A robust fractional-order sliding mode control technique for piezoelectric nanopositioning stages in trajectory-tracking applications

High-precision control of the piezoelectric nanopositioning stages is becoming a key technique in some precision manufacturing equipment. However, the piezoelectric nanopositioning stages suffer from the hysteresis effect and load disturbance, which damage its positioning accuracy. This paper proposes a fractional-order sliding mode tracking control method combining the fractional-order sliding mode surface and a new two-power reaching law to achieve high-precision tracking control of the piezoelectric nanopositioning stages under different loads. The fractional-order sliding mode surface effectively alleviates its chattering problem. The new two-power reaching law improves the convergence rate of the proposed controller. We conduct a rigorous theoretical analysis of the convergence interval and stability of the proposed controller. To evaluate the performance of the proposed controller, we carry out comparative trajectory tracking experiments on the piezoelectric nanopositioning stages. Results show that the proposed controller exhibits a satisfactory tracking performance even under different loads. Moreover, comparisons show that the proposed fractional-order sliding mode tracking controller outperforms the conventional PID and sliding mode control methods. The tracking performance of the proposed fractional-order sliding mode control method is improved by 59.17% and 39.42% compared with the PID and sliding mode control methods when tracking a sinusoidal signal with a frequency of 100 Hz.