Adaptive displacement control with hysteresis modeling for piezoactuated positioning mechanism

An adaptive displacement control with hysteresis modeling for a piezoactuated positioning mechanism is proposed in this paper because the dynamic performance of piezosystems is often severely deteriorated due to the hysteresis effect of piezoelectric elements. First, a new mathematical model based on the differential equation of a motion system with a parameterized hysteretic friction function is proposed to represent the dynamics of motion of the piezopositioning mechanism. As a result, the mathematical model describes a motion system with hysteresis behavior due to the hysteretic friction. Then, by using the developed mathematical model, the adaptive displacement tracking control with the adaptation algorithms of the parameterized hysteretic function and of an uncertain parameter is proposed. By using the proposed control approach on the displacement control of the piezopositioning mechanism, the advantages of the asymptotical stability in displacement tracking, high-performance displacement response, and robustness to the variations of system parameters and disturbance load can be provided. Finally, experimental results are illustrated to validate the proposed control approach for practical applications.