Performance preserving controller reduction via additive perturbation of the closed-loop transfer function

Abstract

In this note, a new performance preserving controller order reduction method is proposed. Here performance preservation indicates that the norm bound of the closed loop transfer function with reduced-order controller is not greater than the norm bound of the closed loop transfer function with full order controller. We assume additive perturbations to the closed-loop transfer function and obtain a sufficient condition for performance preservation. Two kinds of useful weightings are derived, and the controller reduction problem is solved via a frequency weighted model reduction problem.

Fixed-order H^∞ controller design via HIFOO, a specialized nonsmooth optimization package

“…Longitudinal dynamics of an experimental highly maneuverable (HIMAT) airplane make a well-known benchmark example for reduced-order robust controller design [17], [30]. The generalized plant has 20 states and the optimal H ∞ norm achieved in closed-loop by a full-order controller is 0.9708.…”

“…The controller reduction techniques in [17], [30] use frequency-weighted model reduction preserving H ∞ performance. We applied HIFOO to the HIMAT example as an alternative to controller reduction.…”

Dimension Reduction of Large-Scale Systems

“…In (9.2) and (9.3) the weights have usually special forms to enforce either closed-loop stability [AL89,LAL90] or to preserve the closed-loop performance bounds for H ∞ controllers [GG98,Gu95,WSL01,EJL01]. The main appeal of coprime factorization based techniques is that in many cases (e.g., feedback controllers resulting from LQG, H 2 or H ∞ designs) fractional representations of the controller can be obtained practically without any computation from the underlying synthesis approach.…”

“…However, to be useful, the low order controller resulting in this way must provide an acceptable performance degradation of the closed loop behavior. This led to methods which try to enforce also the preservation of closed-loop performance [AL89,GG98,Gu95,WSL01,EJL01].…”

Direct Synthesis of Fixed-Order <inline-formula> <tex-math notation="TeX">${\cal H}_{\infty}$</tex-math></inline-formula> Controllers

“…In general, the effects of such reductions on the stability and performance cannot be determined apriori. However, when reduction is applied to the controller, some sufcient only conditions have been developed to guarantee stability or performance [7] [10]. Reduction of the plant model is usually not preferred since appropriate approximation of the system requires some prior knowledge of the controller [5].…”