Dynamic pull-in of parallel-plate and torsional electrostatic MEMS actuators

An analysis of the dynamic characteristics of pull-in for parallel-plate and torsional electrostatic actuators is presented. Traditionally, the analysis for pull-in has been done using quasi-static assumptions. However, it was recently shown experimentally that a step input can cause a decrease in the voltage required for pull-in to occur. We propose an energy-based solution for the step voltage required for pull-in that predicts the experimentally observed decrease in the pull-in voltage. We then use similar energy techniques to explore pull-in due to an actuation signal that is modulated depending on the sign of the velocity of the plate (i.e., modulated at the instantaneous mechanical resonant frequency). For this type of actuation signal, significant reductions in the pull-in voltage can theoretically be achieved without changing the stiffness of the structure. This analysis is significant to both parallel-plate and torsional electrostatic microelectromechanical systems (MEMS) switching structures where a reduced operating voltage without sacrificing stiffness is desired, as well as electrostatic MEMS oscillators where pull-in due to dynamic effects needs to be avoided.     

On the dynamic pull-in of electrostatic actuators with multiple degrees of freedom and multiple voltage sources

This study considers the dynamic response of electrostatic actuators with multiple degrees of freedom that are driven by multiple voltage sources. The critical values of the applied voltages beyond which the dynamic response becomes unstable are investigated. A methodology for extracting a lower bound for this dynamic pull-in voltage is proposed. This lower bound is based on the stable and unstable static response of the system, and can be rapidly extracted because it does not require time integration of momentum equations. As example problems, the dynamic pull-in of two prevalent electrostatic actuators is analyzed.     

Analytical approach and numerical /spl alpha/-lines method for pull-in hyper-surface extraction of electrostatic actuators with multiple uncoupled voltage sources

This work presents a systematic analysis of electrostatic actuators driven by multiple uncoupled voltage sources. The use of multiple uncoupled voltage sources has the potential of enriching the electromechanical response of electrostatically actuated deformable elements. This in turn may enable novel MEMS devices with improved and even new capabilities. It is therefore important to develop methods for analyzing this class of actuators. Pull-in is an inherent instability phenomenon that emanates from the nonlinear nature of the electromechanical coupling in electrostatic actuators. The character of pull-in in actuators with multiple uncoupled voltage sources is studied, and new insights regarding pull-in are presented. An analytical method for extracting the pull-in hyper-surface by directly solving the voltage-free K-N pull-in equations derived here, is proposed. Solving simple but interesting example problems illustrate these new insights. In addition, a novel /spl alpha/-lines numerical method for extracting the pull-in hyper-surface of general electrostatic actuators is presented and illustrated. This /spl alpha/-lines method is motivated by new features of pull-in, that are exhibited only in electrostatic actuators with multiple uncoupled voltage sources. This numerical method permits the analysis of electrostatic actuators that could not have been analyzed by using current methods.     

Influence of van der Waals force on the pull-in parameters of cantilever type nanoscale electrostatic actuators

In this paper, the influence of the van der Waals force on two main parameters describing an instability point of cantilever type nanomechanical switches, which are the pull-in voltage and deflection are investigated by using a distributed parameter model. The fringing field effect is also taken into account. The nonlinear differential equation of the model is transformed into the integral form by using the Green’s function of the cantilever beam. The integral equation is solved analytically by assuming an appropriate shape function for the beam deflection. The detachment length and the minimum initial gap of the cantilever type switches are given, which are the basic design parameters for NEMS switches. The pull-in parameters of micromechanical electrostatic actuators are also investigated as a special case of our study by neglecting the van der Waals force.     

压电作动器在基于声辐射模态的ASAC中的应用

控制作动器的选取和设计是实现主动结构声学控制的关键一环。利用压电材料的逆压电效应,选择矩形压电片作为控制作动器应用于基于声辐射模态的主动结构声学控制中,提出了基于声辐射模态的压电作动器主动控制策略,并得到了最佳控制电压的获取方法。以简支板为例,通过压电作动器控制效果分析,揭示了压电作动器控制的内在规律;通过与单点力控制效果的比较分析,验证了压电作动器控制策略的优越性。     

