Disturbance rejection: A polynomial approach

A detailed analysis of the disturbance rejection problem in single-input single-output linear systems is presented. The analysis is based on an external polynomial model and employs the algebra of polynomials. All solutions are expressed in a parametric form and solvability conditions are given for a number of constraints including those of internal stability and arbitrary pole placement. Measurable and unmeasurable disturbances are distinguished, and the effect of output feedback is investigated. A simple design procedure is then proposed, which provides a stable dynamical solution and which can be extended so as to minimize its order. The procedure consists of solving two linear polynomial equations and yields the compensator in a compact form suitable for direct realization.