Fuzzy-logic control of dynamic systems: from modeling to design M. Reza Emami*, Andrew A. Goldenberg, I. Burhan TuÈrksen Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ont., Canada M5S 3G8 Received 1 September 1998; accepted 1 June 1999 Abstract A systematic methodology for the synthesis and analysis of fuzzy±logic controllers for multi-input multi-output nonlinear dynamic systems is proposed in this paper. A robust model-based control structure is suggested that includes the fuzzy±logic dynamics model of the system and several robust fuzzy control rules. The fuzzy±logic model is systematically constructed from the input-output data, and the robust control rules are designed using the sliding-mode control theory. The stability and completeness of the control structure is guaranteed, based on a generalized formulation of the sliding-mode control developed in this paper. The proposed fuzzy±logic control scheme has been applied to trajectory control of a four-degree-of-freedom robot manipulator, and was compared with high-gain PID controllers. Superior tracking performance was achieved. # 2000 Elsevier Science Ltd. All rights reserved. Keywords: Variable structure systems; Sliding-mode control; Fuzzy-logic control; Robust control; Fuzzy systems; Robot manipulators 1. Introduction The major part of the research on fuzzy±logic con- trol (FLC) has focused on practical implementations, and successful results have been reported in a wide range applications. Despite the diversity of the approaches used in the development of fuzzy control- lers, most of them are designed based on `trial and error'. Although this could be eective in some cases, it limits the rise of systematic approaches fuzzy±logic control. One route to the systematic synthesis and analysis of the fuzzy±logic systems is to consider the FLC as a particular class of nonlinear systems, and to apply tools taken from the classical nonlinear control sys- tems theory. A promising approach in this direction is based on the fact that the FLC is a variable structure system (VSS). Variable structure control systems con- stitute a class of nonlinear feedback control systems whose structure varies, depending on the state of the system. Recently, new eorts have been made to inves- tigate the connection between fuzzy±logic and variable structure control (Kawaji and Matsunaga, 1991; Ghalia and Alouani, 1995; Wu and Liu, 1996). Based on the analysis of these two control approaches, it was concluded that, due to the partitioning of the input- output space, the FLC is a qualitative extension of the sliding-mode control. Some guidelines were speci®ed for deriving the fuzzy IF-THEN control rules, and for analyzing the stability and robustness of the fuzzy± logic control, based on the variable structure system theory (Palm, 1992), an approach that can be referred to as `fuzzy sliding-mode control'. However, in the above-mentioned eorts, only single-input single-out- put systems are considered. For multi-input multi-out- put (MIMO) nonlinear systems, due to the state interactions, more information from the system is required, leading to a model-based fuzzy±logic control approach that is the focus of this paper. A few researchers have attempted to apply the fuzzy sliding mode control approach to robot manipulators (Chen et al., 1994; Tsay and Huang, 1994; Begon et al., 1995). Despite successful results, the lack of a sys- tematic approach to the design and analysis of FLC, Engineering Applications of Arti®cial Intelligence 13 (2000) 47±69 0952-1976/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved. PII: S0952-1976(99)00031-7 www.elsevier.com/locate/engappai * Corresponding author. Tel.: +1-416-946-3357; fax: +1-416-978- 7753. E-mail address: emami@mie.utoronto.ca (M.R. Emami).