PD control for global stabilization of an n-TORA system

This paper concerns a global stabilization problem for an n-TORA (Translational Oscillator with a Rotational Actuator) system which consists of n carts connected to the fixed walls and each other by n + 1 linear springs with each cart having an eccentric rotational proof-mass actuator moving in the horizontal plane. First, this paper derives the motion equation of the n-TORA system. Then, by using Lyapunov stability theory and physical properties of mechanical parameters of the n-TORA system, this paper proves that the global stabilization of the n-TORA system can be achieved by the PD control of the angle of the rotational proof-mass of each TORA. This paper presents numerical simulation results for the 2- and 3-TORA systems to validate the result of the global stabilization.