Piezoelectric Cantilever Actuator Research Articles

Sparse Lissajous scanning reflectance confocal microscope with an adjustable field of view and fast iterative Fourier filtering reconstruction.

Medical imaging devices are becoming increasingly compact, necessitating optimization research into different methods of actuation. Actuation influences important parameters of the imaging device such as size, weight, frame rate, field of view (FOV), and image reconstruction for imaging devices point scanning techniques. Current literature around piezoelectric fiber cantilever actuators focuses on device optimization with a fixed FOV but neglects adjustability. In this paper, we introduce an adjustable FOV piezoelectric fiber cantilever microscope and provide a characterization and optimization procedure. To overcome calibration challenges, we utilize a position sensitive detector (PSD) and address trade-offs between FOV and sparsity with a novel inpainting technique. Our work demonstrates the potential for scanner operation when sparsity and distortion dominate the FOV, extending the usable FOV for this form of actuation and others that currently only operate under ideal imaging conditions.

Theoretical Modeling of Piezoelectric Cantilever MEMS Loudspeakers

Piezoelectric microelectromechanical system (MEMS) loudspeakers have received extensive attention in recent years. In particular, the piezoelectric cantilever MEMS loudspeaker, which uses multilayer piezoelectric cantilever actuators (MPCAs), has attracted attention because of its small size, low cost, ease of manufacture, and desirable piston movement. However, owing to the complex driving principles of MPCAs, no adequately efficient and appropriate method currently exists that can be used to analyze and predict the performance of piezoelectric cantilever MEMS loudspeakers. In this study, the equivalent circuit method (ECM) is adopted to theoretically model piezoelectric cantilever MEMS loudspeakers, and an ECM model with a special MPCA transformer for electromechanical conversion is proposed. With the proposed ECM model, the performance characteristics of piezoelectric cantilever MEMS loudspeakers, such as the displacement and sound pressure response, can be calculated efficiently and conveniently. To verify the accuracy of the ECM model, the finite element method is adopted for simulation, and the simulated results are compared with those of the ECM models. A satisfactory agreement was found, which verifies the accuracy of the proposed ECM model.

Investigation of Deformation in Bimorph Piezoelectric Actuator: Analytical, Numerical and Experimental Approach

Piezoelectric actuators are widely used in many fields such as medical instruments, optics, and aerospace due to their small size and high reliability. Piezoelectric cantilever actuators are used in different configurations such as unimorph and bimorph. In this paper, a 3-D lead zirconate titanate (PZT) bimorph was modeled in COMSOL Multiphysics software for investigation of series and parallel configuration. Theoretical analysis has been developed for the measurement of deformation of a piezoelectric cantilever in inverse piezoelectric effect. The experiment was also performed to examine the deformation of piezoelectric bimorph cantilever. It is found that under a constant applied electric field of 100 V bimorph piezoelectric actuator produces maximum deformation at 100 mm length, 30 mm width, and 20 mm thickness. It is also found that piezoelectric series benders have relatively less deformation than piezoelectric parallel benders. Experimental results show good agreement with theoretical and Numerical results.

Optimal Design of Piezoelectric Cantilevered Actuators for Charge-Based Self-Sensing Applications

Charge-based Self-Sensing Actuation (SSA) is a cost and space-saving method for accurate piezoelectric based-actuator positioning. However, the performance of its implementation resides in the choice of its geometry and the properties of the constituent materials. This paper intends to analyze the charge-based SSA’s performances dependence on the aforementioned parameters and properties for a piezoelectric cantilever. A model is established for this type of Piezoelectric Actuator (PEA), and a multi-objective function is defined. The multi-objective function consists of the weighted actuator and sensor objective functions of the PEA. The analytical optimization approach introduced herein aims to assess the evolution of the defined multi-objective function across a defined set of geometrical parameters and material properties and highlights the existence of a subset of solutions for an optimal charge-based SSA’s implementation. The commercially-available finite element analysis software, COMSOL Multiphysics, is used on the parametric model of the given structure to validate the analytical model. Then, experiments are conducted to corroborate the numerical and analytical modeling and analysis.

