摘 要

可變結構控制系統中的滑動模式控制已發展了三十幾年，藉著控制系統結
構的切換和引入適合的滑動模式，系統狀態可被拉到滑動線(面)上，可變
結構控制對干擾或不確定系統具有極佳的不敏性。然而當滑動模式控制器
以數位電腦來實現時，其滑動條件與傳統的連續系統並不相同，因此，有
必要針對間時系統另外設計符合間時滑動條件的控制器，再者，當系統出
現隨機干擾時，在只知道干擾訊號統計特性的情況下，如何使滑動條件滿
足並設計最佳到達控制律成為本文之研究重點。 本文針對非線性間時系
統提出一套新的間時滑動模式設計法則:間時滑動模式控制器是根據
Lyapunov 函數而設計，保證可以滿足穩定的間時滑動條件；並運用統計
上考慮期望值最佳化的原理，在隨機干擾的情況下，設計了一則最佳的到
達控制律；此外，文中也提出一種新的切換法則以降低顫動現象。依上列
所提之研究結果，作用在線性及非線性間時系統上，經由電腦軟體模擬均
獲得有效驗證。

Abstract

Sliding mode controller within the domain of variable structure
control has been developed over thirty years. It applied
suitable sliding mode by means of switching the structure of
control systems. The system states might be pulled above sliding
line (plane). Variable structure controller has very good
insensitivity for disturbance or uncertainty system. But when
the study uses digital computer to achieve sliding model control
, the sliding condition of sliding mode controller is different
from that of traditional continuous system. Therefore, it is
necessary to design a controller which can correspond to
discrete sliding condition. Furthermore, when the system has
exogenous disturbances , and we only know the statistic
characteristic of these disturbances, how to satisfy the sliding
condition and design optimal hitting control law turn into main
points of the study.

In this thesis, we propose a new method to design discrete
sliding mode controller for nonlinear systems. Discrete sliding
mode controller is designed based on Lyapunov function. The
approach is guaranteed to satisfy the stable discrete time
sliding mode condition. It also manipulate the theory of optimal
expectation value of statistics. An optimal hitting control law
is designed based on the consideration of stochastic
disturbance. Besides, a switching algorithm is presented to
attenuate the chattering phenomenon. Base on the above research
results, It can get effective verification by means of computer
software simulation, when acts on linear and nonlinear system.
Abstract