In this paper, an adaptive swarm learning process (SLP) algorithm for designing the optimal proportional integral and derivative (PID) parameter for a multiple-input multiple-output (MIMO) control system is proposed. The SLP algorithm is proposed to improve the performance and convergence of PID parameter autotuning by applying the swarm algorithm and the learning process. The adaptive SLP algorithm improves the stability, performance and robustness of the traditional SLP algorithm to apply it to a MIMO control system. It can update the online weights of the SLP algorithm caused by the errors in the settling time, rise time and overshoot of the system based on a stable learning rate. The gradient descent is applied to update the weights. The stable learning rate is verified based on the Lyapunov stability theorem. Additionally, simulations are performed to verify the superiority of the algorithm in terms of performance and robustness. Results that compare the adaptive SLP algorithm with the traditional SLP, a neural network (NN), the genetic algorithm (GA), the particle swarm and optimization (PSO) algorithm and the kidney-inspired algorithm (KIA) based on a two-wheel inverted pendulum system are presented. With respect to performance and robustness, the adaptive SLP algorithm provides a better response than the traditional SLP, NN, GA, PSO and KIA.
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The authors thank the Petchra Pra Jom Klao scholarship and the Department of Electronic and Telecommunication Engineering, Faculty of Engineering at King Mongkut’s University of Technology Thonburi, for the funding of this research.
Jirapun Pongfai received her bachelor of engineering degree in computer engineering from Naresuan University (NU), Pitsanulok, Thailand, in 2015 and a master of engineering degree in electrical and information Engineering from King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, Thailand, in 2017. Her research interests are intelligence control, optimal and predictive controller design and artifitial intelligence and embedded system design.
Chrissanthi Angeli received her master of science degree in intelligent systems from the University of Plymouth and a D.Phil. in intelligent fault detection techniques from the University of Sussex. Currently she is a professor at the Technological Education Institute of Piraeus. Her current research interests include real-time expert systems, web-based expert systems and artificial intelligence techniques for fault detection.
Peng Shi received his Ph.D. degree in electrical engineering from the University of Newcastle, Australia; a Ph.D. degree in mathematics from the University of South Australia. He was awarded a Doctor of Science degree from the University of Glamorgan, UK in 2006, and a Doctor of Engineering degree from the University of Adelaide in 2015. He is now a professor at the University of Adelaide, and Victoria University, Australia. He was a professor at the University of Glamorgan, UK; and a senior scientist in the Defence Science and Technology Organisation, Australia. His research interests include system and control theory, computational intelligence, and operational research. He has actively served in the editorial board of a number of journals, including Automatica, IEEE Transactions on Automatic Control; IEEE Transactions on Fuzzy Systems; IEEE Transactions on Cybernetics; IEEE Transactions on Circuits and Systems-I: Regular Papers; and IEEE Access. He is a Fellow of the Institution of Engineering and Technology, and the Institute of Mathematics and its Applications. He was the Chair of Control Aerospace and Electronic Systems Chapter, IEEE South Australia Section. Currently he serves as an IEEE Distinguished Lecturer, and a Member of Australian Research Council, College of Expert.
Xiaojie Su received his bachelor’s degree from Jiamusi University, China, in 2008; a master’s degree from Harbin Institute of Technology, China, in 2010 and a Ph.D. from Harbin Institute of Technology, China, in 2013. Currently, he is a professor at the College of Automation, Chongqing, China. His research interests are in fuzzy systems, optimal filtering, optimal controller design, and model reduction. He serves as an associate editoe for IEEE Access, Information Sciences, Signal Processing, IET Electronic Letter, Neurocomputing, Asia Journal of Control, and International Journal of Control, Automation, and System. Additionally, he is an associate editor for conference editorial board, IEEE Control System Society.
Wudhichai Assawinchaichote received his B.S. degree with honor in electrical engineering from Assumption University, Bangkok, Thailand, in 1994; an M.E. degree in electrical engineering from Pennsylvania State University (Main Campus), PA, USA, in 1997; and a Ph.D. degree in electrical engineering from the University of Auckland, New Zealand, in 2004. Currently, he is an Associate Professor at the department of Electronic and Telecommunication Engineering, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, Thailand. He has published a research monograph and more than 20 research papers in international refereed journals indexed by SCI/ESCI (Clarivate Analytics). His current research interests include fuzzy control, robust control, optimal control, system and control theory, computational intelligence, and PID controller design. He currently serves as an Associate Editor for a number of journals and also serve as a reviewer, including Automatica; IEEE Transactions on Industrial Electronics; IEEE Transactions on Fuzzy Systems; IEEE Transactions on Cybernetics; IEEE Transactions on Systems, Man and Cybernetics: Systems; Neural Computing and Applications; and IEEE Access.
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Pongfai, J., Angeli, C., Shi, P. et al. Optimal PID Controller Autotuning Design for MIMO Nonlinear Systems Based on the Adaptive SLP Algorithm. Int. J. Control Autom. Syst. 19, 392–403 (2021). https://doi.org/10.1007/s12555-019-0680-6
- inverted pendulum
- learning algorithm
- multiple-input/multiple-output (MIMO)
- optimal control
- PID controller
- swarm algorithm