A new approach to the perfect regulation and the bounded peaking in linear multivariable control systems

Abstract

This paper presents a new approach to the perfect regulation (p.r.) and the bounded peaking (b.p.) in linear multivariable control systems, based on the pole and the eigenvector assignment technique. Roughly speaking the p.r. represents an ideal control action which reduces the settling time to 0, while the b.p. simply means the bounded overshoot in this ideal situation. Simple frequency domain characterizations of the p.r. and the b.p. are derived. They reveal some invariance properties of the p.r. and the b.p. that provide a powerful tool for achieving the p.r. and the b.p. The existence condition for the p.r. is derived, which turns out to be identical to the result obtained in the optimal regulator theory. This result is extended to a more general control objective of attaining the p.r. for one output while keeping the b.p. for another output. A condition on which the p.r. is realized by an output feedback is also derived. A simple design algorithm is proposed for achieving the p.r. which is essentially the eigenvector assignment procedure. Finally, an application to a real system is discussed.