Limit cycles analysis of reset control systems with reset band

Baños, Alfonso; Dormido, Sebastián; Barreiro, Antonio

doi:10.1016/j.nahs.2010.07.004

Cited by 18 publications

(11 citation statements)

References 13 publications

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“…When D 1 or D 2 are crossed, the control u toggles between u 1 and u 2 , like in Section 2. The reset law in (25b) is similar to the reset band considered in [4,5]. On the other hand, when the branch D 0 is crossed, the system resets its actuation u to the rest value u 0 , which globally stabilizes the equilibrium (y 0 , 0), with y 1 < y 0 < y 2 , from any point of C 0 := R 2 .…”

Section: General Theorymentioning

confidence: 99%

“…In comparison to [4,5,[30][31][32], here we consider sustaining and damping oscillations (in a mechanical system) as complementary. The nature of the approach in [30][31][32] is close to our approach for the case of sustained oscillations, although we do not require any a priori knowledge about the existence of a hybrid periodic solution (as, for instance, in [30,Assumption 4.5, item 4)]).…”

Section: Introductionmentioning

confidence: 99%

“…The nature of the approach in [30][31][32] is close to our approach for the case of sustained oscillations, although we do not require any a priori knowledge about the existence of a hybrid periodic solution (as, for instance, in [30,Assumption 4.5, item 4)]). In [4,5], limit cycles are an undesired dynamics arising when stabilizing through linear resets the origin of a linear system; [5] relies on the matrix exponential for the Poincaré map, and [4] utilizes the approximate method of the describing function [25,Section 7.2]. Our underlying system is instead a nonlinear (one-degree-of-freedom) mechanical system; our approach is based on Poincaré map and Lyapunov analysis.…”

Section: Introductionmentioning

confidence: 99%

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Relay-based hybrid control of minimal-order mechanical systems with applications

et al. 2018

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Relay-based hybrid control of minimal-order mechanical systems with applications. Automatica, Elsevier, 2018, 97, pp. AbstractThis work explores the potential of relay-based control on a one-degree-of-freedom nonlinear mechanical system, in the contexts of both sustaining and damping oscillations. For both cases we state our main results building upon a simple reset formulation (relay feedback) and providing intuitive basic equations from classical mechanics. With a more rigorous description following a hybrid system formalism, we establish then the global asymptotic stability of the corresponding (compact-set) attractors through hybrid Lyapunov tools. The aspects of sustaining and damping oscillation are seen as complementary, because they reduce to a suitable mirroring of the reset surface. Finally, we discuss two applications of our results to the case of a hopping mass and an automotive suspension.

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Section: General Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Relay-based hybrid control of minimal-order mechanical systems with applications

et al. 2018

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“…The chosen tool is the Poincaré Map (PM) [14]. In this way the results here are complementary to the results in [2], where the analysis tool was the Describing Function. PM has been applied to piecewise linear systems in [9], this approach is similar to ours (with switching in place of resetting) and provides estimations of the domain of attraction of the limit cycles.…”

Section: Introductionmentioning

confidence: 88%

“…In particular, we obtain the fixed point x LC 2 = 0.105 and half-period τ 0 = 3.418 sec., and thus f ′ (x LC 2 ) = (A r EA r E) (2,2) = 0.2866 < 1.…”

Section: Limit Cycles and Poincaré Mapsmentioning

confidence: 99%

Reset Control Systems with Reset Band: Well-posedness and Limit Cycles Analysis

Barreiro

Baños

Dormido

2011

2011 19th Mediterranean Conference on Control &Amp; Automation (MED)

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Reset controllers provide a simple way to improve performance when controlling strongly traded-off plants. A reset controller operates most of the time as a linear system, but when some condition holds, it performs a zero resetting action on its state. Recently, some generalizations have been proposed: anticipation of the condition with the so-called reset band, relaxation of the action applying partial reset, etc.There is a lack of analysis tools for reset systems with reset band. In this paper we address the problem of existence, detection and stability of limit cycles by means of Poincaré maps. The results give also information on pathologies such as Zenoness. The presented approach is complementary to describing function analysis, in order to reveal the ability of reset controllers for overcoming fundamental limitations in the frequency domain.

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Performance improvement of SISO linear control systems by hybrid state resetting and sector confinement of trajectories

González

Barreiro

Dormido

et al. 2016

Intl J Robust & Nonlinear

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Summary Reset control techniques have been proposed to overcome fundamental limitations of linear controllers by means of their transformation into hybrid models that combine continuous flow and discrete jump dynamics. The hybrid nature in the control loop involves some difficulties when analyzing the performance of the controller and some drawbacks on the controller design related to the stability conditions. The technique that we propose is based on sector confined target dynamics of the continuous flow mode by means of the application of the discrete reset jumps. This behavior, in the error plane (e(t),ė(t)), is correlated with certain preferred sectors that lead to fast and over‐damped responses. The paper studies how to design a hybrid resetting version of a linear controller that achieves the required fast and over‐damped responses to arbitrary references. Copyright © 2016 John Wiley & Sons, Ltd.

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Limit cycles analysis of reset control systems with reset band

Cited by 18 publications

References 13 publications

Relay-based hybrid control of minimal-order mechanical systems with applications

Relay-based hybrid control of minimal-order mechanical systems with applications

Reset Control Systems with Reset Band: Well-posedness and Limit Cycles Analysis

Performance improvement of SISO linear control systems by hybrid state resetting and sector confinement of trajectories

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