A Smplified Predictive Control for a Shell Amd Tube Heat Exchanger

8/3/2019 A Smplified Predictive Control for a Shell Amd Tube Heat Exchanger

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S. Rajasekaran et al. / International Journal of Engineering Science and TechnologyVol. 2 (12), 2010, 7245-7251

A SIMPLIFIED PREDICTIVE CONTROL

FOR A SHELL AND TUBE HEAT

EXCHANGERS.RAJASEKARAN*

Research Scholar, Anna University of Technology, CoimbatoreCoimbatore, India-641048

[email protected]

Dr.T.KANNADASAN

Director-Research,Anna University of Technology, Coimbatore

Coimbatore, [email protected]

Abstract:In this paper a simplified predictive control design is applied for the controlling a temperature of a fluid stream usingthe shell and tube heat exchanger. The predictive control design based on Dynamic Matrix Control (DMC) involvesthe complicated inversion computation for higher dimensional matrix. Using DMC for controlling a temperature ofthe shell and tube heat exchanger, there is still a need for optimization of conversation of energy. The simplified

predictive control is based on DMC, which reduces the computational complexity by exploring its internalmechanism. Finally the simplified Predictive Control is applied to shell and tube heat exchanger and the results ofthis control algorithm compared with the conventional PID controller and DMC based PID Controllers.

Keywords: PID; Dynamic Matrix Control; Shell and Tube Heat Exchanger.

1. Introduction

To exchange heat among the two fluids with of the different temperature with higher efficiency for this process, theHeat exchanger are commonly used in the industries such as gas processing, petrochemical industries etc., and alsoit has the advantages of lower cost and compact structures. For the external load variations and regulation, inindustries the transient resulting are done by the heat exchanger and their networks frequently used. The simulationsof the transient response of heat exchanger is necessary in many industries are processed by the operation such asnuclear reactors, power plants and chemical process. The regulations, optimal operations and the real time control allthese are demand the heat exchanger to behave as the more accurate description of the time domain and therefore forthe best performance and of the heat exchanger the control parameters should be maintained carefully. The two maincontrol parameters are to be controlled they are hot fluid and cold fluid temperature. It is very important to developthe model before tuning the optimum controller settings. The process of determining a mathematical expression thatdescribes the process is called as modeling. Determining the model from first principles involves the mathematical

and scientific equations that must be accepted the physics principles of a given process [1]. To determining themodel for the system there are two methods, first principle with mathematical and scientific equations. Themathematical system is in the differential form which describes how the system changes with respect to a steadystate. The laplace transform of a time domain differential equation, it is mainly based on the dynamic model yieldsand a transform model in S-domain which is being used to simulate the process.Mainly the accuracy may increase the insertion of dynamic equation to which it affects the process. All dynamicsare not taken in a account practically. Empirically for determining the model it involves subjecting a system to userdefined inputs and the datas are collected by the system responds. The data using black box approach, the modelwas identified. Dynamic matrix control (DMC) algorithm is one of the important representative model predictive

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control algorithm which is delivered by J.Richalet etc. in 1978, and has advanced a lot over the years [8]. The modelof DMC control algorithm is based on step response prediction model. Traditional autocorrecting of single step

prediction is extended to multiple step prediction. Based on the practical feedback information, repeatingoptimization of the algorithm restrains effectively the algorithm sensitive to parameter change of the model. Basedon combining the features of prediction function in DMC with feedback structure of PID, a dynamic matrix controlwith PID structure (PID-DMC) is derived. Using DMC algorithm it requires the inversion computation of higherdimensional matrix and the computation required for the PID-DMC algorithm complicated than that in traditionalDMC algorithm. Traditional feedback control algorithm-PID control is simple in principle, easy to understand andimplement in engineering, which is still widely used for controlling temperature of heat exchanger. Many advancedcontrol algorithm is based on PID control algorithm. Heat exchanger process is highly nonlinear and time varyingfunction. Using conventional PID control for heat exchanger, it cannot achieve ideal control effect because of itsnonlinear and time varying behavior. In order to solve these problems, the predictive PID controller has derived.Using simplified DMC-PID algorithm for controlling temperature of shell and tube heat exchanger. The steady stateand transient response of shell and tube heat exchanger using simplified DMC-PID control is simulated andcompared with Conventional DMC-PID algorithms. It is found that the simplified DMC-PID performs well than theconventional PID, DMC-PID and results are tabulated.

