Modeling and Control of CSTR using Model based Neural Network Predictive Control

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					                                                           (IJCSIS) International Journal of Computer Science and Information Security,
                                                           Vol. 10, No. 7, July 2012




    Modeling and Control of CSTR using Model based
           Neural Network Predictive Control

                                                          Piyush Shrivastava
                                                          Assistant Professor,
                                           Electrical& Electronics EngineeringDepartment,
                                          Takshshila Institute of Engineering & Technology,
                                                   Jabalpur, Madhya Pradesh, India
                                                                    .


Abstract—this paper presents a predictive control strategy based            consider plant behavior over a future horizon in time. Thus, the
on neural network model of the plant is applied to Continuous               effects of both feedforward and feedback disturbances can be
Stirred Tank Reactor (CSTR). This system is a highly nonlinear              anticipated and eliminated, fact which permits the controller to
process; therefore, a nonlinear predictive method, e.g., neural             drive the process output more closely to the reference
network predictive control, can be a better match to govern the             trajectory. The classical MBPC algorithms use linear models of
system dynamics. In the paper, the NN model and the way in                  the process to predict the output of the process over a certain
which it can be used to predict the behavior of the CSTR process            horizon, and to evaluate a future sequence of control signals in
over a certain prediction horizon are described, and some                   order to minimize a certain cost function that takes account of
comments about the optimization procedure are made. Predictive
                                                                            the future output prediction errors over a reference trajectory,
control algorithm is applied to control the concentration in a
continuous stirred tank reactor (CSTR), whose parameters are
                                                                            as well as control efforts. Although industrial processes
optimally determined by solving quadratic performance index                 especially continuous and batch processes in chemical and
using the optimization algorithm. An efficient control of the               petrochemical plants usually contain complex nonlinearities,
product concentration in cstr can be achieved only through                  most of the MPC algorithms are based on a linear model of the
accurate model. Here an attempt is made to alleviate the                    process and such predictive control algorithms may not give
modeling difficulties using Artificial Intelligent technique such as        rise to satisfactory control performance [3, 4]. Linear models
Neural Network. Simulation results demonstrate the feasibility              such as step response and impulse response models are
and effectiveness of the NNMPC technique.                                   preferred, because they can be identified in a straightforward
                                                                            manner from process test data. In addition, the goal for most of
   Keywords-Continuous Stirred Tank Reactor; Neural Network                 the applications is to maintain the system at a desired steady
based Predictive Control; Nonlinear Auto Regressive with                    state, rather than moving rapidly between different operating
eXogenous signal.                                                           points, so a precisely identified linear model is sufficiently
                                                                            accurate in the neighborhood of a single operating point. As
                       I.    INTRODUCTION                                   linear models are reliable from this point of view, they will
    One of the main aims in industry is to reduce operating                 provide most of the benefits with MPC technology. Even so, if
costs. This implies improvements in the final product quality,              the process is highly nonlinear and subject to large frequent
as well as making better use of the energy resources. Advanced              disturbances; a nonlinear model will be necessary to describe
control systems are in fact designed to cope with these                     the behavior of the process. Also in servo control problems
requirements. Model based predictive control (MBPC) [1,2] is                where the operating point is frequently changing, a nonlinear
now widely used in industry and a large number of                           model of the plant is indispensable. In situations like the ones
implementation algorithms due to its ability to handle difficult            mentioned above, the task of obtaining a high-fidelity model is
control problems which involve multivariable process                        more difficult to build for nonlinear processes.
interactions, constraints in the system variables, time delays,
etc. The most important advantage of the MPC technology                         In recent years, the use of neural networks for nonlinear
comes from the process model itself, which allows the                       system identification has proved to be extremely successful [5-
controller to deal with an exact replica of the real process                9]. The aim of this paper is to develop a nonlinear control
dynamics, implying a much better control quality. The                       technique to provide high-quality control in the presence of
inclusion of the constraints is the feature that most clearly               nonlinearities, as well as a better understanding of the design
distinguishes MPC from other process control techniques,                    process when using these emerging technologies, i.e., neural
leading to a tighter control and a more reliable controller.                network control algorithm. The combination of neural
                                                                            networks and model-based predictive control seems to be a
   Another important characteristic, which contributes to the               good choice to achieve good performance in the control. In this
success of the MPC technique, is that the MPC algorithms                    paper, we will use an optimization algorithm to minimize the



