PID) controller has been used inindustries for various process control applications. Itprovides control action to the discrepant values fromthe desired values in process output. Henceappropriate control action is needed to maintain thisprocess in the desired condition. The PI controlleryields an overshoot and long settling time, whichexacerbate the process. Hence it is not well suited formany complex processes in industries. ModelPredictive Control (MPC) is found to be very accurateand reliable in controlling the process variable. MPChas the ability to anticipate the future events andtakes action accordingly. In this research workcomparison of PI controller with MPC is made andthe best controller for this CSTR temperature controlprocess is to be selected.II.The first principles model of the continuous stirred tankreactor and the operating data as specified in the Pottman andSeborg [1] has been used in the simulation studies. Highlynonlinear CSTR is common in chemical and petrochemicalplants. The process considered for the simulation study is shownin Figure 2.1. Here an irreversible, exothermic chemicalreaction A B occurs in constant volume reactor that is cooledby a single coolant stream. A feed material of composition CA0enters the reactor at temperature T0, at a constant volumetricflow rate ‘q’. Product is withdrawn from the reactor at the samevolumetric flow rate ‘q’. The mixing is assumed to be efficientenough to guarantee homogeneity of the liquid content withinthe reactor. In a jacketed CSTR the heat is added or removed byvirtue of the difference between the jacket fluid and the reactorfluid. Often, the heat transfer fluid is pumped through theagitation nozzles that circulate the fluid through the jacket at ahigh velocity. The coolant flows at a flow rate of ‘qc’ and at afeed temperature Tc0. The exit temperature of the coolant fluidis Tc.Index Terms— Continuous Stirred Tank Reactor,Proportional Integral Derivative, Overshoot, Long settlingtime, Model Predictive ControlI.DESCRIPTION OF CSTR PROCESSINTRODUCTIONIn any manufacturing process, where a chemical change istaking place, a chemical reactor is the heart of the plant.Depending on the mode of operation, reactors are classified asbatch-wise or continuous. In batch-wise mode, reactants arecharged at the beginning of the reaction and products areremoved at the end of the reaction. In continuous stirred tankreactor (CSTR), reactants are continuously charged andproducts are continuously removed.Chemical reaction systems are usually nonlinear dynamicalsystems.Process control has become an integral part of process plants.An automatic controller must be able to facilitate the plantoperation over a wide range of operating conditions. Theproportional-integral (PI) or proportional-integral-derivative(PID) controllers are commonly used in many industrial controlsystems. These controllers are tuned with different tuningtechniques to deliver satisfactory plant performance. However,specific control problems associated with the plant operationsseverely limit the performance of conventional controllers. The175

International Journal of Emerging Technology in Computer Science & Electronics(IJETCSE) ISSN: 0976-1353 Volume 23 Issue 1 –JUNE 2016.Where CAs, Ts, qs, qcs are the steady state values of effluentconcentration, reactor temperature, feed flow rate and coolantflow rate respectively.The Jacobian matrix A is given as,The Jacobian matrix B is given byThe output matrix C is given byFigure 1.TABLE I.Schematic diagram of a continuous stirred tankreactor.MATHEMATICAL MODELLINGThe following assumptions are made to obtain the simplifiedmodelling equations of an ideal CSTR:2.2.1Reactor Mass BalanceWhere, CA is the product (effluent) concentration ofcomponent A in the reactor and rA is the rate of reaction