Design and testing of a hybrid polymeric electrostrictive/piezoelectric beam with bang–bang control

Electrostrictive materials, hard ceramics and soft polymers, have been used as precision actuators in many engineering applications. This study is to examine bang–bang control performance of a hybrid Plexiglas beam laminated with polymeric electrostrictive (RTV 270) actuator and piezoelectric polyvinylidene fluoride (PVDF) sensor layers using both analytical and experimental techniques. Material characteristics are calibrated via static testing first; a hybrid beam model is then fabricated and an experiment set-up, consisting of a bang–bang controller, high-voltage amplifier, data acquisition system and the hybrid beam system, is designed to evaluate vibration control characteristics (i.e., damping ratio estimation) of the hybrid beam subjected to various control conditions. Due to the quadratic behaviour of electrostrictive materials, the controller activates the electrostrictive actuator only in upward motion of the beam, with reference to signals generated from the piezoelectric sensor. Base on constitutive equations and dynamic/control characteristics, a mathematic hybrid beam model is also derived from the electrostrictive thin shell theory and its dynamic responses, based on the finite difference discretization, are simulated to predict damping ratios resulting from control forces induced by the electrostrictive actuators. Dynamic responses (with and without control) of the physical beam model are measured and compared with simulation results. Favourable comparison suggests that the mathematical model describes the experimental model very well and its application to other advanced structures can be proceeded.     

Optimal control of structural vibrations using a mixed-mode magnetorheological fluid mount

In this work, a mixed-mode magnetorheological (MR) mount is proposed and applied to the vibration control of a flexible beam structure subjected to external disturbances. On the basis of non-dimensional Bingham number, an appropriate size of the MR mount is designed and manufactured. After experimentally evaluating the field-dependent damping force of the MR mount, a structural system consisting of a flexible beam and vibrating rigid mass is established. The governing equation of motion of the system is derived and expressed as a state space control model. A linear quadratic Gaussian (LQG) controller is then designed in order to attenuate the vibration of the structural system. The controller is empirically realized and control responses such as acceleration and displacement of the structural system are evaluated and presented in frequency domain.     

周期性机械振动主动控制算法

为提高周期性机械装置的隔振性能,减少其对底座(或地面)及周围环境的影响,采用由弹性橡胶和压电堆作动器组成的主动悬置(active control mount, ACM).针对压电堆作动器输出位移较小的情况,设计液压位移放大机构.通过对压电作动器和橡胶主簧性能的分析,建立由主动悬置构成的隔振系统的力学模型.周期性机械振动系统,其周期振动信号可用作控制同步信号,因此控制系统采用基于同步滤波-X LMS(least mean square)算法的自适应控制策略,传递到机座的残余力作为误差信号,实现对周期性机械振动系统的主动控制.计算机仿真实验结果表明,采用这种主动悬置和同步滤波-X LMS算法的主动控制系统,相对于采用普通橡胶悬置的被动系统,明显减少了对底座的力传递,减振效果明显.     

Hybrid controller of a linear piezoelectric walking stage relying on stack/shear piezoelectric actuators

This paper proposes a hybrid control strategy of a novel linear piezoelectric walking stage based on two sorts of piezoelectric actuators, which takes the load variation into account. The proposed stage consists of two parallel 4-bar lever amplification mechanisms with flexure hinges actuated by piezoelectric stacks to heighten the vertical distance (that is more tolerable to the assembly discrepancy), two compression springs (that is able to maintain a fixed linear position without powering), and two shear piezoelectric actuators (that can achieve longer and equivalent to walking motion) in a small form factor. The proposed stage has two operating modes, namely a coarse positioning mode with a more extensive travel range and a fine positioning mode with a nanometer-level resolution, to possess excellent performance for the linear piezoelectric walking stage of load variations. One multimodal switching controller and one feedforward-feedback controller conduct the coarse mode and fine mode, respectively. The optimal frequency for a specific load is obtained through a backpropagation neural network in the multimodal switching control. In the feedforward-feedback control, the inverse mathematical model based on the Bouc-Wen hysteresis model is used to mitigate the hysteresis effect in the feedforward part while the proportional–integral–derivative controller in the feedback part handles the external system disturbances. Experimental results show the proposed hybrid coarse/fine mode control strategy's effectiveness to satisfy an efficient and accurate positioning task.     

