Robust non-fragile dynamic vibration absorbers with uncertain factors

In this paper, the design problem for non-fragile dynamic vibration absorbers (DVAs) is investigated. Due to the imprecision of the manufacturing process or the variation during the operation, uncertainty in the parameters of the DVA is unavoidable. The uncertainty may degrade the performance of the designed DVA or even deteriorate the system. Hence, it is practically demanding to propose a design method for a non-fragile DVA, i.e., when the parameters of the DVA vary in an admissible range, an expected vibration suppression level should be guaranteed. The uncertainty of the DVA is feasibly assumed to be norm-bounded. Then, the design problem for the DVA is converted into a static output feedback (SOF) control problem. Sufficient condition for the existence of the non-fragile DVA with a prescribed H_∞ level is derived by using a bilinear matrix inequality (BMI). An iterative linear matrix inequality (ILMI) method is employed to solve the BMI condition. Finally, a design example is given to show the effectiveness of the proposed approach.     

Active vibration control in Duffing mechanical systems using dynamic vibration absorbers

This paper deals with the multi-frequency harmonic vibration suppression problem in forced Duffing mechanical systems using passive and active linear mass–spring–damper dynamic vibration absorbers. An active vibration absorption scheme is proposed to extend the vibrating energy dissipation capability of a passive dynamic vibration absorber for multiple excitation frequencies and, simultaneously, to perform reference position trajectory tracking tasks planned for the nonlinear primary system. A differential flatness-based disturbance estimation scheme is also described to estimate the unknown multiple time-varying frequency disturbance signal affecting the differentially flat nonlinear vibrating mechanical system dynamics. Some numerical simulation results are provided to show the efficient performance of the proposed active vibration absorption scheme and the fast estimation of the vibration disturbance signal.     

Brake squeal reduction of vehicle disc brake system with interval parameters by uncertain optimization

An uncertain optimization method for brake squeal reduction of vehicle disc brake system with interval parameters is presented in this paper. In the proposed method, the parameters of frictional coefficient, material properties and the thicknesses of wearing components are treated as uncertain parameters, which are described as interval variables. Attention is focused on the stability analysis of a brake system in squeal, and the stability of brake system is investigated via the complex eigenvalue analysis (CEA) method. The dominant unstable mode is extracted by performing CEA based on a linear finite element (FE) model, and the negative damping ratio corresponding to the dominant unstable mode is selected as the indicator of instability. The response surface method (RSM) is applied to approximate the implicit relationship between the unstable mode and the system parameters. A reliability-based optimization model for improving the stability of the vehicle disc brake system with interval parameters is constructed based on RSM, interval analysis and reliability analysis. The Genetic Algorithm is used to get the optimal values of design parameters from the optimization model. The stability analysis and optimization of a disc brake system are carried out, and the results show that brake squeal propensity can be reduced by using stiffer back plates. The proposed approach can be used to improve the stability of the vehicle disc brake system with uncertain parameters effectively.     

具有不确定参数的Liu混沌系统的同步

基于控制Lyapunov函数,对具有不确定参数的Liu混沌系统提出一种同步控制方法,控制律只依赖参数变化范围而不必知道参数的具体数值. 与已有结果相比,该设计比较简单,有较强的鲁棒性,能克服较大参数误差对同步的影响. 仿真结果说明了所提方法的有效性. 关键词： 参数系统 同步 鲁棒控制 控制Lyapunov函数     

Anticontrol of chaos for discrete-time fuzzy hyperbolic model with uncertain parameters

This paper proposes a new method to chaotify the discrete-time fuzzy hyperbolic model （DFHM） with uncertain parameters. A simple nonlinear state feedback controller is designed for this purpose. By revised Marotto theorem, it is proven that the chaos generated by this controller satisfies the Li-Yorke definition. An example is presented to demonstrate the effectiveness of the approach.     

黏弹材料动力学参数的宽频测试

利用改进的波速法,对黏弹性材料连续宽频范围的动力学参数进行测试。利用有限元方法,对波速法的测试过程进行了仿真,验证了利用长短棒波速法测量宽频动力学参数的有效性。采用可控脉冲生成技术,在激振器上产生了用于宽频测试的短脉冲信号。黏弹性长短棒在上述宽带短脉冲激励下作纵向强迫振动,利用激光测振仪测量长短两棒自由端的纵向振动速度,从而可得两振动信号在连续宽频范围的幅值比和相位差,进而可根据波速法原理计算得到材料在连续宽频范围的储能模量和损耗因子。测试结果表明,该系统通过较少次数测试,可直接计算得到1~5 kHz连续宽频范围的动力学参数,测试结果与黏弹仪数据吻合。通过对幅值比和相位差进行线性最小二乘拟合,可以进一步拓展测量的频率范围。该方法准确可靠、简便快速,具有实际应用价值。     

