A new driving method for piezo deformable mirrors: open loop control and MOAO made easy

Nanopositioning stages with piezoelectric actuators have been widely used in fields such as precision mechanical engineering, but the nonlinear start-up accuracy problem under open-loop control has still not been solved, and more errors will accumulate, especially under open-loop control. This paper first analyzes the causes of the starting errors from both the physical properties of materials and voltages: the starting errors are affected by the material properties of piezoelectric ceramics, and the magnitude of the voltage determines the magnitude of the starting errors. Then, this paper adopts an image-only model of the data separated by a Prandtl-Ishlinskii model (DSPI) based on the classical Prandtl-Ishlinskii model (CPI), which can improve the positioning accuracy of the nanopositioning platform after separating the data based on the start-up error characteristics. This model can improve the positioning accuracy of the nanopositioning platform while solving the problem of nonlinear start-up errors under open-loop control. Finally, the DSPI inverse model is used for the feedforward compensation control of the platform, and the experimental results show that the DSPI model can solve the nonlinear start-up error problem existing under open-loop control. The DSPI model not only has higher modeling accuracy than the CPI model but also has better performance in terms of compensation results. The DSPI model improves the localization accuracy by 99.427% compared to the CPI model. When compared with another improved model, the localization accuracy is improved by 92.763%.

A meter-scale piezoelectrically active composite re ector has been developed and tested. The active re ector consists of a spherically curved, graphite face sheet, aluminum honeycomb core composite panel augmented with a network of distributed piezoelectric composite actuators. The piezoelectric actuator system may be used for controlling the structural dynamic response of the re ector, or for correcting low-order, thermally-induced quasistatic distortions of the panel. In this study, thermally-induced surface deformations of 1 to 5 microns were deliberately introduced onto the re ector, then measured using a speckle holography system. The re ector surface gure was subsequently corrected to a tolerance of 100 nm using a lattice of 90 piezoelectric composite actuators distributed across the re ector’s back face sheet. Initial experimental investigations consisted of open-loop gure control to determine in uence functions and control authority for each individuallyaddressable actuator, followed by a closed-loop gure control implementation. This paper will describe the design, construction, and testing of the active composite re ector system under thermal loads, and subsequent correction of thermal deformations via distributed piezoelectric actuation.

Hysteresis and creep compensation for piezoelectric actuator in open-loop operation

Nearly every new large-scale laser system application at LLNL has requirements for beam control which exceed the current level of available technology. For applications such as inertial confinement fusion, laser isotope separation, laser machining, and laser the ability to transport significant power to a target while maintaining good beam quality is critical. There are many ways that laser wavefront quality can be degraded. Thermal effects due to the interaction of high-power laser or pump light with the internal optical components or with the ambient gas are common causes of wavefront degradation. For many years, adaptive optics based on thing deformable glass mirrors with piezoelectric or electrostrictive actuators have be used to remove the low-order wavefront errors from high-power laser systems. These adaptive optics systems have successfully improved laser beam quality, but have also generally revealed additional high-spatial-frequency errors, both because the low-order errors have been reduced and because deformable mirrors have often introduced some high-spatial-frequency components due to manufacturing errors. Many current and emerging laser applications fall into the high-resolution category where there is an increased need for the correction of high spatial frequency aberrations which requires correctors with thousands of degrees of freedom. The largest Deformable Mirrors currently availablemore » have less than one thousand degrees of freedom at a cost of approximately $1M. A deformable mirror capable of meeting these high spatial resolution requirements would be cost prohibitive. Therefore a new approach using a different wavefront control technology is needed. One new wavefront control approach is the use of liquid-crystal (LC) spatial light modulator (SLM) technology for the controlling the phase of linearly polarized light. Current LC SLM technology provides high-spatial-resolution wavefront control, with hundreds of thousands of degrees of freedom, more than two orders of magnitude greater than the best Deformable Mirrors currently made. Even with the increased spatial resolution, the cost of these devices is nearly two orders of magnitude less than the cost of the largest deformable mirror.« less