per unitvolume. The Arrhenius expression is normally used for the rateof reaction. A first order reaction results in the followingexpression.Where, ko is the reaction rate constant, E is the activationenergy, R is the ideal gas constant and T is the reactortemperature on an absolute scale (Kelvin).STEADY STATE OPERATING DATAParametersSymbolsValuesProduct concentrationReactor temperatureCoolant flow rateFeed flow rateFeed concentrationFeed temperatureInlet coolant temperatureCSTR volumeHeat transfer termReaction rate constantActivation energy termCATqcq0.0882 mol/l441.2 K100 l/min100 l/min1 mol/l350 K350 K100 l7x105cal/(min K)7.2x1010 min-11x104 KCA0T0Tc0VhAkoE/RHeat of reaction-2x105cal/molLiquid densities1x103 g/lSpecific heat1 cal/(g K)2.2.1 Steady State AnalysisThe steady-state analysis shows the behaviour of the systemin the steady-state and results in optimal working point in thesense of maximal effectiveness and concentration yield.Mathematical meaning of the steady-state is that derivativeswith respect to time variable are equal to zero. (d(.)/dt 0). Thereactant and cooling heat must be equal in the steady-state,Hence, Qr Qc, The equations (2.4) and (2.5) can be rewrittenas,2.2.1 Reactor Energy BalanceWhere, (- H) is the heat of reaction, hA is the heat transfercoefficient, T0 is the feed temperature and Tc0 is the inletcoolant temperature.and results in relations for these heats Qr and Qc:2.2.1 LinearizationThe nonlinear equations are linearized and cast into the statevariable form as follows:If Qr and Qc are computed for various values of thetemperature from 300K to 500K for operating point q 100Where matrices A and B represent the Jacobian matricescorresponding to the nominal values of the state variables andinput variables, x̃, ũ and ỹ represent the deviation variables.The output matrix is represented as C. .l/min andgiven in176 100 l/min, three steady-states are obtained as

International Journal of Emerging Technology in Computer Science & Electronics(IJETCSE) ISSN: 0976-1353 Volume 23 Issue 1 –JUNE 2016.TABLE III. EIGEN VALUES AT THE THREE OPERATING POINTS OFTHE IDEAL CSTROperating point123TABLE IV.-3.0764 2.8533j-1.9837 3.0573j-1.0493 2.9064jRGA MATRICES AT THE THREE OPERATING POINTSOperatingPoint1Figure 2. Heat balance inside the reactorIt can be clearly seen that, this system has two stable steadystates (S1 and S2) and one unstable steady state (N1). Thesteady-state values of the state variables in these points are:The steady-state model is described by the set of nonlinearfunctionsEigen valueRGA 2.07638 3.076380 3.076380 2.07638 2 2.269567 3.2695670 3.2695670 2.269567 3 2.58955 3.58955 3.589550 2.58955 From the above table, it can be inferred that the process isstable at all the operating points as the eigen values havenegative real parts.III.PID controllers have been used widely in the industry due tothe fact that they have simple structures and they assureacceptable performance for the majority of the industrialprocesses. Because of their simple structures, PID controllersare easy to design, operate and maintain. Consequently, PIDcontrollers earn their popularity among practitioners in theindustry. Beginning with Zeigler and Nichols work, variousparameter tuning methods for conventional PID controllers havebeen proposed. On the other hand, controlling MIMO systems isnot straight forward due to the interactions between thechannels. The interactive multivariable systems can becontrolled by either of the following:1. a multivariable or centralized MIMO controller or2. a set of SISO controllersThe graph between temperature vs. concentration is given inFig.2.3. From the Fig. 2 and Fig. 32.2.1Design of Decentralized ControllersThe decentralized controllers are designed for the local linearmodels at the three chosen operating