Input performance limitations of feedback control

Abstract

This paper deals with input performance limitations of feedback control. The achievable input performance depends on the joint controllability and observability of unstable poles and is exactly quantified for single input single output (SISO) and multi input multi output (MIMO) systems with and without time delay. We also present a modification of µ-interaction measure to assess the feasibility of decentralized stabilization with independent designs of loops. The results are useful for various purposes including designs of the process, control structure and optimal controller synthesis.

Multi‐loop control synthesis for unstable systems and its application: An approach based on µ interaction measure

“…The initiative to solve this problem was taken by Kariwala et al [13,14,19], in which the -IM condition was represented in terms of control sensitivity function. With slight modifications, the following result was obtained.…”

“…This is because, it offers a dynamic measure of interactions, and is also applicable to high-order systems. Its equal applicability to block pairings and other elegant properties have attracted the attention of many researchers in the field of decentralized control [5,12,14,15,[17][18][19]. Based on the -IM, the method proposed by Grosdidier and Morari [15] utilize an independent design approach.…”

“…Many other ideas also came into picture and subsequently improved, some were really interesting and innovative, but finding a (block) diagonal-approximated system that possesses the same number of unstable poles as the system itself still remains an open question. In [14,19], a step toward solving this approximation problem for unstable systems was carried out. It presents a numerical approach, where the decentralized controller is designed based on the (block) diagonal approximation of an unstable plant.…”