Simultaneous damping and tracking control of a piezoelectric nanopositioning stage via time-weighted error optimization in dual-loop state feedback

Abstract Piezoelectric-driven nanopositioning stages typically suffer from lightly damped resonance and inherent hysteresis nonlinearity, which leads to pronounced overshoot, oscillation, limited bandwidth, and positioning inaccuracies, severely degrading positioning accuracy and stability. Traditional control methods often fail to simultaneously suppress resonance and achieve fast, smooth transient performance. Moreover, in conventional dual loop designs, the damping and tracking loops are tuned separately, resulting in suboptimal overall performance. To address these issues, this paper proposes a dual loop state feedback control framework. The framework integrates an augmented system with integral action for zero steady state error and adopts the integral of time multiplied by absolute error (ITAE) criterion for direct optimization of time domain transient metrics. A specially constructed set of state variables is introduced to avoid direct differentiation of the output signal and to suppress the amplification of measurement noise in the feedback loop; subsequently, a state observer is implemented to enable full-state feedback. In conjunction with this dual-loop structure, a feedforward compensator based on the inverse Prandtl–Ishlinskii model is incorporated to mitigate hysteresis nonlinearity. Experimental comparisons with a traditional PI controller and a Butterworth-based pole-placement method demonstrate that the proposed ITAE-optimized controller achieves ideal transient performance, including less than 3.1% overshoot, a settling time below 7 ms. Furthermore, it extends the closed-loop bandwidth to over 92 Hz, which is more than four times the bandwidth achieved by PI control. The proposed method provides a practical solution for nanopositioning systems that combines high speed, low overshoot, and high precision.