區間二型多項式模糊控制系統之基於SOS強健控制器設計

Design of SOS-based Robust Controller for Interval Type-2 Polynomial Fuzzy Logic Control Systems

黃冠福(Guan-Fu Huang)

指導教授 ： 余國瑞

國立中正大學/工學院/光機電整合工程研究所/碩士(2015年)

摘要

本文提出運用區間二型模糊邏輯系統建立多項式模糊模型，並設計區間二型多項式模糊控制器。由於區間二型模糊邏輯系統比一型模糊邏輯系統具有較佳對抗模式不確定性之能力，且多項式模糊模控制系統之狀態矩陣，允許為多項式矩陣，大幅降低模糊規則數，因此，本文提出四個區間二型多項式模糊控制系統穩定定理。分別為區間二型多項式模糊系統對於衰退率之 SOS 穩定條件，區間二型多項式模糊系統對於外部干擾之 SOS 穩定條件，區間二型多項式模糊系統對於模式不確定性之 SOS 穩定條件，以及區間二型多項式模糊系統對於外部干擾與模式不確定性之 SOS 強健 穩定條件。最後採用Tanaka與Lam之多項式模糊模型範例，驗證區間二型多項式模糊控制系統，比一型多項式模糊控制系統更具寬鬆與一般性。

關鍵字

外部干擾 ； 多項式模糊控制系統 ； 區間二型多項式模糊控制系統 ； 模式不確定性 ； 強健控制

並列摘要

This thesis presents an application of an interval type-2 (IT2) fuzzy logic system to construct a polynomial fuzzy model and design an IT2 polynomial fuzzy controller. The IT2 fuzzy logic system was used because of its greater robustness against model uncertainty compared with type-1 (T1) fuzzy logic systems. A polynomial fuzzy control system (FCS) enables representing a state matrix with a polynomial, substantially reducing the number of fuzzy rules. Therefore, this thesis presents four theorems for IT2 polynomial FCS stability conditions: sum of squares (SOS)-based stability condition for designing an IT2 polynomial FCS involving decay rates, SOS-based stability condition for designing an IT2 polynomial FCS involving external disturbances, SOS-based stability condition for an IT2 polynomial FCS by assessing model uncertainty, and SOS-based stability condition for an IT2 polynomial FCS involving both external disturbances and model uncertainty. Finally, the results compared with the examples of Tanaka and Lam confirmed that the proposed IT2 polynomial fuzzy control system was more relaxed and general compared with a traditional T1 polynomial fuzzy control system.

並列關鍵字

External disturbance ； Polynomial fuzzy control systems ； Interval Type-2 polynomial fuzzy control system ； Model uncertainty ； Robust control

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