압전 액추에이터(Piezoelectric actuator)는 빠른 응답 특성, 넓은 대역폭, 우수한 반복 정밀도, 그리고 높은 분해능의 특성으로 인하여 다양한 산업분야에서 폭넓게 사용되고 있다. 하지만, 압전 액추에이터에는 히스테리시스 효과(Hysteresis effect)가 발생되는 단점이 있으며, 이는 시스템의 성능을 저하시키는 주요한 원인으로 알려져 있다. Generalized Prandtl-Ishlinskii(GPI) model을 이용한 기존 연구에서는 히스테리시스 효과를 제거하기 위하여 히스테리시스를 수리적으로 모델링하고, 그 결과로부터 역 히스테리시스를 도출하였다. 하지만 모델링된 변수 값에 따라서는 역 히스테리시스 루프를 형성하지 못하는 치명적 문제점이 발생된다. 따라서 본 논문에서는 이러한 문제점을 해결하기 위하여 Inverse Generalized Prandtl-Ishlinskii(IGPI) model을 이용하여 역 히스테리시스를 직접 모델링하는 방법을 제안하였다. 또한 모델링 정밀도는 다양한 입력신호를 이용한 실험 결과를 기반으로 검증하였다. Piezoelectric actuators have been widely used in various applications because they have many advantages such as fast response time, repeatable nanometer motion, and high resolution. However Piezoelectric actuators have the strong hysteresis effect. The hysteresis effect can degrade the performance of the system using piezoelectric actuators. In past study, the parameters of the inverse hysteresis model are computed from the identified parameters using the Generalized Prandtl-Ishlinskii(GPI) model to cancel the hysteresis effect, however according to the identified parameters there exist the cases that can't form the inverse hysteresis loop. Thus in this paper the inverse hysteresis modeling mothod is proposed using the Inverse Generalized Prandtl-Ishlinskii(IGPI) model to handle that problem. The modeling results are verified by experimental results using various input signals.

The Piezoelectric Actuator Drive (PAD) is a type of rotary motor that transforms the linear motion of piezoelectric stack actuators into a precise rotational motion. The very high stiffness of the actuators employed make this type of motor suited for open-loop control, but the inherent hysteresis exhibited by piezoelectric ceramics causes losses. Therefore, this paper presents a straightforward method to measure piezoelectric stack actuator equivalent parameters that includes nonlinearities. By folding the nonlinearities into a newly-defined coupling coefficient, the inherent hysteretic behavior of piezoelectric stack actuators can be greatly reduced through precompensation. Experimental results show a fitting accuracy of 98.8 % between the model and measurements and a peak absolute error reduction by a factor of 10 compared to the manufacturer-provided parameter. This method improves both the static and dynamic performance of the Piezoelectric Actuator Drive (PAD) while still permitting open-loop control.

We characterize the errors associated with open-loop control of a microelectromechanical system deformable mirror (DM) using an approach that combines sparse calibration of the electrostatic actuator state space with an elastic plate model of the mirror facesheet. We quantify sources of measurement error and modeling error and demonstrate that the DM can be shaped in a single step to a tolerance of ∼8nm of that achievable with iterative feedback-based closed-loop control. Zernike polynomials with up to 2.5μm amplitude were made with this approach and yielded a shape error of <25nm rms in most cases. Residual errors were shown to be due primarily to spatial resolution limits inherent in the DM (e.g., uncontrollable errors).

Piezoelectric actuators are increasingly popular for high-accuracy and high-speed nanopositioning systems. However, nonlinear rate-dependent hysteresis of piezoelectric actuators leads to many difficulties in accurately analyzing the dynamic characteristics of piezoelectric nanopositioning systems in a wide frequency band. This paper proposes fractional-order model methods to characterize the hysteresis of piezoelectric actuators in time and frequency domains. Input voltage and output displacement of the piezoelectric actuator in time domain are employed to identify the parameters of the fractional-order model. Moreover, amplitude and phase errors are utilized to obtain the fractional model in frequency domain. Simulations and experiments are performed to validate the effectiveness of the proposed fractional-order model. The results show that the identified model in frequency domain is preferable in a wider frequency range from 1 to 200 Hz, and the maximum error is about 4.47%.

Nanopositioning proposes a high demand for its control system. However, hysteresis, a common nonlinear phenomenon existing in piezoelectric actuator, decreases precision of nanopositioning. In this paper, active disturbance rejection control (ADRC) is designed to estimate and cancel the influence of hysteresis, and integral time absolute error (ITAE) optimal index is chosen to determine the parameters of ADRC. Simulations are performed on the basis of mathematic model of nanopositioning system, and numerical results show that ADRC is effective in the control of nanopositioning.

