Robust impulsive control of motion systems with uncertain friction

Wouw, van de N Nathan; Leine, Remco I.

doi:10.1002/rnc.1694

Cited by 25 publications

(20 citation statements)

References 34 publications

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“…In [8], and references therein, it is seen that the first-order necessary conditions for the optimization of a quadratic cost problem subjected to systems with unilateral constraints result in differential equations with measures. Other than the optimization problems, control of mechanical systems in the presence of friction may necessitate the use of impulsive (or measure) control for stabilization [45]. The basic problem in studying the solution of MDE (2) comes due to the product g(·)du.…”

Section: Literature Overviewmentioning

confidence: 99%

Stability notions for a class of nonlinear systems with measure controls

Tanwani

Brogliato

Prieur

2015

Math. Control Signals Syst.

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We consider the problem of stability in a class of differential equations which are driven by a differential measure associated with inputs of locally bounded variation. After discussing some existing notions of solution for such systems, we derive Lyapunov-based conditions on the system's vector fields for asymptotic stability under a specific class of inputs. These conditions are based on the stability margin of the Lebesgue-integrable and the measure-driven components of the system. For more general inputs which do not necessarily lead to asymptotic stability, we then derive conditions such that the maximum norm of the resulting trajectory is bounded by some function of the total variation of the input, which generalizes the notion of integral input-to-state stability in measure-driven systems.

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Section: Literature Overviewmentioning

confidence: 99%

Stability notions for a class of nonlinear systems with measure controls

Tanwani

Brogliato

Prieur

2015

Math. Control Signals Syst.

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“…The proposed feed-forward approximation is used in a composite controller/observer strategy that forces the average square integral of the position tracking error to an arbitrarily small value. Some robust set-point stabilization problem for motion systems subject to friction is analyzed in [26]. Uncertainties in the friction model are unavoidable, therefore an impulsive feedback control design that robustly stabilizes the setpoint for a class of position-, velocity-and time-dependent friction laws with an uncertainty is proposed.…”

Section: Friction Modeling In Contact Mechanics and Control Of Disconmentioning

confidence: 99%

An approximation method for the numerical solution of planar discontinuous dynamical systems with stick-slip friction

Olejnik¹,

Awrejcewicz²,

Fečkan³

2014

ams

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The time moment of appearance of zero relative velocity during displacements of contacting bodies in dynamical systems with dry friction can be precisely computed. In this work, there is proposed an event driven numerical scheme allowing for integration of discontinuous differential equations. The study shows, that a direct application of standard integration methods may produce some inaccurate estimations of stick-slip transitions observed during frictional relative displacements. Results of numerical computations obtained by means of the proposed method of approximation of one degree-of-freedom dynamical system with dry friction confirm good accuracy of the determination of sticking phases. By comparison of two apparently similar solutions there has been shown and explained a significant difference in their smoothness and accuracy of estimation of the sticking phase's boundaries. The P. Olejnik, J. Awrejcewicz and M. Fečkan phase observed in an approximate solution of the analyzed discontinuous counterpart is smooth, and its ends are more precisely estimated. Reasonable accuracy of the solution could be obtained by a decrease of fitting parameter of the proposed approximate method to an exact sticking phase. For a comparison, three numerical procedures performed in Python and Matlab have been included. The usefulness of this method was verified by calculation of elementary work against the friction force to yield an acceptable accuracy.Mathematics Subject Classification: 65D30, 68W25, 34A36, 74M10

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“…Non-model-based control techniques do not aim at friction compensation, but change the effect of friction on the closed-loop system to obtain the desired performance. Examples are impulsive control [7] or dithering-based controllers [8]. A drawback of these control schemes is that the use of impulsive control forces may result in excitation of unmodeled, high-frequency system dynamics.…”

Section: Introductionmentioning

confidence: 99%

Hybrid PID control for transient performance improvement of motion systems with friction

Beerens

Bisoffi

Zaccarian

et al. 2018

2018 Annual American Control Conference (ACC)

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We present a novel reset control approach to improve transient performance of a PID-controlled motion system subject to friction. In particular, a reset integrator is applied to circumvent the depletion and refilling process of a linear integrator when the system overshoots the setpoint, thereby significantly reducing settling times. Moreover, robustness for unknown static friction levels is obtained. A hybrid closed-loop system formulation is derived, and stability follows from a discontinuous Lyapunov-like function and a meagre-limsup invariance argument. The working principle of the controller is illustrated by means of a numerical example.

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Robust impulsive control of motion systems with uncertain friction

Cited by 25 publications

References 34 publications

Stability notions for a class of nonlinear systems with measure controls

Stability notions for a class of nonlinear systems with measure controls

An approximation method for the numerical solution of planar discontinuous dynamical systems with stick-slip friction

Hybrid PID control for transient performance improvement of motion systems with friction

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