Design of Takagi-Sugeno Fuzzy Region Controller Based on Rule Reduction, Robust Control, and Switching Concept

Abstract

This paper presents a new structure of Takagi-Sugeno (T-S) fuzzy controllers, which is called T-S fuzzy region controller or TSFRC for short. The fuzzy region concept is used to partition the plant rules into several fuzzy regions so that only one region is fired at the instant of each input vector being coming. Because each fuzzy region contains several plant rules, the fuzzy region can be regarded as a polytopic uncertain model. Therefore, robust control techniques would be essential for designing the feedback gains of each fuzzy region. To improve the speed of response, the decay rate constraint is imposed when deriving the stability conditions with Lyapunov stability criterion. To design TSFRC with the linear matrix inequality (LMI) solver, all stability conditions are represented in terms of LMIs. Finally, a two-link robot system is used to prove the feasibility and validity of the proposed method.

In-situ bioremediation for petroleum contamination: A fuzzy rule-based model predictive control system

“…The use of linguistic fuzzy if-then rules exploits the tolerance for imprecision and uncertainty of expert experience. Fuzzy rule based systems have been used widely and successfully for process control of various industrial processes, and the work has been reported in Tsoi and Gao (1999), El-Shal and Morris (2000), Klepiszewski and Schmitt (2002), and Sun et al (2007).…”

T-S Fuzzy H∞ Tracking Control of Input Delayed Robotic Manipulators

“…To show the effectiveness of the proposed controller design method, the stability control of the robotic manipulator with and without input delays is firstly evaluated. For comparison purpose, we introduce a so-called robust controller from (Sun, et al, 2007), which was designed using a region based rule reduction approach and obtained with one rule to reduce the complexity caused by the number of fuzzy rules. The design result for this controller with a decay rate 0.5 was given as -115.…”

“…It is observed that the state variables do not converge to equilibrium states in this case and hence controller (23) is not able to stabilise the system when input time delays are given as 24 ms. Following the similar idea given in (Sun, et al, 2007), a robust controller which uses only one rule and considers the fuzzy model as a polytopic uncertain model can also be designed using the presented conditions (19-21). We now use the reference model as r 010 0 -6 -5 0 0 A= 00 0 1 00 6 5 =30 ms, d 2 =0.1, d 3 =0.1, d 4 =0.1, and define 1 0000-1 00 0 0 C= 0 0 10 0 0 0 10 0 To check the stability control performance of the designed controller (24), the reference input and external disturbances are all set as zero, and the initial conditions are same to the above used values.…”