Partial eigenstructure assignment for undamped vibration systems using acceleration and displacement feedback

A new method for partial eigenstructure assignment using acceleration and displacement feedback for undamped vibration systems is presented in this paper. Firstly, a necessary and sufficient condition is proposed for the incremental mass and stiffness matrices that modify some eigenpairs while keeping other eigenpairs unchanged. Secondly, based on this condition, an algorithm for determining the required control gain matrices of acceleration and displacement feedback, which assign the desired eigenstructure, is developed. This algorithm is easy to implement, and works directly on the second-order system model. More importantly, the algorithm allows the control matrix to be specified beforehand and also leads naturally to a small norm solution of the feedback gain matrices. Finally, some numerical examples are given to demonstrate the effectiveness and accuracy of the proposed algorithm.     

Tuneable vibration absorber design to suppress vibrations: An application in boring manufacturing process

Dynamic vibration absorbers are used to reduce the undesirable vibrations in many applications such as electrical transmission lines, helicopters, gas turbines, engines, bridges, etc. Tuneable vibration absorbers (TVA) are also used as semi-active controllers. In this paper, the application of a TVA for suppression of chatter vibrations in the boring manufacturing process is presented. The boring bar is modeled as a cantilever Euler–Bernoulli beam and the TVA is composed of mass, spring and dashpot elements. In addition, the effect of spring mass is considered in this analysis. After formulation of the problem, the optimum specifications of the absorber such as spring stiffness, absorber mass and its position are determined using an algorithm based on the mode summation method. The analog-simulated block diagram of the system is developed and the effects of various excitations such as step, ramp, etc. on the absorbed system are simulated. In addition, chatter stability is analyzed in dominant modes of boring bar. Results show that at higher modes, larger critical widths of cut and consequently more material removal rate (MRR) can be achieved. In the case of self-excited vibration, which is associated with a delay differential equation, the optimum absorber suppresses the chatter and increases the limit of stability.     

Active vibration control of beam structures using acceleration feedback control with piezoceramic actuators

In this study, the active vibration control of clamped–clamped beams using the acceleration feedback (AF) controller with a sensor/moment pair actuator configuration is investigated. The sensor/moment pair actuator is a non-collocated configuration, and it is the main source of instability in the direct velocity feedback control system. First, the AF controller with non-collocated sensor/moment pair actuator is numerically implemented for a clamped–clamped beam. Then, to characterize and solve the instability problem of the AF controller, a parametric study is conducted. The design parameters (gain and damping ratio) are found to have significant effects on the stability and performance of the AF controller. Next, based on the characteristics of AF controllers, a multimode controllable single-input single-output (SISO) AF controller is considered. Three AF controllers are connected in parallel with the SISO architecture. Each controller is tuned to a different mode (in this case, the second, third and fourth modes). The design parameters are determined on the basis of the parametric study. The multimode AF controller with the selected design parameters has good stability and a high gain margin. Moreover, it reduces the vibration significantly. The vibration levels at the tuned modes are reduced by about 12 dB. Finally, the performance of the AF controller is verified by conducting an experiment. The vibration level of each controlled mode can be reduced by about 12 dB and this value is almost same as the theoretical result.     

Active vibration control using optimized modified acceleration feedback with Adaptive Line Enhancer for frequency tracking

Modified acceleration feedback (MAF) control, an active vibration control method that uses collocated piezoelectric actuators and accelerometer is developed and its gains optimized using an optimal controller. The control system consists of two main parts: (1) frequency adaptation that uses Adaptive Line Enhancer (ALE) and (2) an optimized controller. Frequency adaptation method tracks the frequency of vibrations using ALE. The obtained frequency is then fed to MAF compensators. This provides a unique feature for MAF, by extending its domain of capabilities from controlling a certain mode of vibrations to any excited mode. The optimized MAF controller can provide optimal sets of gains for a wide range of frequencies, based on the characteristics of the system. The experimental results show that the frequency tracking method works quite well and fast enough to be used in a real-time controller. ALE parameters are numerically and experimentally investigated and tuned for optimized frequency tracking. The results also indicate that the MAF can provide significant vibration reduction using the optimized controller. The control power varies for vibration suppression at different resonance frequencies; however, it is always optimized.     

