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Mathematical Problems in Engineering
Volume 2014, Article ID 765858, 11 pages
Research Article

Complex-Coefficient Frequency Domain Stability Analysis Method for a Class of Cross-Coupled Antisymmetrical Systems and Its Extension in MSR Systems

1Department of Space Equipment, Equipment Academy, Beijing 101416, China
2School of Instrumentation Science & Opto-electronics Engineering, Beihang University, Beijing 100191, China

Received 25 July 2013; Revised 13 December 2013; Accepted 16 December 2013; Published 20 February 2014

Academic Editor: Asier Ibeas

Copyright © 2014 Yuan Ren and Jiancheng Fang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper develops a complex-coefficient frequency domain stability analysis method for a class of cross-coupled two-dimensional antisymmetrical systems, which can greatly simplify the stability analysis of the multiple-input multiple-output (MIMO) system. Through variable reconstruction, the multiple-input multiple-output (MIMO) system is converted into a single-input single-output (SISO) system with complex coefficients. The pole locations law of the closed-loop system after the variable reconstruction has been revealed, and the controllability as well as observability of the controlled plants before and after the variable reconstruction has been studied too, and then the classical Nyquist stability criterion is extended to the complex-coefficient frequency domain. Combined with the rigid magnetically suspended rotor (MSR) system with heavy gyroscopic effects, corresponding stability criterion has been further developed. Compared with the existing methods, the developed criterion for the rigid MSR system not only accurately predicts the absolute stability of the different whirling modes, but also directly demonstrates their relative stability, which greatly simplifies the analysis, design, and debugging of the control system.