The State Space and Transfer Function Approaches in Practical Linear Multivariable Systems Design

Abstract

A great deal of attention has been paid recently to the application of state space formalism to linear multivariable time-invariant system design. It is shown that this approach is inherently very limited for practical use and has led to some naive results. The design based on state space formulation does not cope with the whole problem of practical design and its results are more easily derived by transform methods. There is then much greater awareness of practical constraints and therefore it is easier to avoid the unrealistic conclusions often reached by state space approach. Transfer function formalism is then used to present a procedure for stabilizing a multivariable feedback system with significant plant uncertainty. The method is to shape the nominal loop functions and decrease their magnitudes with frequency as rapidly as possible such that the system is stable over the range of plant uncertainty. The procedure is to handle them one by one such that each stage is basically a single loop shaping problem. A demonstrative example is given.