TY - JOUR

T1 - Saturating PI Control of Stable Nonlinear Systems Using Singular Perturbations

AU - Lorenzetti, Pietro

AU - Weiss, George

N1 - Publisher Copyright:
© 1963-2012 IEEE.

PY - 2023/2/1

Y1 - 2023/2/1

N2 - 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).

AB - 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).

KW - Lyapunov methods

KW - nonlinear systems

KW - proportional-integral (PI) control

KW - saturating integrator

KW - singular perturbation method

KW - synchronverter

KW - windup

UR - http://www.scopus.com/inward/record.url?scp=85124197160&partnerID=8YFLogxK

U2 - 10.1109/TAC.2022.3147167

DO - 10.1109/TAC.2022.3147167

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AN - SCOPUS:85124197160

SN - 0018-9286

VL - 68

SP - 867

EP - 882

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 2

ER -