Complexity reduction of explicit MPC based on fuzzy reshaped polyhedrons for use in industrial controllers

Abstract

The explicit model predictive control (EMPC) generates the rules of control defined for a set of polyhedral regions. Online EMPC calculations consist of searching a look-up table to find the appropriate control law according to a particular state. This paper discusses the complexity of online computation and the memory required to store data in an EMPC implementation. Therefore, a new reshaping method is applied to the active regions so that the definition of the polyhedron has regular boundaries. This approach has made some improvements. First, the usable memory will be a lot less for the actual implementation compared to the traditional EMPC approach. Second, the small number of new clusters reduces search time in explicit lookup tables and speeds up overall implementation. To this end, fuzzy clustering is used to introduce a novel method of transforming polyhedrons in the context of fuzzy explicit model predictive (FEMPC) control, followed by a new fuzzy-based piece-wise affine (PWA) explicit formulation for control law calculations. The stability of the proposed method is investigated using the Lyapunov stability criteria. The proposed algorithm has been tested on a nonlinear continuous stirred tank reactor (CSTR) benchmark system and simulation tests show that the proposed approach involves a compromise between storage space requirements and online efficiency.

KEYWORDS:

• Explicit model predictive control (EMPC)
• multi-parametric programming
• complexity reduction
• polyhedrons
• fuzzy explicit MPC (FEMPC)

Data availability statement

The data used to support the findings of this study are available from the corresponding author upon request.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Nematollah Changizi

Nematollah Changizi received an M.S. degree in Control Engineering from IAU, Gonabad Branch, Iran in 2011. Currently, he is a Ph.D. student of Control Engineering at IAU, Science and Research Branch, Tehran, Iran. He has published over 12 papers in peer-reviewed journals and international conferences. He has two national inventions and the second rank of scientific articles in Khorasan Razavi province, Iran, and has also been introduced as a superior professor in Alborz province, Iran. He is also active in the instrumentation and automation of industrial projects. His research interests include the implementation of control strategies in industrial processes and instrumentation.

Karim Salahshoor

Karim Salahshoor received the M.S. and Ph.D. degree in Control Engineering from UMIST at Manchester, England. He is a Professor in the Department of Instrumentation and Automation, Petroleum University of Technology (PUT), Ahvaz, Iran. His research interests include system identification, fault-tolerant control, and industrial process control.

Mehdi Siahi

Mehdi Siahi received the B.Sc. degree in Electrical Engineering from Yazd University, Yazd, Iran in 2001 and M.Sc. degree in Control Engineering from the Shahrood University of Technology, Shahrood, Iran, in 2003. He obtained the Ph.D. degree in Control Engineering from Shahrood University of Technology, Shahrood IRAN, in 2008. He is now an associate Professor and has been with Faculty of Electrical Engineering, Islamic Azad University, Iran from 2004. His current research is on Fault Tolerant Control Systems, Robust Control and Nonlinear Systems.