Control of Piezo Actuated Structures using Interval Method

Abstract

A Fast output sampling feedback controller is designed and implemented for vibration control of piezoelectric actuated beam structure using an interval method. Uncertainties which are assumed in the model, are identified through on line recursive least square parameter estimation. The control and identification process is done by using Simulink modeling software and a dSPACE DS 1104 controller board.     

Vibration control of a frame structure using electro-rheological fluid mounts

A squeeze-mode electro-rheological (ER) mount has been designed, manufactured, and applied to the vibration control of a frame structure subjected to external excitations. After verifying that the damping force of the ER mount can be controlled by controlling the applied voltage, a frame structure system supported by spring mounts and the proposed ER mounts has been assembled. The governing equation of the structural system is derived in the modal coordinate and is rewritten as a state-space control model. An optimal controller, which consists of the velocity feedback signal of the frame structure and the force feedback signal transmitted from the exciting point to the mount position, is formulated in order to attenuate the imposed excitations. The controller has been optimized experimentally and control responses such as the acceleration of the frame structure and the transmitted force at each mount position are presented in both time and frequency domains.     

Controller design for high-frequency cutting using a piezo-driven microstage

Controller design consists of a feedforward and a feedback controller to support a microstage with flexure hinge structure driven by piezoelectric ceramic actuator for high-frequency nanoscale cutting is developed in this article. The feedforward controller is designed based on a hysteresis dynamic model in order to reduce the nonlinear hysteresis effect of piezoelectric actuator. The position feedback controller is designed based upon an exponentially weighted moving average (EWMA) method embedded in an internal model control (IMC) structure constructing a run-to-run IMC (RtR-IMC) control scheme in order to deal with system bias or modeling inaccuracy. Also, disturbance due to temperature rise will influence actuator's performance, hence an additional compensator is included in the IMC structure. Surfaces dimple micro-machining utilizes piezoelectric-driven microstage for high-speed cutting is selected as an example to investigate system performance. The developed control algorithm is implemented on a DSP-based system to provide 1 kHz operating speed. In experiment, the proposed feedforward and feedback controller is verified to be able to overcome those negative factors efficiently and preserve good positioning accuracy.     

Finite element based model predictive control for active vibration suppression of a one-link flexible manipulator

This paper presents a unique approach for active vibration control of a one-link flexible manipulator. The method combines a finite element model of the manipulator and an advanced model predictive controller to suppress vibration at its tip. This hybrid methodology improves significantly over the standard application of a predictive controller for vibration control. The finite element model used in place of standard modelling in the control algorithm provides a more accurate prediction of dynamic behavior, resulting in enhanced control. Closed loop control experiments were performed using the flexible manipulator, instrumented with strain gauges and piezoelectric actuators. In all instances, experimental and simulation results demonstrate that the finite element based predictive controller provides improved active vibration suppression in comparison with using a standard predictive control strategy.     

Ultra-precise tracking control of piezoelectric actuators via a fuzzy hysteresis model

In this paper, a novel Takagi-Sugeno (T-S) fuzzy system based model is proposed for hysteresis in piezoelectric actuators. The antecedent and consequent structures of the fuzzy hysteresis model (FHM) can be, respectively, identified on-line through uniform partition approach and recursive least squares (RLS) algorithm. With respect to controller design, the inverse of FHM is used to develop a feedforward controller to cancel out the hysteresis effect. Then a hybrid controller is designed for high-performance tracking. It combines the feedforward controller with a proportional integral differential (PID) controller favourable for stabilization and disturbance compensation. To achieve nanometer-scale tracking precision, the enhanced adaptive hybrid controller is further developed. It uses real-time input and output data to update FHM, thus changing the feedforward controller to suit the on-site hysteresis character of the piezoelectric actuator. Finally, as to 3 cases of 50 Hz sinusoidal, multiple frequency sinusoidal and 50 Hz triangular trajectories tracking, experimental results demonstrate the efficiency of the proposed controllers. Especially, being only 0.35% of the maximum desired displacement, the maximum error of 50 Hz sinusoidal tracking is greatly reduced to 5.8 nm, which clearly shows the ultra-precise nanometer-scale tracking performance of the developed adaptive hybrid controller.     

