Optimal H2 And H∞ Fixed Order Dynamic Compensation Using Canonical Forms

This paper presents a technique for designing fixed order dynamic compensators in controller canonical form which are robust to both structured and unstructured uncertainty. The formulation uses an approach which combines an H₂ and H_∞ optimization process. Specificaly, a quadratic performance index is minimized subject to a constraint on the H_∞, norm of the closed loop transfer function from disturbances to controlled outputs. This provides robustness to unstructured uncertainty. To provide robustness to structured uncertainty, an upper bound is computed for the worst case parameter variations, and it is then included in the derivation of the optimality conditions. For the specific case of no structured uncertainty, the results of this approach using the canonical form compensator are analytically related to the previously published results for a fixed or dynamic compensator. It is demonstrated that the use of the canonical form greatly simplifies the system of necessary conditions.