Frequency Domain Criteria for Synthesizing Robustly Stabilizing Compensators for a Class of Interval Plants

[+] Author and Article Information
Yongdong Zhao, Suhada Jayasuriya

Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843

J. Dyn. Sys., Meas., Control 117(2), 241-247 (Jun 01, 1995) (7 pages) doi:10.1115/1.2835185 History: Received September 01, 1991; Online January 22, 2008


Considered in this paper is the robust stabilization of a special family of single-input single-output, interval plants in which only the denominator polynomial or the plant poles are uncertain. Two frequency domain necessary and sufficient conditions are derived for the robust stability of the closed-loop system. The first stability criterion reduces to a question of whether or not a specially constructed polar plot intersects the box [−1, 1] × [−1, 1] in the complex plane and the second reduces to a question of whether or not the polar plot of the nominal loop transfer function intersects a specially constructed frequency dependent domain in the complex plane. Both criteria can be used for synthesizing controllers for the special class of interval plants considered. A loop shaping technique is proposed for the synthesis of a robustly stabilizing compensator. For the special class of interval plants considered, the polar plot of the nominal loop transfer function must not intersect a frequency dependent parallelogram. The four corners of the parallelogram can be explicitly computed at each frequency.

Copyright © 1995 by The American Society of Mechanical Engineers
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