Two-parameter robust repetitive control with application to a novel dual-stage actuator for noncircular Machining

This work presents a robust repetitive controller design for a novel dual-stage actuator system. The dual-stage actuator, which consists of an electrohydraulic actuator for 25-mm-gross motion and a piezoelectric actuator for 40-μm fine motion, is designed for noncircular machining application. The controller is designed through a sequence of two single-input-single-output (SISO) designs by exploiting the triangular structure of the two by two actuator system dynamics. The tracking error from the first stage electrohydraulic actuator is used as reference for the second stage piezoelectric actuator. In this master-slave control arrangement, the overall sensitivity function is the product of two sensitivity functions from each actuator´s servo loop. Thus, performance is improved at the frequencies where the sensitivity values are already well less than one. In the real-time control implementation, the effects of finite word length are analyzed and addressed via controller order reduction and realization. In an experiment of tracking an automotive cam profile at the rate of 10 cycles per second (600 rpm), the proposed dual-stage servo system generated tracking error of 4-μm peak-to-valley and 0.80-μm root-mean-square (RMS) value, showing a substantial improvement over the 16 micron peak-to-valley and 2.64-μm RMS errors generated by the electrohydraulic servo system alone.