A Study of T–S Model-Based SMC Scheme With Application to Robot Control

Yew-Wen Liang, Sheng-Dong Xu, Der-Cherng Liaw, Cheng-Chang Chen
2008 IEEE transactions on industrial electronics (1982. Print)  
In light of the remarkable benefits and numerous applications of the Takagi-Sugeno (T-S) fuzzy system modeling method and the sliding mode control (SMC) technique, this paper aims to study the design of robust controllers for a set of secondorder systems using a combination of these two approaches. The combined scheme is shown to have the merits of both approaches. It alleviates not only the online computational burden by using the T-S fuzzy system model to approximate the original nonlinear
more » ... iginal nonlinear one (since most of the system parameters of the T-S model can be computed offline) but also preserves the advantages of rapid response and robustness characteristic of the classic SMC schemes. Moreover, the combined scheme does not need to online compute any nonlinear term of the original dynamics, and the increase in the number of fuzzy rules does not create extra online computational burdens for the scheme. The proposed analytical results are also applied to the control of a two-link robot manipulator and compared with the results using classic SMC design. Simulation results demonstrate the benefits of the proposed scheme. Index Terms-Robot manipulators, robust control, slidingmode control (SMC), Takagi-Sugeno (T-S) fuzzy system model. I. INTRODUCTION D UE to the efficiency and merits of solving complex nonlinear system identification and various control problems, fuzzy set theory and fuzzy system modeling have recently attracted considerable attention in both academic research and practical applications [3], [26], [27] . Among the existing fuzzy system modeling approaches, the so-called T-S fuzzy system model proposed by has turned out to be one of the most popular modeling themes in the favor of its conceptual simplicity. The basic idea of the T-S approach is first to decompose a nonlinear system into several linear models according to different cases in which the associated linear models best fit the nonlinear one and, then, to aggregate each individual linear model into a single nonlinear one in terms of each model's membership functions. Although the concept is simple, the T-S fuzzy system model has been theoretically justified as a universal approximator [26] , [27] , which makes the T-S fuzzy system model become particularly useful, particularly Manuscript
doi:10.1109/tie.2008.2005138 fatcat:2dmdmtxxhrcs3ifzvgubsg4fv4