A methodology and model for the pull-in parameters of magnetostatic actuators

Magnetostatic actuators exhibit bistability similarly to the pull-in phenomena of electrostatic actuators. In this paper a methodology and model for the extraction of the magnetic Pull-In parameters of magnetostatic actuators are derived. The flux-controlled magnetostatic actuator is analyzed based on the energy representation and the magnetomotive force-controlled magnetostatic actuator is analyzed in the thermodynamic potential energy (or co-energy) representation. An algebraic equation, referred to as the magnetic Pull-In equation, for each of the two cases (flux-controlled and magnetomotive force-controlled actuators) is derived. By solving these Pull-In equations either analytically or numerically, the magnetic Pull-In parameters are obtained. Several case studies, covering displacement and torsion magnetic actuators, are presented and analyzed, illustrating the usefulness of the proposed methodology, its relative simplicity as well as the adaptability and practical usage in wide spectrum of magnetic actuators. [1425].     

Design of large deflection electrostatic actuators

Electrostatic, comb-drive actuators have been designed for applications requiring displacements of up to 150 /spl mu/m in less than 1 ms. A nonlinear model of the actuator relates the resonant frequency and the maximum stable deflection to the actuator dimensions. A suite of experiments that were carried out on deep reactive ion etched (DRIE), single-crystal silicon, comb-drive actuators confirm the validity of the model. Four actuator design improvements were implemented. First, a folded-flexure suspension consisting of two folded beams rather than four and a U-shaped shuttle allowed the actuator area to be cut in half without degrading its performance. Second, the comb teeth were designed with linearly increasing lengths to reduce side instability by a factor of two. Third, the folded-flexure suspensions were fabricated in an initially bent configuration, improving the suspension stiffness ratio and reducing side instability by an additional factor of 30. Finally, additional actuation range was achieved using a launch and capture actuation scheme in which the actuator was allowed to swing backward after full forward deflection; the shuttle was captured and held using the backs of the comb banks as high-force, parallel-plate actuators.     

Fabrication of piezoelectric multilayer thin-film actuators

In this study, we fabricated multilayer ceramics (MLCs) composed of multilayered Pb(Zr,Ti)O₃ (PZT) piezoelectric thin films with internal electrodes and evaluated their dielectric and piezoelectric properties. The stack of PZT ferroelectric layers (550 nm) and SrRuO₃ (SRO, 80 nm) electrodes were alternatively deposited on Pt/Ti-coated silicon-on-insulator substrates by radio-frequency magnetron sputtering. The MLCs composed of one, three, and five PZT layers were fabricated by the alternate sputtering deposition of PZT ferroelectric layers and SRO electrodes through the movable shadow mask. The capacitances of MLCs were proportionally increased with the number of PZT layers, while their relative dielectric constants were almost same among the each MLC. The MLCs exhibited symmetric and saturated P–E hysteresis loops similar to the conventional PZT thin films. We estimated that the piezoelectric properties of MLCs by FEM simulation, and confirmed that the effective transverse piezoelectric coefficients (d _31,eff ) increased with the number of PZT layers. The piezoelectric coefficients calculated to be d _31,eff  = ?2964 pC/N at 25 PZT layers, which is much higher than those of conventional single-layer piezoelectric thin films.     

比例模糊控制在压电陶瓷执行器中的应用

针对压电陶瓷的逆压电效应,提出了一种以压电陶瓷驱动精密流量阀为执行器,采用压电陶瓷驱动流量阀阀芯,控制其开口大小,从而达到精确控制流过阀的液体流量的目的.在减压出口处安装了金属橡胶材料,以达到消除流体通过节流口后压力剧烈变化所产生的纹波现象,并就其驱动电压一输出位移一输出流量之间的数学关系建立模型.由于压电陶瓷的非线性、迟滞、蠕变等特性影响控制精度且控制复杂,提出了一种比例模糊控制方法,取得了较通常采用的控制方法更为理想的效果.     

Linear electrostatic actuators: Gap maintenance via fluid bearings

This paper addresses a novel actuator for manufacturing applications, the “electrostatic artificial muscle.” Artificial muscle is composed of a dense array of small linear actuators. Its promise lies in the prospect of high performance (e.g. higher force-to-weight ratio and peak acceleration than a comparable magnetic motor), clean, quiet operation, and design versatility (especially the elimination of transmissions in many applications). The characteristics of artificial muscle are particularly appealing for applications in robotics and high-speed automation.A model of a linear electrostatic induction motor is presented to illustrate the potential for high performance as well as the difficulty of “gap maintenance.” Gap maintenance refers to the demanding task of preserving a uniform, narrow gap between “slider” and stator in the presence of destabilizing electrostatic forces. A novel approach to gap maintenance, the use of dielectric fluid bearings, is presented. Analysis of a simple, 2-D motor model shows that gap maintenance and motor efficiency may be characterized by two nondimensional parameters: a levitation number, and a gap aspect ratio. It is shown that achieving both low-speed levitation and high efficiency requires long, narrow gaps (high aspect ratio). The results of this analysis are extended to a more complex model featuring an unconstrained, rigid slider. An experimental study of fluid bearings is also presented.     

