A Stable Control of a Cstr with Input Multiplicities Using Artificial Neural Network Based Narma-l2

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Communications in Control Science and Engineering (CCSE) Volume 2, 2014

A Stable Control of a Cstr with Input Multiplicities Using Artificial Neural Network Based Narma-l2 Prabhaker Reddy Ginuga*, Radha Krishna Poondla Dept. of Chemical Engineering, University College of Technology, Osmania University, Hyderabad, INDIA *gpreddy_ouct@yahoo.com; rkpoondla@yahoo.com Abstract In this paper, the Neural network based NARMA-L2 controller is analyzed to an isothermal continuous stirred tank reactor (CSTR) which exhibits input multiplicities in space velocity on product of B. i.e., two values of space velocity will give the same value of product B. The Performance of Neural network based NARMA-L2 controller and conventional PI controller have been evaluated through simulation studies. As the NARMA-L2 controller provides always the two values of space velocity for control action and by selecting the value nearer to the operating point, it is found to give stable and better responses than conventional PI controller.

The PI controller results in unstable condition or switch over from initia l lower input space velocity to higher input space velocity vice versa. Thus, NARMA-L2 controller is found to overcome the control problems of PI controller due to the input multiplicities.

Keywords NARMA-L2 Controller; Isothermal CSTR; Input Multiplicities; Unstable

Introduction The t erm In put multi pli cit y mean s, more t han on e val ue of in put variable producing the same val ue of output. It is a kind of nonlinearity in the process. Input multiplicity occurs due to the competing effect s in t he processes.

Dyn amic an d steady st ate behaviour of t he process wit h input multiplicity will remain di stinct at different input values for the same output. Processes wit h multiple reacti ons, multi react ors or recycle struct ures are shown t o [1, 2] . Conventional linear PI controller will have control problems like in stability, oscill atory exhi bit in put multiplicities [3-5] due to in put multipli cities in t he process. an d l ess economi cal In t he l ast t wo decades, a n ew direction to control has gained consi derable attention. This new approach to control is called ‘Intelligent control’. The term ‘intelligent control’ addresses to more general control probl ems. It may refer to systems, which cannot be adequatel y described by a differential equations framework. There are three basic approaches to intelligent control: knowledge- based expert s systems, fuzzy l ogi c an d n eural n et works. The t erm ‘conventional control’ refers to theories and methods that are employed to control dynamic systems whose beh aviour is pri marily described by differential equations. Among these intelligent controllers, neural networks control has [6, 7] for control of dynamic process, demonstrating the ability of handling non linearity. become popular tool In this work, the design and eval uation of neural n etwork based NARMA-L2 controller are present ed to overcome the control problems associated with conventional PI controller due to input multipliciti es.

Description of CSTR with Input Mu ltiplicities We consider here a continuous stirred tank reactor (CSTR) with the following isothermal series an d parallel reactions; A

k1

2A

k2

B k3

C D

(1) (2)

The product B is the desired one. The mass balance equations for A an d B are given by: 2

Where,

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dX 1/dt = - k1*X 1 – k3*X 1 + (CA,0 – X 1)*u

(3)

dX 2/dt = k1*X 1 – k1*X 2+ X 2*u

(4)

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X 1=CA, X 2=CB , u=F/V

(5)

and F is the flow rate (l/min), CA and C B are the concentration of A and B in the reactor (mol /l) and CA,0 is the feed concentration of A (mol/l).The st eady state solutions of equations (3) and (4) are given by 2

X 1,s = {-b + [b +4*k3 CA,0 Us]0.5}/2*k1 us = {f2 ±

2 [f 2

(6)

0.5

– 4 * f1*f3 ] }/(2*f1)

(7)

Where b = k1 + U s 2 f1 = d 2 -1 2 f2 = - 2*d2 d1 = 2*k1+ d3 2 2 f3 = d1 – k 1 2 d1=(2k1*k2*X 2+k 1)/k1 d2=(2k3*X 2+k1)/k1 d3=4k3* CA,0 -1

-1

-

The parameters considered for the present work are given by k1 = 0.8333 (min ), k 2 = 1.6667 (min ), k3 = 0.16667 (mol -1 1 *min ), CA,0 = 10 (mol/l). The val ues of X 2 vs us are shown in Fig 1. Which shows steady state input multiplicities in us on the product concentration (X 2,s ). Th at is two same values of X 2,s .for example, X 2 = 1.117 can be obtained at us = -1 -1 0.5714 an d al so at us=2.8746. The gain is +0.5848 at U = 0.5714 Min where as the gain is -0.1208 at U= 2.8746 min .

FIG.1 STEADY STATE RESPONSE SPACE VELOCITY OF A CSTR

Design of a Neural Network Based NARMA – L2 Controller of a CSTR Generally, nonlinear process is given by the following discrete model, y(k + d) = {f[y(k), y(k - 1)...y(k - n + 1), u(k - 1) ...u(k - m + 1] + g[y(k), y(k - 1)... y(k - n + 1), u(k - 1)...u(k - m + 1].u(k)}

(8)

This model is in companion form, where the next controller input u(k) is not contained insi de the nonlinearity. The advantage of this form is that it can solve for the control input that causes the system out put to follow the set point, y(k + d) = y r(k + d). The resulting controller will have the form, u(k) =

Yr(k + d) - f[y(k), y(k - 1)...y(k - n + 1), u(k - 1)...u(k - m + 1] g[y(k), y(k - 1)...y(k - n + 1), u(k - 1)...u(k - m + 1]

(9)

Using this equation, directly it can sol ve control problems, because it may determine the control input, u(k) based on the output at the same time, y(k). From Eq.(9) the NARMA-L2 controller for CSTR, the space velocity is given as, u(k) =

Yr - f[x 2 (k), x 2 (k - 1)...x 2 (k - n + 1), u(k - 1)...u(k - m + 1] g[x 2 (k), x 2 (k - 1)...x 2 (k - n + 1), u(k - 1)...u(k - m + 1]

(10)

Simu lation Results and Discussion The performance of proposed neural network based NARMA-L2 controller an d conventional P I controller to the isothermal CSTR in space velocity is evaluated using SIMULINK model shown in Fig.2 below .