Strain rate self-sensing for a cantilevered piezoelectric beam

This paper deals with the analytical modeling, and the experimental verification of the strain rate self-sensing method using a hybrid adaptive filter for a cantilevered piezoelectric beam. The piezoelectric beam consists of two laminated lead zirconium titanates (PZT) on a metal shim. A mathematical model of the beam dynamics is derived by Hamilton’s principle and the accuracy of the modeling is verified through the comparison with experimental results. For the strain rate estimation of the cantilevered piezoelectric beam, a self-sensing mechanism using a hybrid adaptive filter is considered. The discrete parts of this mechanism are realized by the DS1103 DSP board manufactured by dSPACE^TM. The efficacy of this method is investigated through the comparison of experimental results with the predictions from the derived analytical model.     

悬臂梁振动自适应模糊控制及DSP实现

以粘贴压电自感作动器的悬臂梁为研究对象,推导了悬臂梁振动主动控制的压电元传感方程和作动方程的传递函数,给出了压电自感作动器位置配置优化方法,设计了硬件电路以及软件流程.试验结果表明,利用压电自感作动器和模糊自适应控制器可有效地抑制悬臂梁振动.     

压电机敏结构嵌入式控制器的开发与验证

为探索压电主动机敏结构测控单元微型化及高速处理技术,设计开发了一种以ARM和DSP为核心的双核嵌入式控制器;阐述了系统构成与核心部件、系统软硬件设计思路、功能指标和开发过程;通过构建模型结构和试验平台,结合自适应滤波前馈振动控制算法,进行了压电机敏柔性结构振动主动控制试验。试验结果验证了所设计嵌入式控制器的可行性和有效性,并在压电机敏结构测控系统微型化方面获得有益结果。     

Supervisory hybrid control of piezoelectric actuators utilized in tracking piecewise continuous trajectories

This article presents a supervisory hybrid control design for piezoelectric actuators utilized in tracking trajectories with intermittent jump discontinuities. We use a previously developed robust adaptive controller and a standard PID controller to construct this hybrid control strategy. We show that when the sub-controllers are used for step tracking, while primarily tuned for continuous trajectory tracking, large undesirable oscillations occur. Conversely, when the controllers are retuned for step tracking, their performance degrades in tracking high-frequency continuous trajectories. Thus, a supervisory hybrid controller is developed to track desired trajectories with occasional discontinuities, using both the robust adaptive and the PID controllers. The robust adaptive controller performs as the primary controller for tracking the continuous segments of the desired trajectory, while the PID controller is activated when the steps occur. Results indicate that the proposed supervisory hybrid controller outperforms both sub-controllers in tracking high-frequency trajectories with intermittent discontinuities.     

高速弹性连杆机构振动的复模态主动控制研究

应用 Hamilton虚功原理 ,建立了含有压电元件的弹性机构振动主动控制有限元模型。运用复模态理论 ,研究了机构的独立模态振动主动控制问题 ,给出了一种简便的包含状态反馈和干扰前馈的混合主动控制技术。针对一曲柄摇杆机构 ,进行了动态分析和主动振动控制的数值仿真。计算结果表明 ,本方法可以有效地控制系统的弹性振动     

橡胶压缩性在悬置结构有限元分析中的应用

合理修正橡胶压缩性对于正确进行橡胶悬置结构有限元分析具有重要意义。以圆柱型橡胶悬置为研究对象,进行悬置径向刚度的有限元分析与试验,通过对比可知,假设橡胶材料为不可压缩或接近不可压缩时,悬置的计算刚度远大于试验刚度,有限元计算存在较大误差。针对以上问题分析,提出进行橡胶体积可压缩性修正的必要性。采用调整橡胶材料泊松比的方法修正橡胶可压缩性,当悬置计算刚度与试验刚度吻合较好时,橡胶可压缩修正模型的泊松比应为0.42。应用修正的橡胶材料模型对悬置结构进行优化改进,并对改进结构进行刚度有限元分析与试验,结果表明,改进结构的刚度计算曲线与试验曲线变化趋势基本一致,吻合较好。从而验证了橡胶体积可压缩模型修正方法合理,具有一定的工程应用价值。     

