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 poles 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.