Design and Implementation of Decentralized Pi Controller for Pilot Plant Binary Distillation Column

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1 International Journal of ChemTech Research CODEN (USA): IJCRGG, ISSN: , ISSN(Online): Vol.1 No.1 pp , 217 Desin and Implementation of Decentralized Pi Controller for Pilot Plant Binary Distillation Column Vinayambika S. Bhat 1, I. Thirunavukkarasu 2*, S. Shanmua Priya 3 1, 2 Dept. of Instrumentation and Control Enineerin, 3 Dept. of Chemical Enineerin, Manipal Institute of Technoloy, Manipal University, Karnataka-India Abstract : The article presents a decentralized Proportional Interal (PI) controller for a pilot plant binary distillation column and discusses, the basic theory of the decentralized control technique. The Relative Gain Array (RGA) approach is used for input output pairin. The PI controller is desined based on process parameters such as time constant and time delay of the process transfer function matrix. The alorithm is compared with cross- control technique, and the performance is evaluated with Interal Square Error (ISE) and Interal Absolute Error (IAE)criteria. The simulation technique has been adopted to study the main effect and the interaction effect of the plant model for the identified distillation column. Moreover, servo and reulatory response are evaluated. Further, the simulated results are validated in real- time environment for the identified Two Input Two Output (TITO) distillation column model. Keywords : Pilot Plant, Decentralized PI Controller, Relative Gain Array, Interal Square Error, Interal Absolute Error. I. Introduction The Proportional Interal Derivative (PID) control technique is one of the commonly used control technique, which has the advantaes of simple structure, reliability, easy operation, and tunin alon with fairly ood control performance over its counterparts 1-4.It is evident from the available academic literature that more than 95% of the process industry uses thepi/pid control technique 5.The academic literature discusses several PI/PID control schemes for sinle or multi Input/Output (I/O) processes 6. The control of the Multiple Input Multiple Output (MIMO) system is challenin because of loop interaction, multiple delays,etc 7, 8. The interactive MIMO systems can be controlled either by centralized or decentralized control techniques 9.Complex structure and lack of interity are the major drawbacks of the centralized control technique 1.The decentralized PI/PID control technique is most widely used in multivariable process control industries. This is mainly due toits hardware simplicity, easy tunin, and capacity to satisfy the control objectives.however, the control structure performance is limited because of interaction between the loops 11.This is due to the existence of nonzero off diaonal elements in the process plant transfer function matrix. The academic literature hihlihts two major issues of the decentralized controller,namely, pairin problem (to identify which output should be controlled by which input) and tunin problem (to identify and tune individual controllers) 12.The reduced loop interaction can be achieved by proper pairin of manipulated and controlled variables 13.The Relative Gain Array (RGA)- based control confiuration is most commonly used for loop interaction in MIMO process industries 14. The RGA- based control technique uses steady state ain of the system to identify the interaction effects in the MIMO system 1. Thus, the current research adopts the RGA approach to interpret the interaction

2 I. Thirunavukkarasu et al /International Journal of ChemTech Research, 217,1(1): effect of the pilot plant distillation column. Further, in the present work, the PI controller is desined based on process parameters (T and τ) alon with the tunin parameters, δ 1 and δ 2. The Distillation Process is one of themost commonly used separation technique in the process industry 15, 16. Effective control of the distillation process is necessary to reduce enery consumption in the process control industry 17, 18. The article presents adecentralized PI control technique for effective control of the identified distillation column transfer function matrix 19.The closed loop responses of the distillation column model for both, setpointchane and load disturbance, are noted. Further, the result is compared with thecrosscontrol scheme. The ISE and IAE values are listed to check the performance ability of both the control techniques. The rest of the article is structured as follows: Section 2 briefly discusses the experimental setup of the pilot plant binary distillation column; the decentralized control scheme is discussed in section 3; andin section 4, the cross- controller alorithm iscompared with the decentralized control technique. The simulation and experimental result verification are discussed in section 5, followed by concludin remarks. II. Brief Discussion on Experimental Setup The objective of the distillation column is to separate the mixture of two or more components either by the application of heat or by the removal of heat 2, 21. The application of the distillation column is found in many fields such as industrial distillation, azeotropic distillation, food processin,etc 22. The laboratory setup of apilot plant binary distillation column used to separate isopropyl alcohol and water is shown in Fi (1). In the present setup, the reboiler is connected to the bottom of the column for the necessary separation. The condenser, connected at the top of the column, is usedto condensate the vapour. Later, the condensated vapour liquid is stored in the reflux drum. Both, there boiler and the condenser, act as heat exchaner. The DAQ card is used to acquire the temperature of the tray usin MATLAB@215 Simulink environment. The temperature at tray 3-T 3 (near the bottom of the column) reads hiher temperature than the temperature at tray 6-T 6 (near the top of the column). The reboiler power rate and reflux flow rate are the two manipulated variables, whereas T 3 and T 6 are the two controlled variables in the present research work. The reboiler power rate is controlled with the help of Solid State Relay (SSR), and the reflux flow rate is controlled usin theperistaltic pump connected atthe top of the column. Fi. 1. Laboratory setup of binary distillation column