2. Experimental Setup and Identification

The temperature control of shell and Tube exchanger setup is shown in the Fig. 1:

Fig.1. Experimental Setup of Heat Exchanger

THO = Hot water outlet temperatureTH1 = Hot water inlet temperature

TCO = Cold water outlet temperatureTC1 = Cold water inlet temperatureH = HeaterR1, R2 = Rota meterV1, V2, V3, V4, V5, V6 = ValvesT1, T2 = Cold, Hot water tank

Here a fluid-fluid two pass countercurrent type heat exchanger is used. The mass flow of the two streams, inlettemperature and outlet temperature of the two streams and flow rates of two streams are process variables associated

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with the function of heat exchanger. Here the hot fluid temperature is taken as controlled variable and cold fluidflow rate is taken as manipulated variable. For a system tested by a step input, a general model that can be fitted to

be a FOPDT [2]. The experimental data were fitted and found transfer function is given by,

0.53S0.7eG S

1.8 1S

(1)

3. PID and Predictive Control

The PID controller is widely applied in industrial field [12]. Apart from its simple structure and relatively easytuning, one of the main reasons for its popularity is that it provides the ability to remove offset by using integralaction. It improves the performance of the robustness in the steady state against noise and uncertainties. Moreover,since PID controller are so widely used, one might expect that the structure should arise naturally given reasonableassumptions on system internal dynamics and control performance specifications. Model predictive control is afamily of controllers that employ a distinctly identifiable model of the process to predict its future behavior over anextended prediction horizon. A performance objective to be minimized is defined over the prediction horizon,usually as a sum of quadratic set point tracking error and control effort terms. This cost function is minimized byevaluating a profile of the manipulated input moves to be implemented at successive instants over control horizon.This idea behind predictive control is at each iteration to minimize a criterion of the following type,

P M

22

N iJ t, u t [ r t i Y t i ] P u t i 1

t (2)

Where, Y= Prediction of output, u = Control input, = Difference operator N = minimum cost horizon, P =Prediction horizon, M = Control horizon

3.1.Dynamic Matrix Control

One of the important predictive control algorithm is DMC which was originally developed by shell oil company in1960s and 1970s, it is based on step response model. The process model employed in this formulation is the stepresponse of the plant while the disturbance is considered to keep constant along the horizon. The procedure to obtainthe prediction as follows [12],

The predictive model of the system output represented by,

Ym (t+1) =A U (t) + A0U (t-1) (3)

Where, U (t) is unknown control increment vector. Ym (t+1) is the output vector of predictive model in futuristic Pinstants under the action ofU (t) at future instants. U (t-1) is the known control vector.

Ym (t+1) = [ ym(t+1), ym(t+2), ym(t+3),.,ym(t+P) ]T (4)

U (t) = [ u(t), u(t+1), u(t+2),., u(t+M-1) ] T (5)

U (t-1) = [ u(t-N+1), u(t-N+2),,u(t-1) ] T (6)

1

2 1

P P 1 P M 1

a 0 . . 0

a a . . 0. . . . .

. . . . .

a a . . a

A

(7)

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N N 1 N 1 N 2 2

N N 1 3

0

P 1

a a a a . . a

0 a a . . a

. . . . .

. . . . .

0 0 . . a

A

(8)

P is the predictive horizon; M is control horizon; A is the P x M Dynamic matrix; N is the time domain length ofmodel.

As interference and error exist in the predictive model output, after compensated by the measured error, theprediction of output can be computed as:

YP (t+1) = ym(t+1)+h[y(t)- ym(t)] = A U (t) + A0U (t-1) + he(t) (9)

where,

YP (t+1) is predictive output vector,

YP (t+1) = [ yp(t+1), yp(t+2), yp(t+3),.,yp(t+P) ]T; h is coefficient of recursive error; e(t) is the error between theactual and predicted model output at time t;

e(t) =y(t)- ym(t)

So the cost function of the conventional DMC is given by,

J = [Yp(t+1) Yr(t+1) ]TQ[Yp(t+1) Yr(t+1)] + U(t)

TU(t) (10)

Where, Q = error weighting matrix; is the control weighting matrix; Yr(t+1) is the desired reference trajectory.