Speed-energy optimization of electrostatic actuators based onpull-in

The speed and total energy required to accomplish pull-in switching of a generic electrostatic actuator is examined. It is found that the value of the source resistance of the voltage drive used for switching has a profound effect on both switching speed and energy requirements. The source resistance governs the charging time for the actuating capacitor. As long as this time is slower than the time required to accelerate the moving mass to maximum speed in the presence of damping, the total energy required for switching can be dramatically reduced without a significant increase in switching time. Indeed, there exists a clear optimum source-resistance value that minimizes the product of switching time and switching energy. These findings are demonstrated theoretically and then applied to specific examples from the literature. In addition, the limiting case of very large source resistance, essentially a current drive, is evaluated and compared to the voltage-driven case. It is found that for equivalent switching times, the current drive requires less total energy for a switching event     

Auto-calibration of capacitive MEMS accelerometers based on pull-in voltage

This paper describes an electro-mechanical auto-calibration technique for use in capacitive MEMS accelerometers. Auto-calibration is achieved using the combined information derived from an initial measurement of the resonance frequency and the measurement of the pull-in voltages during device operation, with an estimation of process-induced variations in device dimensions from layout and deviations in material properties from the known nominal value. An experiment-based analytical model is used to compute the required electrostatic forces required to simulate external accelerations allowing the electro-mechanical calibration of the accelerometer. Measurements on fabricated devices confirm the validity of the proposed technique and electro-mechanical calibration is experimentally demonstrated.     

Comprehensive review of low pull-in voltage RF NEMS switches

Microsystem Technologies - The present study focuses on state-of-the-art of the demand, operating principles, design parameters, different materials for beam and dielectric, already existing...     

压电智能结构的主动控制及压电执行器布局优化

本文对压电梁、板结构振动主动控制进行了研究,分别建立了压电悬臂梁的耦合动力学方程以及Kirchhoff假设下矩形压电薄板的耦合动力学方程,通过采用独立模态空间控制法,实现了对压电智能结构前两阶模态的主动振动控制.为提高主动控制的抑振效果,通过仿真实例分析了压电执行器在梁上的不同布局对于主动控制抑振效果的影响,得到了压电执行器粘附于悬臂梁上的最佳布局.最后实验验证了压电悬臂梁在自由振动以及模态共振下压电执行器对于悬臂梁响应控制的可行性和有效性.     

Optimization of clamped circular piezoelectric composite actuators

This paper addresses the design of clamped circular piezoceramic composite unimorph and bimorph configurations, specifically the conflicting requirements of maximum volume displacement for a prescribed bandwidth. An optimization problem is formulated that implements analytical solutions for unimorph and bimorph configurations using laminated plate theory, including the use of oppositely polarized piezoceramic patches. A range of actuator geometric parameters are studied, and bounds for volume displacement and natural frequency of optimal designs are determined and presented via design curves. In the selected design space, Pareto optimization results for unimorph and bimorph configurations show that optimal volume displacement is related to the bandwidth by a universal power law such that the product of the square of the natural frequency and the displaced volume, a “gain-bandwidth” product, is a constant. Characteristic trends are also described that are independent of the actuator radius for the Pareto optimal piezoceramic patch thickness and radius versus normalized bandwidth. The results are relevant, for example, in the design of zero-net mass-flux or synthetic jet actuators used in flow control applications.     

