消隔组合X型减振器设计与动力学分析

本文将一种X型结构与线性弹簧阻尼减振器相结合构成一种兼具消振和隔振性能的新型X型减振器.基于拉格朗日方法建立单自由度线性振子耦合消隔组合X型减振器系统的动力学方程,应用谐波平衡法得到系统稳态响应的近似解析解,并通过Runge Kutta法得到系统的数值解验证解析解的正确性.讨论了不同的基础激励下新型X型减振器对系统的响应幅值以及位移传递率的减振效果.此外,分析了不同参数对系统的幅频响应曲线以及位移传递率的影响.研究结果表明,新型X型减振器不仅可以将线性刚度转化为非线性刚度,还可以为系统提供负刚度,拥有优秀的消振和超低频隔振性能.     

Feedback Control of Limit Cycle Amplitudes from A Frequency Domain Approach

In this paper, a problem in feedback control of limit cycle amplitudes is studied. A graphical approach for this bifurcation control problem is developed by means of higher-order harmonic balance approximations for both amplitude and frequency of the system oscillatory outputs. The approach starts with the familiar Hopf bifurcation mechanism, and employs the second, fourth, and sixth-order harmonic balance approximations to generate a sequence of graphical tests for convergence analysis of the system oscillatory outputs. This sequential graphical testing leads to accurate approximations of limit cycles of small amplitudes in the system outputs. Degenerate Hopf bifurcation theory is used to formulate an appropriate control objective of capturing small-amplitude limit cycles, which can avoid reaching unstable equilibria or other undesirable limit sets. A rich cubic planar model is presented for illustration of the proposed control method.     

Limits of linearity in squeeze film behavior of a single degree of freedom microsystem

This paper presents a theoretical investigation of squeeze film flow in systems employing microplates parallel to a substrate and undergoing large amplitude normal vibration. Most previous models of squeeze film damping assume small oscillation amplitude with linear system behavior, but it is often unclear how small the vibrations must be to actually elicit this response. In addition, fluid inertia effects are usually overlooked. This study provides a compact nonlinear solution for the incompressible hydrodynamic forces with specific terms describing fluid inertia and viscous damping. Numerical analysis (the explicit Runge-Kutta method) is applied to solve the nonlinear governing equation. The effects of frequency, oscillation amplitude, aspect ratio (of gap to length), and Reynolds number on the dynamic response of the system are investigated. The overall system response depends strongly on the actuation frequency and system properties. It is found that a simple criterion of validity for the linear system assumption is not possible. Near resonance, the vibration input amplitude (relative to the initial gap) must be very small indeed for linearity (～0.001), while in other cases the relative amplitude can be greater than one.     

Feedback limitations of linear sampled‐data periodic digital control

We present a set of feedback limitations for linear time‐invariant systems controlled by periodic digital controllers based upon an analysis of the inter‐sample response of the closed‐loop system to sinusoidal inputs. Fundamental sensitivity and complementary sensitivity functions govern the fundamental and harmonic components of the continuous closed‐loop response. The continuous and discrete response of the system is sensitive to variations in the analog plant at frequencies integer multiples of ω_s/N away from the excitation frequency, where ω_s is the sampling frequency and N is the period of the controller. These functions satisfy interpolation and integral constraints due to open‐loop non‐minimum phase zeros and unstable poles. In addition, the use of periodic digital control may result in a reduction in closed‐loop bandwidth. Copyright © 2000 John Wiley & Sons, Ltd.     

Rejection of harmonic disturbances at the controller input via hybrid adaptive external models

The problem of rejecting harmonic disturbances occurring at the input of a linear controller in a stable loop is addressed. The task is to recover regulation of the plant output, using only information corrupted by harmonic noise of unknown frequency. The solution is provided by an adaptive external model (a device placed outside the stabilizing loop), which possesses a hybrid system structure due to the specific form of the associated certainty-equivalence solution. The geometric characterization of the solution is emphasized throughout the paper, and its relation with the internal model principle is discussed. The important issue of convergence in absence of persistence of excitation is addressed in full. Experimental results validate the proposed approach.     

