非線性系統之觀測器為基礎輔以間接適應模糊控制器設計

AN OBSERVER-BASED INDIRECT ADAPTIVE FUZZY CONTROL FOR NONLINEAR SYSTEMS

吳秶菘(Tzu-Sung Wu)

指導教授 ： 游文雄

大同大學/電機資訊學院/電機工程學系所/博士(2011年)

摘要

在本論文中，針對非線性系統具有延遲時間以及輸出延遲的問題，我們提出以觀測器為基礎之間接適應模糊控制方法。

首先，假設已知系統所有狀態，並且利用追蹤誤差向量設計適應法則以調整適應模糊控制器的模型參數。接著，由於在實際運用上，系統狀態是未知或部分已知的，並且可能存在模型誤差。本文提出可變節構結合以觀測器為基礎之模糊系統設計去估測系統的實際狀態以及補償非線性項、系統未確定項及外在干擾的影響，使得非線性系統的模糊模型參數可以連續調整以及其穩定性、收斂性與強健性獲得改善。因此，使用可變結構結合以觀測器為基礎之適應模糊控制器所得到的模糊模型將會比傳統適應模糊控制器得到的模糊模型更為精確，而控制結果也會更佳。

此外，針對非線性系統具有輸出延遲現象提出以觀察器為基礎之模糊適應控制器設計，在模糊線性控制方法中，提供模糊線性模型去近似非線性控制系統，並根據李普若夫穩定準則及線性矩陣不等式設計控制法則使得估測及追蹤誤差皆能收斂至預先設定的有限區域，並且達到所要求的$H_infty$追蹤性能。此外，針對非線性系統只有部份狀態可以量測以及具有輸出延遲的現象，本文提出雙層模糊狀態觀察器來重建系統狀態。其設計方法為利用模糊線性動態模型來表示蔡氏電路具有輸出延遲之狀態觀測器之局部線性關係，接著使用一個雙層模糊觀測重建蔡氏系統的系統狀態，其中在第一層中，針對每一段延遲時間設計m+1個T-S模糊子觀測器，第二層使用延遲輸出誤差狀態作為其語言變量。

最後，以雙連桿搖擺車具有延遲時間和蔡氏電路系統具有輸出延遲為模擬例子，並根據模擬結果可以驗證本文提出的控制機制之有效性。

關鍵字

輸出延遲 ； 蔡式電路系統 ； 線性矩陣不等式 ； 狀態回授控制 ； 雙層模糊觀察器 ； 模糊適應觀察器 ； 均勻終極有界 ； 搖擺車系統

並列摘要

In this dissertation, we propose an observer-based indirect adaptive fuzzy control design method for the nonlinear systems with delayed time and output delay.
First, it is assumed that the system states can be measured and the adaptive laws are designed as the function of the tracking error vector for tuning the parameters of the fuzzy model as well as for the design of adaptive fuzzy controller.
Next, since the system states may be unknown or partially known for the practical application and there may exist modeling errors, the variable structure combining with the observer-based adaptive fuzzy control design is used to estimate the system states and compensate the effects of nonlinearities, system uncertainties and external disturbances such that the stability and robustness of the nonlinear systems, and parameters convergence of the fuzzy model can be guaranteed.

As for the nonlinear systems with output delay, the proposed fuzzy linear control method using two-layer fuzzy observer to estimate the state of the nonlinear control system.
Estimation and tracking errors can be proved to converge to a bounded pre-specified region by using the Lyapunov Theorem and linear matrix inequalities (LMIs), and to achieve the $H_infty$ tracking performance in the closed-loop system.
First, a fuzzy linear dynamic model described by fuzzy If-Then rules is proposed to represent local linear input/output relations as well as a two-layer fuzzy state observers of nonlinear system with delayed output where the first layer consists of $m+1$ T-S fuzzy sub-observers for each delayed time slice, and the linguistic variables of each fuzzy observer are given by the estimated fuzzy observer delayed states, and the second layer using delayed output error states as its linguistic variables is defuzzified from the $m+1$ fuzzy sub-observers in the first layer.

Finally, two numerical example of a two-links rolling cart and Chua's circuit system with delayed time and output delay, respectively, are given, and according to simulation results can demonstrate the validity of the proposed control scheme.

並列關鍵字

chaotic Chua's circuit system ； uniformly ultimately bounded (UUB) ； $H_infty$ tracking performance ； linear matrix inequalities (LMIs) ； state feedback control ； two-layer fuzzy observer ； output time-delay ； Fuzzy adaptive observer-based control ； rolling cart system

參考文獻

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