Multipurpose controllers for multivariable systems

Abstract

The primary purpose of this paper is to outline a new procedure for designing controllers which simultaneously achieve a variety of desired design goals in deterministic, unity feedback, linear multivariable systems. More specifically, we will present a new algorithm for the systematic design of a "three-part" multivariable controller which simultaneously ensures: 1) a noninteractive or decoupled closed-loop design, 2) complete and arbitrary closed-loop pole placement, which implies desired (single-loop) transient performance as well as closed-loop stability, 3) zero steady-state errors between the plant outputs and any nondecreasing deterministic inputs, 4) complete steady-state output rejection of nondecreasing deterministic disturbances, and 5) robustness with respect to stability, disturbance rejection, and zero error tracking for rather substantial plant parameter variations. Our development will employ the more "modern" (Laplace-transformed) differential operator approach for controller synthesis, which involves transfer matrix factorizations and the manipulation of polynomial matrices in the Laplace operator <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</tex> .