Precise, Long-Time Displacement Self-Sensing of Piezoelectric Cantilever Actuators Based on Charge Measurement Using the Sawyer–Tower Circuit**Supported by the National Natural Science Foundation of China under Grant No 11521202.

Previous studies show that near linearity exists between displacement and charge of piezoelectric actuators, while studies under higher fields are lacking and long-time displacement self-sensing is still a challenge. Here we indicate that precise, long-time displacement self-sensing can be accomplished using the Sawyer–Tower circuit, where a high-impedance electrometer and a non-leaky capacitor are used to measure the charge. Calibrating the results on a piezoelectric unimorph cantilever shows that the displacement resolution of charge self-sensing is ∼3 nm, much better than that of ∼40nm for the calibrating laser sensor. Testing results under a unipolar field up to 2 kV/mm with different periods indicate that a direct proportional relationship holds between charge and displacement with the maximum error of 4.65%. The self-sensing time can be over 20 min or even longer if a higher-impedance electrometer is used.

Internal model-based feedback control design for inversion-free feedforward rate-dependent hysteresis compensation of piezoelectric cantilever actuator

This study proposes a new rate-dependent feedforward compensator for compensation of hysteresis nonlinearities in smart materials-based actuators without considering the analytical inverse model. The proposed rate-dependent compensator is constructed with the inverse multiplicative structure of the rate-dependent Prandtl–Ishlinskii (RDPI) model. The study also presents an investigation for the compensation error when the proposed compensator is applied in an open-loop feedforward manner. Then, an internal model-based feedback control design is applied with the proposed feedforward compensator to a piezoelectric cantilever actuator. The experimental results illustrate that the proposed feedforward–feedback control scheme can be used in micro-positioning motion control applications to enhance the tracking performance of the piezoelectric cantilever actuator under different operating conditions.

Analysis of the actuating effects of triple-layer piezoelectric cantilevers considering electromechanical coupling correction

A dynamic analytical model is developed to predict the performance of a triple-layer piezoelectric cantilever as actuators in relation to materials with large piezoelectric and electromechanical coupling (EMC) coefficients under axial stress and plane strain conditions. The dynamic electromechanical behavior of a symmetrical triple-layer piezoelectric cantilever (STLPC) actuator is investigated. The analytical model of STLPC based on electromechanical coupling correction coefficient (EMCC) is established in one-dimensional (1D) form and applied to 1D and 2D deformations. Furthermore, the theoretical analysis of the EMCC model is critically evaluated and compared with the simulations using a finite element method (FEM). Results show that the EMCC model can be accurately applied to analyze the actuation performance of STLPC. Analyzed results show that the proposed model is accurately applied to large and small piezoelectric coupling conditions. The piezoelectric cantilever with large piezoelectric and EMC coefficients can be accurately analyzed by the proposed model accounted for small EMC condition in a traditional model. Design optimization based on actuators is also discussed. Optimal thickness ratios between elastic and piezoelectric layers are effectively calculated and obtained.

The constituent equations of piezoelectric cantilevered three-layer actuators with various external loads and geometry

This paper presents test results for deformation conditions of three-layer, piezoelectric cantilever converters subjected to various electrical and mechanical boundary conditions. A general solution has been developed based on implementation of piezoelectric triple segments (PTS) to the beam. A working mechanism and conditions for strain of the PTS segment have been determined. Basing on the general solution, for the cantilever actuator subjected to an external force (of single and dual PTS segments) and a uniform load (of single PTS segment), particular solutions have also been developed. Moreover, dimensionless frequencies of the oscillating motion for the analyzed converters have been determined. In the next step, the influence of such factors as length, quantity and position of PTS segments, their relative stiffness and unit weight on values of the obtained frequencies of vibration have been defined. The resulting analytical solutions have been compared with the developed FEM solution.

A novel microgripper hybrid driven by a piezoelectric stack actuator and piezoelectric cantilever actuators.

