PI control of stable nonlinear plants using projected dynamical systems

TL;DR

This paper introduces a new anti-windup PI controller for stable nonlinear plants using projected dynamical systems theory, ensuring input constraints and stability under certain conditions, validated on power grid applications.

Contribution

It proposes a novel controller design that enforces input constraints via projected dynamical systems and provides stability guarantees for nonlinear plants.

Findings

Ensures plant input constraints through projection methods.

Guarantees local exponential stability with small enough gain.

Validated on power system power regulation.

Abstract

This paper presents a novel anti-windup proportional-integral controller for stable multi-input multi-output nonlinear plants. We use tools from projected dynamical systems theory to force the integrator state to remain in a desired (compact and convex) region, such that the plant input steady-state values satisfy the operational constraints of the problem. Under suitable monotonicity assumptions on the plant steady-state input-output map, we use singular perturbation theory results to prove the existence of a sufficiently small controller gain ensuring closed-loop (local) exponential stability and reference tracking for a feasible set of constant references. We suggest a particular controller design, which embeds (when possible) the right inverse of the plant steady-state input-output map. The relevance of the proposed controller scheme is validated through an application in the power systems domain, namely, the output (active and reactive) power regulation for a grid-connected synchronverter.