points. Figure 3.1 showsthe block diagram representation of decentralized control of anideal CSTR. The manipulated variables are the feed flow rate(u1) and coolant flow rate (u2). The outputs are the effluentconcentration (y1) and reactor temperature (y2).The controller parameters of the two loops such as gc1 andgc2 are obtained using IMC based design procedure.The nonlinear CSTR has been linearized at three stableoperating points using the data given in Table 2.1. Theoperating points selected for the linear models are presented inTable 2.2. The eigen values, damping factor obtained at therespective operating points are presented in Table 2.3.TABLE II.OperatingPointSTEADY STATE OPERATING POINTS FOR THE 0882441.21030.1055436.83DESIGN OF GAIN SCHEDULING IMC BASEDPID CONTROLLER97177

International Journal of Emerging Technology in Computer Science & Electronics(IJETCSE) ISSN: 0976-1353 Volume 23 Issue 1 –JUNE 2016.Operating pointgl1gl2q 103,qc 97,CA 0.0748, T 445.31.84960.8010q 100,qc 100,CA 0.0882, T 441.21.73770.8290q 97,qc 103,CA 0.1055, T 436.81.62910.8508The static decouplers are designed as follows:Figure 2. Block diagram representation of decentralized controlscheme for the ideal CSTRIMC Based tuning procedure for tuning the PI controllerparameters IMC based tuning approach is taken up and theprocedure proposed by Bequette (2003) yields the followingcontroller parameters. The PI controller parameters at the threeoperating points are presented in Tables 3.2 and 3.3. It shouldbe noted that the controller gain has been found to be a functionof the filter parameter λ. The filter parameter values are chosenby trial and error method and the selection of the appropriatefilter parameter value is decided by the performance indexmeasured in the closed loop.g l1 g12 (0)g11 (0)gl 2 g 21 (0)g 22 (0)TABLE V.IMC BASED PI CONTROLLER SETTINGS FOREFFLUENT CONCENTRATION CONTROL USING DECENTRALIZEDCONTROL SCHEMEOperating pointKcKiq 103,qc 97,CA 0.0748,T 445.367.6114193.9954Figure 3. Block diagram representation of decoupled controlscheme for the ideal CSTRq 100,qc 100, CA 0.0882,T 441.217.891981.73940q 97,qc 103, CA 0.1055,T 436.831.1897104.75157In the presence of decouplers, the multivariable systembehaves like two independent loops, for which the controllerscan be designed independently. The static decouplers at thethree operating points are given in Table 3.4.TABLE VII. STSTIC DECOUPLERS AT THE THREEOPERATING POINTSTABLE VI. IMC BASED PI CONTROLLER SETTINGS FOR ONTROLOperating pointOperating pointKcKiq 103,qc 97,CA 0.0748,T 445.30.03800.4148q 100,qc 100,CA 0.0882,T 441.20.11360.3807q 97,qc 103,CA 0.1055,T 436.80.03040.13852.2.2gl1gl2q 103,qc 97,CA 0.0748,T 445.31.84960.8010q 100,qc 100,CA 0.0882,T 441.21.73770.8290q 97,qc 103,CA 0.1055,T 436.81.62910.8508The equations for the two loops of a 2 x 2 multivariablesystem including the decouplers are given byDesign of Decoupling ControllersThe Block diagram representation of decoupled controlscheme for the multivariable control of CSTR is given in Fig.3.2. The manipulated variables are the feed flow rate (u1) andcoolant flow rate (u2). The outputs are the effluent concentration(y1) and reactor temperature (y2). In this work, the decouplersare designed using static decoupling method, to reduce theinteraction brought inby cross coupling. It consists of two steps: first, to designthe decouplers and second, to design the controllers fordecoupled systems.Substituting the values of gij in equations (3.12) and (3.13),the controllers are designed using IMC based tuning method.The PI controller parameters obtained at different operatingpoints are given in Tables 3.5 and 3.6.178

