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 -