Saturating PI control of stable nonlinear systems using singular perturbations

TL;DR

This paper develops a saturating PI control method for stable nonlinear systems, ensuring exponential stability and zero steady-state error, with global stability under certain conditions, validated through power converter applications.

Contribution

It introduces a saturating integrator-based PI controller with stability guarantees for nonlinear plants using singular perturbations theory.

Findings

Existence of an upper bound on controller gain for stability.

Exponential stability with a large region of attraction.

Global asymptotic stability for small gains if the plant has the asymptotic gain property.

Abstract

This paper presents an anti-windup PI controller, using a saturating integrator, for a single-input single-output stable nonlinear plant, whose steady-state input-output map is increasing. We prove that, under reasonable assumptions, there exists an upper bound on the controller gain such that for any constant reference input, the corresponding equilibrium point of the closed-loop system is exponentially stable, with a "large" region of attraction. When the state of the closed-loop system converges to this equilibrium point, then the tracking error tends to zero. The closed-loop stability analysis employs Lyapunov methods in the framework of singular perturbations theory. Finally, we show that if the plant satisfies the asymptotic gain property, then the closed-loop system is globally asymptotically stable for any sufficiently small controller gain. The effectiveness of the proposed PI controller is proved by showing how it performs as part of the control algorithm of a synchronverter (a special type of DC to AC power converter).