非線性系統之強健型切換式模糊控制

Robust Switching Fuzzy Control for Nonlinear System

吳祖錚(Tsu-Cheng wu)

指導教授 ： 練光祐

中原大學/工學院/電機工程研究所/碩士(2002年)

https://doi.org/10.6840/cycu200200201

摘要

在本論文中，針對兩種非線性系統，離散混沌系統及非完整約束系統，我們分別提出一新的強健型模糊控制器。這強健型模糊控制器是以T-S模糊模式為發展基礎之下，利用線性矩陣不等式技術去設計此控制器的控制增益。首先，對離散混沌系統輸出回授模式追蹤控制作一探討，當被控廠之系統矩陣與參考模式之系統矩陣產生參數誤差時，此誤差容易造成混沌系統的不穩定，因此我們先設計部份控制器以補償此誤差。接下來，當有系統狀態未知時，我們設計一T-S模糊估測器作估測。同時，完成控制器之其餘架構的設計以達到追蹤參考模式。當我們將模糊估測器及參考模式之追蹤控制器合成一誤差系統，可將以上控制器的增益設計轉換成線性矩陣不等式問題，利用MATLAB之工具盒求得。我們利用一Henon Map離散混沌系統作理論上的驗證。
針對非完整約束系統，首先討論不可積之約束條件及運動方程之推導。對其一般系統模式，以T-S模糊模型建立近似主要模式。切換式模糊控制器則以模糊平行分佈補償器來設計，解決了系統不確定、外界干擾、與模糊模式誤差等對系統性能的影響。並且經由較為寬鬆之線性矩陣不等式條件的滿足，控制系統可達到強健穩定化與模式追蹤的成果。最後利用單腳跳動機器人做數值模擬，以驗證預定之效益。

關鍵字

T-S模糊估測器 ； 強健型模糊控制 ； T-S模糊模式 ； 切換式模糊控制

並列摘要

In this thesis, new robust fuzzy controllers are proposed for two class of nonlinear systems, namely discrete-time chaotic systems and nonholonomic systems. The robust controllers are developed based on T-S fuzzy model, where as the LMI technique is used to design the control gain. Fordiscrete-time chaotic systems, we investigate the issue of fuzzy outputfeedback model following control. Here we consider mismatched parameters
occuring in the system matrix of the plant and reference model. To obtain immeasurable states, a T-S fuzzy observer and, in turn, a T-S fuzzy
controller are designed. The stability conditions of the overall error system are formulated into LMI problem. Since simultaneous solution to the
parameter compensation gains, control gain, and estimation gain are not trivial, we address a three steps method to solve the LMIs. The proposed
methodology is applied to the chaotic Henon Map. The numerical simulations results reveal the validity of theoretical derivation. The nonholonomic systems arising from a no-slip constraint or a constraint on the conservation of generalized momentum. For this class of systems, a general approxmation T-S fuzzy model is introduced to assure that the controllability of all local linear subsystems in fuzzy rules can be held. Then, based on this fuzzy model, a switching fuzzy controller via PDC concept is proposed for the control issues of stabilization and model following. The stability condition and, in turn, the control gain design are reformulated to an LMI problem. The proposed methodology is applied to a one-leg hopping robot, a typical nonholonomic system. The numerical simulations illustrates satisfactory results.

並列關鍵字

T-S Fuzzy Model ； Robust Fuzzy Control ； T-S Fuzzy observer ； Switching Fuzzy Control

參考文獻

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