International Journal of Emerging Technology in Computer Science & Electronics(IJETCSE) ISSN: 0976-1353 Volume 23 Issue 1 –JUNE 2016.TABLE VIII. IMC BASED PI CONTROLLER SETTINGS FOREFFLUENTCONCENTARATIONCONTROLUSINGDECENTRALIZED CONTROL SCHEMEOperating pointKcKiq 103,qc 97,CA 0.0748,T 445.356.3117161.3464q 100,qc 100,CA 0.0882,T 441.235.7523120.0243q 97,qc 103,CA 0.1055,T 436.820.827095.0907TABLE IX. IMC BASED PI CONTROLLERREACTOR TEMPERATURE CONTROL USING(b) Variations in feed flow rateFigure 3.2 Servo response for reactor temperature control usingdecentralized control schemeSETTINGS FORDECENTRALIZEDCONTROL SCHEMEOperating pointKcKiq 103,qc 97,CA 0.0748,T 445.30.017300.64660q 100,qc 100,CA 0.0882,T 441.20.015090.18498q 97,qc 103,CA 0.1055,T 436.80.010100.31190(a) Variations in effluent concentration(a) Variations in effluent concentration(b) Variations in coolant flow rateFigure 3.3 Regulatory response for effluent concentrationcontrol using decentralized control scheme(b) Variations in coolant flow rate(c)Figure 3.1 Servo response for effluent concentration controlusing decentralized control scheme(a) Variations in reactor temperature(a) Variations in reactor temperature(b) Variations in feed flow rateFigure 3.4 Regulatory response for reactor temperaturecontrol using decentralized control scheme179

International Journal of Emerging Technology in Computer Science & Electronics(IJETCSE) ISSN: 0976-1353 Volume 23 Issue 1 –JUNE 2016.(b) Variations in coolant flow rate(a) Variations in effluent concentrationFigure 3.7 Regulatory response for effluent concentrationcontrol using decoupled control scheme(b) Variations in coolant flow rateFigure 3.5 Servo response for effluent concentration controlusing decoupled control scheme(a) Variations in reactor temperature(b) Variations in feed flow rate(a)Variations in reactor temperatureFigure 3.8 Regulatory response for reactor temperature controlusing decoupled control schemeDESIGN OF MODEL PREDICTIVE CONTROLLER(c) Variations in feed flow rateFigure 3.6 Servo response for reactor temperature controlusing decoupled control schemeFig. 4.1. Model Predictive Control block diagramDESIGN CONTROLLERThis shows how to design a model predictive controllerin Simulink. We have built a nonlinear plant model in Simulink.We want to design an MPC controller at a specific equilibriumoperating point. This shows that model-based design workflow.We linearized the plant at the desired operating point, design theMPC controller and validate it with nonlinear simulation. Itincludes steps as per state space model are follows:(a) Variations in effluent concentration180

International Journal of Emerging Technology in Computer Science & Electronics(IJETCSE) ISSN: 0976-1353 Volume 23 Issue 1 –JUNE 2016.presented in the following Fig. 5.1.The set point variations inthe reactor temperature is given and the responses are displayedin Fig. 5.2.1. Define the plant in discrete form.2. Obtain the state space model of the plant.3. Define prediction horizon and control horizon.4. Predict future output and control effort based on previousinput, output and control effort.5. Verify the robustness of the controller in presence ofuncertainties in the plant model.6. Verification of the performance of controller with differentweighting functions7. Verification of the performance of controller with constraintson the control effort.8. Evaluation of performance of controller with differentprediction horizons.Fig. 5.1 Servo response for Effluent concentration4.4.1 SELECTION OF DESIGN AND TUNINGPARAMETERSA number of design parameters must be specified inorder to design an MPC system. In this section, we consider keydesign issues and recommended values for the parameters.Several design parameters can also be used to tune the MPCcontroller.1. N and tThese parameters should be selected so that N t open-loopsettling time. TypicalValues of N:30 N 120(4.3)2. Prediction Horizon, PIncreasing P results in less aggressive control actionSet P N M(4.4)3. Control Horizon, MIncreasing M makes the controller more aggressive andincreases computationalEffort, typically:1 M 20(4.5)4. Weighting matrices Q and RDiagonal matrices with largest elements corresponding tomost important variablesFig. 