                                                                       38                              http://sites.google.com/site/ijcsis/
                                                                                                       ISSN 1947-5500
                                                         (IJCSIS) International Journal of Computer Science and Information Security,
                                                         Vol. 10, No. 7, July 2012




cost function and obtain the control input. The paper analyses a         More complex optimization functions can consider the control
neural network based nonlinear predictive controller for a               effort. It is the specific case of GPC (Generalized Predictive
Continuous Stirred Tank Reactor (CSTR), which is a highly                Control), where the optimization index J can be expressed as:
nonlinear process. The procedure is based on construction of a
neural model for the process and the proper use of that in the
optimization process.
    This paper begins with an introduction about the predictive                                                                                   (4)
control and then the description of the nonlinear predictive             where:
control and the way in which it is implemented. The neural               y(k ) - is the output plant estimation at instant = k
model and the way in which it can be used to predict the
behavior of the CSTR process over a certain prediction horizon           Δu - is the control action increment.
are described, and some comments about the optimization                  N1 - is the minimum horizon of prediction.
procedure are made. Afterwards, the control aims, the steps in           NU - is the control horizon.
the design of the control system, and some simulation results            NY - is the maximum horizon of prediction.
are discussed.
                                                                         The objective of the control problem is to minimize the index
                   II.   PREDICTIVE CONTROL                              J, with respect to the control actions, looking for the points
The predictive controller, in summary, is characterized by               where the first order differential is null.
computing future control actions based on output values
predicted by a model, with vast literature and academic and
industrial interest (Clarke, 1987; Garcia et all, 1989; Arnaldo,                 III.    NEURAL NETWORK PREDICTIVE CONTROL
1998) [4]. This section presents the concepts of predictive              By the knowledge of the identified neural model of the
control based on NPC, using the usual optimization functions             nonlinear plant which is capable of doing multi step ahead
and control laws, applied to the conventional predictive                 predictions, Predictive control algorithm is applied to control
controllers.                                                             nonlinear process. The idea of predictive control is to
                                                                         minimize cost function, J at each sampling point:
                                                                                        N2                     2    Nu                    2

                                                                          J(t,U(k)) = ∑[ r(k +i) − y (k+i)] + ∑ρ[ Δu(k +i −1)]
A. Optimization functions
                                                                                                   ˆ
The optimization function, usually represented by the index J,
                                                                                        t=N1                        i=1
represents the function that the control action tries to                                                                                       
minimize. In an intuitive way, the error between the plant                                                                                        (5)
output and the desired value is the simplest example of an                                                                             
optimization function, and it is expressed by:                           With respect to the Nu future controls,

                                                                                                  U ( k ) = [u ( k ).....u ( k + N u − 1)]T (6) 
                                                             (1)
Where:                                                                   and subject to constraints:
y(k) represent the plant output
y k ref ( )represent the desired response
e(k) represent the estimation error
                                                                                        Nu ≤ i ≤ ( N2 − nk )                                      (7) 
k is the sample time
                                                                                  Using the predictive control strategy with identified
One of the most usual optimization functions is based on the             NARX model (NNMPC) it is possible to calculate the optimal
square error and it is represented as:                                   control sequence for nonlinear plant. Here, term r(k+i) is the
                                                                                                               ˆ
                                                                         required reference plant output, y (k+i) is predicted NN
                                                              (2)        model output, Δ u ( k + i − 1) is the control increment, N1 and
But the optimization index can take forms of more complex
functions. For predictive controllers, whose models are                  N2 are the minimum and maximum prediction (or cost)
capable to predict N steps ahead, the simple application of the          horizons, Nu is the control horizon, and ρ is the control
square error approach can present satisfactory results. This             penalty factor[4].
case admits that the optimization function is not limited to an                   The predictive control approach is also termed as a
only point, but an entire vector of N predicted errors. It seeks         receding horizon strategy, as it solves the above-defined
to optimize the whole trajectory of the future control actions in        optimization problem [5] for a finite future, at a current time
a horizon of N steps ahead.                                              and implements the first optimal control input as the current
                                                                         control input. The vector u = [Δu(k),Δu(k+1),…Δu(k + Nu-1)]
                                                                         is calculated by minimizing cost function, J at each sample k
                                                              (3)
                                                                         for selected values of the control parameters {N1, N2, Nu, ρ}.