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FIG.2 SIMULINK MODEL OF NN- NARMA-L2 AND PI CONTROL OF A CSTR

The responses of Neural Network based NARMA L2 and P I controllers for set point change of 1.117 to 1.2 mol /l is shown in Fig.3. Here, Neural networks based controller gives faster response than conventional PI controller (kc=1.87, Ï„I=1.1). The correspon ding control actions are shown in Fig.4 and it shows a smooth action.

FIG. 3 RESPONSES OF NEURAL NETWORKS BASED NARMA L2 AND PI CONTROLLERS IN CONCENTRATION OF B VERSUS TIME FOR SETPOINT CHANGE FROM 1.117 TO 1.2 MOL/L AT LOWER INPUT SPACE VELOCITY

FIG. 4 CONTROL ACTIONS OF NEURAL NETWORKS BASED NARMA L2 AND PI IN SPACE VELOCITY FOR THE RESPONSES SHOWN IN FIG.3

Next, the performance of both the Neural networks based NARMA l2 an d convrntional PI controllers is evaluated at higher input space velocity. The responses of both controllers for a set point change of 1.117 to 1.2 mol/l are given in Fig.5. Here, The Neural n etworks based NARMA l2 results in stable and smooth response whereas PI controller leads to unstable response due to negative process gain at higher input space velocity. The proposed Neural networks

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controller always provides two input values of space velocity for control action and it selects control action which is nearer to operating point. Thus, Neural networks based controller is superior than contional PI controller.

FIG. 5 RESPONSES OF NEURAL NETWORKS BASED NARMA L2 AND PI CONTROLLERS IN CONCENTRATION OF B VERSUS TIME FOR SETPOINT CHANGE FROM 1.117 TO 1.2 MOL/L AT HIGHER INPUT SPACE VELOCITY

FIG. 6 CONTROL ACTIONS OF NEURAL NETWORKS BASED NARMA L2 AND PI IN SPACE VELOCITY FOR THE RESPONSES SHOWN IN FIG.5

Now, the performance of present NN NARMA L2 and PI designed for higher input space velocity is eval uated. So, the responses of NN based NARMA-L2 controller and PI controller for a set point change of 1.117 to 1.2 mol /l are presented in Fig.6. It shows responses of both controllers are smooth an d fast.. Fig.7 gives control actions in space velocity for this set point change.

The response of present NN NARMA L2 an d conventional PI controller designed (kc = -4.0,Ï„I=0.17) for higher input is shown in Fig.8 for set point change from 1.117 to 1.2 at lower input space velocity. As expected, it shows unstable response due to positive process gain at lower input space velocity. How ever, the present NN NARMA L2 controller gives a stable respon se. Th us controller PI controller designed for higher input space velocity will give unstable response. And the proposed NN NARMA controller is stable at both the input space velocities.

FIG 7 RESPONSES OF NEURAL NETWORKS BASED NARMA L2 AND PI CONTROLLERS IN CONCENTRATION OF B VERSUS TIME FOR SETPOINT CHANGE FROM 1.117 TO 1.2 MOL/L AT HIGHER INPUT SPACE VELOCITY

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Communications in Control Science and Engineering (CCSE) Volume 2, 2014

FIG.8 CONTROL ACTIONS OF NEURAL NETWORKS BASED NARMA L2 AND PI IN SPACE VELOCITY FOR THE RESPONSES SHOWN IN FIG.7

FIG 9 RESPONSES OF NEURAL NETWORKS BASED NARMA L2 AND PI CONTROLLERS IN CONCENTRATION OF B VERSUS TIME FOR SETPOINT CHANGE FROM 1.117 TO 1.2 MOL/L AT LOWER INPUT SPACE VELOCITY

FIG.10 CONTROL ACTIONS OF NEURAL NETWORKS BASED NARMA L2 AND PI IN SPACE VELOCITY FOR THE RESPONSES SHOWN IN FIG.9

Conclusions In the present study, the performance of conventional PI controller an d Neural Network based controller is studied for the set point changes at lower an d higher input dilution rates. Based on the above st udies, the following conclusions are made. At lower input dilution rate, response of PI controller for set point change from 1.117 to 1.2 mol/l is stable. Whereas proposed neural network based NARMA- L2 controller is giving stable response for the both set point changes. Similarl y, at higher input dilution rate, the con ventional PID is found to be unstable and the

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NARMA-L2 controller i s stable. Thus, the proposed NN based NARMA-L2 is found to overcome the control problems due to input multiplicities.

ACKNOWLEDGEMENT Authors are grateful to TEQIP-II project of MHRD, Govt . of Indi a for financial support.

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D.B.Anuradha, G.Prabhaker Reddy*, J.S.N.Murthy, Direct Inverse Neural Network Control of A Continuous Stirred Tank Reactor, Proc. IMECS, .2, Hong Kong 2009, 236-241.

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