On the structure of a two-degree-of-freedom H ∞ loop shaping controller

Abstract

Explicit state-space formulae are presented for a two degree-of-freedom (2-DOF) controller that stabilizes an augmented plant with respect to unstructured additive coprime factor perturbations whilst simultaneously providing robust model following. The 2-DOF problem was known to inherit certain features of the McFarlane-Glover loop shaping design method, from which it is derived. In this paper, the precise structure of one admissible controller is derived. That structure is shown to comprise a state-estimator, an on-line step-response model, and an augmented state estimate feedback law. The formulae derived herein are applied to a classical nonlinear stabilization problem.