Robust control of uncertain asymmetric hysteretic nonlinear systems with adaptive neural network disturbance observer

In this article, a novel command-filtered adaptive control scheme is proposed for uncertain asymmetric hysteretic nonlinear systems with unknown external disturbances, where the hysteresis nonlinearities are described by an asymmetric Bouc–Wen model. Firstly, the hysteresis model uncertainties are considered, a robust hysteresis state observer is constructed to compensate the asymmetric hysteresis nonlinearity. Secondly, both tracking errors and prediction errors are employed to develop the adaptive neural networks (NNs) for approximating unknown nonlinear functions of the system, where the acquisition of the prediction error avoids the need to differentiate the state measurements. Then, a nonlinear disturbance observer with the filtered control input and system states is constructed to estimate a total disturbance resulting from both the NN approximation errors and the external disturbances. With the help of filtering differentiators, a command-filtered backstepping control law is designed by using the adaptive NN approximators, the disturbance observers, and the hysteretic compensator. The effects of the filtering errors, the disturbance estimation errors, and the hysteresis compensation error on the closed-loop stability are rigorously analyzed. Finally, the proposed control algorithm is applied to a piezoelectric micro-displacement servo system, the real-time experimental results indicate that the relative average error and the relative maximal error of the sinusoidal trajectory tracking are 0.04% and 0.06%, respectively. Compared with the existing adaptive robust control algorithm, a significant improvement on the tracking accuracy is achieved.