Piezo-actuated stages have become more and more promising in nanopositioning applications due to the excellent advantages of the fast response time, large mechanical force, and extremely fine resolution. Modeling and control are critical to achieve objectives for high-precision motion. However, piezo-actuated stages themselves suffer from the inherent drawbacks produced by the inherent creep and hysteresis nonlinearities and vibration caused by the lightly damped resonant dynamics, which make modeling and control of such systems challenging. To address these challenges, various techniques have been reported in the literature. This paper surveys and discusses the progresses of different modeling and control approaches for piezo-actuated nanopositioning stages and highlights new opportunities for the extended studies.

Modeling and Control of Piezo-Actuated Nanopositioning Stages: A Survey

Recent interest in high-speed scanning probe microscopy for high-throughput applications including video-rate atomic force microscopy and probe-based nanofabrication has sparked attention on the development of high-bandwidth flexure-guided nanopositioning systems (nanopositioners). Such nanopositioners are designed to move samples with sub-nanometer resolution with positioning bandwidth in the kilohertz range. State-of-the-art designs incorporate uniquely designed flexure mechanisms driven by compact and stiff piezoelectric actuators. This paper surveys key advances in mechanical design and control of dynamic effects and nonlinearities, in the context of high-speed nanopositioning. Future challenges and research topics are also discussed.

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Invited review article: high-speed flexure-guided nanopositioning: mechanical design and control issues.

Position sensors with nanometer resolution are a key component of many precision imaging and fabrication machines. Since the sensor characteristics can define the linearity, resolution and speed of the machine, the sensor performance is a foremost consideration. The first goal of this article is to define concise performance metrics and to provide exact and approximate expressions for error sources including non-linearity, drift and noise. The second goal is to review current position sensor technologies and to compare their performance. The sensors considered include: resistive, piezoelectric and piezoresistive strain sensors; capacitive sensors; electrothermal sensors; eddy current sensors; linear variable displacement transformers; interferometers; and linear encoders.

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A review of nanometer resolution position sensors: Operation and performance

In this paper, a general skeleton on modeling, controller design, and applications of the piezoelectric positioning stages is presented. Toward this framework, a general model is first proposed to characterize dynamic behaviors of the stage, including frequency response of the stage, voltage-charge hysteresis and nonlinear electric behavior. To illustrate the validity of the proposed general model, a dynamic backlash-like model is adopted as one of hysteresis models to describe the hysteresis effect, which is confirmed by experimental tests. Thus, the developed model provides a general frame for controller design. As an illustration to this aspect, a robust adaptive controller is developed based on a reduced dynamic model under both unknown hysteresis nonlinearities and parameter uncertainties. The proposed control law ensures the boundedness of the closed-loop signals and desired tracking precision. Finally, experimental tests with different motion trajectories are conducted to verify the proposed general model and the robust control law. Experimental results demonstrate the excellent tracking performance, which validates the feasibility and effectiveness of the proposed approach.

Motion Control of Piezoelectric Positioning Stages: Modeling, Controller Design, and Experimental Evaluation

A review of recent studies on non-resonant piezoelectric actuators

http://www.mate.tue.nl/mate/pdfs/10617.pdf

Velocity and acceleration estimation for optical incremental encoders

Piezoelectric actuators are commonly used for micropositioning systems at nanometer resolution. Increasing demands regarding the speed and accuracy are inducing the need for new actuators and new drive principles. A nonresonant piezoelectric actuator is used to drive a stage with 1-DOF through four piezoelectric drive legs. In order to improve the positioning accuracy of the stage, a new drive principle and control strategy for the walking piezomotor are proposed in this paper. The proposed drive principle results in overlapping tip trajectories of the drive legs, resulting in a continuous and smooth drive movement. Gain scheduling feedback in combination with feedforward control further improves the performance of the stage. With the developed drive principle and control strategy, the piezomotor is able to drive the stage at constant velocities between 100 nm/s and 1 mum/s with a tracking error below the encoder resolution of 5 nm. Constant velocities up to 2 mm/s are performed with tracking errors below 400 nm. Point-to-point movements between 5 nm and the complete stroke of the stage are performed with a final static error below the encoder resolution.

http://www.mate.tue.nl/mate/pdfs/9634.pdf

Using a Walking Piezo Actuator to Drive and Control a High-Precision Stage

Velocity and Acceleration Estimation for Optical Incremental Encoders

Piezo actuators are used in high-precision systems that require nanometer accuracy. In this paper, we consider a nano-motion stage driven by a walking piezo actuator, which contains four bimorph piezo legs. We propose a (model-based) optimization method to derive waveforms that result in optimal driving properties of the walking piezo motor. A model of the stage and motor is developed incorporating the switching behavior of the drive legs, the contact deformation, and stick-slip effects between the legs and the stage. The friction-based driving principle of the motor is modeled using a set-valued friction model, resulting in a model in terms of differential-algebraic inclusions. For this model, we developed a dedicated numerical time-stepping solver. Experiments show a good model accuracy in both the drive direction and the perpendicular direction. The validated model is used in an optimization, resulting in waveforms with optimal driving properties of the stage at constant velocity. Besides the model-based optimization, also a direct experimental data-based waveform optimization is performed. Experiments with the optimized waveforms show that compared to existing sinusoidal and asymmetric waveforms in literature the driving properties can be significantly improved by the model-based waveforms and even further by the data-based waveforms.

Modeling and Waveform Optimization of a Nano-motion Piezo Stage

Atomic Force Microscopes (AFMs) are widely used for the investigation of samples at the nanometer scale. The metrological AFM used in this work uses a 3 degrees-of-freedom (DOFs) stage, driven by piezo-stack actuators, for sample manipulation in combination with a fixed cantilever. The piezostack actuators suffer from hysteresis, which acts as a nonlinear disturbance on the system and/or can change the system dynamics. The contributions of this paper are the application of feedback control to all 3 DOFs of the metrological AFM and the design and application of a hysteresis feedforward for the asymmetric hysteresis present in the system. The amount of coupling between the DOFs is assessed by a non-parametric multiple-input-multipleoutput (MIMO) identification. Since the dynamics appear to be decoupled in the frequency range of interest, feedback controllers are designed for each DOF separately. For the modeling of the asymmetric hysteresis an extended Coleman-Hodgdon model is proposed. This model is used for feedforward compensation of the hysteresis. The combination of feedback control for all DOFs and the asymmetric hysteresis feedforward enables the AFM to track scanning profiles within the sensor bound of 5nm. Real-time imaging of the sample is possible with an accuracy of 2nm.

http://www.mate.tue.nl/mate/pdfs/9726.pdf

R. J. E. Merry

Papers

Velocity and acceleration estimation for optical incremental encoders

Using a Walking Piezo Actuator to Drive and Control a High-Precision Stage

Velocity and Acceleration Estimation for Optical Incremental Encoders

Modeling and Waveform Optimization of a Nano-motion Piezo Stage

Identification, control and hysteresis compensation of a 3 dof metrological afm