  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).

Optimization and Control