For the piezo-driven microgripper, one issue is to enlarge the grasping stroke and realize parallel grasping movement in the compact design. Piezoelectric stack actuator (PSA) and piezoelectric cantilever actuator (PCA) are two kinds of typical piezoelectric actuators. In this study, a novel microgripper hybrid driven by a PSA and two PCAs is proposed, which can be a better solution for the issue, compared with the previous microgripper using PSA-driven multi-stages displacement amplification mechanism (DAM) or using longer and narrower PCAs. A compact one-stage orthogonal DAM is proposed for the PSA in the microgripper, which can enlarge the grasping stroke and realize parallel grasping movement. The proposed orthogonal DAM is a triangulation amplification-based mechanism with undetermined structural parameters. Bidirectional symmetric input forces/displacements are not required in the proposed design. The number of the undetermined parameters and the solution principle are analyzed. Finite element analysis is used to verify the proposed DAM. The gripper arms are designed as two PCAs, for which the grasping and parasitic movements of the free end are modeled. Piezoelectric-static coupling finite element analysis is used to verify the models. The PCAs-driven grasping with considerable parasitic movement can be used in the coarse positioning. The integration of the hybrid-driven microgripper is presented, and its performances are presented and verified by experiments.

A novel rate-dependent hysteresis modeling and position control technique for piezo-actuated bimorph beams

Piezoelectric cantilever actuators are widely used in micro/nano-positioning applications due to their relatively accurate response and large operating bandwidth. One of the main obstacles in the way of implementing high-accuracy position tracking in high frequencies is the piezoelectric hysteresis phenomenon. It is known from previous research that piezoelectric materials exhibit a rate-dependent hysteresis loop. The purpose of this article is to obtain a novel hysteresis model that can accurately describe the output of the piezoelectric actuator. This is done by introducing a hysteresis model in the form of an actuated linear dynamic system. This model provides the ability to capture both rate-dependence and magnitude characteristics of the system, and it is simple and easy to implement in real-time. As a result, the proposed method accurately predicts the position of the piezo-actuated beam in a wide range of input frequencies and amplitudes. To demonstrate its effectiveness, the proposed hysteresis model is used along with a robust control loop to track the position of a piezo-actuated beam plant. It is shown using experimental results that utilizing this model leads to accurate position control in a wide range of frequencies.

Getting Started with PEAs-Based Flapping-Wing Mechanisms for Micro Aerial Systems

This paper introduces recent advances on flapping-wing Micro and Nano Aerial Vehicles (MAVs and NAVs) based on Piezoelectric Actuators (PEA). Therefore, this work provides essential information to address the development of such bio-inspired aerial robots. PEA are commonly used in micro-robotics and precise positioning applications (e.g., micro-positioning and micro-manipulation), whereas within the Unmanned Aerial Vehicles (UAVs) domain, motors are the classical actuators used for rotary or fixed-wing configurations. Therefore, we consider it pertinent to provide essential information regarding the modeling and control of piezoelectric cantilever actuators to accelerate early design and development stages of aerial microrobots based on flapping-wing systems. In addition, the equations describing the aerodynamic behavior of a flapping-wing configuration are presented.

Simultaneous Displacement/Force Self-Sensing in Piezoelectric Actuators and Applications to Robust Control

Self-sensing technique consists of using an actuator as a sensor at the same time. This is possible for most actuators with physically reversible principle such as piezoelectric materials. The main advantages of self-sensing are: 1) the embeddability of the measurement technique, and 2) its low cost as no additional sensor is required. This paper presents a self-sensing technique for piezoelectric actuators used in precise positioning applications like micromanipulation and microassembly. The main novelty is that both displacement and force signals can be simultaneously estimated. This allows a feedback control using one of these two signals with a display of the other signal. To demonstrate this advantage, a robust $H_\infty$ feedback control on displacement with real-time display of the force is used as an application of the proposed self-sensing technique. In this paper, experimental results obtained with a piezoelectric cantilever actuator validate and demonstrate the efficiency of the proposed self-sensing.

