Piecewise affine modeling and compensation in motion of linear ultrasonic actuators

Ultrasonic actuators used in high-precision mechatronics possess strong frictional effects, which are among the main problems in precision motion control. Traditional methods apply model-based nonlinear feedforward to compensate the friction, thus requiring closed loop stability and safety constraint considerations. In this article, model-based parametric controllers are developed to obtain an optimal positioning control for these motors. A systematic approach which uses piecewise affine models greatly simplifies the friction model compared to the traditional methods. Issues about the nonlinear effects of the friction are addressed by designing a robust control law near zero speed. These developments result in a gain-scheduling optimal input, which is simple to carry out in real-time applications. The controller is expected to improve the safety constraints and the tracking performance for actuator operation.