Wednesday , June 20 2018

Tuning of Multivariable Decentralized
PID Controller Using State Transition Algorithm


1 Department of Instrumentation and control Engineering,
Kalasalingam University, Krishnankoil, Tamilnadu, India;;
2 Department of Electronics and Communication Engineering,
PSR Engineering College, Sivakasi, India

3 Department of Electrical and Electronic Engineering,
National Engineering College, Kovilpatti, India
4 Department of Automation and Applied Informatics,
“Aurel Vlaicu” University of Arad, Romania

Abstract: Implementation of State Transition Algorithm (STA) for the tuning of multivariable Proportional Integral Derivative (PID) controller is reported. Two input and two output binary distillation column plant model by Wood and Berry is considered as a benchmark. Simulations are performed for three cases such as multivariable PID controller with decoupler, without decoupler and multivariable PI controller without decoupler. Integral of Time weighted Absolute Error (ITAE) and Integral of Absolute Error (IAE) are chosen as objective functions for the first case while Integral of Absolute Error alone is chosen for remaining couple of cases. Simulations are carried out for 20 independent trials by STA and STA with SBX crossover. Comparison of fitness value and time domain parameters for three cases against PBPSO is reported. Statistical performance measures of STA and STA-SBX algorithms are presented and simulation result implies that STA is a potential algorithm which provides better fitness for all the three cases and has global search capability. SBX crossover is enhanced by the consistency of the algorithm.

Keywords:  Multivariable PID Controller Tuning, State Transition Algorithm, Distillation column, MIMO process.

>>Full text>>
G. SARAVANAKUMAR, K. VALARMATHI, M. PALLIKONDA RAJASEKARAN, Seshadhri SRINIVASAN, M. WILLJUICE IRUTHAYARAJAN, Valentina E. BALAS, Tuning of Multivariable DecentralizedPID Controller Using State Transition Algorithm, Studies in Informatics and Control, ISSN 1220-1766, vol. 24 (4), pp. 367-378, 2015.


Proportional Integral Derivative controller is one of the simplest and most commonly used ones in various industries for control applications. Despite significant advancements in control technology, over 80% of industrial control loops are incorporated with PID controller. Though it is widely accepted, it should be properly tuned to meet desired behavior. Extensive work of Ziegler and Nichols [1] is the breakthrough in tuning methodology and Cohen Coon, Lambda tuning, and Chen Hrown Reswick (CHR) methods are a few of the other tuning methods reported in the literature [2]. Existing tuning methods are classified [3] based on nature and usage as analytical methods, Heuristic method, Frequency response method, Optimization method and Adaptive tuning methods. Among those, optimization method is widely utilized around the globe as it is conceptually simple and widely accepted one for tuning PID controller [2]. In this method, controller parameters are adjusted based on the chosen objective function chiefly integral performance measures. A classical optimization technique namely gradient method is often used to find optimal values. The shortcoming of gradient descent methods is sensitivity to the selection of initial values and their tendency to lock into a local extreme point [4]. Evolutionary Computation techniques are proposed to tune the PID controller by taking all non-linearity and additional process characteristics into account [5], [6]. Genetic Algorithm (GA) has the capability to solve nonlinear and complex optimization problems [7]. Porter and Jones proposed a GA-based simple and generic method of tuning digital PID controller [8].

Numerous work is available in the literature related to Distillation column control strategy [9-14]. Very recently, various optimization techniques such as Covariance Matrix Adaptation Evolution Strategy (CMAES), Particle Swarm Optimization (PSO), Differential Evolution (DE), Tribes Algorithm (TA), Ant Colony Optimization (ACO), Tabu Search Algorithm (TSA) and different Binary Particle Swarm Optimization are used to tune the PID control parameters [15-19]. Modified firefly algorithm for the tuning ofmultivariable PID controller is implemented for distillation column [20].

Iruthayarajan and Baskar compared the performance of various Real Coded Genetic Algorithm (RGA), Differential Evolution (DE), Modified Particle Swarm Optimization (MPSO) and Covariance Matrix Adaptation Evolution Strategy (CMAES) in the multivariable distillation column [21]. Discrete Binary PSO (DBPSO) algorithm, Probability based discrete binary PSO (PBPSO) and Modified Discrete Binary PSO (MDBPSO) are proposed to tune multivariable PID controller for the distillation column and compared the results with the RGA, MPSO and CMAES [22].

Amongst, PBPSO provided the best optimal value for all the three cases such as multivariable PID controller with decoupler, without decoupler and multivariable PI controller without decoupler. Recently proposed State transition Algorithm (STA) is applied to different benchmark problems which has the ability to reach a global optimal solution and shown that it has good convergence property when compared with a Real coded genetic algorithm (RCGA), Complementary Learning Particle Swarm optimization (CLPSO) and Strategy adaptation Differential Evolution (SaDE) [23]. Herein, Implementation of State Transition Algorithm (STA) and STA-SBX Algorithm to tune multivariable PID controller for the distillation column is proposed and compared with already reported best results.


