一般多變數控制系統設計的困難點，在於如何處理各個變數之間的動態耦合效應。由於多變數系統的動態不確定性及因系統模式複雜而造成的運算負荷，使以模式為基礎的解耦控制策略，很難應用於及時控制系統。本研究發展了四種智慧型適應控制器來處理上述問題，這些控制器以模糊系統或神經網路為主要架構，依據或免除Kalman-Yacubovich lemma，搭配以Lyapunov穩定準則為理論基礎的適應控制法則，來追蹤一個預設的參考模式。並採用奇異激勵(singular perturbation)的概念，先將非對稱式多變數系統解耦成數個階數較低且具不同時間常數的獨立對稱式多變數子系統，使系統穩定性可以分開確定。這些智慧型系統的可調參數的初值可設為零，然後使用一個根據Lyapunov穩定準則所推導的適應法則，將其調整至適當值。在適應法則中，並加入兩個增加系統強健性的修正項；一個是邊界層函數，可使因參數誤差及模式誤差而造成的狀態誤差收斂至一定值；另一個是e-修正項，可使系統在無持續激勵下，也可確保系統參數收斂至適當值。
本研究利用三個模擬系統及兩個實驗載具，來驗證智慧型適應控制器的性能。分別是：(1)以解耦適應模糊滑動模式控制器(DAFSMC)控制單桿及雙桿倒單擺模擬系統，用來驗證奇異激勵技巧的解耦效用。(2)以參考模式適應模糊控制器(MRAFC)控制雙連桿機器手臂模擬系統及五軸機器人系統，用來驗證以MIMO為設計觀點的控制器的性能、穩定性、及強健性。(3)以解耦參考模式適應模糊滑動模式控制器(DMRAFSC)及解耦適應神經網路控制器(DANC)控制一個半車主動式懸吊實驗平台，以驗證多變數解耦控制器的效用，並將實驗結果與被動式懸吊系統做一比較。
所有的模擬及實驗結果顯示，智慧型適應控制器具有極佳的控制性能、穩定性及強健性。

Generally, the difficulty of multi-variable systems control is how to overcome the coupling effects among each degree of freedom. Due to computational burden and dynamic uncertainty of multi-variable systems, the model based decoupling approach is hard to implement in real-time control system. In this study, four intelligent adaptive controllers are proposed to handle these behaviors. The structure of these model-free new controllers are based on fuzzy/neural systems of which adaptive laws are derived based on Lyapunov stability theory to control the system for tracking a user-defined reference model. The requirement of Kalman-Yacubovich lemma is fulfilling or relaxing. In addition, a non-square multi-variable system can be decoupled into several reduced-order isolated square multi-variable subsystems by using the singular perturbation scheme for different time-scale stability analysis. The adjustable parameters of these intelligent systems can be initialized at zero, then, the novel online parameters tuning algorithms are developed based on Lyapunov stability theory. A boundary-layer function is introduced into these updating laws to cover the parameter errors and modeling errors, and to guarantee the state errors converge into a specified error bound. An e-modification is added into these updating laws to release the assumption of persistent excitation and obtain the optimal values of the adjustable parameters of intelligent systems.
To evaluate the control performance of the proposed controllers, three simulation systems and two experimental rigs are chosen as the implemental systems. (1)A decoupled adaptive fuzzy sliding-mode controller (DAFSMC) is implemented on the single/double link inverted pendulum systems for verifying the decoupled ability of the singular perturbation scheme. (2)A model reference adaptive fuzzy controller (MRAFC) is applied to a two-link robot system and 5 degree-of-freedom (DOF) laboratory robot system to demonstrate the control performance, stability and robustness of the MIMO based controller based on numerical simulations and experiment results, respectively. (3)A decoupled model reference adaptive fuzzy sliding-mode controller (DMRAFSC) and a decentralized adaptive neural controller (DANC) are implemented on the active suspension system of a half vehicle test rig for verifying the performance of these decoupled MIMO controllers. In addition, the experimental results of these two controllers are compared with that of the passive suspension.

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