Adaptive Sub-Nanometer Control of a Piezoelectric Positioning Platform

This paper reports an asymmetric Bouc-Wen (ABW) hysteresis model and a hybrid control algorithm based on multi-modal Bayesian gradient optimization (MBGO) for trajectory tracking in the micro-positioning phase of a piezoelectric positioning platform. First, a system-level dynamic model capable of expressing hysteresis nonlinearity is established based on the asymmetric Bouc-Wen model. Second, an MBGO parameter identification algorithm based on Particle Swarm Optimization (PSO) is proposed to improve the characterization capability of the hysteresis model. Subsequently, a feedforward adaptive fuzzy PID (FF-AFPID) composite controller is designed by compensating the hysteresis nonlinearity through the ABW inverse model while dynamically adjusting PID parameters with adaptive fuzzy rules. Through triangular and sinusoidal trajectory tracking experiments, the root mean square errors were reduced to 0.112 nm and 0.103 nm by the FF-AFPID, with an improvement of 74.944%, 57.088% (triangular) and 77.511%, 57.083% (sinusoidal) over the FF-PID and FF-FPID algorithms, respectively. The results demonstrate that the trajectory tracking of performance the positioning platform in micro-positioning phase was significantly enhanced by FF-AFPID, with the maximum error being suppressed to sub-nanometer levels.