Nonlinear control for linear motors with friction - Application to an inverted pendulum system

International audienceA linear motor is used here as an actuator for a cart-pendulum system. The global, upward stabilization of the inverted position is aimed at. In such an under-actuated situation, (i) constraints on the motor motion (limited length) have to be taken into account and (ii) friction effects may have a strong influence (limit cycles). A two-step path planning-plus-tracking strategy allows for dealing with constraint (i). Regarding point (ii), and since friction effects are hardly modeled, a second-order sliding mode algorithm is chosen. The resulting controller is designed without any knowledge of neither the electromagnetic circuits of the linear motor (the model is a simple gain), nor the friction models (only upper bounds for the friction forces acting on both the linear motor and pendulum are required). Experimental results show good performances in tracking and regulation, both for the swing-up and stabilization phases of the inverted pendulum