Feedback control of multibody systems with joint clearance and dynamic backlash: a tutorial

Brogliato, Bernard

doi:10.1007/s11044-017-9585-4

Cited by 21 publications

(31 citation statements)

References 78 publications

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“…The major issues for the control of such systems are the under-actuation. More recently, Brogliato [468] studied the problem of feedback control of mechanisms with joint clearance, and three important feedback controllers, mainly the impactless trajectories with persistent contact, control through collisions, the stabilization of equilibrium points, and the trajectory tracking control, were comparatively analyzed. Zhao and his co-authors [469] presented a methodology to improve the accuracy prediction of dynamic behavior of planar mechanism with dry clearance joints, with particular application to a reciprocating compressor.…”

Section: Optimization and Control Of Mechanisms With Clearance Jointsmentioning

confidence: 99%

A comprehensive survey of the analytical, numerical and experimental methodologies for dynamics of multibody mechanical systems with clearance or imperfect joints

Tian

Flores

Lankarani

2018

Mechanism and Machine Theory

306

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A comprehensive survey of the literature of the most relevant analytical, numerical, and experimental approaches for the kinematic and dynamic analyses of multibody mechanical systems with clearance joints is presented in this review. Both dry and lubricated clearance joints are addressed here, and an effort is made to include a large number of research works in this particular field, which have been published since the 1960's. First, the most frequently utilized methods for modeling planar and spatial multibody mechanical systems with clearance joints are analyzed, and compared. Other important phenomena commonly associated with clearance joint models, such as wear, non-smooth behavior, optimization and control, chaos, and uncertainty and links' flexibility, are then discussed. The main assumptions procedures and conclusions for the different methodologies are also examined and compared. Finally, future developments and new applications of clearance joint modeling and analysis are highlighted.

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Section: Optimization and Control Of Mechanisms With Clearance Jointsmentioning

confidence: 99%

A comprehensive survey of the analytical, numerical and experimental methodologies for dynamics of multibody mechanical systems with clearance or imperfect joints

Tian

Flores

Lankarani

2018

Mechanism and Machine Theory

306

View full text Add to dashboard Cite

show abstract

“…This property holds generically for DIs with compact, convex valued and upper semicontinuous right-hand sides [249], and we note that the DIs considered in [495] satisfy these assumptions. The stability analysis in [131] uses the results in [385].…”

Section: Other Resultsmentioning

confidence: 99%

“…The feedback control problem for crawlers, which has engineering interest [98], remains largely open and could certainly benefit from the studies on the control of FOSwP. When masses are non zero, they belong to the class of so-called "juggling systems" whose structure is particular [140,131]. It is noteworthy that so-called play operators of hysteresis (as in Figure 2.3 (b) [440,149,85], and naturally yields Lur'e set-valued systems [20,561].…”

Section: Compliant Contact/impact Modelsmentioning

confidence: 99%

“…The Aubin/Lipschitz property of GEs with parameters (which characterizes how solution sets of GEs vary with parameters) is studied in [18,15] when F (•) in (6.1) is a subdifferential. Contact mechanics equilibria without Coulomb friction are studied in [131] [130,Section 7.5.2], and with Coulomb friction in [76,83,82,330,482], where the GEs for equilibria are analysed in great detail. In the latter setting, the equilibria usually are not unique (sets of equilibria exist) due to the set-valuedness of friction.…”

Section: (62)mentioning

confidence: 99%

“…• The Lejeune-Dirichlet (or Lagrange-Dirichlet) Theorem is extended to frictionless multicontact systems in [131,126], and to the case with set-valued friction in [386,385,547]. • Stability through finite accumulation of impacts (the so-called Zeno equilibria) is analysed in [453,452,383,147,568], with Lyapunov function [453,383].…”

Section: Sufficient Lyapunov Conditions Let Us Now Provide Brief Insmentioning

confidence: 99%

See 2 more Smart Citations

Dynamical Systems Coupled with Monotone Set-Valued Operators: Formalisms, Applications, Well-Posedness, and Stability

Brogliato¹,

Tanwani²

2020

SIAM Rev.

Self Cite

117

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This survey article addresses the class of continuous-time systems where a system modeled by ordinary differential equations (ODEs) is coupled with a static and time-varying setvalued operator in the feedback. Interconnections of this form model certain classes of nonsmooth systems including sweeping processes, differential inclusions with maximal monotone right-hand side, complementarity systems, differential and evolution variational inequalities, projected dynamical systems, some piecewise linear switching systems. Such mathematical models have seen applications in electrical circuits, mechanical systems, hysteresis effects, and many more. When we impose a passivity assumption on the open-loop system, and regard the set-valued operator in the feedback as maximally monotone, we obtain a set-valued Lur'e dynamical system. In this article we review the mathematical formalisms, their relationships, main application fields, well-posedness (existence, uniqueness, continuous dependence of solutions), and stability of equilibria. An exhaustive bibliography is provided.

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Control of systems with time varying unilateral constraints using robust and optimal controllers: A homogeneity framework

Oza

Orlov

2020

Intl J Robust & Nonlinear

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Summary A tracking problem is studied in this article where a time‐varying unilateral constraint and disturbances are present. An extension to the method of nonsmooth state transformation is developed. The proposed framework enables synthesis and analysis of control of a rigid body colliding with a time‐varying unilateral constraint. Both the translational and rotational dynamics in three dimensions are covered. The control problem encompasses continuous and discontinuous controllers in the presence of impacts and discontinuous disturbances. This leads to new results in the area of control of systems with impacts and dry friction, a well‐known challenging direction in nonsmooth mechanics. Major contribution of the article is in achieving finite‐time tracking for a class of unilaterally constrained systems where the system dynamics with impacts are converted into one without impacts. Stability results are obtained via the homogeneity of differential inclusions. Numerical simulations are shown to demonstrate specific examples of the theoretical development.

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Feedback control of multibody systems with joint clearance and dynamic backlash: a tutorial

Cited by 21 publications

References 78 publications

A comprehensive survey of the analytical, numerical and experimental methodologies for dynamics of multibody mechanical systems with clearance or imperfect joints

A comprehensive survey of the analytical, numerical and experimental methodologies for dynamics of multibody mechanical systems with clearance or imperfect joints

Dynamical Systems Coupled with Monotone Set-Valued Operators: Formalisms, Applications, Well-Posedness, and Stability

Control of systems with time varying unilateral constraints using robust and optimal controllers: A homogeneity framework

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