具時間延遲及參數不確定性之區間型type-2 T-S模糊奇異網路控制系統強健H∞控制

Robust H∞ Control for Interval Type-2 T-S Fuzzy Singular Networked Control Systems with Delay and Parameter Uncertainty

賴怡霖(Yi-Lin Lai)

指導教授 ： 曾傳蘆

國立臺北科技大學/電資學院/電機工程系研究所/碩士(2013年)

摘要

本篇論文探討具有相依時間延遲及封包遺失的非線性奇異網路控制系統之強健H∞控制器設計，其中延遲部份包含了輸入延遲及狀態延遲，並且在系統中也考慮了造成系統擾動的不定參數。
首先，將所考慮的非線性系統以區間型type-2 T-S模糊控制理論建立數學模型，並且使用平行分布補償法的概念設計出區間型type-2 T-S模糊控制器。在穩定性分析部份，採用李亞普諾夫穩定度定理作為分析工具，並在選擇李亞普若夫泛函時，考慮了相依時間延遲特性，且在分析過程中加入的自由權重矩陣以減少保守性，再以線性矩陣不等式推導出奇異網路控制系統的穩定度充分條件。在控制器方面，利用穩定度分析結果，本論文導入對偶性技巧求出滿足性能指標的強健H∞控制器設計條件。
最後，本論文利用Matlab LMI Toolbox進行數值範例模擬及分析。由模擬結果可得知，設計出的強健H∞控制器在具有干擾與不定參數的環境下，確實具有強健穩定性並能達到所要的性能指標，驗證了設計方法的正確性。

關鍵字

奇異網路控制系統 ； 區間型type-2 T-S模糊模型 ； 李亞普若夫穩定度 ； 不定參數 ； H∞控制

並列摘要

This thesis investigates the robust H∞ controller design for nonlinear singular networked control systems with packet loss and delays. The delays include input and state delays. The parameter uncertainty is also considered in this work.
Firstly, the nonlinear system is modeled by using the interval type-2 T-S fuzzy theory. The concept of parallel distributed compensation is adopted to design the interval type-2 T-S fuzzy controller. To analyze the stability, this work adopts the Lyapunov stability theory as a tool. While choosing the Lyapunov functional, the delay-dependent characteristic is considered. Moreover, free weighting matrices are involved for reducing the conservativeness. Then, using the linear matrix inequality technique, the sufficient condition for the stability of singular networked control system is obtained. As to the controller design, this work introduces the concept of duality. Along with the stability condition, the desired robust H∞ controller design can be derived.
Finally, two numerical examples are simulated and analyzed by using the Matlab LMI toolbox. According to the simulation results, the designed controller stabilizes the nonlinear systems and achieves the H∞ performance. It verifies the correctness of the proposed controller design method.

並列關鍵字

Singular Networked Control Systems ； Interval Type-2 T-S Fuzzy Model ； Lyapunov Stability ； Uncertainty ； H∞ control

參考文獻

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