A Finite-Time Sliding-Mode Controller Based on the Disturbance Observer and Neural Network for Hysteretic Systems with Application in Piezoelectric Actuators.

Piezoelectric actuators (PEAs) have the benefits of a high-resolution and high-frequency response and are widely applied in the field of micro-/nano-high-precision positioning. However, PEAs undergo nonlinear hysteresis between input voltage and output displacement, owing to the properties of materials. In addition, the input frequency can also influence the hysteresis response of PEAs. Research on tracking the control of PEAs by using various adaptive controllers has been a hot topic. This paper presents a finite-time sliding-mode controller (SMC) based on the disturbance observer (DOB) and a radial basis function (RBF) neural network (NN) (RBF-NN). RBF-NN is used to replace the hysteresis model of the dynamic system, and a novel finite-time adaptive DOB is proposed to estimate the disturbances of the system. By using RBF-NN, it is no longer necessary to establish the hysteresis model. The proposed DOB does not rely on any priori knowledge of disturbances and has a simple structure. All the solutions of closed-loop systems are practical finite-time-stable, and tracking errors can converge to a small neighborhood of zero in a finite time. The proposed control method was compiled in C language in the VC++ environment. A series of comparative experiments were conducted on a platform of a commercial PEA to validate the method. According to the experimental results of the sinusoidal and triangular trajectories under the frequencies of 1, 50, 100, and 200 Hz, the proposed control method is feasible and effective in improving the tracking control accuracy of the PEA platform.