3 I. Thirunavukkarasu et al /International Journal of ChemTech Research, 217,1(1): III. Decentralized Pi Controller Consider the decentralized control structure of the TITO system as shown in Fi (2), where the process to be controlled has two inputs - u 1 and u 2, and two output variables y 1 andy 2. The process transfer function matrix is iven in Eq. (1). y( s) G ( s) u( s) (1) Where, p y(s)=[y 1 (s), y 2 (s)] T and u(s)=[u 1 (s), u 2 (s)] T Fi. 2.Decentralised control structure for TITO system G p (s) is the transfer function matrix of the process in Eq. (2). p11 p12 G p( s) (2) p21 p22 Where, the transfer function is in the First Order Plus Time Delay (FOPTD)form. The RGA technique is wellestablished for the desin of MIMO control systems. In this technique, multivariable process interactions are reduced by pairin correct controlled and manipulated variables. This process of precise pairin also results in ood performance and stability marins. Thus, the RGA approach will select the control loop pairin with minimum interaction 23, 24. The RGA is determined by steady state ain matrix of the plant transfer function, which is shown in Eq. (3). Thus, the present work employs RGA techniqueto interpret the interaction effects. i.e., RGA G ( )* ( ( )) T p s Gp s (3) In eneral, the decentralized controller matrix structure is iven by Eq. (4). c11 Gc () s (4) c22 1 In Eq. (4), c11 and c22 is desined based on the process parameters of p11 and p11, respectively. δ 1 and δ 2 are the tunin parameters 23. The recommended rane of δ 1 and δ 2 are in the rane of -2. Thus, in PI controller and τ I =δ 2 τ, here, T and τ are time constants and time delay of the respective plant transfer function in the transfer function matrix form of the TITO system.

4 I. Thirunavukkarasu et al /International Journal of ChemTech Research, 217,1(1): IV. Cross- Controller It is difficult to attain satisfactory control performance of the interactions between the variables in themimo system. But, such cases can be effectively handled by imposin a decoupled network in order to cancel the interaction effect in the process. This would results as a sinle loop control system. Thus, an additional controller is introduced alon with the PI decentralized controllers to compensate for any interactions. In a MIMO system, controller variables relatin to the manipulated variables throuh the diaonal matrix is called a decoupled system. Thus, the controller added to the decentralized control confiuration is called cross- controller/ decoupler 23.The cross- controllerstructure for TITO system is shown in Fi(3). Fi. 3.Cross- control structure for TITO system The TITO plant structure as iven in Eq. (2) is considered here by inorin the time delay. In Fi (3), the controller and decoupler structure for the system is as shown in Eq. (5) and Eq. (6). c11 c 12 G c( s) (5) c21 c22 v1 G v( s) (6) v2 Thus, the controller structure of the cross- controller to yield a completely decoupled system is iven by Eq. (7). G ( s) G G G (7) dc p v c The interaction effect is eliminated by puttin off-diaonal elements to zero in Eq. (7)and the same is shown in Eq. (8). dc11 G dc( s) (8) dc22 Where, dc 11 ( s) p11v1c11 p12v2c21(9) s (1) dc22 ( ) p21 v1 c12 p22 v2 c22 Further, c12 (s) and c21 (s) obtained from Eq. (7)by puttin off- diaonal elements to zero, is iven by Eqs. (11) and (12), respectively. p12v2c22 c 12 ( s) (11) p11 v1

