Integral control of stable nonlinear systems based on singular perturbations

Lorenzetti, Pietro; Natarajan, Vivek

doi:10.1016/j.ifacol.2020.12.1698

Cited by 8 publications

(4 citation statements)

References 30 publications

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“…The approach taken in Reference 18 is somewhat different to that here, as there the low‐gain integral parameter is viewed as “sufficiently small” so that the closed‐loop feedback system may be rewritten as a standard singular perturbation model, and singular perturbation techniques applied. The recent paper 20 effectively generalises and strengthens, 18 by weakening various assumptions and by including an anti‐windup component in the integrator. The conclusions of Reference 20 are local, but only local assumptions are imposed, and also does not consider ISS properties.…”

Section: Low‐gain Pi Control For Discrete‐time Forced Lur'e Systemsmentioning

confidence: 93%

“…The recent paper 20 effectively generalises and strengthens, 18 by weakening various assumptions and by including an anti‐windup component in the integrator. The conclusions of Reference 20 are local, but only local assumptions are imposed, and also does not consider ISS properties.…”

Section: Low‐gain Pi Control For Discrete‐time Forced Lur'e Systemsmentioning

confidence: 93%

“…Given the importance of output regulation in applied settings, much attention has been devoted to the extension of integral control, and related notions, to nonlinear plants, with early contributions including References 18, and 19,20 are recent papers in the area. These latter works both contain a bibliographic overview of contributions to integral control in the nonlinear setting, see also Reference 21, the research monograph 22 and the references therein.…”

Section: Introductionmentioning

confidence: 99%

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Low‐gain integral control for a class of discrete‐time Lur'e systems with applications to sampled‐data control

Guiver

Rebarber

Townley

2022

Intl J Robust & Nonlinear

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We study low-gain (P)roportional (I)ntegral control of multivariate discretetime, forced Lur'e systems to solve the output-tracking problem for constant reference signals. We formulate an incremental sector condition which is sufficient for a usual linear low-gain PI controller to achieve exponential disturbance-to-state and disturbance-to-tracking-error stability in closed-loop, for all sufficiently small integrator gains. Output tracking is achieved in the absence of exogenous disturbance (noise) terms. Our line of argument invokes a recent circle criterion for exponential incremental input-to-state stability. The discrete-time theory facilitates a similar result for a continuous-time forced Lur'e system in feedback with sampled-data low-gain integral control. The theory is illustrated by two examples.

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Section: Low‐gain Pi Control For Discrete‐time Forced Lur'e Systemsmentioning

confidence: 93%

Section: Low‐gain Pi Control For Discrete‐time Forced Lur'e Systemsmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Low‐gain integral control for a class of discrete‐time Lur'e systems with applications to sampled‐data control

Guiver

Rebarber

Townley

2022

Intl J Robust & Nonlinear

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“…We believe that the new singular perturbations approach is much more elegant, and more suitable for generalizations. A preliminary and partial presentation of our results, without applications, is in our recent conference paper [31], again considering only integral control. Moreover, the global stability results from Section V here are substantially stronger than those in [31].…”

Section: Introductionmentioning

confidence: 99%

Saturating PI control of stable nonlinear systems using singular perturbations

Lorenzetti¹,

Weiss²

2021

Preprint

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This paper presents a PI controller with antiwindup, using a saturating integrator, for a single-input singleoutput 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).

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PI control of stable nonlinear plants using projected dynamical systems

Lorenzetti

Weiss

2022

Automatica

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Integral control of stable nonlinear systems based on singular perturbations

Cited by 8 publications

References 30 publications

Low‐gain integral control for a class of discrete‐time Lur'e systems with applications to sampled‐data control

Low‐gain integral control for a class of discrete‐time Lur'e systems with applications to sampled‐data control

Saturating PI control of stable nonlinear systems using singular perturbations

PI control of stable nonlinear plants using projected dynamical systems

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