H_∞ Observations Weighted Control Law

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.