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

2020/03/03 by John W. Simpson-Porco, Simpson-Porco, John W.
Engineering · Mathematics · #Control and Stability of Dynamical Systems #Numerical methods for differential equations #Stability and Control of Uncertain Systems

paper · pdf · doi:10.48550/arxiv.2003.01348

Abstract

Relaxed conditions are given for stability of a feedback system consisting of\nan exponentially stable multi-input multi-output nonlinear plant and an\nintegral controller. Roughly speaking, it is shown that if the composition of\nthe plant equilibrium input-output map and the integral feedback gain is\ninfinitesimally contracting, then the closed-loop system is exponentially\nstable if the integral gain is sufficiently low. The main result is illustrated\nwith an application arising in frequency control of AC power systems. We\ndemonstrate how the contraction condition can be checked computationally via\nsemidefinite programming, and how integral gain matrices can be synthesized via\nconvex optimization to achieve robust L2 performance in the presence of\nnonlinearity and uncertainty.\n

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