Stabilizing Switching Force Control for the Hunt-Crossley Model

This paper proposes a switching control scheme for the Hunt-Crossley model, which represents the behavior of contact between two surfaces in mechanical systems. The scheme comprises a PID force feedback controller and a position/velocity feedback controller. Its objective is to apply the desired amount of pressure while ensuring closed-loop stability. The PID force feedback controller operates in contact mode, while the position/velocity feedback controller operates in non-contact mode. For the PID control, a non-quadratic Lyapunov function is devised together with an invariant domain of attraction within the contact region, including the equilibrium steady state. For the non-contact region where the state trajectories stay only temporarily, the position/velocity feedback control is equipped with a disturbance compensation term on the basis of a Lyapunov min-max approach, which leads to a quadratic Lyapunov function. Notice the two different ways of achieving infinite gain operation for handling modeling errors and disturbances: infinite gain at DC, resulting from integral action in the contact mode, and infinite gain at equilibrium, resulting from the use of a signum function in the non-contact mode. The asymptotic stability of the overall switching control system is proven by demonstrating that the two Lyapunov functions defined in the contact and non-contact regions satisfy certain decreasing properties. Simulations confirm that the applied force closely tracks the desired value in the presence of a DC disturbance and model uncertainty.