This paper presents a novel redundantly piezo-actuated three-degree-of-freedom XYθz compliant mechanism for nano-positioning, driven by four mirror-symmetrically configured piezoelectric actuators (PEAs). By means of differential motion principle, linearized kinematics and physically bi-directional motions in all the three directions are achieved. Meanwhile, the decoupled delivering of three-directional independent motions at the output end is accessible, and the essential parallel and mirror symmetric configuration guarantees large output stiffness, high natural frequencies, high accuracy as well as high structural compactness of the mechanism. Accurate kinematics analysis with consideration of input coupling indicates that the proposed redundantly actuated compliant mechanism can generate three-dimensional (3D) symmetric polyhedral workspace envelope with enlarged reachable workspace, as compared with the most common parallel XYθz mechanism driven by three PEAs. Keeping a high consistence with both analytical and numerical models, the experimental results show the working ranges of ±6.21 μm and ±12.41 μm in X- and Y-directions, and that of ±873.2 μrad in θz-direction with nano-positioning capability can be realized. The superior performances and easily achievable structure well facilitate practical applications of the proposed XYθz compliant mechanism in nano-positioning systems.

At the University of California's Lick Observatory, we have implemented an on-sky testbed for next-generation adaptive optics (AO) technologies. The Visible-Light Laser Guidestar Experiments instrument (ViLLaGEs) includes visible-light AO, a micro-electro-mechanical-systems (MEMS) deformable mirror, and open-loop control of said MEMS on the 1-meter Nickel telescope at Mt. Hamilton. In this paper we evaluate the performance of ViLLaGEs in open- and closed-loop control, finding that both control methods give equivalent Strehl ratios of up to ~ 7% in I-band and similar rejection of temporal power. Therefore, we find that open-loop control of MEMS on-sky is as effective as closed-loop control. Furthermore, after operating the system for three years, we find MEMS technology to function well in the observatory environment. We construct an error budget for the system, accounting for 130 nm of wavefront error out of 190 nm error in the science-camera PSFs. We find that the dominant known term is internal static error, and that the known contributions to the error budget from open-loop control (MEMS model, position repeatability, hysteresis, and WFS linearity) are negligible.

The piezoelectric actuators have high resolution, wide operating frequency and low power consumption, but they suffer hysteresis which affects their linearity. In this paper are presented comparatively the analog and digital techniques for improvement (reducing) of nonlinear behavior of this type of actuators using charge amplifiers. First an analog charge amplifier and its performance analysis are presented. Then a model of digital charge amplifier with linearity performance considerably improved (91% reduced), but which shows a pronounced drift is presented. In the last section several methods for drift reducing are presented and analyzed, one of them having a reduction with 87%. A number of functional diagrams and response graphs for the developed techniques and methods are presented. Introduction The application area of the piezoelectric actuators has been spectacular developed, especially due to their remarkable qualities. Compared to other nano-positioning actuators, these have high resolution, high force, wide operating frequency and low power consumption. It is enough to mention some of their applications [1, 2, 3]: in micro and nano-devices for mechanical positioning with below micrometrics accuracy (optical and electronics microscopy, high precision cutting devices (error correction), robotics and positioning of magnetic heads and optical recordingplayback); in deformable mirrors (adaptive optics systems); in ultrasonic motors; in the impact controlled on/off devices; in fuel injectors of diesel engines etc. But, the piezoelectric materials have important non-linear characteristics determi-ned by the existence of hysteresis and creep, which can reduce the positioning accuracy of a piezoelectric actuator. When it is applied to a piezoelectric actuator a sudden voltage, the length will quickly respond then it will change slowly due to the creep effect. Creep is the polarization result of the piezoelectric actuator which continues to change after the applied voltage reaches its final value. Commonly, this effect is an issue at low frequencies and it is not important for higher frequencies [4]. Hysteresis is another undesired effect: when the input voltage is gradually increased, the actuator displacement is different from when the voltage is decreased for the same voltage value applied. For hysteresis reducing, many techniques have been implemented: the model-based control [5]; the displacement feedback control [6]; the charge control [7]. Without going into details, it is worth mentioning that, none of these techniques do not provide an acceptably hysteresis dimi-nution to allow the piezoelectric actuators to do the very high precisions displacement. In this paper, a model of digital charge amplifier is presented. By this model, a significant reduction of the piezoelectric actuators nonlinear behaviour is obtained. 94 | T h e 3 9 t h A R A P r o c e e d i n g s In the following sections we present this digital model. The analog charge amplifier To make the transition to digital charge amplifier, we present a simple analog charge amplifier in this section. In Figure 1(a) the circuit diagram of this analog charge amplifier is shown. It contains a comparator (Ʃ) and amplifier (K), a stack piezoelectric (SP) with capacity, Cpa, a sensing capacitor with capacitance, CS. R1 is used to model the operational amplifier (OA) input terminal leakage, and R2 is due to the leakage of the sensing capacitor. The circuit feedback loop is used to equalize the reference voltage, Vr, with the actual voltage across the sensing capacitor. If the OA, SP and sensing capacitor would be ideal, R1 and R2 can be removed and ideal Laplace transfer function would be:

