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On the Prevention of Vibrations in the Problem of the Time-Optimal Control of a System with Two Degrees of Freedom

  • OPTIMAL CONTROL
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Journal of Computer and Systems Sciences International Aims and scope

Abstract

We study a mechanical system with two degrees of freedom, consisting of two absolutely rigid bodies (material points) connected to each other by a weightless rectilinear viscoelastic rod that can be stretched or compressed. The bodies can move translationally along a fixed straight line. A control force limited in absolute value is applied to one of them, whose vector is directed along the rod. A continuous piecewise-linear control in time, which transfers the system from one equilibrium position to another in a length of time close to the minimum possible time, is constructed. In the absence of viscosity, with the constructed quasi time-optimal control, unwanted vibrations of the bodies are not excited either during the transition process or when it ends. In contrast to the time-optimal relay control, the constructed continuous control is also robust with respect to the uncertainty of the design parameters.

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Funding

This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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  1. Institute of Mechanics, Lomonosov Moscow State University, 119991, Moscow, Russia

    Yu. D. Selyutskiy & A. M. Formalskii

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  1. Yu. D. Selyutskiy
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  2. A. M. Formalskii
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Correspondence to Yu. D. Selyutskiy or A. M. Formalskii.

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Selyutskiy, Y.D., Formalskii, A.M. On the Prevention of Vibrations in the Problem of the Time-Optimal Control of a System with Two Degrees of Freedom. J. Comput. Syst. Sci. Int. 62, 956–967 (2023). https://doi.org/10.1134/S1064230723060096

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  • DOI: https://doi.org/10.1134/S1064230723060096

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