A numerical method for optimal pole/zero-polynomial allocation in multivariable systems

For controllable and observable systems the transfer function matrix determines the system characteristics. The poles determine the system stability and the individual zeros and gains determine the shape of the response. All the design methods reported so far in feedback and compensator methods for acheiving acceptable response deal with pole allocation and steady-state properties. With all these methods the pole allocation moves the individual zeros in an undetermined and complicated way and hence the transient response shaping in multivariable systems is still an unresolved problem. In the paper we consider a new method for designing, simultaneously, the gains, poles, and zeros of transfer function matrices. The method is based on the extension of a method developed by the first author for the exact systhesis of transfer matrices. In the proposed method we start from a desired, but inadmissible, gain/pole/ zero configuration in the transfer function matrix and, by using hill-climbing algorithem, search in the general pole/zero-polynomial space for the nearest point in the admissible sub-space. The method is illustrated by numerical examples.