Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

A Time-optimal Problem of Stopping a Two-link Pendulum on a Movable Mount

Author(s):

Anton Pavlovich Potapov

Technician of Laboratory 38 of Instute of Control Sciences RAS (ICS RAS),
4th year student of the Department of Physical and Mathematical Methods of Control,
Faculty of Physics, Moscow State University M.V. Lomonosov (MSU)

potapov@ipu.ru

Andrey Alekseevich Galyaev

Doctor of Technician Sciences, Corresponding Member RAS,
Head of the Laboratory 38 of Instute of Control Sciences RAS (ICS RAS),
Head of the Department of Physical and Mathematical Methods of Control,
Faculty of Physics, Moscow State University M.V. Lomonosov (MSU)

galaev@ipu.ru

Abstract:

We consider a time-optimal problem of stopping a two-link pendulum on a movable mount. Given nonlinear system with the lack of and limitation on the control resource is linearized in the neighborhood of a stable equilibrium position. For a linearized system the Pontryagin maximum principle is used and the optimal control law obtained. To estimate parameters of the law basing on finding out an orthogonal subspace was an algorithm developed for constructing a time-optimal system control. A software module has been developed in the Matlab environment with the help of which a comparison of the dynamics of linear and nonlinear systems with the obtained control law was made.

Keywords

• Pontryagin maximum principle
• time-optimal problem
• two-link pendulum

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