Dual-layer sliding mode motion control of piezoelectric stick-slip actuator based on nonlinear extended state observer

Abstract In this article, a dual-layer sliding mode control scheme based on a nonlinear extended state observer (NESO) is designed to achieve displacement tracking of the piezoelectric stick-slip actuator (PSSA). A simple and continuous friction model is constructed based on the Coulomb friction model and the hyperbolic tangent function, and the electromechanical-rigid-flexible-friction coupled dynamics of the PSSA is established. By introducing a tracking differentiator, the overshoot that adversely affects displacement control is effectively suppressed, while the unknown nonlinear characteristics of the PSSA are actively estimated through the NESO. The convergence speed and control accuracy of the PSSA are enhanced by the designed dual-layer sliding mode controller, and the stability of both the NESO and the controller is analyzed using the Lyapunov method and finite-time control theory. Finally, experimental results on motion control demonstrate that the proposed dual-layer sliding mode approach effectively achieves the desired positioning and trajectory tracking performance of the PSSA.