Piezoelectric Nanopositioning Stage Research Articles

Design and disturbance rejection control of a piezoelectric nanopositioning stage

The article covers structural design and disturbance rejection control of a flexure-based compliant piezoelectric nanopositioning stage. The stage is devised using four-bar amplification mechanisms, auxiliary guiding mechanisms, and a compound parallelogram mechanism. Static and dynamic models of compliant mechanisms are analyzed based on a compliance matrix method. A modified Prandtl-Ishlinskii (PI) model with dead zone operators is used to describe the asymmetric hysteresis. Then, a global electromechanical dynamic model is built and identified. A comprehensive disturbance rejection controller (CDRC) combining a robust H∞ control and a disturbance observer-based (DOB) control is proposed for high trajectory tracking accuracy and anti-disturbance performance. The trajectory tracking accuracy of the stage can be up to 3 nm in experiments. As amplitudes of reference signals increases, relative tracking errors gradually decrease. System instability and oscillation caused by strong external disturbances are also reduced. Experimental results prove the effectiveness of the developed CDRC.

Dynamic Modeling and Attitude Decoupling Control for a 3-DOF Flexible Piezoelectric Nano-Positioning Stage Based on ADRC.

The paper proposes a three-degrees-of-freedom flexible nano-positioning stage constructed from compliant flexures and piezoelectric thin-sheet actuators, featuring a compact size and fast dynamic responses, which can be extensively applied to the typical micro/nano-positioning applications. Meanwhile, the dynamic model of the flexible PZT nano-positioning with distributed parameter characteristics is established to distinctly reflect the piezoelectric–mechanical coupling relationship between the four flexible PZT actuators and the three outputs of such a system. Furthermore, the attitude decoupling control for the 3-DOF flexible piezoelectric nano-positioning stage is achieved by the Active Disturbance Rejection Control (ADRC) method to compensate for the positioning errors in the actual positioning process. After this, a real-time experimental apparatus with two Position-Sensitive Detectors (PSDs) is also proposed and fabricated to test the three outputs of the flexible piezoelectric thin-sheet (PZT-5A) nano-positioning stage and validate the effectiveness of the dynamic modeling method and attitude decoupling control in the piezoelectric nano-positioning stage ranges.

Design and control of an x-y-θz parallel piezoelectric nanopositioning stage with a large moving platform

This paper introduces the design and control of a new type of x- y-θ z parallel piezoelectric nanopositioning stage. Using the spatial cross-distributed double parallel four-bar linkage (DPFL), the mirror symmetrically distributed driving unit and auxiliary unit are designed. Then, a parallel piezoelectric nanopositioning stage with a large moving platform and good guidance and decoupling performance are designed. The workspace and frequency response characteristics of the stage are analyzed based on the stiffness and dynamic models. To improve the static and dynamic characteristics of the stage, the structural size is optimized, and the optimization results are verified by Finite Element Analysis (FEA). To reduce the response time, hysteresis nonlinearity, and external disturbance of the stage, a compound controller combining a rate-dependent Prandtl–Ishlinskii (PI) hysteresis compensator and a proportional-integral controller is designed. Finally, the prototype of the stage is made by Wire Electro-Discharge Machining (WEDM) technology. The open-loop performance of the stage is tested experimentally. The results show that the maximum relative coupling error between x and y directions is less than 0.5%. Also, the experimental control results show that the designed compound controller has a fast response speed, good positioning, and tracking performance.

Robust tracking for nanopositioning stages using sliding mode control with active disturbance rejection: Design and implementation

This paper presents the design and implementation of a novel sliding mode control integrated with active disturbance rejection (SMCDR) for precise robust trajectory tracking of piezoelectric nanopositioning stages. The model uncertainties, nonlinearity, and external disturbances of the piezoelectric nanopositioning stage are regarded as a lumped disturbance, which is estimated by an extended state observer. The active disturbance rejection control (ADRC) strategy is used to realize a preliminary trajectory tracking, while the sliding mode control is adopted to handle the estimation error and residual uncertainties, and to improve the tracking performance. The exponential stability of the proposed SMCDR is proved using Lyapunov’s direct method. The proposed SMCDR controller combines the strength of both ADRC and sliding mode control, exhibits a simple structure, requires only the position measurements, and does not require any information of model parameters except for an approximate constant gain. Experimental results reveal the robustness of the SMCDR approach in suppressing the hysteresis of piezoelectric actuator, and illustrate the superior performance over conventional ADRC, integral sliding mode controller (ISMC) and PID controller for trajectory tracking control of piezoelectric nanopositioning stages.