4.5 Servo response for Reactor temperatureTable 5.1 provides the performance measures for servoproblemand Table 5.2 provides the performance measures for regulatoryproblem using decentralized control scheme. Table 5.3 providesthe performance measures for servo problem and Table 5.4provides the performance measures for regulatory problemusing decoupled controllers. The comparison of theperformance measures such as IAE and ISE values between thedecentralized and decoupled control schemes show that theperformance is better with the decoupled controllers than withthe decentralized controllers.PERFORMANCE ANALYSIS OF THE CONTROLLERSTable 5.1 Performance measures for servo problem (EffluentConcentration)(a) Variations in effluent concentrationOPDecentralized 948x10-71(b) Variations in feed flow rateFigure 3.6 Servo response for reactor temperature control usingdecoupled control schemeThe closed loop simulation studies are carried out on the CSTRmodel with decentralized control, decoupled control using IMCtuned PI and MPC controller settings. In order to assess thetracking capability of the designed controllers, set pointvariation in effluent concentration is given and the responses are181MPC

International Journal of Emerging Technology in Computer Science & Electronics(IJETCSE) ISSN: 0976-1353 Volume 23 Issue 1 –JUNE 2016.Table 5.2 Performance measures for regulatory problem(Effluent Concentration)OPDecentralized x10-71REFERENCES[1]MPC[2][3][4]Table 5.3 Performance measures for servo problem (ReactorTemperature)OP123Decentralized .289.0967.5002.4952.06523.54MPC[5]ISE[6][7]Table 5.4 Performance measures for regulatory problem(Reactor Temperature)OP123[8]Decentralized E[9]CONCLUSIONAn improved MPC (Model Predictive Control) techniqueis presented and it has been shown to be a simple and efficientalgorithm for multivariable control. Simulation results for acontinuous fermenter demonstrate the superiority of the MPCcompared with the original IMC-PID. MPC maintains a highlevel of closed-loop performance in both servo and regulatoryproblems, despite appreciable variations in process dynamicsand strong interactions between the manipulated variables. Inthis work we do not attempt to study the influence of tuningconstant sample time on closed-loop performance for thecontrollers in the multivariable case. In the example, sampletime fixed as the inverse of the process gain matrix.It is clear that to improve the performance of thecontroller, it is necessary to consider the tuning constant inoptimization of the IAE and ISE criterion. The qualitative andquantitative comparison of the closed loop simulation studiesconducted on the CSTR using decentralized ,decoupled andMPC control schemes reveal that the MPC control schemeprovides better set point tracking and load disturbance rejectionthan others control scheme.[12][13][14][15]182KiamHeongAng, Gregory Chong and Yun Li (2005), PIDControl System Analysis, Design, and Technology, IEEEtransactions on control systems technology, vol. 13, no. 4.A.Albagul , M.saad and Y.Abujeela,” Design andimplementation of PI and PIFL controllers for ContinuousStirred Tank Reactor system, “ International Jouranal ofComputer Science and Electronics Engineering (IJCSEE)Volume 2, Issue 2, 2014.J Prakash and K Srinivasan, “Design of nonlinear PIDcontroller and nonlinear model predictive controller for acontinuous stirred tank reactor,” ISA Transactions, 48,2009.IOSR Journal of Electrical and Electronics Engineering(IOSR-JEEE) e-ISSN: 2278 