Abstract

In the kinematic formulation, two problems are considered for the time-optimal control of the position of a single-link pendulum fixed on a movable base that can move along the horizontal axis. In the first problem, the initial position of the pendulum is the lower, stable position of the pendulum; it is required to transfer it to the upper, unstable position resting either in an arbitrary or a given place along the horizontal axis. In the second problem, the initial position is, on the contrary, the upper position. It is required to move the pendulum along the horizontal axis, while maintaining its original vertical position at the end. Both problems are considered based on nonlinear equations. The numerical solution of the problems is preceded by an analysis of the optimality conditions arising from the maximum principle in the case of the kinematic control of these objects.

中文翻译：

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关于通过摆的运动控制摆的垂直位置的快速动作

摘要

在运动学公式中，在时间最优控制固定在可沿水平轴移动的可移动基座上的单连杆摆的位置时，考虑了两个问题。在第一个问题中，摆的初始位置是摆的较低的稳定位置。需要将其转移到水平轴上任意位置或给定位置的不稳定上部位置。在第二个问题中，相反，初始位置是较高位置。需要沿水平轴移动摆锤，同时在末端保持其原始垂直位置。基于非线性方程考虑了两个问题。