Active disturbance rejection control for nanopositioning: A robust U-model approach

Hysteresis severely reduces positioning performance of a piezoelectric nanopositioning stage. Linear active disturbance rejection control (LADRC) is a practical solution to improve the positioning accuracy. However, the PD controller utilized in the LADRC is not effective enough to suppress the uncancelled total disturbance, and high-order pure integrators are difficult to be stabilized just by a PD controller. In this work, a robust U-model active disturbance rejection control (RUADRC) is proposed by incorporating the core idea of the U-model control and the Glover–McFarlane control. Then, the controlled plant can be dynamically transformed to a unit. Difficulties in stabilizing high-order pure integrators are decreased, the phase lag between the input and output of a controlled plant is reduced, and the closed-loop responses is sped up. In addition, the influence of both inaccurate total disturbance estimation and imperfect approximation is also minimized by the Glover–McFarlane control Closed-loop stability, steady-state tracking error, and the phase advantage of the RUADRC have been analysed. Theoretical results show that the RUADRC promises a timelier and more accurate positioning. Experimental results still confirm the advantages of the RUADRC over the LADRC on both reference tracking speed, accuracy and disturbance rejection ability.

Damping and tracking control of nanopositioning stages with double delayed position feedback.

This paper presents a new damping control scheme for piezoelectric nanopositioning stages with double delayed position feedback (DDPF). The DDPF in the inner loop is proposed to suppress vibration of the nanopositioning stage, which leads to a double time-delay system. A new numerical differential method is proposed to determine the parameters of the DDPF with pole placement. Then, a high-gain proportional-integral (PI) controller is designed in the outer loop to achieve a low level of tracking errors, which includes the hysteresis nonlinearity, disturbance, and modeling uncertainties. Experimental tests with various control schemes are conducted on a piezoelectric nanopositioning stage to verify the effectiveness of the proposed method. Experimental results reveal that the control bandwidth of the system is improved from 79Hz (with the PI controller), 416Hz (with the conventional delayed position feedback based controller), and 422Hz (with the recursive delayed position feedback based controller) to 483Hz (with the proposed controller).

Design of Composite Disturbance Observer and Continuous Terminal Sliding Mode Control for Piezoelectric Nanopositioning Stage

The nonlinearities of piezoelectric actuators and external disturbances of the piezoelectric nanopositioning stage impose great, undesirable influences on the positioning accuracy of nanopositioning stage systems. This paper considers nonlinearities and external disturbances as a lumped disturbance and designs a composite control strategy for the piezoelectric nanopositioning stage to realize ultra-high precision motion control. The proposed strategy contains a composite disturbance observer and a continuous terminal sliding mode controller. The composite disturbance observer can estimate both periodic and aperiodic disturbances so that the composite control strategy can deal with the disturbances with high accuracy. Meanwhile, the continuous terminal sliding mode control is employed to eliminate the chattering phenomenon and speed up the convergence rate. The simulation and experiment results show that the composite control strategy achieves accurate estimation of different forms of disturbances and excellent tracking performance.

Fractional delay filter based repetitive control for precision tracking: Design and application to a piezoelectric nanopositioning stage

The development of nanotechnology requires a precision tracking of periodic signals in order to complete repetitive industrial or scientific tasks. Although repetitive control is an intuitive choice to realize precisely periodic signal’s tracking, an integer number should match the period of signals for a digital control system otherwise the performance would be deteriorated significantly. Thus, in this paper, a fractional delay filter based repetitive control (FDFRC) is developed to achieve precision signal tracking with arbitrary periods. According to the internal model principle, a fractional delay filter with the spectrum-selection property is designed by using of a Farrow structure to address integer/non-integer delays. The stability of FDFRC is also given and analyzed in frequency domain to facilitate controller implementation. The proposed FDFRC allows an easy, simple and practical realization with only one parameter to be adjusted for different integer/non-integer delays. Comparative experiments with different frequencies of triangular waves for x axis and Lissajous scanning for x–y plane on a piezoelectric nanopositioning stage are conducted to further verify the significant improvements on the tracking performance of the proposed controller.

