Force Ripple Compensation in Linear Motors Based on Closed-Loop Position-Dependent Identification

Permanent-magnet linear synchronous motors can serve as direct-drive actuators for machine tools and production machines, whenever high dynamic performance are required. Since compliance in transmission elements is eliminated, higher control bandwidths can be achieved, when compared to traditional solutions based on conversion from rotational to linear motion. Like their rotational counterparts, these motors are, however, affected by a ripple, in the form of parasitic and undesired force pulsations. In this paper, a compensation scheme of force ripple is proposed, based on a simple and compact model of the disturbance. The compensation requires a preliminary identification stage that simply consists of a couple of controlled motions at constant and very low velocity. The compensation term is then applied in parallel to the position/velocity controller, as a function of the linear position of the motor. A robustness analysis is performed based on a convenient formulation of the closed-loop system, as well as on a Lyapunov argument. Experiments that demonstrate the effectiveness of the method are reported, even when compared to a traditional force disturbance observer.