A Canonical Form For The Reduction of Linear Scalar Systems

Consideration is given to the problem of the reduction of order of a scalar system S (A,B,C) described by a transfer function g (s). On the assumption that the reduced order model is to be used for feedback control systems design, a canonical form is derived equivalent to a system decomposition related to the asymptotes, intercepts and finite zeros of the system root-locus. A model reduction procedure, based on the canonical form, is suggested and shown to be capable of providing a good approximation to both the dominant pole and dominant zeros of g (s) and to make possible the matching of the desired number of high and low frequency moments. The canonical form can also be used to provide an estimate of a suitable reduced model order. Two examples are described.