A Parametric Study of Mechanical Cross-Coupling in Parallel-Kinematics Piezo-Flexural Nano-Positioning Systems

Piezo-electric nano-positioning stages are being widely used in applications in which precision and accuracy in the order of nano, and high scanning speeds are paramount. This paper presents a Finite Element Analysis (FEA) of the parallel piezo-flexural nano-positioning (PPNP) stages to investigate motion interference between their different axes. Cross-coupling is one of the significant contributors to undesirable runouts in the precision positioning of PPNP actuators. Using ABAQUS/CAE 2018 software, a 3D model of a PPNP stage was developed. The model consists of a central elastic body connected to a fixed frame through four flexural hinges. A cylindrical stack of multiple piezoelectric disks is placed between the moving central body and the fixed frame. Extensive simulations were carried out for three different friction coefficients in the piezoelectric disks’ contact surfaces, different frame materials, and different geometrical configurations of the stage and the hinges. As a result, it was observed that the primary root cause of the mechanical cross-coupling effect could be realized in the combination of the slip and rotation of the piezoelectric disks due to their frictional behavior with the stage moving in the tangential direction, concurrent with changes in the geometry of the stage.

Bandwidth enhancement in damping control for piezoelectric nanopositioning stages with load uncertainty: Design and implementation

High bandwidth and fast tracking of desired trajectories are eagerly required in various applications that use piezoelectric nanopositioning stages, especially in atomic force microscopes where the vibration stemming from lightly damped modes of stages is a challenging control problem. In this study, a bandwidth-enhanced positive acceleration, velocity, and position feedback damping controller is presented to achieve the tracking bandwidth exceeding the first resonant frequency through using a novel pole-shift method. The stability of the positive feedback damped loop is examined by a mixed passivity, small-gain approach, and Nyquist theorem framework. Also, in conjunction with a proportional–integral tracking controller, robust stability is addressed for load uncertainties. Experimental application to a piezoelectric nanopositioning stage demonstrates that a closed-loop bandwidth of 282.5 Hz is achieved, which exceeds the dominating resonance of the stage at 210 Hz. The achieved bandwidth is 1.35 times larger than the dominating resonance, which is a competitive result among most existing damping control approaches. Comparative tracking results verify the effectiveness of the proposed control scheme on the suppression of low-frequency hysteresis and tracking performance of high-speed triangular waves under load variations.

An Adaptive Fuzzy Predictive Controller with Hysteresis Compensation for Piezoelectric Actuators

Piezoelectric actuators (PEAs) are the pivotal components of many nanopositioning systems because of their superiorities in bandwidth, mechanical force, and precision. Unfortunately, the intrinsic nonlinear property, hysteresis, makes it difficult to achieve the precise control of PEAs. Considering this drawback, diversified feedback control approaches have been studied in the literature. Inspired by the idea that the involvement of feedforward terms can upgrade the tracking performance, our previous conference paper proposed a novel feedforward–feedback control approach (model predictive control with hysteresis compensation). Following the previous work, an adaptive fuzzy predictive controller with hysteresis compensation is further studied in this paper. The major improvement of the proposed method is the employment of adaptive fuzzy model, by which the dynamic model of PEAs is able to adjust in real time, resulting in a better control performance. To validate the effectiveness of the proposed method, extensive experiments are conducted on a Physik Instrumente P-753.1CD piezoelectric nanopositioning stage. Comparisons with several existing control approaches are carried out, and the root mean square tracking error of the proposed method is reduced to 30% of that under the previously proposed neural network model–based predictive control, when tracking 100 Hz sinusoidal reference.

