A survey of simple transfer-function derivations from high-order state-variable models

The problem of the derivation of simple transfer function models from high order state variable models is reviewed. Methods of reduction are classified according to whether they involve

1. (a) the computation of the time or frequency responses

2. (b) the derivation, as an intermediate step, of a transfer function which is the ratio of two polynomials, the denominator being of the same order as the state variable model, or

3. (c) a set of characterising functions.

Particular reduction methods considered are those based on fitting the step or frequency responses, on determining the intermediate, high order transfer function and reducing it by continued fraction expansion and on fitting the moments of the impulse response. An example illustrating these methods is given. The form of the simple model, the criteria of goodness of fit and the practical difficulties involved in the use of these methods are discussed.