MODEL-REDUCTION WITH BALANCED REALIZATIONS

This paper considers the use of balanced realizations in the context o f plant and controller order reduction. The emphasis is placed on redu ced-order models obtained by residualizing the less controllable and o bservable states of a balanced realization. The residualized system, u nlike a truncated system or an optimal Hankel-norm approximation, main tains the steady-state gain of the system, In addition, balanced resid ualization is seen to give good matching at low and medium frequencies . This is favourable with regards to both plant and controller reducti on. The method is demonstrated on examples and detailed comparisons ma de with balanced truncation and optimal Hankel-norm approximation. The importance of DC-gain matching and scaling in different set-ups is hi ghlighted. Ways of reducing the 2-DOF (degree of freedom) H-infinity c ontroller of Hoyle ef al. (1991) are discussed and important conclusio ns drawn. A new proof of the error bound for balanced residualization is given in an appendix.