  1. NICHOLS, N. B., J. G. ZIEGLER, Optimum Settings for Automatic Controllers, ASME, 64, 1942.
  2. ASTROM, K., PID Controllers: Theory, Design and Tuning, 1995.
  3. ANG, K., G. CHONG, Y. LI, PID Control System Analysis and Design, Control Systems, IEEE 26, 2006, pp. 32-41.
  4. GE, H.-W., Y.-C. LIANG, M. MARCHESE, A Modified Particle Swarm Optimization-based Dynamic Recurrent Neural Network for Identifying and Controlling Nonlinear Systems, Computers & Structures, vol. 85, 2007, pp. 1611-1622.
  5. BACK, T., U. HAMMEL, H.-P. SCHWEFEL, Evolutionary Computation: Comments on the History and Current State, Evolutionary Computation, IEEE Transactions on, vol. 1, 1997, pp. 3-17.
  6. DRACOPOULOS, D. C., Evolutionary Learning Algorithms for Neural adaptive Control, Springer-Verlag New York, Inc., 1997.
  7. KROHLING, R., J. REY, Design of Optimal Disturbance Rejection PID Controllers using Genetic Algorithms, Evolutionary Computation, IEEE, vol. 5 2001, pp. 78-82.
  8. JONES, A. H., B. PORTER, Genetic Tuning of Digital PID Controllers, Electronics Letters, vol. 28, 1992, pp. 843-844.
  9. LEMAIRE, J., M. MORARI, B. OGUNNAIKE, W. RAY, Advanced Multivariable Control of a Pilot Plant Distillation Column, AIChE Journal, vol. 29, 1983, pp. 632-640.
  10. ESCOBAR, M., J. O. TRIERWEILER, Multivariable PID Controller Design for Chemical Processes by Frequency Response Approximation, Chemical Eng. Science, vol. 88, 2013, pp. 1-15.
  11. COELHO, L. D. S., M. W. PESSÔA, A Tuning Strategy for Multivariable PI and PID Controllers using Differential Evolution Combined with Chaotic Zaslavskii Map, Expert Systems with App., vol. 38, 2011, pp. 13694-13701.
  12. KIM, C., K. LEE, J. LEE, M. LEE, Analytical Design of Multiloop PID Controllers for Desired Closed-loop Responses, AIChE Journal, vol. 50, 2004, pp. 1631-1635.
  13. DORMIDO, S., F. MORILLA, F. VÁZQUEZ, An Iterative Method for Tuning Decentralized PID Controllers, Proc. 14th IFAC World, 1999.
  14. GANGULY, S., S. MAITI, N. D. SARAF, Some New Approaches for the Control of a Distillation Column and Their Experimental Evaluation on a Pilot Plant, Computers & Chemical Engineering, vol. 19, 1995, pp. 399-404.
  15. BERNERT, D. L. A., D. L. S. COELHO, L. DOS, PID Control Design for Chaotic Synchronization using a Tribes Optimization Approach, Chaos, Solitons & Fractals, vol. 42, 2009, pp. 634-640.
  16. DUAN, H., D. WANG, X. YU, Novel Approach to Nonlinear PID Parameter Optimization using Ant Colony Optimization Algorithm, J. of Bionic Engineering, vol. 3, 2006, pp. 73-78.
  17. JAN, R.-M., R.-J. LIU, C.-S. TSENG, Robust PID Control Design for Permanent Magnet Synchronous Motor: A Genetic Approach, Electric Power Systems Research, vol. 78, 2008, pp. 1161-1168.
  18. KIM, T. T.-H., I. MARUTA, T. SUGIE, Robust PID Controller Tuning Based on the Constrained Particle Swarm Optimization, Automatica, vol. 44, 2008, pp. 1104-1110.
  19. DU, H., S. WANG, J. ZHANG, J. ZHUANG, Self-organizing Genetic Algorithm based Tuning of PID Controllers, Information Sciences, vol. 179, 2009, pp. 1007-1018.
  20. COELHO, L., V. MARIANI, Firefly Algorithm Approach based on Chaotic Tinkerbell Map Applied to Multivariable PID Controller Tuning, Computers & Mathematics with Applications, vol. 64, 2012, pp. 2371-2382.
  21. BASKAR, S., M. IRUTHAYARAJAN, Evolutionary Algorithms based Design of Multivariable PID Controller, Expert Systems with Applications, vol. 36, 2009, pp. 9159-9167.
  22. FEI, M., M. I. MENHAS, H. PAN, L. WANG, Comparative Performance Analysis of Various Binary Coded PSO Algorithms in Multivariable PID Controller Design, Expert Systems with Applications, vol. 39, 2012, pp. 4390-4401.
  23. GUI, W., C. YANG, X. ZHOU, State Transition Algorithm, Journal of Industrial and Management Optimization. vol. 8, 2012, pp. 1039-1056.
  24. BERRY, M., R. WOOD, Terminal Composition Control of a Binary Distillation Column, Chemical Eng. Science, vol. 28, 1973, pp. 1707-1717.
  25. HAMZAÇEBI, C., F. KUTAY, Continuous Functions Minimization by Dynamic Random Search Technique, Applied Mathematical Modelling, vol. 31, 2007, vol. 2189-2198.
  26. DEB, K., A. KUMAR, Real-coded Genetic Algorithms with Simulated Binary Crossover: Studies on Multimodel and Multiobjective Problems, Complex Systems, vol. 9 1995, pp. 431-454.