Harmonic Balance Nonlinear Identification of a Capacitive Dual-Backplate MEMS Microphone

This paper describes the application of a nonlinear identification method to extract model parameters from the steady-state response of a capacitive dual-backplate microelectromechanical systems microphone. The microphone is modeled as a single-degree-of-freedom second-order system with both electrostatic and mechanical nonlinearities. A harmonic balance approach is applied to the nonlinear governing equation to obtain a set of algebraic equations that relate the unknown system parameters to the steady-state response of the microphone. Numerical simulations of the governing equation are also performed, using theoretical system parameters, to validate the accuracy of the harmonic balance solution for a weakly nonlinear microphone system with low damping. Finally, the microphone is experimentally characterized by extracting the system parameters from the response amplitude and phase relationships of the experimental data.     

分段阻尼隔振系统的动力学特性分析

针对传统线性隔振器在降低共振峰值的同时会牺牲隔振性能的矛盾,设计了一种含分段阻尼的隔振器.首先,采用移动凸轮变阻尼装置,通过凸轮廓线的设计使系统的垂向阻尼系数的受振动位移大小控制并呈现分段线性特征,分析了该装置的阻尼特性.然后将分段阻尼装置应用于隔振器中,建立了含分段阻尼的积极隔振系统模型及其动力学方程,通过能量等效原理求出了分段阻尼系统的等效线性阻尼系数,求解了简谐力激励下系统响应的理论解,并用四阶龙格-库塔法数值仿真验证了理论解的正确性.最后研究了分段阻尼隔振系统的动态特性,分析了主要参数对幅频响应特性与力传递率特性的影响.结果表明,通过合理的参数选择,分段阻尼隔振器可兼顾无阻尼隔振器与线性阻尼隔振器的优点,既能有效降低系统的共振峰值,又能保证高频区域的优秀隔振性能,为新型非线性隔振器的设计提供了理论依据.     

含时滞轨道吸振器的建筑结构的动力学分析

本文研究了具有时滞轨道非线性吸振器的建筑结构的动力响应及其控制效果.采用谐波平衡法和弧长延拓法给出了简谐激励作用下主结构的幅频响应曲线,并与龙格库塔法的结果进行了对比.考察了不同参数情况下幅频曲线的变化情况,揭示了系统的复杂运动现象.结果表明,轨道非线性会导致幅频曲线向左偏转.时滞反馈控制能够降低主结构的位移幅值,并可抑制混沌响应.     

Model reduction based on limited‐time interval impulse response Gramians

In this paper, three new Gramians are introduced namely ‐ limited‐time interval impulse response Gramians (LTIRG), generalized limited‐time Gramians (GLTG) and generalized limited‐time impulse response Gramians (GLTIRG). GLTG and GLTIRG are applicable to both unstable systems and also to systems which have eigenvalues of opposite polarities and equal magnitude. The concept of these Gramians is utilized to develop model reduction algorithms for linear time‐invariant continuous‐time single‐input single‐output (SISO) systems. In the cases of GLTIRG and GLTG based model reduction, the standard time‐limited Gramians are generalized to be applied to unstable systems by transforming the original system into a new system which requires the solution of two Riccati equations. Two numerical examples are included to illustrate the proposed methods. The results are also compared with standard techniques.     

Approximate solutions for nonlinear transverse vibrations of elastically restrained tapered beams

This paper introduces the approximate solutions of the mathematical model of an elastically restrained tapered beam. At the beginning of the study, the equation of motion is derived in a detailed way. The frequency–amplitude relation is deduced and solved numerically. The nonlinear natural frequencies for the transverse vibrations of an elastically restrained tapered beam are provided using Mathematica software. The max–min approach, the frequency–amplitude method and the parameter-expansion method are applied in order to obtain an approximated solution. The approximate analytical results are further compared with the numerical results for both small and large amplitude oscillations, and very good agreement is observed.     

