Abstract
In this paper, a control law to stabilize the amplitude or rotational speed of a variable length pendulum to a desired value by periodically changing the position of the center of gravity is proposed. First, the motion of the pendulum oscillating around a lower equilibrium point is analyzed using the averaging method, and a first-order differential equation for the amplitude of the pendulum is derived. Subsequently, using the derived equation of motion, a control law is designed to control the amplitude of the pendulum to the desired value. Similarly, the motion of a pendulum rotating continuously around the rotation axis is analyzed, the first-order differential equation for the angular velocity of the pendulum is derived, and then a control law of the rotational speed is designed. The derived nonlinear feedback control law consists of the amplitude, angle, and angular velocity of the pendulum in the case of amplitude control, and in the case of rotational speed control, the rotational velocity and angular acceleration of the pendulum. Finally, by using the proposed control method, it is shown that the amplitude and rotational speed of the pendulum can be controlled to the desired values.
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