Robust stability and performance with fixed-order controllers
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abstract
This paper deals with the problem of synthesizing or designing a feedback controller of fixed dynamic order for a linear time-invariant plant for a fixed plant, as well as for an uncertain family of plants containing parameter uncertainty, so that stability, robust stability and robust performance are attained. The desired closed-loop specifications considered here are given in terms of a target performance vector representing a desired closed-loop design. In general, these point targets are unattainable with a fixed-order controller. By enlarging the target from a fixed-point set to an interval set the solvability conditions are relaxed and a solution is enabled. Results from the parametric robust control literature can be used to design the interval target family so that the poles and zeros of the closed-loop system are guaranteed to remain in a prescribed region of the complex plane, and closed-loop performance, measured for instance in the H norm are attained, even when plant uncertainty is present. It is shown that it is possible to devise a computationally simple linear programming approach that attempts to meet the desired closed-loop specifications. The approach developed here gives the entire set of controllers attaining the specifications as a convex set and also can be recast to give the lowest-order controller attaining specifications.
