Modeling and Two-Input Sliding Mode Control of Rotary Traveling Wave Ultrasonic Motors

Traveling wave ultrasonic motors are actuators relying on piezoelectric ceramics that combine many advantageous features, such as high stalling torque, fast response, compactness, and magnetic resonance compatibility. However, they suffer from nonlinear dynamics, load-dependent dead zones, and the difficulty to control low speeds. In this paper, we present a novel second-order model for traveling wave ultrasonic motors. It is based on a dry friction driving principle and features dead zone effects. Based on the model, a two-input sliding mode controller is designed. It controls both phase difference and frequency of the traveling wave, without the necessity of implementing a signum function. With this controller, the state-of-the-art is extended to the position control case, while at the same time using fine-grained phase difference control for low velocities. Moreover, we show global uniform asymptotic stability for bounded disturbances and that velocity jumps do not appear when the control domains of phase difference and frequency are switched. Finally, both the model and the controller are evaluated via simulations and experiments that include the response to a position step input under various opposing torques.