Modeling hysteresis in piezoelectric actuators using NARMAX models

This paper presents a non-linear moving average model with exogenous inputs (NMAX) and a non-linear auto-regressive moving average model with exogenous inputs (NARMAX) respectively to model static and dynamic hysteresis inherent in piezoelectric actuators. The modeling approach is based on the expanded input space that transforms the multi-valued mapping of hysteresis into a one-to-one mapping. In the expanded input space, a simple hysteretic operator is proposed to be used as one of the coordinates to specify the moving feature of hysteresis. Both the modified Akaike's information criterion (MAIC) and the recursive least squares (RLS) algorithm are employed to estimate the appropriate orders and coefficients of the models. The advantage of the proposed approach is in the systematic design procedure which can on-line update the model parameters so as to accommodate to the change of operation environment compared with the classical Preisach model. Moreover, the obtained model is non-linear in variables but linear in parameters so that it can avoid the problem of sticking in local minima which the neural network based models usually have. The results of the experiments have shown that the proposed models can accurately describe static and dynamic behavior of hysteresis in piezoelectric actuators.     

Extending the travel range of analog-tuned electrostatic actuators

The pull-in instability limits the travel distance of elastically suspended parallel-plate electrostatic microactuators to about 1/3 of the undeflected gap distance. In this paper, we examine the “leveraged bending” and “strain-stiffening” methods for extending the travel range of electrostatic actuators. The leveraged bending effect can be used to achieve full gap travel at the cost of increased actuation voltage. The strain-stiffening effect can be used to minimize actuation voltage for a given travel range. An analytical approximation shows that the strain-stiffening effect can be used to achieve a stable travel distance up to about 3/5 of the gap. A tunable reflective diffraction grating known as the polychromator has been designed using these actuation techniques, and selected designs have been fabricated and tested for actuation behavior. Gratings with 1024 flat, closely packed grating-element actuators have been fabricated with over 1-cm-long mirrors, achieving stable vertical travel distances of more than 1.75 μm out of a 2-μm gap     

Active control of building structures using piezoelectric actuators

Active control strategy is an innovative method for enhancing structural functionality against strong ground motions. In this paper the performance of piezoelectric actuators for active control of the seismic responses of tall buildings is investigated. Three-dimensional modeling of the building is considered where three degrees of freedom including displacements in two perpendicular horizontal directions and rotation about the vertical axis are corresponded to each floor. The piezoelectric actuators are hosted at the bottom of the columns and the controlling forces produced by actuators are considered in the equations of motion of the buildings. Linear quadratic regulator (LQR), supervisory fuzzy controller (SFC) and fuzzy logic controller (FLC) are applied in the control designs. For the numerical studies, a real 10 story building subjected to an ensemble of 20 worldwide acceleration records is considered. Since there are many possible positions for placement of piezoelectric actuators in the test building, genetic algorithm is used for finding the optimal arrangement of actuators in order to achieve maximum reduction in building responses. The comparison of the controlled and uncontrolled responses of the test building indicates that the piezoelectric actuators are able to provide considerable reductions in buildings’ seismic responses. Also the performance of the above three controllers reveals that the fuzzy controller is much more effective than the two others.     

Design considerations of rectangular electrostatic torsionactuators based on new analytical pull-in expressions

An important design issue of electrostatic torsion actuator is the relative locations of the actuating electrodes, where the bias voltage is applied. These geometrical design parameters affect both the pull-in angle as well as the pull-in voltage. In this paper, a new approximated analytical solution for the pull-in equation of an electrostatic torsion actuator with rectangular plates is derived. The analytical expression is shown to be within 0.1% of the one degree of freedom (1DOF) lumped-element model numerical simulations. Moreover, the analytical expressions are compared with the full coupled-domain finite-elements/boundary-elements (FEM/BEM) simulations provided by MEMCAD4.8 Co-solve tool, showing excellent agreement. The approach presented here provides better physical insight, more rapid simulations and an improved design optimization tool for the actuator     

A hybrid model for rate-dependent hysteresis in piezoelectric actuators

A hybrid model is proposed in this paper to describe the static nonlinear and dynamic characteristics of rate-dependent hysteresis in piezoelectric actuators. In this model, a neural network based submodel is implemented to approximate the static nonlinear characteristic of the hysteresis while a submodel with the first-order differential operators is constructed to describe the dynamic behavior of the hysteresis. In this paper, a special hysteretic operator is proposed to extract the hysteretic feature of the hysteresis. Then, an expanded input space with such special hysteretic operator is constructed. Based on the constructed expanded input space, the neural network can be implemented to approximate the hysteresis phenomenon. The submodel to describe the dynamics is a sum of the weighted first-order differential operators. Finally, the experimental results of applying the proposed method to the modeling of hysteresis in a piezoelectric actuator are also presented.