Adaptive Third-Order Fixed-Time Integral Sliding-Mode Control for Piezoelectric-Driven Microinjectors

This paper presents an adaptive third-order fixed-time integral sliding-mode control (A3-FTISMC) scheme for a piezoelectric-driven microinjector. High-order sliding-mode and integral control techniques are adopted to suppress the hysteresis nonlinearity of piezoelectric actuators and eliminate chattering simultaneously. The adaptive laws are designed to remove the reliance on prior knowledge of disturbance upper bounds. The global fixed-time stability of the closed-loop system is rigorously proven, ensuring that the upper bound of the settling time is independent of initial system states and enabling fast stabilization even under large initial deviations from the reference. Both simulations and experiments validate the effectiveness of the proposed method. When tracking a sinusoidal reference signal with 50 µm amplitude, 0.5 Hz frequency and 100 µm bias, the settling time and steady-state error are 0.276 s and 1.12 µm in simulations, and 0.4 s and 2.7 µm in experiments, respectively. Comparative results reveal that the proposed algorithm outperforms existing methods in convergence speed and tracking accuracy. Moreover, the controller achieves fast stabilization under diverse initial conditions and exhibits strong robustness in tracking reference trajectories with varying frequencies and amplitudes. This work lays a theoretical basis for high-performance control of piezoelectric microinjectors and offers practical value for industrial applications of piezoelectric actuation systems.