模糊控制的穩定條件與其應用：使用LMI方法

Stabilization Conditions of Fuzzy Control and Its Application: Using LMI Approaches

In terms of Lyapunov's direct method, this paper proposed stability conditions of fuzzy logic control (FLC) and its application for structural and mechanical systems approximated by Tagagi-Sugeno (T-S) fuzzy model. External forces or disturbances are not considered in these controlled systems. In the design controller procedure, a parallel distributed compensation (PDC) scheme was utilized to construct a global FLC by blending all linear local state feedback controllers. A stability criterion was carried out not only for the fuzzy model but also for a real mechanical system. Furthermore, this controller design problem can be reduced to an linear matrix inequalities (LMI) problems by Schur Complements and efficient interior-point algorithms are now available in Matlab toolbox to solve this problem. Simulation results show the utility of the FLC design method based on LMI's proposed in this paper. 基於李雅普諾夫直接法（Lyapunov's direct method）和T-S模糊模型（Takagi-Sugeno Fuzzy model）的使用，本文推導一個使結構機械系統穩定的條件方程式並且設計一個能夠使系統達到穩定的模糊邏輯（Fuzzy Logic Controller, FLC）控制器。在控制器的設計過程中，吾人將使用平行分散補償（Parallel Distributed Compensation, PDC）的技巧整合所有局部狀態回饋控制，並進一步建構一個完整的模糊邏輯控制器。文中，除了探討模糊模型的穩定性分析之外，還將模糊模型應用於實際的結構機械系統；另外，使用Schur Complements將控制問題簡化成解線性矩陣不等式（Linear matrix inequalities, LMI）的問題，使吾人更有效的利用Matlab工具箱所提供的演算法來解決此問題。文末，舉一實例並藉由數值模擬證實此模糊控制方法可行。