3.2.PID Controller Based on DMC

From the last analysis the conventional cost function contains only the integral functions, the new cost function is

obtained by introducing proportion, integral and differential into the cost function. The procedure of PID controllerbased on DMC and the Simplification was delivered by Ping Ren, Guang-Yi Chen, Hai-long pei in the year 2008[10].Then the new cost function is obtained,

J = [Yp(t+1) Yr(t+1) ]T Ki [ Yp(t+1) Yr(t+1) ]+ [Yp(t+1) Yr(t+1) ]

T Kp [ Yp(t+1) Yr(t+1) ] + [

2Yp(t+1) 2Yr(t+1) ]

T Kd [ 2Yp(t+1)

2Yr(t+1) ] + U(t)TU(t) (11)

Where

Yp(t+1) = [ yp(t+1), yp(t+2), yp(t+3),., yp(t+P) ]T

Yr(t+1) = [ yr(t+1), yr(t+2), yr(t+3),., yr(t+P) ]T

2Yp(t+1) = [2yp(t+1), 2yp(t+2), 2yp(t+3),., 2yp(t+P)]

2Yr(t+1) = [

2yr(t+1), 2yr(t+2),

2yr(t+3),., 2yr(t+P) ]

yp(t+i) = yp(t+i) - yp(t+i-1) (12)

yr(t+i) = yr(t+i) yr(t+i-1) (13)

2yp(t+i) = yp(t+i) - yp(t+i-1) (14)

2yr(t+i) = yr(t+i) - yr(t+i-1) (15)

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i = 1,2,3.,P

Kp, Ki, Kd are proportion, integral, differential factor respectively.Define

E0(t) = Yp(t+1) - Yr(t+1) = [e0(t+1),..,e0(t+P)]T (16)

E0(t) = Yp(t+1) - Yr(t+1) = [e0(t+1),.., e0(t+P)]T (17)

2E0(t) =

2Yp(t+1) -2Yr(t+1) = [

2e0(t+1),.., 2e0(t+P)]

T (18)

By substituting (16),(17),(18) into (11) the new cost function is rewritten as

J = E0(t)T Ki E0(t) + E0(t)

T KpE0(t) + 2E0(t)

T Kd2E0(t) + U(t)

TU(t) (19)

The predicted error of the PID based DMC contorl is given by,

e0(t+i) = yp(t+i) - yr(t+i) = yp(t+i) - yr(t+i) ( yp(t+i-1) yr(t+i-1)) = e0(t+i) - e0(t+i-1)

In the same way,

2e0(t+i) = e0(t+i) - e0(t+i-1) (20)

Specially, define e0(t) = e0(t) = 0

Introduce a matrix

1 . . 0

1 1 . .

. . . .

0 . 1 1

S

Then,

E0(t) = SE0(t); 2E0(t) = S2 E0(t) (21)

Substituting the (21) into (19), we can get cost function as following,

J = E0(t)T Ki E0(t) + E0(t)

T KpE0(t) + 2E0(t)

T Kd2E0(t) + U(t)

TU(t) = E0(t)TR E0(t) + U(t)

TU(t) (22)

Where, R = KiI + KpSTS + Kd (S

2)T S2

Differentiating (22) with respect U(t) and setting this equal to zero, we obtain the optimal control:

U(t) = ( I + ATRA)-1 AT R[Yr(t+1) A0U(t-1) he(t)] (23)

Set DT = [1 0 0]1xP then the demanded control could be obtained,

u(t) = DT( I + ATRA)-1 AT R[Yr(t+1) A0U(t-1) he(t)] (24)

4. Simplified PID- DMC Algorithm

Conventional PID-DMC control algorithm uses output reference trajectory to soften output. A Simplified PID-DMCcontrol algorithm is extended to soften the input control actions, rolling optimization strategy of predictive controllercan increased by softening the input control actions. By softening the input control actions, the control incrementtends to 0 smoothly in the control horizon (M). The adjustments taken only in control horizon M. in order to makeu(t + j ) come to 0 in M steps little by little, the control increment is given by[10],

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u(t+j) =

q

k

k j

u(t) (25)

Where, k>0 , q>1 are considered as designed parameters, j=0,1,2,.,M-1

then the prediction of output (9) can be rewritten asYp(t+1)= A.A1u(t)+ A0U(t-1)+he(t) (26)

Let A2=A.A1

Substitute 26 into cost function (22), the cost function of Simplified PID-DMC is given by

u(t) = (A1TA1+ A2

TRA2)-1A2

TR[Yr(t+1)-A0U(t-1)-he(t)] (27)

This Simplified PID-DMC algorithm constrains the rolling optimization sequence and softens the input signals.