                                                                    39                                 http://sites.google.com/site/ijcsis/
                                                                                                       ISSN 1947-5500
                                                                            (IJCSIS) International Journal of Computer Science and Information Security,
                                                                            Vol. 10, No. 7, July 2012




The ese control p parameters de              redictive control
                                 efines the pr                                                                   e            al
                                                                                                     The purpose of our neura network mo    odel is to do
per               is             t                           the
   rformance. N1 i usually set to a value 1 that is equal to t                                    eries prediction of the plant output. Given a series of
                                                                                            time se              n            t             n
  me                             ne          on
tim delay, and N2is set to defin the predictio horizon i.e. tthe                            control signals
                                                                                                  l            % d                              to
                                                                                                               u and past data yt it is desired t predict the
nummber of time-st               ure          he
                  teps in the futu for which th plant respon nse
is r              dicted.
   recursively pred                                                                               output series yN.The network is trained to do one step
                                                                                            plant o                             k
                                                                                            ahead p                                            put
                                                                                                   prediction[9], i.e. to predict the plant outp yt+1 given
                                                                                                  rrent control si
                                                                                            the cur                           plant output yt . The neural
                                                                                                                 ignal ut and p
                                                                                                  k            ent          n
                                                                                            network will impleme the function
                                                                                                        yt +1 = f (ut , yt )
                                                                                                        ˆ                                                         (12)

                                                                                            As it is discussed above, yt h                         in
                                                                                                                                   has to contai sufficient
    Figure 1: NNMP principle app
    F            PC            plied to CSTR ch
                                              hemical process                               informa ation for this p
                                                                                                                   prediction to be possible.It is assumed that
                                                                                                                                  e
                                                                                            yt is mu                                              od
                                                                                                    ultivariable. One problem is that this metho will cause
    e              n                          s
The minimization of criterion, J in NNMPCis an optimizatiion                                a rapidly increasing d divergence due to accumulati of errors.
                                                                                                                                  e                ion
prooblem minimi    ized iterativel
                                 ly. Similar t NN traini
                                             to          ing                                       efore puts high demands on a
                                                                                            It there               h               accuracy of the model. The
                                                                                                                                                  e
   ategies, iterativ search meth
stra               ve            hods are appli to determi
                                              ied        ine                                        the
                                                                                            better t model mat      tches the actua plant the les significant
                                                                                                                                   al             ss
the minimum.                                                                                the acc                 r.                            as
                                                                                                   cumulated error A sampling time as large a possible is
                                                                                            an effe                                e
                                                                                                   ective method to reduce the error accum       mulation as it
θ (ii+1) =θ (i ) +μ (i) .d(i)                   (8) where θ ( i ) specif
                                                        e,             fies                 effectiv
                                                                                                   vely reduces t number of steps needed for a given
                                                                                                                   the            f              d
the current iterate (number ‘i’), d (i) is the sea
                  e                              arch direction a
                                                                and                         time ho                 ural
                                                                                                   orizon. The neu network tr                     ne
                                                                                                                                   rained to do on step ahead
                                                                                                    ion             l             he              of
                                                                                            predicti will model the plant. Th acquisition o this model
μ (ii)                        us
      is the step size. Variou types of a    algorithms exiist,                                     referred to as S
                                                                                            is also r              System Identifification.
cha                           w
   aracterized by the way in which search di               tep
                                             irection and st
   e
size are selecte               p
                 ed. In the present work Newton bas        sed
Levvenberg–Marqu  uardt (LM) allgorithm is immplemented. TThe                                     IV
                                                                                                   V.     MODELIN OF NEURAL NETWORK PRE
                                                                                                                NG                    EDICTIVE
sea              applied in LM algorithm is:
  arch direction a             a                                                                                           NPC)
                                                                                                                 CONTROL (NN
                                                                                                  ree          ved        N            opment are
                                                                                            The thr steps involv in the ANN model develo
 ˆ
(H[U i (t)] +λ i I)d i = -G[U i (t)]
                   d                            (9)                                         A. Gen               put-Output data
                                                                                                   neration of Inp             a
                                    nt           Hessian matrix as:
                         with Gradien vector and H                                                ata             o
                                                                                            The da generated to train the netw work should coontain all the
                                                                                                  nt
                                                                                            relevan information about the dyn               e
                                                                                                                               namics of the CSTR. The
                   ∂ J(t,U(t))                                                                    was             he           al           he
                                                                                            input w given to th conventiona model of th CSTR and
    G[U i (t)] =               |                                                            from t                nal         he
                                                                                                   the convention model, th input and output were
                      ∂ U(t) U ( t ) =U ( t )
                                       i

