Tracking Control of Piezo-actuated Nanopositioners for High-speed Scanning


Student thesis: Doctoral Thesis

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Awarding Institution
  • Hanxiong LI (Supervisor)
  • LiMin Zhu (External person) (External Supervisor)
Award date1 Jun 2021


With the rapid development of nanotechnology, atomic force microscope (AFM) has been proven to be a versatile investigative tool in nanomeasurement and nanomanipulation. In the past few years, driven by the ever-growing demand of atomic-scale characterizations in nano-technology and biological researches, special attention has been paid to improving the accuracy and the scanning speed of AFM. Due to its high performance in high-resolution, fast response time and low cost, the piezo-actuated nanopositioners are adopted in AFM for realizing the scanning operations. However, there exist three main challenges for the piezo-actuated nanopositioners to achieve high-speed and high-accuracy scanning: i) the piezoelectric actuators suffer from the inherent rate-dependent nonlinear hysteresis, which would reduce the tracking accuracy of the nanopositioner especially in high-speed scanning; ii) the mechanical structure of the piezo-actuated nanopositioner has the lightly damped resonance. In high-speed scanning, the system resonance would reduce the tracking accuracy, and even causes system instability. In order to avoid vibration, the tracking frequency is generally restricted to less than 1%~10% of the first resonant frequency of the nanopositioner; iii) the cross-coupling effect between axes poses a bottleneck that limits the multi-axis nanopositioners to achieve precise tracking operations especially in large scanning range and high speed. Additionally, the hysteresis nonlinearity of the piezoelectric actuator and the lightly damped resonance of the nanopositioner are usually coupled to affect the tracking accuracy of the nanopositioner and limit the scanning speed.

To address these issues, this thesis presents the modeling and compensation of the hysteresis and the cross-coupling effect, the precise tracking control of the non-raster scanning trajectories, and the high-bandwidth control. The main research contents and achievements are listed as follows.

(1) A Gaussian-Process-based rate-dependent hysteresis model is proposed to characterize the rate-dependent hysteresis of the piezoelectric actuator. By introducing both the voltage value and its changing rate to the model input, the proposed model is capable of describing the nonlinear memorability as well as rate-dependence of hysteresis. The usage of the kernel function makes the model flexible and accurate without specifying a function form and the parameters. A hysteresis compensator is developed based on the inverse model for eliminating the tracking error caused by the hysteresis. Further, since the Gaussian Process is computationally expensive, a frequency-separation-based Gaussian Process (FSGP) modeling method is designed based on the optimal subset selection for making predictions. It can avoid both the high computational burden and the accuracy loss caused by large data quantity. The open loop and closed-loop controllers are designed based on the FSGP model, and the tracking and imaging results demonstrate the effectiveness and superiority of the FSGP-based modeling and compensation method.

(2) Aiming at the precise tracking of sinusoids or sinusoid-based signals in typical sequential non-raster scanning trajectories, a parallel tracking controller composed of several resonant controllers (RCs) is proposed. The selection for each RC in the parallel array is based on two considerations: one is the spectrum of the reference signal, and the other is the harmonics caused by the nonlinearities of the nanopositioner. Thus, the gain of RC at each resonant frequency can be allocated on demand. Since the performance of RC is highly dependent on the accurate placement of the resonant poles, a modified Tustin method is proposed to implement the controller with better accuracy. Furthermore, the fractional-order calculus is introduced to improve the transient performance of the RCs, which could result in a higher convergence speed compared to the original RC. To validate the tracking performance of the proposed method, a comprehensive examination of several types of the non-raster sequential scanning trajectories with a wide frequency range has been carried out on a nanopositioner.

(3) In order to improve the bandwidth and realize the accurate tracking of signals within the bandwidth, a dual loop control method based on state feedback modal control is designed. In this scheme, the state-feedback-based modal controller is firstly designed in the inner loop to enlarge both the damping ratio and natural frequency of the first resonant mode. Then, a proportional-integral (PI) controller is utilized in the outer loop for eliminating the tracking errors caused by other disturbances and nonlinearities including hysteresis and creep. To maximize the control bandwidth of system under the proposed dual-loop scheme, an optimization method is thus proposed for simultaneously tuning the parameters of the inner and the outer loop controllers. This control scheme extends the conventional active damping control which only improves the damping ratio, to the active modal control which improves both damping and stiffness. Moreover, instead of designing the inner-loop controller and the outer-loop controller separately, this work optimizes the parameters of the two loops simultaneously. Therefore, the bandwidth close to or even larger than the first resonant frequency of the nanopositioner can be obtained. Finally, experiments are carried out on a piezo-actuated nanopositioner, which demonstrate the abilities of bandwidth improvement and accuracy enhancement of the proposed control scheme.

(4) The time/space-separation-based Gaussian Process modeling and compensation methods are developed to deal with the spatiotemporal cross-coupling effect of a 2-DOF nanopositioner. In the modeling process, the principle component analysis is introduced firstly to accomplish the time/space separation and to reduce the model dimension, which results in a few spatial basis functions and the corresponding temporal coefficients. The spatial functions represent the spatial distributed behavior of the coupling effect, while the temporal coefficients represent the nonlinear dynamic behavior. Then the FSGP is adopted to model the temporal coefficients for the purpose of describing the nonlinear dynamic behavior of the cross-coupling effect. Finally, with the time/space synthesis, the nonlinear spatiotemporal dynamics is reconstructed. Different from the conventional cross-coupling model, the proposed model has the power for describing both the spatial distributed behavior and the nonlinear dynamics of the cross-coupling effect. In the compensation process, the proposed model is applied, together with an inversion of the system dynamics, to form a feedforward compensator. Hybrid controller composed of the feedforward compensator and PI feedback controller is then constructed. Experiments are presented to demonstrate the merits of the modeling and compensation methods.

    Research areas

  • Piezo-actuated Nanopositioner, Rate-dependent Hysteresis, Tracking Control, Resonant Controller, Active Modal Control, Cross-coupling Effect