High Bandwidth Control of a Piezo-Actuated Nanopositioning System Based on a Discrete-Time High-Order Dual-Loop Framework.

Dual-loop control enhances the bandwidth of piezo-actuated nanopositioning systems via inner-loop state feedback controller suppressing lightly damped resonance and outer-loop tracking controller eliminating hysteresis nonlinearity. However, the traditional framework based on the continuous-time low-order model suffers from control performance degradation. To address this issue, this paper proposes a dual-loop control framework based on the discrete-time high-order model. In this framework, the discrete-time linear quadratic regulator extends theoretical bandwidth through simultaneous parameter optimization, and direct discrete implementation of the high-order state feedback controller and an integrator improves control precision by reducing model mismatch and controller discretization errors. Experiments are conducted on a custom-designed piezo-actuated system. Experimental frequency response of the system with the developed framework agrees well with the theoretical one, and the actual bandwidth is improved to 8248 Hz, which is better than 3920 Hz (continuous-time high-order model) and 6610 Hz (discrete-time low-order model), and exceeds open-loop resonant frequency 6352 Hz. Step response and trajectory tracking tests also demonstrate the effectiveness of the developed framework.