                                                                                            sampled for 0.02 sam               s            uired sampled
                                                                                                                 mpling instants and the requ
                                   %
                                 ∂ U(t) %                                                           e             rain
                                                                                            data are obtained to tr the networ rk.
                       %
    = − 2ϕ T [U i (t)]E(t)+2 ρ            U (t ) |U ( t ) =U i ( t )
                                 ∂ U(t)                               10)
                                                                     (1

                     %
             ∂ 2 J(t,U
                     U(t))
H[U i (t)] =
  U                        |
                ∂U(t 2 U ( t ) =U ( t )                                  
                                  i
                     t)
             ∂ ⎛ ∂Y(t)  ˆ         ⎞       %      %
                                        ∂U (t) ∂U (t )
                                            T
          =        ⎜         E(t) ⎟ +2ρ                |
            ∂U(t) ⎝ ∂U(t)                ∂U(t) ∂U (t ) U ( t ) =U ( t )
                                                                 i

                                  ⎠

                                                                               (1
                                                                                11) 

                 ies
where B(i) specifi the approxi             e             ian
                              imation of the inverse Hessi
  d                                         h
and G[U(i)(t)] is the gradient of the J with respect to tthe
  ntrol inputs. Th most popula formula kno
con              he           ar            own as Broydeen-                                                       e             put
                                                                                                              Figure 2: Input-Outp Sequence
  etcher-Goldfarb
Fle                           GS)          m
                 b-Shanno (BFG algorithm to approxima    ate
the inverse Hessi is used her
                 ian                        posed scheme of
                              re[8]. The prop                                               B. Neu Network A
                                                                                                  ural          Architecture
imp              e
   plementing the NNMPC is sh hown in Figure 2.
                                           e                                                       ed
                                                                                            The fee forward net  twork with sig
                                                                                                                              gmoidal activa
                                                                                                                                           ation function
                                                                                            was ch              on
                                                                                                  hosen based o the trials w with different structures of
  me
Tim Series Predi             ural
               iction with Neu Networks                                                           ayer perceptron
                                                                                            multila             n.




