非線性遲滯現象的自適性模糊控制

Abstract

非線性遲滯現象(Hysteresis)存在於許多物理系統中，如：壓電感測器、致動器和現今汽車中配備的電子節氣門與電磁閥…等。遲滯現象的非線性特性常常會造成控制的複雜度更為提高，有鑑於此，本論文著力於探討遲滯現象所帶來的非線性現象，並提出一種「間接型自適性模糊控制器 (indirect adaptive fuzzy controller, IAFC)」。然而，要鑑別一個系統的遲滯現象需要嚴謹且反覆的測量與實驗；因此，本論文參照現今文獻中廣泛被採用的遲滯曲線數學模型，藉由遲滯特性方程式來模擬特定的遲滯曲線；在許多現存的遲滯模型中，本論文選用「Backlash-like遲滯現象」來進行探討與研究，並基於此遲滯模型，提出有效的控制器。有別於其它自適性控制器的多重限制條件，間接型自適性模糊控制器的限制條件則較為寬鬆，因此可以適用於較廣泛的遲滯系統中。藉由控制法則和自適性法則，間接型自適性模糊控制器能夠反覆地修正與學習，來達到期望的效果；此外在Lyapunov穩定性條件的檢視下，可以確保整個閉迴路系統穩定。本論文選用的驗證平台為由MathWorks所開發的MATLAB軟題，而經由「倒單擺系統」和「單連結機械手臂」等標準的測試系統實驗後，證明本論文所提出之間接型自適性模糊控制器可以有效的處理遲滯現象帶來的非線性特性，此外與文獻中常用的「倒階模糊適應性(adaptive fuzzy backstepping)控制器」相比，本控制器可以得到更為準確的控制結果。

Nonlinear hysteretic phenomena occur in many physical systems, such as electronic throttle and solenoid valves in automobiles, piezoelectric sensors, and many other mechanical actuators. In order to handle these nonlinear properties of hysteretic systems, an indirect adaptive fuzzy controller (IAFC) is proposed in this thesis. However, it is hard to directly identify the unknown hysteretic effects. Therefore, to overcome this problem, some existing hysteretic functions are introduced to construct the nonlinear properties of unknown hysteretic systems; for the purpose of this study, backlash-like hysteresis model is adopted. Based on the backlash-like hysteresis model, the existence of an indirect adaptive controller (IAFC) can be derived in this thesis. Unlike the existing fuzzy control methods, the proposed IAFC can deal with different kinds of hysteretic problems with the adaptive and control laws. Furthermore, based on the learning algorithm, the adaptive and control laws not only can be derived but the stability of the closed-loop system can also be guaranteed by the Lyapunov stability criterion. Then, MATLAB software is used as the verification platform to evaluate the effectiveness of the proposed approach. Finally, compared with the existing backstepping adaptive control method, the proposed IAFC can effectively handle the nonlinear properties in some well-known benchmarks like the Inverted Pendulum System (IPS) and the single-link robotic manipulator.