Tracking Control of a Piezo Positioning Stage with Scalar Sign Function and Digital Redesign Technique

Piezoceramic materials are widely used in various applications, such as vibration control, structural health monitoring and micro-positioning devices. Piezoceramic actuators exhibit hysteresis nonlinearity due to their ferroelectric nature. This nonlinearity results in system inaccuracy and deteriorated performances for precision devices. A scalar sign function-based digital redesign control methodology is developed to establish a linear relationship between input and output of a piezoelectric actuator with absolute value state and input constraints. The scalar sign function is first utilized to obtain an optimal linear model of the constrained non-smooth state and input functions of the piezoelectric system, which has the exact dynamics of the original nonlinear system at the operating point of interest and minimal modeling errors in the vicinity of the operating point on the trajectory. A digitally redesigned optimal state feedback tracking controller with prediction feature is implemented on the nonlinear system. In addition, a prediction based digital observer is designed to estimate the unavailable state variables of the system.