1676, p-ISSN: 2320-3331,Volume 7, Issue 1 (Jul. – Aug. 2013), pp. 88-99. ModelPredictive Control Design for Nonlinear Process ControlReactor Case study: CSTR (Continuous Stirred TankReactor) Mrs. M. Shyamalagowri, M.E., (Ph.D) 1*, Dr R.Rajeswari., M.E., Ph.D2www.iosrjournals.orgM. Nikravesh ,A.E. Farell,T.G. Stanford ,”Control ofnonisothermal CSTR with time varying parameters viadynamic neural network control (DNNC)”, ChemicalEngineering Journal,vol 76,pp.1-16, 2000.K.J. Astrom, T.Hagglund, PID Controller: Theory, Designand tuning, Instrument Society of America, NorthCarolina, 1995.M. Saad, A. Albagul, D. Obiad,”Modelling and ControlDesign of Continuous Stirred Tank Reactor”, 15th WSEASInternational Conference on automatic Control, Modellingand Simulation (ACMOS’13), Brasov, Romania, 2013.B. Nagaraj, P. Vijayakumar, A Comparative study of PIDcontroller tuning using GA,EP, PSO and ACO, Journal ofAutomation, Mobile Robotics & Intelligent Systems,VOLUME 5, 2011.10. S. S. Ge, C. C. Hang, and T. Zhang,” Nonlinearadaptive control using neural networks and its applicationto CSTR systems”, Journal of Process Control, vol.9,pp.313-323, 1998.A. Tewari, Modern Control Design with Matlab andSimulink, john Wiley & Sons Pte Ltd., Asia, 2002.A.Albagul , M.saad and Y.Abujeela,” Design andimplementation of PI and PIFL controllers for ContinuousStirred Tank Reactor system, “ International Jouranal ofComputer Science and Electronics Engineering (IJCSEE)Volume 2, Issue 2, 2014.J Prakash and K Srinivasan, “Design of nonlinear PIDcontroller and nonlinear model predictive controller for acontinuous stirred tank reactor,” ISA Transactions, 48,2009.IOSR Journal of Electrical and Electronics Engineering(IOSR-JEEE) e-ISSN: 2278 1676, p-ISSN: 2320-3331,Volume 7, Issue 1 (Jul. – Aug. 2013), pp. 88-99. ModelPredictive Control Design for Nonlinear Process ControlReactor Case study: CSTR (Continuous Stirred TankReactor) Mrs. M. Shyamalagowri, M.E., (Ph.D) 1*, Dr R.Rajeswari., M.E., Ph.D2 www.iosrjournals.orgQiang Xiong, Wen-Jian Cai, Ming He, A practicalDecentralized PID Auto tuning Method for TITO systemsunder closed loop control, International Journal ofInnovative computing, Information and Control.vol 2,number 2, April 2006.Xiong Q., W.J.Cai, M.J.He.,”Equivalent transfer functionmethod for PI/PID controller design of MIMO processes”,Int.journal of Process control, 17, pp665-673. (2007).

International Journal of Emerging Technology in Computer Science & Electronics(IJETCSE) ISSN: 0976-1353 Volume 23 Issue 1 –JUNE 2016.[16] K.J. Astrom, T.Hagglund, PID Controller: Theory, Design[17][18][19][20][21]and tuning, Instrument Society of America, NorthCarolina, 1995.M. Saad, A. Albagul, D. Obiad,”Modelling and ControlDesign of Continuous Stirred Tank Reactor”, 15th WSEASInternational Conference on automatic Control, Modellingand Simulation (ACMOS’13), Brasov, Romania, 2013.A. Tewari, Modern Control Design with Matlab andSimulink, john Wiley & Sons Pte Ltd., Asia, 2002.Xue ZK, Li SY. Multi-model modeling and predictivecontrol based on Local model networks. Control andIntelligent Systems 2006; 34(2):105–12.Arslan E, Camurdan MC, Palazoglu A, Arkun Y. Multimodel scheduling control of nonlinear systems using gapmetric. Industrial & Engineering Chemistry Research2004; 43:8275–83.Prakash J, Senthil R. Design of observer based nonlinearmodel predictive controller for a continuous stirred tankreactor. Journal of Process Control 2008; 18:504–14.183

2.2.1 Design of Decentralized Controllers The decentralized controllers are designed for the local linear models at the three chosen operating points. Figure 3.1 shows the block diagram representation of decentralized control of an ideal CSTR. The manipulated variables are the feed flow rate (u 1) and coolant flow rate (u 2). The outputs are .