Sliding mode control of a shear-mode type ER engine mount

This paper presents feedback control characteristics of a shear-mode type electro-rheological (ER) engine mount. The field-dependent yield stress of an arabic gum-based ER fluid is obtained using a couette type electroviscometer, and it is incorporated into the governing equation of motion of the ER engine mount, which is derived from a bond graph model. A sliding mode controller which directly represents the field-dependent damping force is formulated by taking into account the stiffness and damping properties of the systems as parameter uncertainties. The controller is then experimentally realized by imposing a semi-active actuating condition. The effectiveness of the proposed ER engine mount is demonstrated showing capabilities of isolating the vibrations due to sinusoidal and random excitations.     

Active robust vibration control of flexible composite beams with parameter perturbations

In this paper, a time domain approach is presented to treat the problem of active controlling simultaneously the bending and torsional vibration of flexible composite beams under both mode truncations and parameter perturbations. In the proposed approach, the residual model, which is known as unstructured uncertainty, is viewed as an additive perturbation to the controlled model. Based on a state space model, which incorporates both bending and torsional deformation effects, of the flexible composite beam with piezoelectric sensors and actuators, a robust stability condition is derived to guarantee that both bending and torsional vibration of the flexible composite beam, which is subject to both mode truncation and linear time-varying parameter perturbations, can be actively controlled by an observer-based controller. The proposed robust stability condition gives an insight into the relationship between the stability margins of the controlled and residual mode subsystems, spillover effects and additive time-varying parameter perturbations. Finally, an active robust vibration control problem of a cantilevered flexible composite beam with piezoelectric sensors and actuators is provided for illustration.     

Design,modeling, and control of a monolithic compliant x-y-θ microstage using a double-rocker mechanism

This paper reports the design, modeling, and control of a novel three-degrees-of-freedom piezoelectric compliant microstage by introducing a new double-rocker mechanism. The double-rocker mechanism combines a first (leverage) amplifier and a second (rocker) amplifier for double-stage displacement amplification and parasitic motion reduction. An analytical model is established to calculate the deformation behavior of the microstage, and the model is verified using finite-element analysis (FEA). An improved Prandtl-Ishlinskii (PI) model is proposed to describe piezoelectric hysteresis characteristics by optimizing the threshold selection. Then, a composite control strategy is designed to achieve precision trajectory control. The control strategy consists of a hysteresis-based feedforward controller and a proportional-integral feedback controller. A prototype of the microstage is manufactured, and an experimental system is established. Several open-loop and closed-loop experiments are conducted, and the experimental results validate the effectiveness of the proposed microstage and the designed control strategy.     

基于速度-加速度时滞反馈的振动主动控制

在振动主动控制中,基于加速度测量信号,并考虑滤波器群时延引入的时滞,研究了一种时滞控制器设计方法。采用等维方法和状态导数反馈思想,提出一种速度-加速度时滞反馈控制器的设计方法。该控制器不含位移信号,可省去两次数值积分和去直流分量、趋势项这两个过程,并可避免由两次数值积分带来的累积误差。以粘帖有压电陶瓷和加速度传感器的智能梁为控制对象,采用该控制器控制其自由振动,并与速度-加速度反馈控制效果进行比较。仿真结果表明,当采用速度-加速度反馈直接控制时滞系统时,若时滞超出其稳定区间,该方法失效,而速度-加速度时滞反馈控制方法则具有良好的控制效果。     

压电复合悬臂梁非线性模型及求解

基于功能材料的复合悬臂梁涉及多物理场耦合,其本构关系的非线性影响悬臂梁的输出及控制精度,采用Helmholtz Gibbs自由能关系建立压电材料的非线性本构模型。基于Boltzmann原理,该模型的内核函数由热能和Gibbs能量平衡决定。将模型与悬臂梁结构进行耦合,利用边界和初始条件导出压电复合悬臂梁的强解形式,并对强解进行弱化,采用Galerkin法对弱解进行离散化,利用三次B样条函数得到悬臂梁的数值解。研究结果表明,与已有文献的实验进行比较,所建立的压电材料非线性本构模型能够较好地预测复合悬臂梁的行为。