Model reduction with balanced realizations

Abstract

This paper considers the use of balanced realizations in the context of plant and controller order reduction. The emphasis is placed on reduced-order models obtained by residualizing the less controllable and observable states of a balanced realization. The residualized system, unlike a truncated system or an optimal Hankel-norm approximation, maintains the steady-state gain of the system. In addition, balanced residualization is seen to give good matching at low and medium frequencies. This is favourable with regards to both plant and controller reduction. The method is demonstrated on examples and detailed comparisons made with balanced truncation and optimal Hankel-norm approximation. The importance of DC-gain matching and scaling in different set-ups is highlighted. Ways of reducing the 2-DOF (degree of freedom) H ∞ controller of Hoyle el al. (1991) are discussed and important conclusions drawn. A new proof of the error bound for balanced residualization is given in an appendix.