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- 1. INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERINGInternational Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – & TECHNOLOGY (IJEET)6545(Print), ISSN 0976 – 6553(Online) Volume 3, Issue 3, October – December (2012), © IAEMEISSN 0976 – 6545(Print)ISSN 0976 – 6553(Online)Volume 3, Issue 3, October - December (2012), pp. 121-129 IJEET© IAEME: www.iaeme.com/ijeet.aspJournal Impact Factor (2012): 3.2031 (Calculated by GISI) ©IAEMEwww.jifactor.com MODEL PREDICTIVE CONTROL TECHNIQUES FOR CSTR USING MATLAB Dr. V.Balaji E.Maheswari Principal, Asst.Professor, Lord Ayyappa Institute of Engineering Sri Sairam Institute of Technology, and Technology, Chennai, India Kanchipuram,India maheseee25@rediffmail.com balajieee79@gmail.com ABSTRACT Model Predictive control (MPC) is shown to be particularly effective for the self-tuning control of industrial processes. Here main objective of DMC controller is to drive the output as close to the set point as possible in a least square sense with the possibility of the inclusion of a penalty term on the input moves. Therefore, the manipulated variables are selected to minimize a quadratic objective that can consider the minimization of future error. The implementation of internal model control(IMC) is also shown here. The control strategy is to determine the best model for the current operating condition and to activate the correspondingcontroller.IMC is a powerful strategy in complex industrial process. A simulated example of the control of nonlinear chemical process is shown. Exothermic stirred tank reactor system with the first order reaction is taken as a nonlinear chemical process. The reaction is assumed to be a perfectly mixed and no heat loss occurs within the system. By using IMC and DMC has simulated control for the total process in CSTR. The simulation results shows the effectiveness of the proposed control strategy. Keywords: MPC, DMC, IMC, CSTRI INTRODUCTION Although the use of Linear control method have been prevalent in the process industries.They have limitation in specially when dealing with nonlinear plants in a wide operating regionhas commonly found in most of the industries. Many economically important operations such asreactors and high purity distillation columns can be very nonlinear and very difficult to controladequately with linear controller. In fact chemical reactors creates some of the most challengingfeedback control problems faced by process control engineers. Complex steady state and dynamicbehavior, such as ignition / extinction behavior and parametric sensitivity create challenges thatare though for traditional linear controller to handle. In recent years, the requirement of quality of 121
- 2. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),ISSN 0976 – 6553(Online) Volume 3, Issue 3, October – December (2012), © IAEMEautomatic control in the process industries increased significantly due to the increased complexityof the plants and sharper specifications of product quality. At the same time available computingpower increased to a very high level. As a result, computer models that are computationallyexpensive became applicable even to rather complex problems. Model based control techniqueswere developed to obtained tighter control. Model predictive control was introduced successfullyin several industrial plants. An important advantage of these control schemes is the ability tohandle constrained of actuated variables and internal variables. In most application of modelpredictive technique, a linear model is used to predict the process behavior over the horizon ofinterest [1, 2]. As most real processes show a nonlinear behavior, some work was done to extendpredictive control techniques to incorporate nonlinear models. [3-5]. The most expensive part of the realization of a nonlinear predictive control scheme is thederivation of the mathematical model. In many cases it is even impossible to obtain a suitablephysically founded process model due to the complexity of the underlying processes or the lack ofknowledge of critical parameters (as, e.g., temperature and pressure dependent mass transfercoefficients or viscosities) of the models. DMC was developed at the end of the seventies byCulter and Rameker [1] of shell oil Co. and has been widely accepted in the industrial world,mainly by petrochemical industries [6]. Nowadays DMC is something more than an algorithm andpart of it success is due to the fact that the commercial product covers topic such as modelidentification or global plant optimization. In many practical cases, however conventionalcontrollers (P/PI/PID-controllers) are already in use at the plant, which stabilize the plant andprovide some basics, sometime sluggish control. The Internal model control (IMC) continues to be a powerful strategy in complexindustrial processes control application. This structure provides a practical tool to influencedynamic performance and robustness to modeling errors transparently in the design. It isparticularly appropriate for the design and implementation of controllers for linear open loopstable system. [2] There are two ways to cope with nonlinear control design for plants subject touncertainty and disturbances: robust and adaptive control. While neural adaptive controller beingextensively developed. [8-11]. The robust technique of internal model control is investigated here.A control system consist of the processes to be controlled and of a controlled device chosen bythe designer which computes the controlled input so as to convey