Stability analysis for systems with saturation and backlash in the loop

Tarbouriech, Sophie; Queinnec, Isabelle; Prieur, Christophe

doi:10.1109/cdc.2013.6760942

Cited by 4 publications

(9 citation statements)

References 20 publications

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“…and M 1 defined in (14), recalling that W = P −1 . The satisfaction of relations (13) and (15) implies both L 0 < 0 and ρ LT 3 Lρ − τ ≤ 0, and then L < 0, for all (x, ϕ 1 , Ψ 1 ,Ψ 1 ) = 0.…”

Section: B Regional Stabilitymentioning

confidence: 97%

“…Proposition 3.1: Theorem 3.1 enjoys the following properties: 1) Given E c = 0, condition (13) is feasible if matrix A 0 is Hurwitz. 2) There always exists E c non null such that condition (13) holds, if matrix A 0 is Hurwitz. Proof: In [15], it has been shown that M 0 < 0 is feasible if matrix A 0 is Hurwitz (that is there exist τ , W , T 3 and S 2 such that M 0 < 0).…”

Section: Feasibilitymentioning

confidence: 99%

“…That leads to a system with a new saturation with a level depending on the magnitude constraint of the previous saturation and on the parameters of the backlash. In [13], the closed-loop system is a dynamical one with nested backlash and saturation operators issued from a static output feedback. The contribution of the current paper can be viewed as an extension of [13] in the sense that we do not consider a static output feedback but a dynamic output feedback and we search for designing an anti-windup term to mitigate the combined effects of saturation and backlash.…”

Section: Introductionmentioning

confidence: 99%

“…In [13], the closed-loop system is a dynamical one with nested backlash and saturation operators issued from a static output feedback. The contribution of the current paper can be viewed as an extension of [13] in the sense that we do not consider a static output feedback but a dynamic output feedback and we search for designing an anti-windup term to mitigate the combined effects of saturation and backlash. Inspired both by [5] and [15], the technique does not intend to invert the backlash element but uses it directly to build the anti-windup loop.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Stability analysis of systems with nested saturation and backlash in the loop via nonstandard anti-windup compensation

Tarbouriech

Queinnec

Prieur

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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This paper deals with control systems subject to backlash and saturation in the loop. One of the goals is to characterize, or at least to approximate, the attractor of such nonlinear dynamical systems. Then, the regional or global asymptotic stability of the closed loop with respect to this attractor is handled. An anti-windup inspired loops is added aiming at improving the quality of the attractor approximation in which converge the closed-loop trajectories and of the basin of attraction of such an attractor. Numerically tractable algorithms with feasibility guarantee are provided, as soon as the linear closed-loop system, obtained by neglecting the backlash and saturation effects, is asymptotically stable. The interest of the results is drawn through an illustrative example.

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Section: B Regional Stabilitymentioning

confidence: 97%

Section: Feasibilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stability analysis of systems with nested saturation and backlash in the loop via nonstandard anti-windup compensation

Tarbouriech

Queinnec

Prieur

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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“…Utilizing generalized sector conditions, stability for systems with backlash and saturation is studied in [16].…”

Section: Compensation For Combined Backlash and Saturationmentioning

confidence: 99%

Backlash compensation for plants with saturating actuators

Rodríguez-Liñán

Heath²

2017

Proceedings of the Institution of Mechanical Engineers, Part I:

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A compensation scheme is proposed for plants subject to both saturation and backlash in series at the actuator. It is shown that the series connection of a backlash inverse, saturation and the backlash itself is equivalent to a saturation function at a different level to the original saturation; we call this the 'saturation equivalence'. Therefore it is proposed to include such a backlash inverse in the compensator. This is shown to be optimal in a sense defined in the paper.It is then straightforward to devise a compensator scheme based on traditional anti-windup. This is illustrated in both simulation and on a laboratory scale rig with severe backlash. A correction for the chattering observed in the control signal due to the discontinuous nature of the nonlinearity inverse is also presented.

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On sensor quantization in linear control systems: Krasovskii solutions meet semidefinite programming

Ferrante

Gouaisbaut

Tarbouriech

2019

IMA Journal of Mathematical Control and Information

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Stability and stabilization for linear state feedback control systems in the presence of sensor quantization are studied. As the closed-loop system is described by a discontinuous right-hand side differential equation, Krasovskii solutions (to the closed-loop system) are considered. Sufficient conditions in the form of matrix inequalities are proposed to characterize uniform global asymptotic stability of a compact set containing the origin. Such conditions are shown to be always feasible whenever the quantization-free closed-loop system is asymptotically stable. Building on the obtained conditions, computationally affordable algorithms for the solution to the considered problems are illustrated. The effectiveness of the proposed methodology is shown in three examples.

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Stability analysis for systems with saturation and backlash in the loop

Cited by 4 publications

References 20 publications

Stability analysis of systems with nested saturation and backlash in the loop via nonstandard anti-windup compensation

Stability analysis of systems with nested saturation and backlash in the loop via nonstandard anti-windup compensation

Backlash compensation for plants with saturating actuators

On sensor quantization in linear control systems: Krasovskii solutions meet semidefinite programming

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