High-bandwidth Control Approaches For Piezo-actuated Nanopositioning Stages

Along with the rapid development of nanoscience and nanotechnology, nanopositioning stages are widely used in many applications. Piezoelectric actuators, which have advantages of fast response, ultra-high resolution and large output force, are usually employed in nanopositioning stages to drive the flexure-based mechanisms. However, the piezoelectric actuator suffers from the inherent complex hysteresis nonlinearity, which seriously degrades the positioning performance of the piezo-actuated system, and even makes the closed-loop system unstable. Moreover, the lightly damped resonant dynamics of the piezo-actuated stage may result in a low-gain margin problem, which limits the bandwidth of the closed-loop system. Input signals with highfrequency components easily excite the vibration, making the system output oscillation. Therefore, it is necessary to compensate for the hysteresis and vibration of the piezo-actuated stage in order to achieve the high-bandwidth nanopositioning control.This dissertation presents high-bandwidth nanopositioning control approaches for the piezo-actuated stage involving with the hysteresis and vibration. The main research contents and achievements are listed as follows.A high-bandwidth control approach is developed based on the closed-loop input shaping, where the piezo-actuated stage is modeled as a cascade of the static hysteresis and the linear dynamics. Firstly, a direct inverse hysteresis compensator is cascaded in the feedforward path to eliminate the hysteresis nonlinearity, which is constructed by using a modified P-I hysteresis model to directly capture the inverse hysteresis effect. Then, a closed-loop input shaper is designed to suppress the vibration of the compensated system, which consists of an inside-the-loop input shaper for active damping and a Smith predictor. The Smith predictor is introduced to prevent the potential closed-loop instability caused by the time delay of the inside-the-loop input shaper. Finally, a high-gain proportional and integral(PI) feedback controller is designed to handle the errors caused by the disturbances and modeling uncertainties together with the hysteresis and creep nonlinearities. Experimental results show that the proposed high-bandwidth controller increases the tracking bandwidth from 22.6Hz to 510 Hz compared with the PI controller.A high-bandwidth control approach for piezo-actuated stages is proposed, which consists of an inner-loop delayed position feedback controller and an outer-loop highgain feedback controller. Firstly, the delayed position feedback controller is developed in the inner loop to suppress the resonant mode of piezo-actuated stages by increasing the damping of the system via pole placement. As the classical pole placement technique cannot be applied for systems with delays, a rightmost pole placement approach based on the generalized Runge-Kutta method is proposed, which calculates the rightmost pole by the GRKM and places it in the desired place by particle swarm optimization algorithm. The benefit of the delayed position feedback control for active damping is its simple structure and ease of implementation. Then, a high-gain proportional-integral(PI) controller is designed to deal with the hysteresis nonlinearity, creep, disturbance and modeling errors. The optimal parameters of the PI controller are found by the trial-and-error method in the stability region, which is given by a graphical method. Experimental results show that the proposed high-bandwidth controller increases the tracking bandwidth from 168 Hz to 710 Hz compared with the PI controller.A rate-dependent Prandtl-Ishlinskii(P-I) model based on the dynamic envelope functions is proposed to describe the static as well as dynamic hysteresis nonlinearity. Different from the commonly used approaches using dynamic weights or dynamic thresholds, the proposed rate-dependent P-I model is formulated by employing dynamic envelope functions into the play operators, while the weights and thresholds of the play operators are still static. By this way, the developed hysteresis model has a relative simple mathematic format with fewer parameters and an easier parameter identification process. The benefit for the developed model also lies in the fact that the existing control approaches can be directly applied to the developed model for hysteresis compensation in real-time applications. A modified particle swarm optimization algorithm is presented to identify the parameters of the hysteresis model, which introduces an effective informed strategy and a mutation operator in the classical particle swarm optimization algorithm. Experimental results on a piezo-actuated stage under different trajectories demonstrate the effectiveness of the proposed hysteresis model.A direct inverse hysteresis compensation method is proposed, in which the ratedependent P-I model based on the dynamic envelope functions is directly utilized to describe the inverse hysteresis effect. With the parameters identified by the modified particle swarm optimization algorithm, the rate-dependent P-I model is cascaded in the feedforward path as a dynamic hysteresis compensator to eliminate the dynamic hysteresis. An open-loop tracking controller and a closed-loop tracking controller are designed to achieve the high-speed tracking. The closed-loop controller is a cascade of a dynamic hysteresis compensator in the feedforward path and a proportional and integral(PI) feedback controller. Experimental results demonstrate that the tracking performance of the piezo-actuated stage is significantly improved by the dynamic hysteresis compensator, which reduces the root-mean-square tracking error by about 80%compared with the static hysteresis compensator.