Global stability for systems with nested backlash and saturation operators

Tarbouriech, Sophie; Prieur, Christophe; Queinnec, Isabelle; Santos, Talía Simões dos

doi:10.1109/acc.2010.5531321

Cited by 4 publications

(6 citation statements)

References 13 publications

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“…Furthermore, the satisfaction of relation (15) ensures that the set S 1 , defined in (17) is included in the region S(G, u 0 ) in which the sector condition on ϕ is satisfied. Hence, in S 1 , we can writeV (x) ≤V (x) − 2ϕ ′ T (sat(Ky) + Gx).…”

Section: B Stability Analysismentioning

confidence: 99%

“…Remark 3: The kind of systems studied in [17] could be addressed by using the framework of the current paper. In [17], the following system is considered:…”

Section: B Stability Analysismentioning

confidence: 99%

“…According to our framework, in the global case (i.e. matrix A is Hurwitz) we can relax the condition (10) in [17] linking up K 1 and K 2 .…”

Section: B Stability Analysismentioning

confidence: 99%

“…In this case, the outer set becomes all the state space, provided that the openloop system is not strictly exponentially unstable. Furthermore, at the opposite of conditions developed in [17], we do not need to use the time-derivative version of the system. Moreover, while [7] addresses the characterization of the global finite-time attractor (no saturation being considered), our approach uses the knowledge of the Lyapunov function and, in this sense, can be considered as bringing a new brick to complement the method proposed in [7].…”

Section: Introductionmentioning

confidence: 99%

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Stability analysis for systems with saturation and backlash in the loop

Tarbouriech

Queinnec

Prieur

2013

52nd IEEE Conference on Decision and Control

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This paper deals with the stability analysis problem for linear systems with saturation and backlash in the loop. The resulting system controlled by a static output feedback is a dynamical model with nested backlash and saturation operators. Uniform ultimate boundedness stability is tackled in a regional (local) or global context depending on the stability property of the open-loop system. Suitable regions of the state space in which the closed-loop trajectories can be captured are characterized, together with estimates of the basin of attraction of such regions. Convex optimization problems are proposed in order to give a constructive solution (in the sense of theoretical conditions associated to numerical procedures).

show abstract

Section: B Stability Analysismentioning

confidence: 99%

“…Remark 3: The kind of systems studied in [17] could be addressed by using the framework of the current paper. In [17], the following system is considered:…”

Section: B Stability Analysismentioning

confidence: 99%

“…According to our framework, in the global case (i.e. matrix A is Hurwitz) we can relax the condition (10) in [17] linking up K 1 and K 2 .…”

Section: B Stability Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stability analysis for systems with saturation and backlash in the loop

Tarbouriech

Queinnec

Prieur

2013

52nd IEEE Conference on Decision and Control

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“…These constraints are included in the MPC design requiring the online solution of a mixed-integer quadratic program. A stability analysis for control systems with such nonlinearities can be found by Tarbouriech et al 14,15 using Lyapunov functions and linear matrix inequalities (LMIs).…”

Section: Introductionmentioning

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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Controller structure for plants with combined saturation and deadzone/backlash

Linan

Heath

2012

2012 IEEE International Conference on Control Applications

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Global stability for systems with nested backlash and saturation operators

Cited by 4 publications

References 13 publications

Stability analysis for systems with saturation and backlash in the loop

Stability analysis for systems with saturation and backlash in the loop

Backlash compensation for plants with saturating actuators

Controller structure for plants with combined saturation and deadzone/backlash

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