多輸入多輸出非線性控制系統之極限環分析

Limit Cycle Analysis of Nonlinear Multi-input Multi-output Control Systems

林致協(Chin-Hsieh Lin)

指導教授 ： 韓光渭

元智大學/工程學院/電機與資訊工程研究所/碩士(1997年)

摘要

本論文之主要目的是對含有多個非線性元件的多輸入多輸出控制
系統(MIMO Control Systems)作極限環(Limit Cycle)分析。本論文
與其他文獻不同之處是將穩定方程式法(Stability Eqution Method)
加以延伸，用以預測極限環的大小和頻率，藉此對多輸入多輸出非線
性控制系統之極限環分析方面建立一有系統的方法。若多輸入多輸出
控制系統之結構有相互對稱之關係時，則可先簡化成多個單輸入單輸
出控制系統，然後用穩定方程式法分析。文中的舉例包含二輸入二輸
出系統和三輸入三輸出系統。另外，對一個有六個非線性體的系統也
加以分析。全部分析結果都用電腦模擬加以比對。

關鍵字

多輸入多輸出控制系統 ； 非線性系統 ； 極限環

並列摘要

The main purpose of this thesis is to analyze the limit
cycles of nonlinear multi-input multi-output control systems.
An extension of the stability-equation method is proposed
to find the amplitudes and frequencies of limit cycles. When
a multi-input multi-output control system is symmetrical, it
can be converted into multiple singal-input singal-output
control systems first, then the stability-equation method is
applied. For illustration, both two-input two-output systems
and three-input three-output control systems are considered.
In addition, a system with six nonlinearities is analyzed.
All the results are checked by computer simulations.

並列關鍵字

MIMO Control Systems ； Nonlinear Systems ； Limit Cycle

參考文獻

[1] K. W. Han,〝Nonlinear Control Systems--Some Practical Methods,〞Academic Cultural Company, Calif., 1977.

[2] K.W. Han and G. J. Thaler,〝High Order System Analysis and Design Using the Root Locus Method,〞J. Franklin Institute, Vol.281, No.2, pp99-113, 1966.

[3] K.W. Han and G. J. Thaler,〝Analysis of Control Systems with Complex Nonlinearities and Transport Lag,〞J. Franklin Institute, Vol.286, No.1, pp76-89, 1968.

[4] T. S. Tsay and K. W. Han,〝Stability Analysis of A Nonlinear Coupled-Core Reactor Control System,〞IEEE Trans. on Nuclear Science, Vol,34, No.6, pp1827-1833, 1987.

[5] K. J. Astrom and T. Hagglund,〝Automatic Tuning of Simple Regulators with Specifications on Phase and Amplitude Margins,〞Automatica , Vol. 20, pp.645-651, 1984.