5 I. Thirunavukkarasu et al /International Journal of ChemTech Research, 217,1(1): p21 v1 c11 c21 ( s) (12) p22v2 Where v1 = v2 =1, c11 =k 1, and c22 =k 2 is of the PI control structure,and desined as discussed in section 3. V. Simulation and Experimental Validation The distillation column model presented 19 is considered here to desin a decentralized PI control alorithm. The TITO distillation column plant transfer function matrix is iven byeq. (13)..1s 1.19s.16e.6e G ( ).1s 1.5s 1 p s.1s. 47s (13).4e.49e.2s 1.19s 1 The steady state ain matrix of Eq. (13) is iven by.16.6 G p (s ) (14).4.49 The RGA of Eq. (14) is obtained usin Eq. (3) as shown in Eq. (15) RGA (15) This implies that the diaonal controller effect is more in comparison with the off-diaonal controller. The most commonly used decentralized control structure, iven in Eq. (4), is utilized in the present research. δ 1 =.1 and δ 2 =1.5 alon with process parameters such as time delay and time constant lead to controller value c11. Further, the tunin value of δ 1 =1 and δ 2 =1.6alon with process parameters represent controller value c22.i.e to find c11 (s):.1 k 1 T p.1.1,.1 k p and I , i.e, ki.1/ Similarly, to find c22 (s): k 1 T p 1. 4,.47 kp and I i.e, k.4/ Thus, the decentralized PI controller for Eq. (13) is iven by Eq. (16) G s c ( s) (16) s The controller desin based on cross- control technique is iven by G dc k ( s) s.133s s.1s.12s 1 I I I (17) 2 k2.21s.41s s.138s.192s 1

6 I. Thirunavukkarasu et al /International Journal of ChemTech Research, 217,1(1): Where, k 1 and k 2 are desined similar to the decentralized PI control technique, iven in Eq. (16) without the neative sin. i.e to find k 1 :.1 k 1 T p.1.1,.1 k p and I , i.e, ki.1/ Similarly, to find k 2 : k 1 T p 1. 4,.47 kp and I i.e, ki.4/ I Thus, in Eq. (17), k1.1 and k2.4. s s I Good performance and stable response is achieved by proper tunin of the controller. The controller desined in the present work ives satisfactory closed loop response for set point chane and load disturbance. The dynamic performance criteria such IAE and ISE are evaluated to verify the performance of the desined controller 4. Further, IAE and ISE are based on the process response. The ISE is used to suppress small errors, whereas IAE is used to suppress larer errors 22.Table 1 summarizes the performance analysis of both the controllersused in the current research work. Moreover, from Table 1, it is evident that the decentralized controller ives asinificantly stable response with less IAE and ISE values. Table 1. Performance analysis Type Decentralized IAE Main effect Interaction effect y 11 y 22 y 12 y PI ISE Cross controller IAE ISE Both controller techniques attain closed loop stable responses in closed loop simulation. Further, the decentralized PI closed loop response is fast with less settlin time as shown in Fis (4) and (5). The Fis (6) and (7) represent the closed loop simulation response of decentralized and cross- control technique, considerin tray temperature as setpoint. The decentralized PI and cross- controller is implemented on a pilot plant distillation column, and its response is shown in Fi (8) and Fi (9) respectively.