Optimal Design of Piezoelectric Cantilevered Actuators With Guaranteed Performances by Using Interval Techniques

Piezoelectric materials are well recognized for the development of systems and actuators working at the micro/nano-scale such as microsystems. This recognition is thanks to the high resolution, high bandwidth, and high force density that they can offer. However, piezoelectric actuators are typified by low range of displacement relative to other actuators like magnetic or thermal actuators. To obtain the sufficient range of displacement with a piezoelectric actuator, either we use high input voltages or we redesign the actuator to have larger dimensions. The former solution may lead to the destruction of the actuators and the latter is not congruent with the objectives of microsystems where the dimensions should be miniaturized. Furthermore, increasing the dimensions of the actuators reduces their rapidity and bandwidth. This paper proposes an approach based on interval analysis to design piezoelectric actuators with cantilever structures. The aim consists in reducing their dimensions while still satisfying some specified performances in term of output range and in term of resonant frequency (and thus bandwidth). The problem of the design is formulated as a set-inversion problem which can be solved using interval techniques. The obtained results, validated with prototype fabrication and experimental characterization, demonstrate the efficiency and the interests of the proposed method for designing systems and actuators working at the micro/nano-scale in general.

Analytical solutions to flexural vibration of slender piezoelectric multilayer cantilevers

The modeling of vibration of piezoelectric cantilevers has often been based on passive cantilevers of a homogeneous material. Although piezoelectric cantilevers and passive cantilevers share certain characteristics, this method has caused confusion in incorporating the piezoelectric moment into the differential equation of motion. The extended Hamilton’s principle is a fundamental approach to modeling flexural vibration of multilayer piezoelectric cantilevers. Previous works demonstrated derivation of the differential equation of motion using this approach; however, proper analytical solutions were not reported. This was partly due to the fact that the differential equation derived by the extended Hamilton’s principle is a boundary-value problem with nonhomogeneous boundary conditions which cannot be solved by modal analysis. In the present study, an analytical solution to the boundary-value problem was obtained by transforming it into a new problem with homogeneous boundary conditions. After the transformation, modal analysis was used to solve the new boundary-value problem. The analytical solutions for unimorphs and bimorphs were verified with three-dimensional finite element analysis (FEA). Deflection profiles and frequency response functions under voltage, uniform pressure and tip force were compared. Discrepancies between the analytical results and FEA results were within 3.5%. Following model validation, parametric studies were conducted to investigate the effects of thickness of electrodes and piezoelectric layers, and the piezoelectric coupling coefficient d31 on the performance of piezoelectric cantilever actuators.

Continuous dynamic modelling of bimorph piezoelectric cantilevered actuators considering hysteresis effect and dynamic behaviour analysis

Bimorph Piezoelectric Cantilevered (BPC) actuators have been of increasing interest in micro-manipulation processes during recent years. Due to properties such as transverse vibration, the performance and manoeuvrability have considerably improved, compared with conventional longitudinal piezoelectric actuators. Therefore, dynamic modelling of such actuators has been the centre of attraction. For this purpose, a target point on the actuator, e.g. the cantilever end tip, is usually considered as the actuator output. One degree of freedom lumped and continuous type dynamic models have been considered in prior research works. These types of modelling lead to two significant issues. First, the effect of higher vibrational modes in the actuator output is disregarded. Second, a minimum phase dynamic system is achievable for all target points regardless of position. In this paper, these two issues will be analytically and experimentally investigated. To this end, a linear continuous dynamic model for a general BPC actuator is derived and discretized by attaining exact mode shapes. The Prandtl–Ishlinskii (PI) model is utilized to model and identify the non-linear hysteresis behaviour. In contrast to previous works, dynamic behaviour analysis elaborates on the effect of higher modes in the actuator output response. In addition, the possibility of non-minimum phase behaviour based on the location of the target point is investigated. Simulation studies and experimental results confirm the validity of the proposed dynamic model and its behaviour analysis.

Control of a Piezoelectric Actuator Using a Bounded-Adaptive Backstepping Scheme and Sliding-Mode Observer

The present paper deals with the motion control of a piezoelectric cantilevered actuator. The motion behavior of the piezoelectric cantilever is affected by two main parasitic effects, the hysteresis and creep effects, which are considered as a generalized disturbance. Additionally, cantilevers's position is the only available measured state. The latter operational scenario reveals that the trajectory-tracking or regulation problem is a non-obvious task. Prior to the controller design, we have focused on the estimation of the velocity using a sliding-mode observer (SMO) in order to avoid the numerical derivative. On the other hand, the control design takes into account the limited response of the control input (bounded states) and it is obtained using the Backstepping framework assuring the stability of origin. Numerical simulations are first presented to verify the efficiency of the observer and controller algorithm, showing that the control objective is fulfilled. The experimental tests were carried out to validate and evaluated the control strategy.