A predictive current control method for shunt active filter with windowing based wavelet transform in harmonic detection

This paper has been established based on harmonic detection and compensation on power system. The present work deals with two powerful methods in harmonic detection field of digital signal processing. The first one is the windowing technique and the other one is wavelet transform. A traditional synchronous fundamental dq-frame algorithm is modified in filtering process. As an improvement, the Fourier-based low pass filter is replaced with a windowing–wavelet method. The adopted windowing aspect is Hamming window to reduce traditional rectangular window effete in frequency domain. In addition, the applied mother wavelet is selected in terms of its effectiveness on transient response, low overshot and low oscillation at frequency domain. Due to these concepts, the db8 is selected as mother wavelet. In harmonic elimination procedure, the detected harmonic is injected using a shunt active filter based on predictive current control technique. The presented method has been verified with MATLAB–SIMULINK model and wavelet toolbox. The results confirm that this method is superior to traditional FFT based and wavelet based filters because of fast transient response and small negligible sidelobes. As a consequence this technique is able to reduce power system harmonic.     

基于平衡截断法的离散时间线性时滞系统的低频域模型降阶

研究在系统工作频率范围为低频区间情形下的离散时间线性时滞系统模型降阶问题. 首先根据时滞系统在零频点处传递函数的性质, 构造了一类匹配其零频响应的带有可调参数的扩展线性时滞系统, 进而在其基础上结合已有的时滞系统平衡截断法给出了新的低频模型降阶算法. 通过调节其中的设计参数, 新方法所得降阶时滞系统模型能够以任意精度逼近原系统的零频响应特性, 进而可以用于改善低频范围内的模型逼近性能. 数值算例验证了所提方法的有效性和优越性.     

带摆动机构的多线切割机的线性H∞张力控制

针对常规张力控制在带摆动机构的多线切割机系统中精度不高,非线性干扰不稳定的问题,本文分析了系统结构和控制难点,采用干扰观测的线性H∞张力控制建立子系统模型,充分考虑系统中具有子系统模型的动态干扰和未建模动态干扰以及参数和结构的不确定性引起的误差,并给出解决方案.研究了线性H∞控制系统的稳定性,并在系统稳定的条件下,利用Chelosky分解方法,得到动态方程的解,大幅提高系统响应速度.样机的实验结果表明该系统具有系统张力波动小,稳定性能好,断线率低的特点.     

Stability and performance of a variable gain controller with application to a dvd storage drive

This paper deals with the control design for optical storage drives. A nonlinear design is suggested to overcome the tradeoff between disturbance rejection, in the sense of tracking error reduction during low-frequency shock and vibration, and playability, in the sense of sensor noise tracking during high-frequency disc surface defects. Based on a variable gain control design, it is shown that improvements in disturbance rejection can be obtained without unnecessarily affecting playability. With this design, additional control is applied beyond a pre-defined error level. Accordingly, it is shown that large vibrations induce additional control effort giving improved disturbance rejection while, at the same time, small vibrations hardly induce any additional control effort thus leaving the playability properties unaffected. The variable gain strategy is studied regarding closed-loop stability and regarding performance. Closed-loop stability is derived on the basis of absolute stability theory. Performance is quantified using a measure derived from the linear sensitivity function. Based on the amplitude of the linear sensitivity function, the maximum absolute values of the periodic nonlinear response subjected to harmonic excitation are computed within a frequency range of interest. Experiments are performed on an industrial setup to validate the numerical results, and to illustrate the applicability of the nonlinear control design in a dvd application.     

Predictive functional control based on fuzzy model: magnetic suspension system case study

Fuzzy model based predictive functional controller (FPFC) is applied to the magnetic suspension system—a pilot plant for magnetic bearing. High quality control requirements are short settle time with a-periodical step response and zero steady-state error. Open loop unstable process was stabilised with linear lead compensator. The FPFC was used as a cascade controller. Due to some model uncertainties, the Takagi–Sugeno fuzzy model of stabilised system was obtained using fuzzy identification. Comparing to PID, it improved quality and robustness performance. With its computational efficiency, it proved to be ideal solution for high sampling frequency systems.     