Optimal active absorber with internal state feedback for controlling resonant and transient vibration

An active, standalone vibration absorber utilizing the state feedback taken from the absorber mass is proposed. Expressions of the optimum absorber parameters are obtained both by optimizing the Η_∞ norm of the frequency response function. For improved transient response featuring low peak response and fast attenuation, the design procedure utilizes the mode equalization followed by the maximization of the damping. An interesting feature of the proposed absorber is that the performance of the absorber does not require having its natural frequency close to the natural frequency of the primary system as is generally the case for tuned passive absorbers or other active and semi-active tuned vibration absorbers. In fact, the performance of the proposed system can be progressively enhanced by increasing the absorber frequency. Compared to the optimum passive absorber, the optimal active absorber can yield wider bandwidth of operation around the natural frequency of the primary system and lower frequency response within the suppression band. The active absorber also offers better transient response compared to the passive absorber both optimized for the best transient responses. The efficacy of the absorber is analyzed both for a single-degree-of-freedom and beam like primary structure.     

Suppression of random vibration in flexible structures using a hybrid vibration absorber

A design method is proposed to suppress stationary random vibration in flexible structures using a hybrid vibration absorber (HVA). While the traditional vibration absorber can damp down the vibration mainly at the pre-tuned mode of the primary structure, active damping is generated by the proposed HVA to damp down all resonant modes of interest of the vibrating structure and the spatial average mean square motion of the vibrating structure can be minimized. Only one absorber and one feedback signal are required to achieve global vibration suppression of a flexible structure under stationary random excitation. A special pole-placement controller is designed such that all vibration modes of the flexible structures become critically damped. It is proved analytically that the proposed HVA damps the vibration of the entire structure instead of just the attachment point of the absorber. The proposed optimized HVA is tested on a beam structure and it shows a superior performance on global suppression of broadband vibration in comparison to other published designs of passive and hybrid vibration absorbers.     

Dynamic behavior of time-delayed acceleration feedback controller for active vibration control of flexible structures

This paper addresses the design problem of the controller with time-delayed acceleration feedback. On the basis of the reduction method and output state-derivative feedback, a time-delayed acceleration feedback controller is proposed. Stability boundaries of the closed-loop system are determined by using Hurwitz stability criteria. Due to the introduction of time delay into the controller with acceleration feedback, the proposed controller has the feature of not only changing the mass property but also altering the damping property of the controlled system in the sense of equivalent structural modification. With this feature, the closed-loop system has a greater logarithmic decrement than the uncontrolled one, and in turn, the control behavior can be improved. In this connection, the time delay in the acceleration feedback control is a positive factor when satisfying some given conditions and it could be actively utilized. On the ground of the analysis, the developed controller is implemented on a cantilever beam for different controller gain–delay combinations, and the control performance is evaluated with the comparison to that of pure acceleration feedback controller. Simulation and experimental results verify the ability of the controller to attenuate the vibration resulting from the dominant mode.     

半导体激光管位移传感器的模型建立及仿真分析

从激光应用系统稳态条件出发,建立了半导体激光管位移传感器系统的数学模型,其仿真结果与有关文献的实验结论相吻合,详细阐述了通过检测ＬＤ注入调制三角波相邻两周期对应点处信号的位相差而完成位移测量的原理。由理论分析提出了提高最大允许位移速度上限和减小测量非线性误差的措施,其结论对激光自混合干涉技术的应用具有重要指导意义     

The effective damping approach to design a dynamic vibration absorber using Coriolis force

In this paper, the vibration reduction of a pendulum structure with dynamic vibration absorber (DVA) using Coriolis force is investigated. When the pendulum structure is subjected to a single harmonic excitation, the effective damping of Coriolis force is used with the second-order approximations to obtain the closed forms of optimal parameters of the DVA. The closed forms obtained show that the natural frequency of the absorber should be tuned to twice that of the pendulum. The closed forms of optimal parameters are verified by numerical optimization. The modified forms of optimal parameters are proposed to be used in case of general excitation. Base on this modified form, the design procedure is demonstrated by the numerical calculation of the free vibration and wind-induced vibration of a ropeway gondola.     

动力吸振器中库仑阻尼对吸振性能的影响

研究了动力吸振器中库仑阻尼(干摩擦)对吸振性能的影响。给出了库仑摩擦模型,在考虑了吸振器中的库仑阻尼的情况下,分析了库仑阻尼引起的主振动系统与附加质量块的2种相对运动状态(滑移和粘滞)以及它们存在和转换的条件,讨论了因库仑阻尼引起的吸振器自由度冻结现象;用Simulink仿真工具对非线性吸振器进行了数值仿真,研究了谐波和白噪声激励下库仑阻尼对吸振器吸振性能的影响以及库仑阻尼与线性阻尼的等效问题。结果显示:弱激励条件下,非线性吸振器减弱吸振效果,强激励条件下增强吸振效果。     

Hybrid vibration absorber with virtual passive devices

A vibration control scheme integrating a passive mass–spring resonator and a linear actuator is developed. A control algorithm is devised to convert the actuator into an additional set of virtual mass–spring structure of programmable characteristic frequency. The relative motion between the primary body and the reaction mass is measured, as well as the acceleration of the reaction mass. This hybrid dynamic vibration absorber is capable of neutralizing a harmonic disturbance regardless of the detailed dynamics of the primary structure and other passive elements. Stability analysis leads to a simple, explicit stability criterion. Distribution of the counter-disturbance force between the active and passive devices is analyzed, and the transient performance is also investigated. Real-time experiments as well as numerical simulations are conducted to confirm the effectiveness of the proposed scheme.     

