以線性矩陣不等式為基礎的非線性系統模糊控制

Abstract

非線性系統的控制是困難的，因為缺乏一套有系統的數學工具以幫助找到必要和足夠的條件去保證他們的穩定性和性能。如果一些受控廠參數是未知的，那問題將變得更複雜。透過使用Takagi–Sugeno (T-S) 的模糊建模，一個非線性系統可以用一些簡單子系統及藉權重的加總來表達。這個模型對一些非線性系統提供一個固定的架構有利於系統的分析。本研究提出一種以線性矩陣不等式(LMI)方法為基礎，對未知參數的非線性系統提供一個線性控制器的設計方法，而受控系統是用T-S模型來表示。這些線性控制器的參數可以透過解一些線性矩陣不等式(LMI)來得到。模擬結果顯示本研究所提出的線性控制器比模糊控制器有一個更簡單的架構，並有較佳的性能。

The control of nonlinear systems is difficult because no systematic mathematical tools are available to find necessary and sufficient condition to guarantee their stability and no systematic methodology exists to design controller to ensure the closed-loop performance. The problem becomes yet more complex if some of the plant parameters are unknown. By using a Takagi-Sugeno (T-S) fuzzy plant model, a nonlinear system can be expressed as a weighted sum of some simple subsystems. This model provides a fixed structure to some nonlinear systems and facilitates the analysis of the systems. In this research, we have presented a linear controller design method for nonlinear plants with unknown parameters based on a LMI approach. The plant is represented by a TSK model. The parameters of the linear controller can be obtained by solving some LMIs. Our linear controller has a simpler structure than that of the fuzzy controller. Simulation results show that the proposed controller provides better performance than that of fuzzy controller.