Frequency Domain Optimization Design of the Dual-Loop Controller for Piezoelectric Tube Scanners With Compound Dynamics

The dual-loop controller (DLC) with both inner damping and outer tracking controllers has demonstrated exceptional performance in high-speed control of piezo-actuated nano-positioners. However, the accurate low-order model of the plant is imperative for designing the damping controller, according to the conventional DLC design principle. This limits its application in controlling piezoelectric tube scanners (PTSs) with compound dynamics. To handle this problem, this study introduces a frequency domain method for designing the DLC based on the frequency response data of the PTS. This method mitigates issues related to modeling errors. Specifically, the Nyquist diagram is employed to provide the stability boundary for parameters determination. A constraint optimization problem is formulated to achieve a high bandwidth with a flat amplitude frequency response. And the differential evolution algorithm is then adopted to find an optimal solution. Experimental validation on a PTS comfirms the effectiveness of this frequency domain design method. The results indicate that the control bandwidth of the optimized DLC achieves 848 Hz for a PTS with the first resonant frequency of 702 Hz. The superiorities of the DLC designed by the proposed optimization method are also validated via comparative tracking experiments involving step and triangular trajectories.
Note to Practitioners
—Frequency response data (FRD)-based methods open a new perspective to the controller design and optimization. Unlike traditional methods relying on transfer function models, the FRD of the system is directly identified and employed for the controller design and optimization, eliminating the need for extensive modeling and system identification efforts, thereby reducing errors. This paper proposes an FRD-based method for the simultaneous optimization of the DLC to achieve a high control bandwidth with a flat amplitude frequency response. This method relieves the requisite of accurate low-order model of the plant in conventional DLC designs. A closed-loop control bandwidth that exceeds the first resonant frequency is obtained for a PTS with complex high-order dynamic models. The proposed method enriches the scope of the DLC for the high bandwidth control, extending its applications to the systems with compound dynamics, which is significant to the high-speed control tasks of nano-positioners, such as the atomic force microscope imaging.