Nonlinear adaptive tracking control of piezoelectric bimorph actuator using hybrid modeling approach

Piezoelectric bimorph actuator has the advantages of small size, fast response speed and high displacement accuracy, but its inherent hysteresis nonlinearity seriously affect the control accuracy and stability of the system. The dead-zone operator was incorporated into classical Prandtl–Ishlinskii model to enable the description of asymmetric hysteresis of piezoelectric bimorph actuator. A hybrid model approach was developed with neural network and improved Prandtl–Ishlinskii model, and it has the advantages of a neural network with ready-made training algorithms and improve the Prandtl–Ishlinskii (PI) model to describe the asymmetric hysteresis. The adaptive control method was derived from training algorithm of neural network, which can update the weight parameters of Play operator and Dead-zone operator in real time. Comparing the results without control, the RMSE of displacement error decreases by 61.35% with classic model, and decreases by 82.93% with hybrid model and proposed adaptive tracking control. Experimental results show that the proposed hybrid model and adaptive control approach can more effectively compensate the hysteresis of piezoelectric bimorph.