Analysis and Synthesis of Low-Gain Integral Controllers for Nonlinear Systems

• 成果类型: Article
• 署名作者: Simpson-Porco, John W.
• 署名单位: University of Toronto
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3035569
• 发表日期: 2021
• 页码: 4148-4159
• 关键词: Integral control; Linear matrix inequalities (LMIs); nonlinear control; output regulation; singular perturbation; slow integrators

摘要

Relaxed conditions are given for stability of a feedback system consisting of an exponentially stable multi-input multi-output nonlinear plant and an integral controller. Roughly speaking, it is shown that if the composition of the plant equilibrium input-output map and the integral feedback gain is infinitesimally contracting, then the closed-loop system is exponentially stable if the integral gain is sufficiently low. The main result is illustrated with an application arising in frequency control of ac power systems. We demonstrate how the contraction condition can be checked computationally via semidefinite programming, and how integral gain matrices can be synthesized via convex optimization to achieve robust L-2 performance in the presence of nonlinearity and uncertainty.