A novel six degree-of-freedom (DOF) parallel micromanipulator with flexure hinges driven by piezoelectric actuators is presented for optical fiber alignment. The micromanipulator is designed based on integration of mechanism, driver and measurement. The 6-SPS mechanism is used to develop the parallel robot, the mechanical parameters of the structure are optimized, and the working space and stiffness analysis is given. Then the modularization of driver and sensor and the controller are integrated together with our own defined internal bus. Finally, the pose of the parallel robot is measured in open loop control and close loop control condition, and the error compensation is executed. Experimental results indicate that the liner precision of the system is 10 nm and the rotation precision of the system is 0.0001deg. The robot has high positioning precision and high reliability, and it can be used expediently in optical fiber alignment system for the high compact structure.

OF THE THESIS Inversion-based Iterative Feedforward-Feedback Control: Application to Nanomechanical Measurements and High-speed Nanopositioning by Yan Zhang Thesis Director: Professor Qingze Zou This thesis presents the development of inversion-based iterative feedforward-feedback (II-FF/FB) approach and its application to achieve high-speed force load in nanomechanical property measurement of soft materials in liquid, and high-speed nanopositioning control using piezoelectric actuators. High-speed nanopositioning is needed in various applications. For example, high-speed precision tracking of the force load is needed to measure the rate-dependent viscoelasticity of a wide range of soft materials in liquid, including live cells. In these applications, however, various adverse effects exist that challenge the precision tracking of the desired trajectory. For instance, during the nanomechanical measurement in liquid, the tracking precision is limited by the thermal drift effect, the reduction of the signal to noise ratio, and the hysteresis and the vibrational dynamics effects of the piezoelectric actuators (used to position the probe relative to the sample), particularly during high-speed measurements. These adverse effects limit the positioning precision not only during quasi-static operation (i.e., lowspeed), but also in high-speed tracking. This research is focused on the development the II-FF/FB technique to tackle these critical issues in practical applications. Motivated by the challenges in high-speed nanomechanical measurement of soft materials in

The Monolithic PiezoActuator (MPA) described in this work proposes the amplification of the piezoelectric deformation by a lever mechanism designed in a bulk piezoceramic plate. The advantages of the monolithic approach are to make the structure compact and to avoid problems of assembling reducing consequently production costs. In addition, several DOF (Degree Of Freedom) MPA can be designed with this approach. The total displacement using the MPA can reach some microns for a few millimeters size device. A numerical model has been used to simulate the static and dynamic behavior of a 1 DOF MPA. Static and dynamic measurements show a maximum displacement of around 6 mm and bandwidths as high as 5 kHz. The second part of this work is devoted to the open-loop position control of the MPA. The piezoelectric actuation is generally known to have a static behavior with a good linearity. Actually, when such an actuator is controlled by the electrical voltage, the typical hysteresis between this voltage and the corresponding deformation of the actuator can reach 20% for a soft PZT. Experimental results show an hysteresis under 10% and weak non-linearity for the MPA compared to standard piezoactuators. In order to linearize the open-loop motions, an open-loop control device which control the quantity of free electrical charges on the micro-actuator has been developed. The implementation of the control method has also given very encouraging results for MPA prototypes used in the laboratory.