Saturating PI Control of Stable Nonlinear Systems Using Singular Perturbations

Pietro Lorenzetti*, George Weiss

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


This article presents an antiwindup propor-tional-integral (PI) controller, using a saturating integrator, for a single-input and single-output (SISO) 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 the 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).

Original languageEnglish
Pages (from-to)867-882
Number of pages16
JournalIEEE Transactions on Automatic Control
Issue number2
StatePublished - 1 Feb 2023


FundersFunder number
Horizon 2020 Framework Programme765579


    • Lyapunov methods
    • nonlinear systems
    • proportional-integral (PI) control
    • saturating integrator
    • singular perturbation method
    • synchronverter
    • windup


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