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International Journal of ChemTech Research CODEN (USA): IJCRGG, ISSN: 0974-4290, ISSN(Online):2455-9555 Vol.10 No.1 pp 284-294, 2017
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Design and Implementation of Decentralized Pi Controller for Pilot Plant Binary Distillation Column
Vinayambika S. Bhat1, I. Thirunavukkarasu2*, S. Shanmuga Priya3
1, 2 Dept. of Instrumentation and Control Engineering,
3 Dept. of Chemical Engineering, Manipal Institute of Technology, Manipal University,
Karnataka-India
Abstract : The article presents a decentralized Proportional Integral (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 pairing. The PI controller is designed based on process parameters such as time constant and time delay of the process transfer function matrix. The algorithm is compared with cross- control technique, and the performance is evaluated with Integral Square Error (ISE) and Integral 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 regulatory 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, Integral Square Error, Integral Absolute Error.
The Proportional Integral Derivative (PID) control technique is one of the commonly used control technique, which has the advantages of simple structure, reliability, easy operation, and tuning along with fairly good control performance over its counterparts1-4.It is evident from the available academic literature that more than 95% of the process industry uses thePI/PID control technique5.The academic literature discusses several PI/PID control schemes for single or multi Input/Output (I/O) processes6. The control of the Multiple Input Multiple Output (MIMO) system is challenging because of loop interaction, multiple delays,etc7, 8. The interactive MIMO systems can be controlled either by centralized or decentralized control techniques9.Complex structure and lack of integrity are the major drawbacks of the centralized control technique10.The decentralized PI/PID control technique is most widely used in multivariable process control industries. This is mainly due toits hardware simplicity, easy tuning, and capacity to satisfy the control objectives.However, the control structure performance is limited because of interaction between the loops11.This is due to the existence of non-zero off diagonal elements in the process plant transfer function matrix. The academic literature highlights two major issues of the decentralized controller,namely, pairing problem (to identify which output should be controlled by which input) and tuning problem (to identify and tune individual controllers)12.The reduced loop interaction can be achieved by proper pairing of manipulated and controlled variables13.The Relative Gain Array (RGA)- based control configuration is most commonly used for loop interaction in MIMO process industries14. The RGA- based control technique uses steady state gain of the system to identify the interaction effects in the MIMO system10. Thus, the current research adopts the RGA approach to interpret the interaction
effect of the pilot plant distillation column. Further, in the present work, the PI controller is designed based on process parameters (T and τ) along with the tuning parameters, δ1 and δ2.
The ‘Distillation Process’ is one of themost commonly used separation technique in the process industry15, 16. Effective control of the distillation process is necessary to reduce energy consumption in the process control industry17, 18. The article presents adecentralized PI control technique for effective control of the identified distillation column transfer function matrix19.The closed loop responses of the distillation column model for both, setpointchange and load disturbance, are noted. Further, the result is compared with thecross- control 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 algorithm iscompared with the decentralized control technique. The simulation and experimental result verification are discussed in section 5, followed by concluding remarks.
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 heat20, 21. The application of the distillation column is found in many fields such as industrial distillation, azeotropic distillation, food processing,etc22. The laboratory setup of apilot plant binary distillation column used to separate isopropyl alcohol and water is shown in Fig (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 exchanger. The DAQ card is used to acquire the temperature of the tray using MATLAB@2015 Simulink environment. The temperature at tray 3-T3 (near the bottom of the column) reads higher temperature than the temperature at tray 6-T6 (near the top of the column). The reboiler power rate and reflux flow rate are the two manipulated variables, whereas T3 and T6 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 using theperistaltic pump connected atthe top of the column.
Fig. 1. Laboratory setup of binary distillation column
Consider the decentralized control structure of the TITO system as shown in Fig (2), where the process to be controlled has two inputs - u1 and u2, and two output variables –y1 andy2. The process transfer function matrix is given in Eq. (1).
(1)
Where, y(s)=[y1(s), y2(s)]T and u(s)=[u1(s), u2(s)]T
Fig. 2.Decentralised control structure for TITO system
Gp(s) is the transfer function matrix of the process in Eq. (2).
(2)
Where, the transfer function is in the First Order Plus Time Delay (FOPTD)form. The RGA technique is well- established for the design of MIMO control systems. In this technique, multivariable process interactions are reduced by pairing correct controlled and manipulated variables. This process of precise pairing also results in good performance and stability margins. Thus, the RGA approach will select the control loop pairing with minimum interaction23, 24. The RGA is determined by steady state gain 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.,(3)
In general, the decentralized controller matrix structure is given by Eq. (4).
(4)
In Eq. (4),gc11 and gc22 is designed based on the process parameters of gp11 and gp11,respectively. δ1 and δ2 are the tuning parameters23. The recommended range of δ1 and δ2 are in the range of 0-2. Thus, in PI controller ⁄ and τI=δ2τ, 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.
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 imposing a decoupled network in order to cancel the interaction effect in the process. This would results as a single loop control system. Thus, an additional controller is introduced along with the PI decentralized controllers to compensate for any interactions. In a MIMO system, controller variables relating to the manipulated variables through the diagonal matrix is called a decoupled system. Thus, the controller added to the decentralized control configuration is called cross- controller/ decoupler23.The cross- controllerstructure for TITO system is shown in Fig(3).
Fig. 3.Cross- control structure for TITO system
The TITO plant structure as given in Eq. (2) is considered here by ignoring the time delay. In Fig (3), the controller and decoupler structure for the system is as shown in Eq. (5) and Eq. (6).
