Synthesis of reduced order multivariable feedback tracking controllers using the Q-parameterization

In this paper we consider the problem of multivariable tracking for stable plants. Specifically, a new method is proposed for constructing a feedback controller which, for certain cases, is of lower order than the controller constructed via the classical robust servomechanism method. Viewed from a tracking standpoint, the servomechanism method results in what may be considered an overdesign. For example, in a two input, two output system, where the first reference input is a step and the second reference input is a sinusoid of a known frequency, ω, the controller obtained via the classical robust servomechanism method allows each output to track a reference input which is of the form A + Bsin(ωt). For many applications, this may not be necessary. As will be shown, the reduced order controller, which is obtained by carefully designing the Q-parameter, does not exhibit this behavior. An example of a two input, two output system is given to illustrate the method.