H∞ Observations Weighted Control Law

[+] Author and Article Information
M. J. Grimble

Industrial Control Unit, Department of Electronic & Electrical Engineering, University of Strathclyde, Glasgow G1 1QE, Scotland

J. Dyn. Sys., Meas., Control 112(3), 337-348 (Sep 01, 1990) (12 pages) doi:10.1115/1.2896150 History: Received August 12, 1988; Revised August 24, 1989; Online March 17, 2008


A H∞ optimal control problem is considered which leads to a particularly simple controller structure. The expression for the optimal controller only requires the solution of one diophantine equation which makes it very appropriate for self-tuning control applications. The controller developed is related to the Observations Weighted control law which involves the minimization of tracking error and control signal variances. The H∞ criterion minimized may be expressed in a signal spectrum minimization form or in a sensitivity minimization form. The system can be guaranteed to be stable under low control weighting (high gain) conditions even for non-minimum phase open-loop unstable plants. The design of the controller depends upon the specification of the cost weighting transfer-functions and this is illustrated in a design example.

Copyright © 1990 by The American Society of Mechanical Engineers
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