5. Results and Discussion

5.1.DMC Controller

Considering the equation (1) and (10) we obtained the simulation results for Conventional PID and DMC controller.The adjustable parameters in this DMC controller that affect closed loop performance include the sample time T,model horizon, N, finite prediction horizon, P, control horizon, M, the move suppressing weights for themanipulated and controlled variables. The tuning parameters are T = .2s, P = 14, M = 2. The weighting parametersare slightly detuned from the originally derived one and controllers tracking performance is as shown in the Fig. 2. Itwas found that the performance of DMC based tuning is better than Conventional PID controller.

Fig.2. Temperature response of PID and DMC

From the fig.2. It was observed that by carefully tuning the DMC method the overshoot of the system has drasticallyreduced when compared to conventional PID controller. It was observed that DMC had almost eliminated theovershoot when compared to PID controller. The settling time was observed to be very less for a DMC and the

performance was much faster also.

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5.2 Simplified Predictive Control

After selection of DMC controller settings we found that the step response of (10) shown in fig 2, and comparedwith PID controller. It is observed that the controller reduces the transient, peak overshoot and settling time.

Fig.3. Temperature response of DMC, PID-DMC, SPID-DMC

For this simulation the values of control parameters are common for DMC, PID-DMC and simplified PID DMC.The values of M and P taken as 5, 50 respectively, the values of proportional, derivative and integral are taken as0.4, 5.6 and 0.8. The simulation of temperature response of shell and tube heat exchanger is given in the Fig.3. Fromthe simulation it was observed that the output of simplified PID-DMC gives a much better control of temperaturerather than classical DMC and PID-DMC.

6. Conclusion

This paper emphasizes on the temperature control aspect of shell and tube heat exchanger. Using simplifiedpredictive controller for temperature control, it reduces the computational complexities and softens the input signalsby constraining the rolling optimization sequence of the controller. The experimental and simulation results showsthat the proposed system obtains a good control effect and can satisfy the requirements of temperature control ofshell and tube heat exchanger. Through simulation, the approach has been shown to be very effective for first order

plus dead time processes. Compared with conventional controllers the simplified predictive controller is more robustto the process variation.

7. References

[1] W.L.Luyben, Process modeling, simulation and control for chemical engineers, second edition, Tata McGraw Hill USA : 1990.[2] S.Nithya.;Abhay Singh Gour;,N.Sivakumaran,.;T.K.Radhakrishnan.; N.Anantharaman..Model based Controller design of shell and tube

Heat exchangerInternational Journal of Sensors & Transducers, Vol .84( 10) ,pp. 1677-686.2007.[3] L. Xia, J. A. De Abreu-Garcia, T. T. Hartley, Modeling and simulation of a heat exchanger, in Proceedings of IEEE International

Conference on Systems Engineering, August 13, 1991, pp. 453-456.[4] Chidambaram, M. and Malleswara Rao, Y. S. N., Nonlinear Controllers for a heat exchangers,J. Proc.Cont., 2, 1, 1992, p. 17-21.[5] W. B. Bequette, Process Control Modeling and Simulation, Prentice Hall, 2003.[6] H. Thal-Larsen, Dynamics of heat exchangers and their models, ASME J. Basic Eng, pp 489 - 504, 1960.[7] E.F. Camacho, C. Bordons, Model Predictive Control in the Process industry, Springer - Velag, London, 1995.[8] J. Richalet, Industrial Applications of Model Based Predictive Control,Automatica 1993, 29 (5), 1251.[9] Katsuhiko ogata, Modern control engineering, fourth edition prentice Hall of India, New Delhi-110001 2005.[10] Ping Ren, Guang-Yi Chen, Hai-long pei, A simplified Algorithm for Dynamic Matrix Control with PID Structure International

conference on intelligent computation technology and automation2008,978-0-7695-3357-5[11] H. Shao,Industrial Process Advanced Control . Shanghai: Shanghai Jiao Tong University Press, 1997.[12] W.Guo, S.Yao, Improved PID dynamic matrix control algorithm based on time domain. Chinese Journal of Scientific Instrument, vol.28,

no.12, pp.2174-2178, 2007.[13] K. J. strm and T. Hgglund, PID Controllers: Theory, Design, and Tuning, Research Triangle Park, NC: Instrument Society of

America, 1995.[14] Diyaz, G., Sen, M., Yang, K.T., McClain, R.L., Simulation of heat exchanger performance by artificial neural networks,Int. J. HVAC and R

Res., 5 (3), pp.195-208, 1999.[15] H. Thal-Larsen, Dynamics of heat exchangers and their models, ASME J. Basic Eng, pp 489 - 504, 1960.

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A Smplified Predictive Control for a Shell Amd Tube Heat Exchanger