黏弹材料动力学参数的宽频测试

利用改进的波速法,对黏弹性材料连续宽频范围的动力学参数进行测试。利用有限元方法,对波速法的测试过程进行了仿真,验证了利用长短棒波速法测量宽频动力学参数的有效性。采用可控脉冲生成技术,在激振器上产生了用于宽频测试的短脉冲信号。黏弹性长短棒在上述宽带短脉冲激励下作纵向强迫振动,利用激光测振仪测量长短两棒自由端的纵向振动速度,从而可得两振动信号在连续宽频范围的幅值比和相位差,进而可根据波速法原理计算得到材料在连续宽频范围的储能模量和损耗因子。测试结果表明,该系统通过较少次数测试,可直接计算得到1~5 kHz连续宽频范围的动力学参数,测试结果与黏弹仪数据吻合。通过对幅值比和相位差进行线性最小二乘拟合,可以进一步拓展测量的频率范围。该方法准确可靠、简便快速,具有实际应用价值。     

模式转换型超声塑焊振动系统的设计

基于弯曲振动理论和耦合振动理论,设计了一种新型大尺寸筒形超声塑焊振动系统。该振动系统由纵向振动换能器及变幅杆、弯曲振动金属圆盘和耦合振动圆筒四部分组成。换能器和变幅杆的纵向振动驱动圆盘的二次弯曲模式振动,圆盘的二次弯曲模式振动激励圆筒的纵向模式振动,实现了工具头在较高频率下谐振。实验结果表明,振动系统的测试频率与计算频率比较符合,在大信号下测试的纵-弯-纵振动模式转换效果很好。研究结果为高频大尺寸超声焊接系统的设计提供了思路。     

Minimization of the mean square velocity response of dynamic structures using an active-passive dynamic vibration absorber

An optimal design of a hybrid vibration absorber (HVA) with a displacement and a velocity feedback for minimizing the velocity response of the structure based on the H(2) optimization criterion is proposed. The objective of the optimal design is to reduce the total vibration energy of the vibrating structure under wideband excitation, i.e., the total area under the velocity response spectrum is minimized in this criterion. One of the inherent limitations of the traditional passive vibration absorber is that its vibration suppression is low if the mass ratio between the absorber mass and the mass of the primary structure is low. The active element of the proposed HVA helps further reduce the vibration of the controlled structure, and it can provide very good vibration absorption performance even at a low mass ratio. Both the passive and active elements are optimized together for the minimization of the mean square velocity of the primary system as well as the active force required in the HVA. The proposed HVA was tested on single degree-of-freedom (SDOF) and continuous vibrating structures and compared to the traditional passive vibration absorber.     

CGZ型机械振动实验系统的研究和应用

CGZ型机械系统是专为工科物理实验专门设计的机械振动类仪器。该实验系统包括振动实验装置、振动测试系统、计算机分析处理系统三大部分,本文将重点介绍实验装置和实验结果分析。     

A trigonometric interval method for dynamic response analysis of uncertain nonlinear systems

This paper proposes a new non-intrusive trigonometric polynomial approximation interval method for the dynamic response analysis of nonlinear systems with uncertain-but-bounded parameters and/or initial conditions.This method provides tighter solution ranges compared to the existing approximation interval methods.We consider trigonometric approximation polynomials of three types:both cosine and sine functions,the sine function,and the cosine function.Thus,special interval arithmetic for trigonometric function without overestimation can be used to obtain interval results.The interval method using trigonometric approximation polynomials with a cosine functional form exhibits better performance than the existing Taylor interval method and Chebyshev interval method.Finally,two typical numerical examples with nonlinearity are applied to demonstrate the effectiveness of the proposed method.     

不确定混沌系统的反同步与参数辨识

针对一类混沌系统,提出了一种系统的混沌反同步设计方案,基于该方案,设计一种自适应控制方法,实现了参数不确定系统的混沌反同步和未知参数的辨识.数值模拟结果表明了提出方法的有效性.     