the desired behavior to thecontrolled system. The controlled device consists of a controller and possibly other elements(observer, filter, internal model). Internal model control system they are characterized by a controldevice consisting of the controller and simulation model of the processes, the internal model. This paper shows the simulink implementation of such a tool, which was also extended forDMC. After the DMC has been trained, it can be used as an independent control strategy. Usingsimulink implementation of internal model control and dynamic matrix control the characteristicsof these approaches have been examined and some limitations of each of them have been pointedout. Continuous Stirred tank Reactor (CSTR) has been used as an example of the nonlinearsystem. The plant exhibits a strongly nonlinear behavior, so that a nonlinear prediction model hasto be used.II MPC Vs. DMC Model predictive control is a strategy, which is based on the explicit use of some kind ofprocesses model to predict the controlled variables over a certain time horizon, the predictionhorizon. Dynamic matrix control (DMC) used here to predict future plant output, based on pastand current values and on the proposed optimal future control action. These actions are calculatedby the optimizer taking into account the cost function (where future tracking error is considered)as well as the constraints. 122
- 3. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),ISSN 0976 – 6553(Online) Volume 3, Issue 3, October – December (2012), © IAEME The control strategy consists of four parts: 1. At each sampling time, the value of the controlled variable y (t+k) is predicted over theprediction horizon k=1…NP. This prediction depends on the future values of the controlled variable u(t+k) within acontrol horizon k=1…NU ,where NU<=NP .If NU<NP then u(t+k)=u (t+NU), k=NU+1….NP 2. A reference trajectory r (t+k), k=1…NP is defined which describes the desired processtrajectory over the prediction horizon. 3. The vector of future controls u (t+k) is computed such that a cost of function dependingon the predicted control error is minimized. The first element of the controlled variable is applied to the process. 4. The prediction error between the measured process output and the predicted output isused for disturbance estimation. Step 1 to 4 is repeated at each sampling instant; this is called a receding horizon strategy. Weused the extended DMC algorithm to explicit use of nonlinear model in the DMC scheme. Inlinear DMC, the prediction of the vector of future values of the controlled variables y is performedusing the dynamic matrix A, which consists of step response coefficients. At the core of MPCalgorithm is a dynamic model until recently most industrial applications have relied on lineardynamic models. This dynamic models have been developed using empirical data obtained fromplant testing. Linear, rather than nonlinear models have been used because of the difficulty indeveloping a generic nonlinear model from empirical data and also because of the computationalexpense involved in using nonlinear models in MPC formulations. The Model Predictive Controller is shown in the figure1 in which optimizer that uses tosolve the control trajectory over a future time horizon based on dynamic model of the process.The Dynamic Matrix Controller is shown in the fig 2. Figure 1 Block diagram of MPC 123
- 4. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),ISSN 0976 – 6553(Online) Volume 3, Issue 3, October – December (2012), © IAEME Figure 2 Block diagram of DMCIII INTERNAL MODEL CONTROL (IMC) The IMC design procedure is a two step approach that although sub-optimal in a generalnorm sense, provides a reasonable tradeoff between performance and robustness. The main benefitof the IMC approach is the ability to directly specify the complementary sensitivity and sensitivityfunctions η and ∈, directly specify the nature of the closed loop response. The IMC designprocedure consists of two main steps. The first step will ensure that q is stable and casual ; thesecond step will require q to be proper. An IMC model provides a practical tool to influencedynamic performance and robustness to modeling errors transparently in the design. IMCphilosophy realizes on that control can be achieved only if the control system encapsulates eitherimplicitly or explicitly some representation of the process to be controlled. If the controlledscheme has been developed based on an exact model of the process, then perfect control ispossible. In IMC control law is easy to implement and requires little computation, its derivation ismore complex. We consider a problem of tracking a set point sequence {r(k)},possibly in thepresence of deterministic disturbances which might occur randomly, and whose effect must becancelled(regulation).The desired dynamical behavior of the control system is chosen to be givenby a stable reference model. In this paper the reference model is selected for process with a delayd and order n; a suitable linear reference model is given by E (q-ı) yr (k)=q-dH (q-ı) r (k) (1) 124
