FPGA-based hybrid control method for high-precision positioning of bipedal stick–slip stepping piezoelectric actuators

Abstract To mitigate the oscillations and backward motion exhibited by stick–slip piezoelectric actuators (PZTs) during operation and enhance their movement speed, this study proposes an field-programmable gate array (FPGA) based hybrid control method for high-precision positioning of bipedal stick–slip stepping PZTs. A composite control strategy is implemented to address hysteresis nonlinearity and achieve sub-micron positioning accuracy. First, a dynamic model integrating piezoelectric nonlinearity, compliant hinge dynamics, and friction effects is established to characterize the actuator’s motion. Second, the Classical-Prandtl–Ishlinskii model is adopted to describe hysteresis behavior, followed by constructing an inverse model to generate feedforward-compensated waveforms, which are output through a DAC controlled by the FPGA. Finally, to achieve dynamic error correction, the FPGA acquires real-time displacement feedback from the sensor via an ADC and dynamically outputs PID control parameters to adjust the driving waveform. Experimental results demonstrate that the compensated waveform improves single-step velocity by 26.9% compared to conventional sawtooth wave excitation. With closed-loop control, the system achieves a steady-state accuracy below 0.1 μm and a millisecond-level response time. This work presents an embedded control solution with high robustness and real-time performance, offering significant potential for applications in micro-electromechanical systems and ultra-precision positioning.