Experimental rotation control of the parametric pendulum using a velocity approach

Abstract

This paper addresses the application of a simple control technique for reaching a stable rotational motion of the parametrically driven pendulum, starting from non-rotating responses. The control action consists of an assistance torque, which is provided conveniently to a pendulum wheel in order to increase its angular velocity. The magnitude of this torque is defined as inversely proportional to the magnitude of the angular velocity of the pendulum, which is computed in real time from angular position measurements. Maximum torque is applied when velocity is zero, while decreasing linearly as velocity increases. The assistance torque takes a very low value when the magnitude of the velocity reaches a threshold, which is defined in terms of the dynamics of the unforced pendulum. The direction of torque application depends on the sign of the angular velocity. The experiments show that rotations can be reached and maintained by means of this technique under a simple harmonic forcing and under an irregular forcing. Besides, since the control law is not dependent on the forcing period, it is intuited that it has the potential to produce good results under pseudo-stochastic forcing. This is of particular importance, with a view to a possible use in ocean wave energy converters, which is nowadays a promising engineering application of parametric pendulum systems. This is in line with the main motivation of this work, which is the implementation of this control technique to maintain the rotational motion of a pendulum-based wave energy converter.