7 Process output Process Output I. Thirunavukkarasu et al /International Journal of ChemTech Research, 217,1(1): Decentralized-y11 Decentralized-y21 Cross-controller-y11 Cross-controller-y Time (secs) Fi. 4. Closed loop response for setpoint chane and load disturbance with SP-y 1 =.8 and SP-y 2 = Decentralized-y12 Decentralized-y22 Cross-controller-y12 Cross-controller-y Time (secs) Fi. 5. Closed loop response for setpoint chane and load disturbance with SP-y 1 = and SP-y 2 =1

8 Process Output Process Output I. Thirunavukkarasu et al /International Journal of ChemTech Research, 217,1(1): T6 T3 SP-T6 SP-T Time (secs) Fi. 6. Closed loop simulation response for decentralized control technique with SP-y 1 =68 and SP-y 2 = T6 T3 SP-T6 SP-T Time (seconds) Fi.7. Closed loop simulation response for cross- control technique with SP-y 1 =71and SP-y 2 =76

9 Tray Temperature (De. Cel) Tray Temperature (De. Cel.) I. Thirunavukkarasu et al /International Journal of ChemTech Research, 217,1(1): Closed loop response of Decentralized Controller based on RGA T3 T6 SP-T6 Reflux Heater SP-T Samplin Instants x 1 5 Fi.8. Implementation of decentralized PI controller on pilot plant binary distillation column for the setpoint trackin of 68 De. Cel for Tray-T 6 and 73 De. Cel for Tray-T 3 1 Closed loop response of Cross Controller T3 T6 SP-T6 SP-T3 Reflux Heater Samplin Instants x 1 5 Fi.9. Implementation of cross controller on pilot plant binary distillation column for the setpoint trackin of 71 De. Cel for Tray-T 6 and 76 De. Cel for Tray-T 3 VI. Conclusions The article presents a decentralized PI control technique for a pilot plant distillation column transfer function matrix. The control structure confiuration is identified throuh the RGA approach. The results show that, the RGA value sinified the 1-1 and 2-2 pairin of the manipulated and controlled variables. Also, the closed loop responsesettles fast,in the presence of load disturbance. The IAE and ISE values were used to

10 I. Thirunavukkarasu et al /International Journal of ChemTech Research, 217,1(1): validate the performance effect of the Decentralized and Cross-controller techniques. The results of this comparison depict that, the decentralized PI control technique results in sinificantly improved performance.further, durinresearch work it was observed that sinificantly improved response is achievedwith both the control techniques. In addition, the simulation responses of the decentralized PI control technique on a pilot plant binary distillation column were validated throuh real-time experimental results. Acknowledment Vinayambika S. Bhat would like to acknowlede the Manalore Institute of Technoloy and Enineerin (MITE), Moodabidri, for sponsorin her Ph.D. proramme. Also, the authors would like to thank the Department of Chemical Enineerin, Manipal Institute of Technoloy, Manipal University, for permittin to use their Distillation Column and supportin accessories to carry out the research work. Nomenclatures and Abbreviations δ 1, δ 2 T 3 T 6 k c τ I T τ PI RGA ISE IAE TITO I/O PID : Tunin parameters : Temperature of Tray-3, near the bottom of the column in Deree Celsius : Temperature of Tray-6, near the top of the column in Deree Celsius : Proportional ain : Interal ain : Time constant in hours : Time delay in hours : Proportional-Interal : Relative Gain Array : Interal Square Error : Interal Absolute Error : Two Input Two Output : Input/Output : Proportional-Interal-Derivative MIMO : Multi Input Multi Output DAQ SSR SP : Data AcQuisition : Solid State Relay : Setpoint References 1. Mahade D. K. and Patre B. M., Decentralized PI/PID controllers based on ain and phase marin specifications for TITO processes, ISA Transactions, 212, 51(4), Malaisamy S., Srinivasan A., Mohamed M. R. and Manimaran M., Power Optimization and Temperature Control in Solar Powered Automated Dryer usin Fuzzy Controller, International Journal of ChemTech Research, 216, 9(5), Kandasamy M., Vijayachitra S. and Saravanan K., Heuristic Alorithm Based Controller Optimization for a Real Time ph Neutralization Process System, International Journal of ChemTech Research, 215, 7(5), Govindarasu R., Parthiban R. and Bhaba P. K., Studies on Implementation of PI Control Techniques in Direct Methanol Fuel Cell, International Journal of ChemTech Research, 214, 6(9), Lenare M. J., Chile R. H. and Wahmare L. M., Desin of decentralized controllers for MIMO processes, Computers and Electrical Enineerin, 212, 38(1), Anil Ch. and Padma Sree R., Tunin of PID controllers for interatin systems usin direct synthesis method, ISA Transactions, 215, 57,

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