Signal-Transformation-Based Repetitive Control of Spiral Trajectory for Piezoelectric Nanopositioning Stages

In this article, a novel signal-transformation-based repetitive controller (STBRC) dedicated to the accurate and fast tracking of spiral trajectory with a time-variant amplitude is proposed and tested. To overcome the requirement of strictly periodic references of conventional repetitive controller, a mapping between spiral trajectory and constant amplitude sinusoid is developed to provide multiple lower gains at the fundamental frequency and its harmonics of the spiral trajectory to ensure zero steady-state errors. The stability of the control method and convergence of steady-state errors are analyzed with a lifted-system representation, respectively, for its time-variant property. Compared with internal model-based controllers for this trajectory, STBRC has the advantages of a simpler structure, fewer parameters, and better performance. The application to a piezoelectric nanopositioning stage verifies the effectiveness of the proposed control method on suppression of cross-coupling errors and improving the tracking performance of high-speed spiral trajectory in comparison with other controllers.

Integrated Modified Repetitive Control With Disturbance Observer of Piezoelectric Nanopositioning Stages for High-Speed and Precision Motion

The tracking performance of piezoelectric nanopositioning stages is vital in many applications, such as scanning probe microscopes (SPMs). Although modified repetitive control (MRC) can improve tracking performance for commonly used periodic reference input, it is sensitive to unexpected disturbances that deteriorate tracking precision, especially for high-speed motion. In order to achieve high-speed and precision motion, in this paper, a new composite control scheme by integrating MRC with disturbance observer (DOB) is developed. To simplify controller implementation, the hysteresis nonlinearity is treated as external disturbance and the proposed method is designed in frequency domain. The stability and robust stability are analyzed, and an optimization procedure to calculate the controller parameters is employed to enhance the performance to the maximum extent. To validate the effectiveness of the proposed method, comparative experiments are performed on a piezoelectric nanopositioning stage. Experimental results indicate that the hysteresis is suppressed effectively and the proposed method achieves high-speed and precision tracking with triangular waves references up to 25 Hz and improves the disturbance rejection ability with disturbances under different frequencies and robustness to model uncertainty through comparing with feedback controllers and MRC, respectively.

High-Precision Tracking of Piezoelectric Actuator Using Iterative Learning Control and Direct Inverse Compensation of Hysteresis

Rate-dependent hysteretic nonlinearity, which is an inherent characteristic of piezoelectric actuators (PEAs), causes a significant challenge in precise motion control of piezoelectric nanopositioning stages. In this paper, by assuming that the model of PEA takes a Hammerstein structure, a novel control strategy that combines iterative learning control (ILC) and the direct inverse of hysteresis is proposed to compensate for both nonlinearities and uncertainties of system simultaneously. Different from those existing direct inverse compensation methods whose control performance highly relies on the accuracy of the hysteresis model, the proposed control strategy is more robust by adding an additional ILC loop. Since ILC is essentially a feedforward control scheme that fully utilizes the input and output information in previous iterations, the tracking precision can be improved promptly in the iteration domain. Comparative experiments are performed to test the efficacy of the proposed algorithm for polynomial, triangular, and step signals. Results show that it is superior to pure proportional–integral (PI) controller and even PI controller combined with inverse compensator in the sense that the root mean square, relative, as well as maximal absolute errors of output tracking have been decreased remarkably within five iterations.

Hysteresis modelling and feedforward compensation of piezoelectric nanopositioning stage with a modified Bouc‐Wen model

Piezoelectric actuators (PEAs) are widely applied in various nanopositioning equipment. However, the strong hysteresis nonlinearity compromises the positioning accuracy. In this work, a novel modified Bouc-Wen (MBW) model with a polynomial function of the differential of the input is established for modelling the hysteresis nonlinearity of the PEA-actuated nanopositioning stages. The particle swarm optimisation algorithm is adopted to identify the parameters of the MBW model with a set of input-output experimental data. The obtained model with the corresponding identification parameters matches well the experimental data with 0.31% relative error. A feedforward compensator based on the obtained model is also applied to compensate the hysteresis nonlinearity. Experiments are conducted to validate the effectiveness of this approach, and the results show the great improvement of positioning accuracy of the stage.

Tracking Control of a Monolithic Piezoelectric Nanopositioning Stage using an Integrated Sensor.

