本論文針對一般非線性系統，及具有不確定之時間延遲非線性輸入的高階
系統，提出一種基於狀態合成函數的單一模糊輸入模糊滑動模態控制器，以解決
模糊控制器過多輸入變數及改善控制器輸出的抖動現象，大略可以分成以下三點
來說明。
1. 在降低輸入變數方面，我們共提出兩種方法，首先在單一模糊輸入類似模糊
滑動模態控制方法中(single-fuzzy-input quasi fuzzy sliding mode control,
SQ-FSMC)，提出了符號距離(signed distance) 的狀態變數合成觀念，在不
影響系統性能的前提下大幅減少規則數，第二種方法為去偶合的單一模糊輸
入模糊滑動控制器(Decoupled single-fuzzy-input fuzzy sliding mode
controller) 的設計，主要針對有偶合特性的系統來完成狀態合成，達到單一
模糊輸入變數的目的。
2. 在改善抖動現象的方面，主要藉著模糊控制器不斷調整在滑動平面附近的控
制輸入，以改善在滑動平面上快速切換的現象，同時又能夠保持系統的強健
性和穩定性。
3. 具有自調機制的單一模糊輸入的控制器(a self-tuning single-fuzzy- input
controllers, ST-SFIC) 能夠有效的處理具有非線性輸入的不確定時間延遲系
統，經過解模糊化推導後的輸入增益調整法則，能夠使得控制輸入的效率大
幅改善，並且在使用上相當方便。
以上各種控制方法係利用倒單擺與球桿系統的平衡模擬以及利用具有不確定時
間延遲非線性輸入的系統模擬來說明方法的可行性，並以實驗的結果驗証系統的
強健性與穩定性。

A practical fuzzy sliding mode controller for uncertain time-delay with nonlinear
input systems and for a class of nonlinear systems is presented. The controller design
deals with the problems of the dimensionality of fuzzy input variables in fuzzy logic
control (FLC) and the chattering phenomena in sliding mode control (SMC)
effectively. The main results of the proposed method are as follows.
1. We propose two methods to reduce the number of fuzzy input variables. First,
without affecting the performance of the system, the proposed single-fuzzy- input
quasi fuzzy sliding mode controller (SQ-FSMC) by way of a composite state
function reduces the number of rules greatly. Second ly, the design of decoupled
single-fuzzy- input fuzzy sliding mode controller (SFI-FSMC) for the fourth-order
coupled systems shows a better performance than previous work.
2. For the chattering problem of the SMC, this phenomenon can be reduced
effectively with the proposed controller by adjusting the control input near the
sliding hyperplane.
3. A self-tuning single-fuzzy-input controller (ST-SFIC) can be easily applied to
uncertain time-delay dynamical systems with nonlinear input. The self-tuning
scheme dramatically improves the control input behavior. Also, the chattering
phenomenon is eliminated effectively. The control algorithm is convenient and
easy to utilize.
The above methods have been illustrated by the simulation results of the pole and the
cart systems as well as the ball and beam systems. In addition, the uncertain
time-delay with a nonlinear input system can be stabilized to the equilibrium. The
experimental results of the present seesaw system with external disturbance are given.

86
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