Linear Control of Time-Domain Constrained Systems

TL;DR

This paper introduces a framework for designing linear controllers that satisfy time-domain constraints using sums-of-squares and LMIs, enabling optimization of performance metrics like settling time and overshoot.

Contribution

It develops a novel control design method combining sums-of-squares techniques with LMIs for constrained linear systems, allowing for both constraint satisfaction and performance optimization.

Findings

Framework successfully enforces time-domain constraints

Allows optimization of steady state errors and settling time

Validated through a numerical example

Abstract

This paper presents a general framework for the design of linear controllers for linear systems subject to time-domain constraints. The design framework exploits sums-of-squares techniques to incorporate the time-domain constraints on closed-loop signals and leads to conditions in terms of linear matrix inequalities (LMIs). This control design framework offers, in addition to constraint satisfaction, also the possibility of including an optimization objective that can be used to minimize steady state (tracking) errors, to decrease the settling time, to reduce overshoot and so on. The effectiveness of the framework is shown via a numerical example.