PI control of stable nonlinear plants using projected dynamical systems

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.(c) 2022 Elsevier Ltd. All rights reserved.

Automated summary

This paper presents a novel anti-windup proportional-integral controller for stable multi-input multi-output nonlinear plants. The controller ensures that the integrator state remains within a desired region, satisfying the operational constraints of the problem. Under suitable assumptions, the existence of a small controller gain is proven to achieve closed-loop exponential stability and reference tracking.