Reduced order models for discrete time systems using remainder matching method

A novel method for reducing the order of a discrete-time transfer function is introduced. The objective of the reduction process is to preserve design parameters of the transfer function so that controllers designed on the basis of the reduced model will satisfactorily compensate the original system. In the remainder matching method, the higher-order terms in the continued fraction expansion are matched to an mth-order transfer function at m chosen frequencies. The mth-order matched transfer function is then substituted in the continued fraction and inverted to obtain the reduced-order model. Such an approach allows the designer to choose significant frequencies such as gain crossover frequency and bandwidth for the matching process. As a result, the compensation for the original system and that for the reduced-order model will have a better match