Robust optimal output-feedback control of piezoelectric motion systems with composite adaptive hysteresis compensation

This article proposes a robust optimal output-feedback control scheme for solving the optimal tracking problem of a piezoelectric motion system, where the model of the piezoelectric motion system is represented by the linear dynamics with both asymmetric input hysteresis nonlinearities and various bounded disturbances. Different from the existing hysteresis model, the neural network is incorporated in the Prandtl-Ishlinskii model to depict the asymmetric feature of the input hysteresis nonlinearity, a novel fast composite adaptive identification method is proposed to obtain the parameters of the asymmetric input hysteresis model. Based on the identified asymmetric hysteresis model, its inverse is constructed to compensate the asymmetric hysteresis nonlinearities of the piezoelectric motion system, and the boundedness of the inverse compensation error is firstly analyzed. In particular, a robust optimal output-feedback controller with a finite-time extend state observer is designed to achieve the optimal tracking of the piezoelectric motion system in the presence of the unknown states and disturbances. Both the convergence of the hysteresis model parameters and the stability of the closed-loop system are analyzed. Finally, the excellent modeling and identification accuracy of the asymmetric input hysteresis nonlinearities and the satisfactory tracking performance of the proposed control scheme are demonstrated by real-time experiments on a piezoelectric motion stage.