A unified framework for input-to-state stability in systems with two time scales

Teel, Andrew R.; Moreau, Luc; Nešić, Dragan

doi:10.1109/tac.2003.816966

Cited by 190 publications

(94 citation statements)

References 59 publications

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“…R. Teel and Aeyels, 1999) and singular perturbations (Christofides and Teel, 1996;Teel et al, 2003) that are tailored for analysis of semi-global practical stability of systems that exhibit time scale separation. Similar to we show that the closed loop system with an extremum seeking controller exhibits two time scales.…”

Section: Introductionmentioning

confidence: 99%

On non-local stability properties of extremum seeking control

2006

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We revisit the extremum seeking scheme whose local stability properties were analyzed in and propose its simplified version that still achieves extremum seeking. We show under slightly stronger conditions that this simplified scheme achieves extremum seeking from arbitrarily large domain of initial conditions if the parameters in the controller are appropriately adjusted. This non-local convergence result is proved by showing semi-global practical stability of the closed-loop system with respect to the design parameters. Moreover, we show at the same time that reducing the parameters typically slows down the convergence of the extremum seeking controller. Hence, the control designer faces a tradeoff between the size of the domain of attraction and the speed of convergence when tuning the extremum seeking controller. We present a simulation example to illustrate our results.

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Section: Introductionmentioning

confidence: 99%

On non-local stability properties of extremum seeking control

2006

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“…Proof of this result is omitted owing to space limitation, it relies upon the results for two-time scale averaged systems given in (Teel et al, 2003) (see in particular Theorem 1). Analyzing the previous result, it can be clarified how the proposed controller satisfies the objectives in a practical way; by the second of (75) we deduce thatθ tends arbitrary close to the power loss term ϕ 0 , while by the first of (75), it can be seen that the power vector x is steered arbitrary close to the reference value x * ϕ 0 .…”

Section: Overall System Stabilitymentioning

confidence: 99%

Analysis, Dimensioning and Robust Control of Shunt Active Filter for Harmonic Currents Compensation in Electrical Mains

Tilli¹,

Marconi²,

Conficoni³

2011

Recent Advances in Robust Control - Theory and Applications in Robotics and Electromechanics

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In this chapter some results related to Shunt Active Filters (SAFs) and obtained by the authors and some coauthors are reported. SAFs are complex power electronics equipments adopted to compensate for current harmonic pollution in electric mains, due to nonlinear loads. By using a proper "floating" capacitor as energy reservoir, the SAF purpose is to inject in the line grid currents canceling the polluting harmonics. Control algorithms play a key role for such devices and, in general, in many power electronics applications. Moreover, systems theory is crucial, since it is the mathematical tool that enables a deep understanding of the involved dynamics of such systems, allowing a correct dimensioning, beside an effective control. As a matter of facts, current injection objective can be straightforwardly formulated as an output tracking control problem. In this fashion, the structural and insidious marginally-stable internal/zero dynamics of SAFs can be immediately highlighted and characterized in terms of sizing and control issues. For what concerns the control design strictly, time-scale separation among output and internal dynamics can be effectively exploited to split the control design in different stages that can be later aggregated, by using singular perturbation analysis. In addition, for robust asymptotic output tracking the Internal Model Principle is adopted.In authors' opinion, SAF case is an illustrative example of common issues in dimensioning and control of complex power electronics equipments, hence the proposed design approach can be generalized for such class of systems (e.g. large-power electric drives; generators and converters, particularly for renewable energies; Uninterruptible Power Supplies, UPS, and power supplies for special applications as particle accelerators). Remarkable the role of "system theory approach" in enlightening crucial sizing issues, this fact strongly testifies how relevant the "control viewpoint" is in all the fields of engineering, particularly when complex dynamic behavior is requested.The presented chapter has been invited for possible publication (after a review process) in the book "Robust Control / Book 1", by INTECH (www.intechweb.org).

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“…LMA forms the mathematical foundation for both the Safety Assurance Monitor (SAM) [11,12,13,14,15] and Correct-by-Construction Artificial Neural Network (CCANN) [8,9,10] which are two applications of the same technology. For an introduction to LMA see the appendix.…”

Section: Safety Assurance Monitor -Sammentioning

confidence: 99%

Management of Test Complexity for Emerging Safety Critical Control Systems Program

Boren¹

2006

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A unified framework for input-to-state stability in systems with two time scales

Cited by 190 publications

References 59 publications

On non-local stability properties of extremum seeking control

On non-local stability properties of extremum seeking control

Analysis, Dimensioning and Robust Control of Shunt Active Filter for Harmonic Currents Compensation in Electrical Mains

Management of Test Complexity for Emerging Safety Critical Control Systems Program

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