未確定非線性系統之適應模糊滑動模式控制器設計

ADAPTIVE FUZZY SLIDING MODE CONTROLLER DESIGN FOR A CLASS OF NONLINEAR UNCERTAIN SYSTEMS

陳帝宏(Ti-Hung Chen)

指導教授 ： 龔宗鈞

大同大學/電機資訊學院/電機工程學系所/博士(2005年)

摘要

本論文針對非線性不確定系統提出適應模糊滑動模式控制器設計。適應模糊滑動模式控制器的設計程序如下：首先，建立一套模糊模型描述非線性不確定系統的輸出/輸入關係；然後，據此模糊模型設計模糊滑動模式控制器以達到控制目標；最後，根據Lyapunov穩定性定理設計適應法則以調整模糊模型的參數。根據目前已發表的文獻可知適應模糊滑動模式控制器是一種非常有效而且具有良好強健性的控制器。然而，適應模糊滑動模式控制器的設計上還有許多值得探討的課題：如何設計適應模糊滑動模式控制器使得系統所有的狀態都能達到所要求的 追蹤表現；如何設計適應模糊滑動模式控制器控制一個系統狀態不是都被能量測的非線性不確定系統。
針對上述的課題，本論文提出三種控制器設計方法：(一)改良式適應模糊滑動模式控制器設計、(二)具有H∞追蹤性能之適應模糊滑動模式控制器設計及(三)具有觀察器適應模糊滑動模式控制器設計。
首先，在第二章中，針對非線性不確定系統提出改良式適應模糊滑動模式控制器設計。在傳統適應模糊控制器的設計上，通常是利用追蹤誤差向量設計適應法則以調整模糊模型參數，在這種設計架構下，當追蹤誤差向量趨近於零的時候，適應法則將不會再調整模糊模型參數，換言之，當追蹤誤差向量趨近於零時，可能依然有模型誤差存在，因此為了補償可能存在的模型誤差，往往需要設計較大的控制力來達成控制目標。不同於傳統適應法則設計，吾人將同時採用追蹤誤差向量和模型誤差向量而設計一套改良式適應法則以調整模糊模型參數，此改良式適應法可以使模糊模型的參數收斂至追蹤誤差向量和模型誤差向量都趨近於零為止。所以，利用改良式適應模糊滑動模式控制器所得到的模糊模型將會比利用傳統適應模糊滑動模式控制器得到的模糊模型更為精確，而控制結果也會更佳。
在第三章中，將針對非線性不確定系統提出具有H∞追蹤性能之適應模糊滑動模式控制器設計，此控制器結合了H∞追蹤控制器與適應模糊控制器的設計方法，並根據Lyapunov穩定準則設計控制法則以使系統狀態變數皆能達到所要求的H∞追蹤性能。最後，並將H∞追蹤控制器的設計問題轉換成一個EVP (eigenvalue problem)以便於運用convex optimization techniques有效率地求解。
第四章則是針對只有部份狀態可以量測的非線性不確定系統，提出具有觀察器之適應模糊滑動模式控制器設計。傳統上，針對此種受控系統設計控制器時，是先設計觀察器估測追蹤誤差向量，再利用所估測追蹤誤差向量設計控制法則，並採用SPR-Lyapunov設計方法設計(strictly-positive-real Lyapunov design approach)適應法則以調整模糊模型參數。不同於SPR-Lyapunov設計方法，吾人利用一組穩定的狀態變數濾波器(state variable filters)過濾觀測誤差以得到過濾觀測誤差向量(filtered observation error vector)，再利用此過濾觀測誤差向量設計適應法則。相較於SPR-Lyapunov設計方法，由於吾人所提出的設計方法僅要求所採用的濾波器需為穩定的，所以將會較容易實現。
根據模擬結果顯示，吾人所提出的三種控制架構皆能達到所預期的控制目標。

關鍵字

模糊控制 ； 適應控制 ； 模糊滑動模式控制

並列摘要

In this dissertation, some adaptive fuzzy sliding mode controller (AFSMC) schemes for a class of nonlinear uncertain systems are presented. The design procedures of AFSMC can be expressed as follows: first, construct the fuzzy models to describe the input/output behavior of the give nonlinear uncertain system. Then, based on the fuzzy model, design a fuzzy sliding mode controller (FSMC) to achieve the control objective. After that, design the adaptive laws for tuning the adjustable parameters of fuzzy model by Lyapunov synthesis approach. Many publications have shown that AFSMC is a powerful and robust control scheme. But, it exist some worth studying topics in design AFSMC, such as how to guarantee the H∞ tracking performance throughout the entire system states, how to treat the system that not all the system states are available for measurement, etc.
Focusing on the above-mentioned topics, this dissertation proposes the following three control strategies: (1) the modified adaptive fuzzy sliding mode controller design (MAFSMC), (2) the H∞ tracking-based adaptive fuzzy sliding mode controller design (H∞AFSMC), and (3) the observer-based adaptive fuzzy sliding mode controller design with state variable filters (O-AFSMC).
Chapter 2 first presents the modified adaptive fuzzy sliding mode controller design (MAFSMC) for a class of nonlinear uncertain systems. Conventionally, the adaptive laws of AFSMC are designed as functions of the tracking error vector. In this scheme, as the tracking error vector approach zero, the adaptive laws of AFSMC would not adjust the parameters of the fuzzy models. Hence, to compensate the modeling error, it needs relatively larger control signal for achieving the control objective. It may occur that the modeling error still exist, while the tracking error vector approaches to zero. Unlike the conventional adaptive algorithm, here, we propose the modified adaptive algorithm utilizes both the tracking error and the modeling error in its adaptive laws, such that the fuzzy model parameters would continuously update until both the tracking error and the modeling error converge to zero. Thus, the fuzzy model obtained by using the proposed MAFSMC will more accurate that of the conventional AFSMC, and the proposed MAFSMC performs better than the conventional AFSMC.
Chapter 3 presents the H∞ tracking-based adaptive fuzzy sliding mode controller design (H∞AFSMC) for a class of nonlinear uncertain systems. This control strategy incorporates the H∞ tracking control scheme into AFSMC and based on the proposed Lyapunov stability criterion, guarantees the H∞ tracking performance throughout the entire system states. After that, the H∞ tracking control problem can be characterized in terms of solving an eigenvalue problem (EVP) to be efficiently solved by using convex optimization techniques.
Chapter 4 presents the observer-based adaptive fuzzy sliding mode controller design with state variable filters (O-AFSMC) for a class of nonlinear uncertain systems, in which not all the states are available for measurement. Conventionally, to treat this controlled system, first, the observer is applied to estimate the tracking error vector. Then, based on the estimated tracking error, the control law is designed. Next, applying strictly- positive-real (SPR)-Lyapunov design approach, design the adaptive laws to adjust the parameters of the fuzzy model. Unlike SPR-Lyapunov design approach, we adopt a set of stable state variable filters to design the adaptive laws. That is, passing the observation error, the difference between the actual tracking error and the estimated tracking error, to a set of state variable filters, obtains a filtered observation error vector, and then, based on the filtered observation error vector, the adaptive laws are designed to adjust the adjustable parameters of the fuzzy model. Since only requiring the selected state variable filters must be stable, the proposed O-AFSMC is more easily to be realized than SPR-Lyapunov design approach.
The simulation results illustrate the design procedure of the proposed control strategies and demonstrate their effectiveness.

並列關鍵字

adaptive control ； fuzzy control ； fuzzy sliding mode control

參考文獻

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