                                                                                       40                                  http://sites.google.com/site/ijcsis/
                                                                                                                           ISSN 1947-5500
                                                         (IJCSIS) International Journal of Computer Science and Information Security,
                                                         Vol. 10, No. 7, July 2012




                 ure       odel
              Figu 3: ANN mo of the CSTR

The lowest error corresponds to 7 neurons in the hidden lay
    e                            o                           yer.
    nce             ed            a
Hen it is selecte as optimal architecture of ANN. The AN     NN
seleected here co                n              e
                   onsists of 4 neurons in the input layer, 7
neuurons in the hid                            n             yer.
                   dden layer and one neuron in the output lay
    e
The ANN archite    ecture used in the present wwork is shown in
Figgure 3. The trai              m
                   ining algorithm used in the C
                                               CSTR modeling is
                                                             g               Fi                            rediction of mo
                                                                              igure 4: (a) One step ahead pr             odel, (b)
   ck               n
bac propagation algorithm. Before traini        ing the proce ess                             ween model ou
                                                                          Prediction error betw                          icted output
                                                                                                           utput and predi
wei                alized to small random numb
    ights are initia                           bers. The weighhts
are adjusted till error gets mi                 all
                                  inimized for a training se ets.                                                                                        idation tests o test set:
                                                                                                                                                      Vali             on
   hen             or             t
Wh the error fo the entire set is acceptably low, the traini  ing
   stopped.
is s
Tab 2 shows th parameters used in developing the AN
   ble              he                                       NN
model for the CST   TR


         Parame  eters                       alues
                                            Va
        Input neu urons                       4
       Output Ne  eurons                      1
         Hidden l layer                       7
           Neuro ons
                 den
      No. of hidd layer                        7
      Activation ffunction                   moidal
                                          Sigm
      Training alggorithm                    g-Marquardt
                                     Levenberg
                 ion
           Iterati                           0000
                                            10                            Figur 5 :(a) one ste ahead predic
                                                                                re           ep             ction of model (validation
         Architec cture                  Feedf
                                             forward                     set), (b Prediction e
                                                                                b)           error between m              nd
                                                                                                           model output an predicted
        Initial weeights                       1                                             output (validati set)
                                                                                             o              ion


              N             or
   Table 2: ANN Parameters fo CSTR model
                                       ling                                                                                    V.                       TINUOUS STIRRE TANK REAC
                                                                                                                                                     CONT            ED        CTOR
                                                                            The Continuous Stirred Tank Reactor [6] is shown in
                                                                               e
                                                                                            model in used a the nonlinea system.
                                                                         Figure 6.This CSTR m             as           ar
C. Model Validat tion
The final step in developing the model is v
    e           n               t             validation of tthe                   mage part with relationship ID rId50 was not found in the file.
                                                                              The im




model [11]. Valid              ormed by evalu
                 dation is perfo              uating the mod del
per             ng              a             a.
   rformance usin trained data and test data The input a    and
   get
targ were prese                 n             the
                 ented to the network and t network w      was
   ined using Lev
trai            venberg-Marqu  uardt algorithm.


                alidation tests on training se
               Va                            et:
                                                                                                                                            Continuous Stir
                                                                                                                                  Figure 6: C                          ctor
                                                                                                                                                          rred Tank Reac

                                                                             The equations w
                                                                               e                        he        model of the
                                                                                           which shows th dynamic m
                                                                         system is



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                                                                                                                                                               ISSN 1947-5500
                                                             (IJCSIS) International Journal of Computer Science and Information Security,
                                                             Vol. 10, No. 7, July 2012




                                       (14)