基于功率流方法的连续参数系统动力吸振器的优化设计

针对附加动力吸振器的连续参数系统,采用两端固支梁模拟连续参数主振系,利用结构导纳理论,引入振动系统的结构导纳修正矩阵和等价结构导纳矩阵,简化了系统的动态特性分析过程。在此基础上,推导系统各环节功率流的矩阵表达式。提出了以注入主阵系的净功率流为控制目标的动力吸阵器优化设计策略,并通过计算数值仿真验证了该方法的有效性。最后,探讨了振源位置对连续参数系统功率流传递特性、吸振器优化参数及其控制效果的影响。     

Improving beampatterns of two-dimensional random arrays using convex optimization

Sensors are becoming ubiquitous and can be combined in arrays for source localization purposes. If classical conventional beamforming is used, then random arrays have poor beampatterns. By pre-computing sensor weights, these beampatterns can be improved significantly. The problem is formulated in the frequency domain as a desired look direction, a frequency-independent transition region, and the power minimized in a rejection-region. Using this formulation, the frequency-dependent sensor weights can be obtained using convex optimization. Since the weights are data independent they can be pre-computed, the beamforming has similar computational complexity as conventional beamforming. The approach is demonstrated for real 2D arrays.     

具有完全不确定参数的五项双曲型混沌系统的投影同步

提出了一个新的简单的双曲型三维自治混沌系统,该三维混沌系统只含有五项, 并且其非线性特征主要依赖于一个非线性二次双曲正弦项和一个非线性二次交叉项. 较已有的三维混沌系统而言, 不仅系统的项要少一些, 而且在参数变化时, 呈现混沌的参数范围也很大. 对系统的一些基本动力学特性进行了数值模拟和理论分析. 同时, 还研究了具有完全不确定参数的该五项双曲型混沌系统的投影同步. 基于Lyapunov指数稳定性理论和Barbalat引理, 设计了一个新的具有参数自适应律的自适应同步控制器, 利用该控制器分别实现了两个结构相同和相异混沌系统的渐进性和全局性投影同步. 数值模拟验证了该方法的有效性和可行性.     

Linear response function for quantum mechanical system

The linear response function for external fields with arbitrary space-time dependence is calculated for various systems in thermal equilibrium. First we derive the general expressions for free fermions and bosons. In particular the superconducting properties of free bosons are investigated. Secondly the influence of a weak repulsion between the bosons on their superconducting properties is investigated. Finally the response function for electrons with the BCS Hamiltonian is calculated exactly in the strong coupling limit.     

Data-free inference of the joint distribution of uncertain model parameters

A critical problem in accurately estimating uncertainty in model predictions is the lack of details in the literature on the correlation (or full joint distribution) of uncertain model parameters. In this paper we describe a framework and a class of algorithms for analyzing such “missing data” problems in the setting of Bayesian statistics. The analysis focuses on the family of posterior distributions consistent with given statistics (e.g. nominal values, confidence intervals). The combining of consistent distributions is addressed via techniques from the opinion pooling literature. The developed approach allows subsequent propagation of uncertainty in model inputs consistent with reported statistics, in the absence of data.     

参数不确定永磁同步电机混沌系统的有限时间稳定控制

针对含有参数不确定性的永磁同步电机混沌系统, 结合主动控制与有限时间稳定控制理论, 提出一种改进的主动有限时间稳定控制器. 该控制器不仅具有较强的鲁棒性, 而且可以通过调整终端吸引子比例系数, 有效地缩短系统的响应时间, 以提高系统的响应能力. 通过仿真实验, 验证了该控制器比传统的控制器的具有更强的鲁棒性和响应能力. 关键词： 永磁同步电机 混沌控制 有限时间稳定 主动控制     

Design optimization of a damped hybrid vibration absorber

In this article, the H_∞ optimization design of a hybrid vibration absorber (HVA), including both passive and active elements, for the minimization of the resonant vibration amplitude of a single degree-of-freedom (sdof) vibrating structure is derived by using the fixed-points theory. The optimum tuning parameters are the feedback gain, the tuning frequency, damping and mass ratios of the absorber. The effects of these parameters on the vibration reduction of the primary structure are revealed based on the analytical model. Design parameters of both passive and active elements of the HVA are optimized for the minimization of the resonant vibration amplitude of the primary system. One of the inherent limitations of the traditional passive vibration absorber is that its vibration absorption is low if the mass ratio between the absorber mass and the mass of the primary structure is low. The proposed HVA overcomes this limitation and provides very good vibration reduction performance even at a low mass ratio. The proposed optimized HVA is compared to a recently published HVA designed for similar propose and it shows that the present design requires less energy for the active element of the HVA than the compared design.     

Adaptive function project synchronization of Rössler hyperchaotic system with uncertain parameters

This Letter addresses the function project synchronization problem of two Rössler hyperchaotic in the presence of unknown system parameters. Based on Lyapunov stability theory an adaptive control law is proposed to make the states of two identical Rössler hyperchaotic systems asymptotically synchronized. Numerical simulations are presented to show the effectiveness of the proposed schemes.