Minimization of a combined H∞ and LQG cost-function for a two-degrees-of-freedom control design

Abstract

The solution to an optimal control problem is presented which allows disturbance rejection and parameter robustness properties to be optimized in addition to tracking performance properties. A two-degrees-of-freedom control law is developed where the feedback controller is designed to optimize H ∞ robustness properties and the reference input controller is selected to achieve good tracking properties in a minimum variance sense. A combined cost-function is posed which includes H ∞ sensitivity and disturbance minimization terms and also minimum variance tracking error and control signal terms. In some problems the criterion will represent the engineering requirements of the designer more realistically than H ∞ or LQG cost terms alone.