- 5. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),ISSN 0976 – 6553(Online) Volume 3, Issue 3, October – December (2012), © IAEME Where r denotes the set point and yr the output of the reference model, and where: E (q-ı) =1+eıq-ı+… +enq-n (2) H (q-ı) =ho+hıq-ı+…+hnq-n (3) q-ı is the backward shift operator. Figure 3 Block diagram of Internal Model Control (IMC)IV EXAMPLE The aim of this simulation is to show the difference of the two controls strategy. Thesimulation is separated into two tasks. First the Dynamic matrix control (DMC) strategy is used.During this period the model and controller parameters for the DMC and IMC are identified .Achemical system, known as a Continuous stirred tank reactor (CSTR), was utilized as an exampleto illustrate the use of proposed DMC and IMC tool. In the CSTR, two chemicals are mixed, andreact to produce a product compound with concentration CA(t). The temperature of the mixer is T(t). The reaction is exothermic, producing heat which acts to slow the reaction down. Byintroducing a coolant flow rate qc(t), the temperature can be varied and hence the productconcentration controlled .This system can be described by the following nonlinear simultaneousdifferential equations: ĆA = q/v (CAf – CA) – k0 CA exp - E/RT (4) Ť = q/v (Tf – T) + (- H) k0 CA / ρCp *exp - E/RT +(ρc Cpc/ρCpV)*qc*[1-exp(-hA/qcρcCpc)]*(Tcf–T) (5) 125
- 6. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),ISSN 0976 – 6553(Online) Volume 3, Issue 3, October – December (2012), © IAEME Figure 4 Continuous stirred tank reactor (CSTR) Figure 5 Open Loop Simulink Model of CSTRV SIMULINK BLOCK IMPLEMENTATION This section explains the application of the dynamic matrix control and internal modelcontrol strategies on the CSTR system for both set point tracking and actual output of the plant. 126
- 7. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),ISSN 0976 – 6553(Online) Volume 3, Issue 3, October – December (2012), © IAEME Figure 6 Dynamic Matrix Control (DMC) Figure 7 Internal Model Control (IMC) Figure. 8 Control signal and actual plant output 127
- 8. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),ISSN 0976 – 6553(Online) Volume 3, Issue 3, October – December (2012), © IAEME Process output with DMC1.4 PROCESS O/P WITH IMC 0.14 alfa=01.2 0.13 0.12 r(t) 1 0.11 0.10.8 Ca (mol/l) 0.090.6 0.08 0.070.4 0.060.2 0.05 u(t) 0.04 0 0 500 1000 1500 2000 2500 3000 0 5 10 15 20 25 30 35 40 45 50 TIME (MIN) Figure 9 DMC strategy, set point tracking Figure 10 IMC strategy, set point trackingVI CONCULSION The overall result showed the capability of employing these control strategies to control anon-linear system such as exothermic reactor (CSTR) use in this case study. Set point trackingbehavior of the DMC and IMC is compared. At every change of operating condition linearizationof nonlinear system is to be carried out. For nonlinear process i.e. Continues stirred tank reactor(CSTR), DMC has stable response around ingratiation point. As operating condition changesDMC became unstable. While for all set point changes, the IMC controller yields a fast responsebut it introduced offset. The IMC requires slightly larger but acceptable control moves. If largercontrol moves are acceptable, faster set point tracking can be obtained by decreasing the pole ofthe set point filter. Proposed IMC strategy is potentially applicable to wide class of process controlproblem. Some oscillatory behavior of the control at the step changes can be seen in both caseswhich can be reduced by using Neural Network.VII REFERENCES[1] C.Culter and B. Ramaker, “ Dynamic matrix controls: A computer controlalgorithm,”Proc.1980 Joint automatic conference.[2] C.E.Garcia and M.Morari, “Internal model control. A Unifying Review and some new results,”Ind. Eng. Chem.Process Des.Dew.21.pp.308-323, 1982.[3]T.Peterson, E.Hernadez, Y.Arkun and F.J.Schor, “Nonlinear predictive control of a semi batchpolymerization reactor by an extended DMC,” Proc. 1989 American controlconference,pp 1534- 1539,1989.[4] E.Hernadez and Y. Arkun, “Neural network modeling and an extended DMC algorithm tocontrol nonlinear system”, Proc.1990 American control conference, pp2454-2459, 1990.[5]D.D.Brenge and W. D.Seider, “Multistep Nonlinear predictive control,”Ind.chem.Eng.Res.28, 128
- 9. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),ISSN 0976 – 6553(Online) Volume 3, Issue 3, October – December (2012), © IAEME pp.1812-1822, 1989.[6] S.J.Qin and T.A.Badgwel, “An overview of industrial model predictive controls technology.In chemical process control: Assesment and new direction for research.”[7] Sanner R., Slotine J.J. “Stable adaptive control of robot manipulators using Neural networks”, Neural computation vol. 7 no.4, 1995,pp 753-790.[8] Narendra K.S., Mukopadhya S: “Adaptive control of nonlinear multivariable system usingneural networks vol.7 no5, 1994,pp 737-752.[9] Morari M., Zafiriou E., Robust process control, Prentice-Hall international editions, 1989.[10] Alverez J., “An internal model controller for nonlinear system”, Prceding of the 3rd European control conference, Rome, Italy, September 1995,pp 301-306.[11] Rivals I., Personaz L., “ Internal model control,” proceeding of the IEEE International symposium on Industrial electronics, June 17-20 1996,Warsaw.ABOUT THE AUTHORS V.BALAJI has 12 years of teaching experience. Now he is working as a principal in Lord Ayyappa Institute of Engineering and Technology, Kanchipuram.His current areas of research are model predictive control, process control, and Fuzzy and Neural Networks. He has published 26 research papers in national and international journals and conferences. He is a member of ISTE, IEEE , IAENG, IAOE and IACSIT. E. Maheswari has 10 years of teaching experience. Now she is working as a AP in Sri Sairam, Institute of Technology Chennai, India. She has published 8 research papers in national and international journals and conferences. Her areas of interest include power electronics and its controlling techniques. she is a member of ISTE, IAOE 129

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