The Design of a Coprime‐Factorized Predictive Functional Controller for Unstable Fractional Order Systems

In this paper, a new approach, called coprime‐factorized predictive functional control method (CFPFC‐F) is proposed to control unstable fractional order linear time invariant systems. To design the controller, first, a prediction model should be synthesized. For this purpose, coprime‐factorized representation is extended for unstable fractional order systems via a reduced approximated model of unstable fractional order (FO) system. That is, an approximated integer model of fractional order system is derived via the well‐known Oustaloup method. Then, the high order approximated model is reduced to a lower one via a balanced truncation model order reduction method. Next, the equivalent coprime‐factorized model of the unstable fractional‐order plant is employed to predict the output of the system. Then, a predictive functional controller (PFC) is designed to control the unstable plant. Finally, the robust stability of the closed‐loop system is analyzed via small gain theorem. The performance of the proposed control is investigated via simulations for the control of an unstable non‐laminated electromagnetic suspension system as our simulation test system.     

串联非线性能量阱的高分支响应研究

本文对比研究了单自由度NES和两自由度串联NES的吸振效能,重点分析了串联NES对高分支响应的抑制作用.运用复变量-平均法,推导出连接串联NES的线性主振子的慢变方程,获得了系统的频率响应曲线.在不同激励幅值下,将连接单自由度NES与连接串联两自由度NES的系统响应进行对比,结果表明,串联NES能够在较大,幅值激励范围内保持较高吸振效能.在两种幅值激励下,分析了串联NES的参数对减振效果的影响.研究结果表明,在小幅激励时,调整一级NES参数对主振子的响应影响较为明显;而在大幅激励时,二级NES参数对减振效果影响较大.     

Harmonic analysis of the vibrations of a cantilevered beam with a closing crack

In this article, the vibrational response of a cracked cantilevered beam to harmonic forcing is analysed. The study has been performed using a finite element model of the beam, in which a so-called closing crack model, fully open or fully closed, is used to represent the damaged element. Undamaged parts of the beam are modelled by Euler-type finite elements with two nodes and 2 d.f. (transverse displacement and rotation) at each node. Recently the harmonic balance method has been employed by other researchers to solve the resulting non-linear equations of motion. Instead, in this study, the analysis has been extended to employ the first and higher order harmonics of the response to a harmonic forcing in order to characterize the non-linear behaviour of the cracked beam. Correlating the higher order harmonics of the response with the forcing term the so-called higher order frequency response function (FRFs), defined from the Volterra series representation of the dynamics of non-linear systems, can be determined by using the finite element model to simulate the time domain response of the cracked beam. Ultimately the aim will be to employ such a series of FRFs, an estimate of which in practice could be measured in a stepped sine test on the beam to indicate both the location and depth of the crack, thus forming the basis of an experimental structural damage identification procedure.     

Optimal anti-windup synthesis for repetitive controllers

Repetitive controllers use internal models that provide very high gain at a selected fundamental frequency and its harmonics, additionally, some of the internal models may result unstable, as in the high order repetitive control approach. These characteristics make the repetitive control system susceptible to exhibit wind-up when actuator saturation occurs. This paper proposes an anti-windup scheme for repetitive control based on the model recovery anti-windup strategy. The proposed scheme provides low order, low computational burden and also isolation of the controller from the saturation effects. The anti-windup compensator is constructed from the plant model and provides an additional linear feedback path aimed at enhancing system performance. This feedback path is designed to obtain a deadbeat behaviour, which makes the system recovery faster. Finally, internal stability and deadbeat features are designed in a compact procedure based on linear matrix inequalities and an optimal linear quadratic design. Experimental validation of the proposed anti-windup compensator is provided using a mechatronic plant.     

Predictive Functional Control Based on Fuzzy Model: Comparison with Linear Predictive Functional Control and PID Control

The implementation of the fuzzy predictive functional control (FPFC) on the magnetic suspension system is presented in the paper. The magnetic suspension system was in our case the pilot plant for magnetic bearing and is an open-loop unstable process, therefore a lead compensator was used to stabilize it. The high quality control requirements were a-periodical step response and zero steady-state error. Adding the integrator to a feedback causes overshoot. The solution to the problem was cascade control with fuzzy predictive functional controller in the outer loop. To cope with the unknown model parameters and the nonlinear nature of the magnetic system, a fuzzy identification based on FNARX model was used. After successful validation the obtained fuzzy model was used for controller design. The FPFC is compared with a cascade linear predictive functional control (PFC) and PID control. The results we obtained with the FPFC are very promising and hardly comparable with conventional control techniques.