An Adaptive Observer for Uncertain Linear Time-Varying Systems with Unknown Additive Perturbations

Pyrkin, Anton A.; Bobtsov, Alexey A.; Romeo, Ortega; Isidori, Alberto

doi:10.48550/arxiv.2112.05497

Cited by 3 publications

(4 citation statements)

References 23 publications

(45 reference statements)

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“…Before closing this section we make the remark that it is actually possible to relax the excitation Assumption 5. Indeed, it has been shown in [15] that global exponential convergence of an LS+FF estimator with dynamic regression extension is ensured with the strictly weaker interval excitation condition [7]. This scheme was also implemented in the simulations but the performance improvement with respect to the LS+FF was negligiblehence, for brevity, the simulated results are omitted.…”

Section: Simulation Resultsmentioning

confidence: 99%

An Almost Globally Stable Adaptive Phase-Locked Loop for Synchronization of a Grid-Connected Voltage Source Converter

Zonetti¹,

Bobtsov²,

Nikolaev³

et al. 2022

Preprint

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In this paper we are interested in the problem of adaptive synchronization of a voltage source converter with a possibly weak grid with unknown angle and frequency, but knowledge of its parameters. To guarantee a suitable synchronization with the angle of the three-phase grid voltage we design an adaptive observer for such a signal requiring measurements only at the point of common coupling. Then we propose two alternative certainty-equivalent, adaptive phase-locked loops that ensure the angle estimation error goes to zero for almost all initial conditions. Although well-known, for the sake of completeness, we also present a PI controller with feedforward action that ensures the converter currents converge to an arbitrary desired value. Relevance of the theoretical results and their robustness to variation of the grid parameters are thoroughly discussed and validated in the challenging scenario of a converter connected to a grid with low short-circuit-ratio.

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Section: Simulation Resultsmentioning

confidence: 99%

An Almost Globally Stable Adaptive Phase-Locked Loop for Synchronization of a Grid-Connected Voltage Source Converter

Zonetti¹,

Bobtsov²,

Nikolaev³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…As expected, this regressor equation is nonlinearly parameterized, which hampers the application of standard estimation techniques. Therefore, we are compelled to appealin Section 4-to the LS+DREM parameter estimator recently reported in (Ortega et al, 2022;Pyrkin et al, 2022). Lemma 1.…”

Section: Regression Equation For Parameter Estimationmentioning

confidence: 99%

“…To estimate the parameters θ from the NLPRE (5) we invoke the recent result of (Ortega et al, 2022), where the LS+DREM estimator proposed in (Pyrkin et al, 2022), which is applicable for linear regression equations, was extended to deal with NLPRE. However, this estimator requires that the mapping of the NLPRE satisfies a monotonicity property, which is not verified by W I (θ) given in (6).…”

Section: Construction Of a Strictly Monotonic Mappingmentioning

confidence: 99%

Parameter Estimation of Two Classes of Nonlinear Systems with Non-separable Nonlinear Parameterizations

Bobtsov¹,

Costa‐Castelló²,

Nikolaev³

2022

Preprint

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In this paper we address the challenging problem of designing globally convergent estimators for the parameters of nonlinear systems containing a non-separable exponential nonlinearity. This class of terms appears in many practical applications, and none of the existing parameter estimators is able to deal with them in an efficient way. The proposed estimation procedure is illustrated with two modern applications: fuel cells and human musculoskeletal dynamics. The procedure does not assume that the parameters live in known compact sets, that the nonlinearities satisfy some Lipschitzian properties, nor rely on injection of high-gain or the use of complex, computationally demanding methodologies. Instead, we propose to design a classical on-line estimator whose dynamics is described by an ordinary differential equation given in a compact precise form. A further contribution of the paper is the proof that parameter convergence is guaranteed with the extremely weak interval excitation requirement.

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“…Before closing this section we make the remark that it is actually possible to relax the excitation Assumption 5. Indeed, it has been shown in Ortega et al 42 that global exponential convergence of the LS+FF estimator with dynamic regression extension is ensured with the strictly weaker interval excitation condition 43 -see also Pyrkin et al 44 This scheme was also implemented in the simulations but the performance improvement with respect to the LS+FF was negligible-hence, for brevity, the simulated results are omitted.…”

mentioning

confidence: 99%

An almost globally stable adaptive phase‐locked loop for synchronization of a voltage source converter to a weak grid

Zonetti,

Bobtsov,

Ortega

et al. 2023

Adv Control Appl

View full text Add to dashboard Cite

In this article, we are interested in the problem of adaptive synchronization of a voltage source converter with a possibly weak grid with unknown angle and frequency. To guarantee a suitable synchronization with the angle of the three‐phase grid voltage we design an adaptive observer for such a signal requiring measurements only at the point of common coupling. Then we propose an alternative certainty‐equivalent, adaptive phase‐locked loop that ensures the angle estimation error goes to zero for almost all initial conditions. Although well‐known, for the sake of completeness, we also present a PI controller with feedforward action that ensures the converter currents converge to an arbitrary desired value. Relevance of the theoretical results and their robustness to variation of the grid parameters are thoroughly discussed and validated in the challenging scenario of a converter connected to a grid with low short‐circuit‐ratio.

show abstract

An Adaptive Observer for Uncertain Linear Time-Varying Systems with Unknown Additive Perturbations

Cited by 3 publications

References 23 publications

An Almost Globally Stable Adaptive Phase-Locked Loop for Synchronization of a Grid-Connected Voltage Source Converter

An Almost Globally Stable Adaptive Phase-Locked Loop for Synchronization of a Grid-Connected Voltage Source Converter

Parameter Estimation of Two Classes of Nonlinear Systems with Non-separable Nonlinear Parameterizations

An almost globally stable adaptive phase‐locked loop for synchronization of a voltage source converter to a weak grid

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