Third-order integral sliding mode control of piezoelectric actuators based on rate-amplitude-dependent Prandtl-Ishlinskii model

Aiming at trajectory tracking control of piezoelectric actuators (PEAs), this article proposes a third-order integral sliding mode control (3-ISMC) based on rate-amplitude-dependent Prandtl-Ishlinskii (PI) inverse model feedforward (3-RAPI) scheme, which can achieve finite time convergence and avoid singular problems, while ensuring the continuity of the control signal. In this control scheme, a rate-amplitude-dependent PI (RAPI) model is proposed to describe the hysteresis characteristics of PEA, and the RAPI hysteresis inverse model is used to realize the feedforward control. The simulation results verify the improvement of the modeling accuracy of the RAPI model compared with the traditional PI model. In order to reduce the influence of modeling error and improve the robustness of the system, a 3-ISMC scheme based on integral non-singular fast terminal sliding mode surface is proposed. Simulation and experimental results demonstrate that the tracking performance of 3-ISMC is improved compared with the existing third-order integral terminal sliding model control (3-ITSMC). Finally, the composite control algorithm is realized by combining the RAPI hysteresis inverse model feedforward with the 3-ISMC algorithm. The experimental results further show that the control algorithm can track the input signal in a wide range of rate and amplitude.