(5)
(6)
Thus, the controller structure of the cross- controller to yield a completely decoupled system is given by Eq. (7).
(7)
The interaction effect is eliminated by putting off-diagonal elements to zero in Eq. (7)and the same is shown in Eq. (8).
(8)
Where, (9)
(10)
Further, gc12(s) and gc21(s) obtained from Eq. (7)by putting off- diagonal elements to zero, is given by Eqs. (11) and (12), respectively.
(11)
(12)
Where gv1=gv2=1, gc11=k1, and gc22=k2 is of the PI control structure,and designed as discussed in section 3.
The distillation column model presented19 is considered here to design a decentralized PI control algorithm. The TITO distillation column plant transfer function matrix is given byEq. (13).
(13)
The steady state gain matrix of Eq. (13) is given by
(14)
The RGA of Eq. (14) is obtained using Eq. (3) as shown in Eq. (15).
(15)
This implies that the diagonal controller effect is more in comparison with the off-diagonal controller. The most commonly used decentralized control structure, given in Eq. (4), is utilized in the present research. δ1=0.1 and δ2=1.5 along with process parameters such as time delay and time constant lead to controller valuegc11. Further, the tuning value of δ1=1 and δ2=1.6along with process parameters represent controller value gc22.i.e to find gc11(s):
,
and , i.e,
Similarly, to find gc22(s): ,
andi.e,
Thus, the decentralized PI controller for Eq. (13) is given by Eq. (16).
(16)
The controller design based on cross- control technique is given by
(17)
Where, k1 and k2 are designed similar to the decentralized PI control technique, given in Eq. (16) without the negative sign.
i.e to find k1:
,
and , i.e,
Similarly, to find k2: ,
andi.e,
Thus, in Eq. (17), and .
Good performance and stable response is achieved by proper tuning of the controller. The controller designed in the present work gives satisfactory closed loop response for set point change and load disturbance. The dynamic performance criteria such IAE and ISE are evaluated to verify the performance of the designed controller4. Further, IAE and ISE are based on the process response. The ISE is used to suppress small errors, whereas IAE is used to suppress larger errors22.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 gives asignificantly stable response with less IAE and ISE values.
Table 1. Performance analysis
Type |
Main effect |
Interaction effect |
||||
y11 |
y22 |
y12 |
y21 |
|||
PI |
Decentralized |
IAE |
1.166 |
5.741 |
1.745 |
1.302 |
ISE |
0.3187 |
2.508 |
0.2102 |
0.08803 |
||
Cross controller |
IAE |
5.463 |
10.48 |
8.187 |
2.383 |
|
ISE |
1.67 |
4.604 |
1.93 |
0.1323 |
Both controller techniques attain closed loop stable responses in closed loop simulation. Further, the decentralized PI closed loop response is fast with less settling time as shown in Figs (4) and (5). The Figs (6) and (7) represent the closed loop simulation response of decentralized and cross- control technique, considering tray temperature as setpoint. The decentralized PI and cross- controller is implemented on a pilot plant distillation column, and its response is shown in Fig (8) and Fig (9) respectively.
Fig. 4. Closed loop response for setpoint change and load disturbance with SP-y1=0.8 and SP-y2=0
Fig. 5. Closed loop response for setpoint change and load disturbance with SP-y1=0 and SP-y2=1
Fig. 6. Closed loop simulation response for decentralized control technique with SP-y1=68 and SP-y2=73
Fig.7. Closed loop simulation response for cross- control technique with SP-y1=71and SP-y2=76
Fig.8. Implementation of decentralized PI controller on pilot plant binary distillation column for the setpoint tracking of 68 Deg. Cel for Tray-T6 and 73 Deg. Cel for Tray-T3
Fig.9. Implementation of cross controller on pilot plant binary distillation column for the setpoint tracking of 71 Deg. Cel for Tray-T6 and 76 Deg. Cel for Tray-T3
The article presents a decentralized PI control technique for a pilot plant distillation column transfer function matrix. The control structure configuration is identified through the RGA approach. The results show that, the RGA value signified the 1-1 and 2-2 pairing 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
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 significantly improved performance.Further, duringresearch work it was observed that significantly 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 through real-time experimental results.
Acknowledgment
Vinayambika S. Bhat would like to acknowledge the Mangalore Institute of Technology and Engineering (MITE), Moodabidri, for sponsoring her Ph.D. programme. Also, the authors would like to thank the Department of Chemical Engineering, Manipal Institute of Technology, Manipal University, for permitting to use their Distillation Column and supporting accessories to carry out the research work.
Nomenclatures and Abbreviations
δ1, δ2 |
: |
Tuning parameters |
T3 |
: |
Temperature of Tray-3, near the bottom of the column in Degree Celsius |
T6 |
: |
Temperature of Tray-6, near the top of the column in Degree Celsius |
kc |
: |
Proportional gain |
τI |
: |
Integral gain |
T |
: |
Time constant in hours |
τ |
: |
Time delay in hours |
PI |
: |
Proportional-Integral |
RGA |
: |
Relative Gain Array |
ISE |
: |
Integral Square Error |
IAE |
: |
Integral Absolute Error |
TITO |
: |
Two Input Two Output |
I/O |
: |
Input/Output |
PID |
: |
Proportional-Integral-Derivative |
MIMO |
: |
Multi Input Multi Output |
DAQ |
: |
Data AcQuisition |
SSR |
: |
Solid State Relay |
SP |
: |
Setpoint |
References
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