                        (15)
                                                                                                    control signal b the controller
                                                                                          Figure 8: c              by
                                d
     where h (t) is the liquid level, Cb(t) is the produ     uct
con                he
   ncentration at th output of th process, w1(t is the flow ra
                                he             t)            ate                        In this pa aper modelin of CSTR has been
                                                                                                                 ng             R
    the
of t concentrate feed Cb1 an w2(t) is the flow rate of t
                   ed           nd                           the              implem                               ral
                                                                                    mented using artificial neur networks. The neural
   uted feed Cb2 .The input con
dilu                             ncentration are set to Cb1=24
                                               e             4.9                                  ned
                                                                              model has been train using data set obtained fr     rom dynamic
   d               he
and Cb2= 0.1.Th constants associated w        with the rate of                equatio             ward neural n
                                                                                     ons. Feed forw               network has b  been used to
connsumption are k1=k2=1.                                                                          he            del
                                                                              model the CSTR. Th neural mod has been d           designed as a
                                                                                     box           he
                                                                              black b model. Th simulation results from conventional
                  e
     The objective of the contro                ntain the produ
                                 oller is to main             uct
con
  ncentration by a adjusting the fl w1 (t), w2 ( =0.1.The lev
                                  low           (t)           vel                     and
                                                                              model a the neural model were co    ompared for th given input
                                                                                                                                he
of t tank h is n controlled. The designed controller uses a
    the           not                                         s                      ons
                                                                              variatio and the re esults have been found satis   sfactory. The
  ural network m
neu                model to pred future CST responses to
                                 dict            TR                           simulat             at
                                                                                     tion shows tha implementat   tion of the Neu Network
                                                                                                                                  ural
pot                signals. The tra
   tential control s              aining data we obtained fro
                                                ere           om              based a             rollers for the s
                                                                                     advanced contr               set-point tracki case were
                                                                                                                                 ing
the nonlinear mod of CSTR.
                  del                                                               o
                                                                              able to force process output varia  ables to their ttarget values
                                                                                     hly
                                                                              smooth and within r                 e
                                                                                                   reasonable rise and settling tiimes.
         VI.      MULATION RES
                SIM          SULTS AND CON
                                         NCLUSION
                                                                                                     VII. REFERE
                                                                                                               ENCES

   e               f               s
The objective of the control strategy is to g      govern theCST  TR          [1]                   E.
                                                                                        Garcia C. E and Morari, M. 1982. In
                                                                                                                    ,             nternal model
dyn                                c
   namics to force the system concentration t track a certa
                                                   to              ain               l-I.            g
                                                                              control “A unifying review and s      some new resu  ults,Industrial
   -points. In this system, the in
set-                              nput is the cool flow rate a
                                                  lant            and         Engine                al
                                                                                    eering Chemica Process ”. De 21, 308--32
                                                                                                                    ev.            23.
                   he               on
the output is th concentratio of the pro           ocess [12]. T  The          [2]      L.G. Lightbody and G. W Irwin, “Neu networks
                                                                                                                  W.              ural
iden               ned
    ntifier is train and initialized before th control acti
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   rts.
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                                   i              udes coolant flo ow         Algoritthms Architect  tures Real-Tim Control, B
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   es               time steps (the sampling time is 20sec).
                                                  e                                 13,
                                                                              pp. 1–1 1992.
   e                               ed             s
The performance of the propose controller is shown in Figu        ure         [3]       D. W. Cla    arke, C. Mo   ohtadi and P S. Tuffs,
                                                                                                                                  P.
   Evidently, the concentration values of the p
7. E                                                              ack
                                                    plant could tra           “Gener ralized Predic ctive Control Basic              Algorithm”,
                   ues              t              d
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                                                                                                                    -
the transient resp ponse, one ma consider a larger predicti
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tim It is rem
  me.             markable to note that bec
                                   n              cause of high   hly                l:             nt
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                                                                                                                                   nd
nonnlinearity natur of CSTR process, using the convention
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                                                                                                           ISSN 1947-5500
                                                        (IJCSIS) International Journal of Computer Science and Information Security,
                                                        Vol. 10, No. 7, July 2012




stability design”, Automatica, vol 32, no. 12, 1701-1706,
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                      AUTHORS PROFILE
Author is presently working as Assistant Professor in
Electrical and Electronics Department of Takshshila Institute
of Engineering and Technology. He received the Masters
degree in Electrical Engineering with specialization in Control
Systems Engineering from Jabalpur Engineering College. His
area of specialization is in Neural Networks, Control Systems,
Fuzzy Logic.




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                                                                                                   ISSN 1947-5500