On-off iterative adaptive controller for low-power micro-robotic step regulation

A novel model-free iterative adaptive controller is presented for low-power control of piezoelectric actuators. The controller uses simple adaptation rules based on known general behavior of piezoelectric actuators to adjust on-off switching times to drive piezoelectric actuators through a desired transient step motion. Adaptation rules are based on small numbers of measurements taken during each iteration of the actuator movement. Combined with the use of only on-off control inputs, controller implementation can be possible at much lower overall power levels than would be needed to implement a conventional control strategy such as through pulse-width-modulation (PWM) with real-time feedback. Such power savings are particularly important for the intended controller application to piezoelectric microactuators driving autonomous terrestrial micro-robots. A method for predicting convergence of systems with nominally linear dynamics and unknown, bounded nonlinearities is described, and applied to a sample target piezoelectric actuator. The controller is tested in simulation and experimentally on a piezoelectric cantilever actuator, and shows predicted convergence to the desired response. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

THERMAL EFFECT ON THE BENDING BEHAVIOR OF CURVED FUNCTIONALLY GRADED PIEZOELECTRIC ACTUATORS

This paper provides a study of the bending behavior of a circularly curved functionally graded piezoelectric cantilever actuator under an applied electric load and heat conduction. As a special case, the curved piezoelectric actuator is assumed to have graded property for the piezoelectric parameter g31 only in the thickness direction, which is expanded by Taylor series. Based on the theory of linear piezoelectricity, the analytical formulations are developed by introducing the Airy stress function. Numerical simulations are made to show the effects of material gradient and heat conduction on the bending behavior of the actuators. It is found that the electroelastic field of the curved actuator is significantly influenced by the thermal load. The results will be very helpful for the design and optimization of curved functionally graded piezoelectric actuators when these devices experience heat transfer.

Analysis of functionally graded and laminated piezoelectric cantilever actuators subjectedto constant voltage

Functionally graded and laminated piezoelectric cantilever actuators are investigated. Eachmaterial parameter of the functionally graded actuator can be an arbitrary continuousfunction of the thickness coordinate of the beam, while the property of each layer in thelaminated actuator is uniform. Piezoelectricity solutions for the two actuatorssubjected to a constant electric potential difference are presented. Firstly, the partialdifferential equations for the plane problem of functionally graded piezoelectricmaterials, which govern the stress function and electric displacement function, arederived. Secondly, the stress function is assumed to be an undetermined function ofthe thickness coordinate, and the electric displacement function is assumed asa linear function of the longitudinal coordinate. In such a case, the stress andelectric displacement function can be acquired through successive integrations. Theanalytical expressions of axial force, bending moment, shear force, displacements,electric displacements and electric potential are then deduced. The analyticalsolutions are finally obtained, with the integral constants completely determined fromthe boundary conditions. Comparisons of the present analytical solutions withbeam theory, finite element method and experiments indicate that the analyticalsolutions are effective and exact, while certain deviations of the beam theory can befound.

Silicon bulk micromachined electromechanical switches with four cantilever piezoelectric actuators

AbstractIn this article, silicon bulk micromachined RF MEMS switch with four cantilever piezoelectric actuators has been designed, fabricated, and characterized for advanced mobile/wireless communication systems. The proposed switch is comprised of four piezoelectric cantilever actuators, a contact metal pad, and a suspended CPW signal line above the silicon substrate. The fabricated piezoelectric switch has an insertion loss of −0.23 dB and an isolation of −44 dB at a frequency of 2 GHz and an operation voltage of 2.5 V, respectively. Also, it has constant performance characteristics at the certain range of applied voltages above the operation voltage that result in high production yield. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 570–573, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22195