Gain margin and time lag tolerance constraints applied to the stabilization problem and robust servomechanism problem

• Published in: IEEE transactions on automatic control Vol. 30; no. 3; pp. 229 - 239
• Main Authors: Davison, E., Copeland, B.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.03.1985; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; Computer science; control theory; systems; Constraint theory; Control system synthesis; Control systems; Councils; Exact sciences and technology; Linear systems; Miscellaneous; Robust control; Robust stability; Robustness; Servomechanisms; Theoretical computing; Time factors; Control robustness; Linear system; Constraint; Stabilization; Servomechanism; Delay
• ISSN: 0018-9286
• DOI: 10.1109/TAC.1985.1103924

Definitions of gain margin tolerance and time lag tolerance for a multivariable linear time-invariant system are given which correspond to a generalization of the notions of gain and phase margin of classical control system theory. Existence conditions are then given to solve the stabilization problem and the robust servomechanism problem with gain margin and time lag tolerance constraints. In particular, the following is shown for a system described in terms of a state-state model: 1) Generically, there exists a controller to stabilize an unstable m -input, r -output system so that the resultant closed-loop system possesses a nonzero gain margin, if and only if min (r, m) = 1 . 2) For stable plants, there always exists a controller to solve the robust servomechanism problem so that it has an arbitrary specified gain margin/time lag tolerance constraint, if and only if there exists a solution to the robust servomechanism problem for the plant. A controller synthesis method is then given which solves the robust servomechanism problem so that it has a specified gain margin/time lag tolerance. Various examples of the proposed algorithm are given to illustrate the type of results that may be obtained.