Measurement of Newton's constant using a torsion balance with angular acceleration feedback

We measured Newton's gravitational constant G using a new torsion balance method. Our technique greatly reduces several sources of uncertainty compared to previous measurements: (1) It is insensitive to anelastic torsion fiber properties; (2) a flat plate pendulum minimizes the sensitivity due to the pendulum density distribution; (3) continuous attractor rotation reduces background noise. We obtain G = (6.674215+/-0.000092) x 10(-11) m3 kg(-1) s(-2); the Earth's mass is, therefore, M = (5.972245+/-0.000082) x 10(24) kg and the Sun's mass is M = (1.988435+/-0.000027) x 10(30) kg.     

动力吸振器中库仑阻尼对吸振性能的影响

研究了动力吸振器中库仑阻尼（干摩擦）对吸振性能的影响。给出了库仑摩擦模型,在考虑了吸振器中的库仑阻尼的情况下,分析了库仑阻尼引起的主振动系统与附加质量块的2种相对运动状态（滑移和粘滞）以及它们存在和转换的条件,讨论了因库仑阻尼引起的吸振器自由度冻结现象;用Simulink仿真工具对非线性吸振器进行了数值仿真,研究了谐波和白噪声激励下库仑阻尼对吸振器吸振性能的影响以及库仑阻尼与线性阻尼的等效问题。结果显示：弱激励条件下,非线性吸振器减弱吸振效果,强激励条件下增强吸振效果。     

Stability and performance limits for active vibration isolation using blended velocity feedback

This paper presents a theoretical study of active vibration isolation on a two degree of freedom system. The system consists of two lumped masses connected by a coupling spring. Both masses are also attached to a firm reference base by a mounting spring. The lower mass is excited by a point force. A reactive control force actuator is used between the two masses in parallel with the coupling spring. Both masses are equipped with an absolute velocity sensor. The two sensors and the actuator are used to implement velocity feedback control loops to actively isolate the upper mass from the vibrations of the lower mass over a broad range of frequencies. The primary concern of the study is to determine what type of velocity feedback configuration is suitable with respect to the five parameters that characterise the system (the three spring stiffnesses and the two masses). It is shown analytically that if the ratio of the lower mounting spring stiffness to the lower mass is larger than the ratio of the upper mounting spring stiffness to the upper mass (supercritical system), feeding back the absolute upper mass velocity to the reactive force actuator results in an unconditionally stable feedback loop and the vibration isolation objective can be fully achieved without an overshot at higher frequencies. In contrast, if the ratio of the lower mounting spring stiffness to the lower mass is smaller than the ratio of the upper mounting spring stiffness to the upper mass (subcritical system), the upper mass velocity feedback is conditionally stable and the vibration isolation objective cannot be accomplished in a broad frequency band. For subcritical systems a blended velocity feedback is proposed to stabilise the loop and to improve the broad-band vibration isolation effect. A simple inequality is introduced to derive the combinations between the two error velocities that guarantee unconditionally stable feedback loops.     

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.     

Vibration control by recursive time-delayed acceleration feedback

This paper presents a theoretical basis of time-delayed acceleration feedback control of linear and nonlinear vibrations of mechanical oscillators. The control signal is synthesized by an infinite, weighted sum of the acceleration of the vibrating system measured at equal time intervals in the past. The proposed method is shown to have controlled linear resonant vibrations, low-frequency non-resonant vibrations, primary and 1/3 subharmonic resonances of a forced Duffing oscillator. The concept of an equivalent damping and natural frequency of the system is also introduced. It is shown that a large amount of damping can be produced by appropriately selecting the control parameters. For some combinations of the control parameters, the effective damping factor of the system is shown to be inversely related to the time-delay in the small delay limit. Selection of the optimum control parameters for controlling the forced and free vibrations is discussed. It is shown that forced vibration is best controlled by unity recursive gain and smaller values of the time-delay parameter. However, the transient response can be optimally controlled by suitably selecting the time delay depending upon the gain. The delay values for the optimal forced response may be different from that required for the optimum transient response. When both are important, a suboptimal choice of the delay parameters with unity recursive gain is recommended.