This article describes a method for tracking control of monolithic nanopositioning systems using integrated piezoelectric sensors. The monolithic nanopositioner is constructed from a single sheet of piezoelectric material where a set of flexures are used for actuation and guidance, and another set are used for position sensing. This arrangement is shown to be highly sensitive to in-plane motion (in the x- and y-axis) and insensitive to vertical motion, which is ideal for position tracking control. The foremost difficulty with piezoelectric sensors is their low-frequency high-pass response. In this article, a simple estimator circuit is used to allow the direct application of integral tracking control. Although the system operates in open-loop at DC, dynamic command signals such as scanning trajectories are accurately tracked. Experimental results show significant improvements in linearity and positioning error.

Precision Motion Control of Piezoelectric Nanopositioning Stage With Chattering-Free Adaptive Sliding Mode Control

This paper presents the precision motion control of a piezoelectric nanopositioning stage using a new scheme of adaptive sliding mode control with uncertainty and disturbance estimation (ASMC-UDE). One uniqueness of the reported ASMC-UDE scheme is that an inherent chattering-free control action is guaranteed by eliminating the use of discontinuous control term. The reported ASMC-UDE strategy is easy to realize because the hysteresis effect is not needed to be modeled. Instead, the hysteresis is estimated and compensated by the robust control scheme. The control scheme is applicable to a system plant with either matched or unmatched disturbances. Unlike the existing UDE-based SMC control schemes, a reference model is not required by the proposed ASMC-UDE scheme. The stability of the chattering-free SMC strategy is proved in theory under the Lyapunov framework. The superiority of the presented control scheme over conventional approaches has been confirmed through comparative experimental studies. Moreover, the robustness of the controller in the presence of model disturbance and external disturbance has been verified.

Design and experimental tests of a dual-servo piezoelectric nanopositioning stage for rotary motion.

A dual-servo nanopositioning stage for high-accuracy rotary motion is presented in this article. A piezoelectric actuator is employed to achieve both the coarse motion and fine motion. By the coarse motion and fine motion, the designed dual-servo nanopositioning stage can obtain large-range rotary motion and high resolution simultaneously. The configuration and motion principle of the dual-servo nanopositioning stage were illustrated and discussed. A prototype was fabricated to test the working performance and the results demonstrate that the maximum speed of the presented dual-servo nanopositioning stage is 32,000 μrad/s and the rotary resolution is about 1.54 μrad. The working performance confirms the feasibility of the dual-servo nanopositioning stage.

An Analytical Approach to Integral Resonant Control of Second-Order Systems

Systems with colocated sensor-actuator pairs exhibit the interesting property of pole-zero interlacing. Integral resonance control (IRC) exploits this property by changing the pole-zero interlacing to zero-pole interlacing. The unique phase response of this class of systems enables a simple integral feedback controller to add substantial damping. Over the past few years, IRC has proven to be extremely versatile and has been applied to a wide variety of systems whose dominating dynamics of interest can be accurately modeled by second-order transfer functions. To date, a manual approach has been employed to determine the parameters of the IRC scheme, namely the feed-through term and the integral gain. In this paper, the relationship between the feed-through term, integral gain, and achievable damping is derived analytically for undamped/lightly damped second-order systems. The relationship between damping controller and an outer servo loop is also derived. These results add to the current understanding of colocated systems and automate the design of IRC controllers with a specified damping and tracking bandwidth. The presented results are applied to design and implement a damping and tracking controller for a piezoelectric nanopositioning stage.

Design of a Topology Nano-Positioning Stage

Nano-positioning technology has been widely used in many fields, such as microelectronics, optical engineering, and micro-technology equipment and manufacture. This paper presents a one-dimensional positioning system, adopting a PZT piezoelectric ceramic nano-positioning stage designed by multi-objective topological optimal synthesis. In order to obtain better performance, wedge-shaped structure has been applied as a precise pretension for the piezoelectric ceramic. Through finite element simulation and experimental verification, better static performance and smaller kinetic coupling are achieved, with up to 10 μm stroke displacement output and 5 nm resolution. This stage provides a novel, flexible, and efficient way in the design and optimization of the nano-positioning system.