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.     

弹性基础隔振系统的简化性能指标和有源控制力

系统研究了基础弹性对单层隔振系统、双层隔振系统及浮筏隔振系统隔振性能的影响。分析了不同隔振系统与不同弹性基础间的振动耦合特性,讨论了不同隔振系统的振级落差和力传递率特性,给出了振级落差和力传递率的简化计算方法。针对不同隔振系统的有源隔振问题,比较了不同作动器安装方式所需的控制力。研究表明,对于所有隔振系统,增加基础的刚度和阻尼有利于提高振级落差和力传递率;对于浮筏隔振系统,增加筏架的刚度和阻尼有利于提高隔振性能和减少有源隔振所需的控制力。      

Simplified performance indices and active control force of vibration isolation systems with elastic base

Influence of the elasticity of the base on vibration isolation performances of single layer, double layer and floating raft vibration isolation systems is investigated systematically.Characteristics of vibration coupling between different vibration isolation systems and different elastic bases are analyzed. Moreover the characteristics of vibration acceleration level difference and force transmissibility of different vibration isolation systems are discussed and their simplified expressions are given. In addition the required control forces of active vibration isolation under different installations of actuators for different vibration isolation systems are compared.The results show that for all vibration isolation systems, the addition of the stiffness and damping of the base can enhance their vibration acceleration level difference and force transmissibility.Moreover for floating raft vibration isolation system, the addition of the stiffness and damping of the raft can enhance its vibration isolation performance and reduce the control force required by active vibration isolation.     

Novel active noise-reducing headset using earshell vibration control

Active noise-reducing (ANR) headsets are available commercially in applications varying from aviation communication to consumer audio. Current ANR systems use passive attenuation at high frequencies and loudspeaker-based active noise control at low frequencies to achieve broadband noise reduction. This paper presents a novel ANR headset in which the external noise transmitted to the user's ear via earshell vibration is reduced by controlling the vibration of the earshell using force actuators acting against an inertial mass or the earshell headband. Model-based theoretical analysis using velocity feedback control showed that current piezoelectric actuators provide sufficient force but require lower stiffness for improved low-frequency performance. Control simulations based on experimental data from a laboratory headset showed that good performance can potentially be achieved in practice by a robust feedback controller, while a single-frequency real-time control experiment verified that noise reduction can be achieved using earshell vibration control.     

空气弹簧隔振台特性试验及信号处理算法研究

超精密测量对环境振动要求非常严格,其仪器设备中多安装隔振装置。为评估某重点实验室圆度仪中使用的仪用小型空气弹簧隔振台的隔振性能,利用压电式加速度传感器设计振动测试试验。根据振动测试中信号的实际情况,设计信号处理算法,对采集到的加速度信号进行预处理、积分运算、频谱分析,消除信号中低频趋势项和干扰噪声,还原实际振动状况,准确获取隔振系统振动位移曲线及其固有频率。试验表明,该空气弹簧隔振系统各项指标满足隔振要求。信号处理算法对振动测试中的加速度信号处理具有一定指导意义,也可作为故障诊断中加速度信号处理的参考。     

FORCE FEEDBACK VERSUS ACCELERATION FEEDBACK IN ACTIVE VIBRATION ISOLATION

This paper compares the force feedback and acceleration feedback implementation of the sky-hook damper when it is used to isolate a flexible structure from a disturbance source. It is shown that the use of a force sensor produces always alternating poles and zeros in the open-loop transfer function between the force actuator and the force sensor, which guarantees the stability of the closed loop. On the contrary, the acceleration feedback produces alternating poles and zeros only when the flexible structure is stiff compared to the isolation system; this property is lost when the flexible modes of the sensitive payload interfere with the isolation system.     

EVALUATING THE VIBRATION ISOLATION OF SOFT SEAT CUSHIONS USING AN ACTIVE ANTHROPODYNAMIC DUMMY

Seat test standards require human subjects to be used for measuring the vibration isolation of vehicle seats. Anthropodynamic dummies, based on passive mass-spring- damper systems, have been developed for testing seats but their performance has been limited at low excitation magnitudes by non-linear phenomena, such as friction in the mechanical components that provide damping. The use of an electrodynamic actuator to generate damping forces, controlled by feedback from acceleration and force transducers, may help to overcome these limitations and provide additional benefits. The transmissibilities of five foam cushions have been measured using an actively controlled anthropodynamic dummy, in which damping and spring forces were supplied by an electrodynamic actuator. The dummy could be set up to approximate alternative single-degree-of-freedom and two-degree-of-freedom apparent mass models of the seated human body by varying motion feedback parameters. Cushion transmissibilities were also measured with nine human subjects, having an average seated weight similar to the dummy. At frequencies greater than 4 Hz, mean cushion transmissibilities measured with subjects were in closer agreement with the transmissibilities obtained with a two degree-of-freedom dummy than with a single degree-of-freedom dummy. However, at frequencies between 2 and 4 Hz, cushion transmissibilities obtained with the two-degree-of-freedom dummy showed consistently larger differences from mean transmissibilities with subjects than single-degree-of-freedom dummies, indicating a need for further development of human apparent mass models to account for the effects of magnitude and spectral content of the input motion. Vertical vibration isolation efficiencies (SEAT values) of the five foams were measured with four input motions, including three motions measured in a car. The SEAT values obtained using the active dummy were highly correlated with the median SEAT values obtained with the nine human subjects, with the two-degree-of-freedom apparent mass dummy giving the highest agreement.     

Effects of isolators internal resonances on force transmissibility and radiated noise

Vibration isolators have been extensively used to reduce the vibration and noise transmitted between the components of mechanical systems. Although some previous studies on vibration isolation considered the inertia of isolators, they only examined its effects on the vibration of single degree-of-freedom (d.o.f.) systems. These studies did not emphasize the importance of the isolators’ inertia, especially from the perspective of noise reduction. This paper shows that the internal dynamics of the isolator, which are also known as internal resonances (IRs) or wave effects, can significantly affect the isolator performance at high frequencies. To study the IR problem, a model of a primary mass connected to a flexible foundation through three isolators is used. In this model, the isolator is represented as a one-dimensional continuous rod that accounts for its internal dynamics. The primary mass is modelled as a rigid body with three d.o.f.'s. The effects of the IRs on the force transmissibility and the radiated sound power from the foundation are examined. It is shown that the IRs significantly increase the force transmissibility and the noise radiation level at some frequencies. These effects cannot be predicted using a traditional model that neglects the inertia of the isolator. The influence of the foundation flexibility on the IRs is also investigated. It is shown that the foundation flexibility greatly affects the noise radiation level but it affects only slightly the force transmissibility, especially at high frequencies where the IRs occur.     

Active isolation of a flexible structure from base vibration

This paper presents a theoretical and experimental investigation into an active vibration isolation system. Electromagnetic actuators are installed in parallel with each of four passive mounts, which are placed between a flexible equipment structure and a base structure which is either flexible or rigid. Isolation of low-frequency vibration is studied, so that the passive mounts can be modelled as lumped parameter springs and dampers. Decentralized velocity feedback control is employed, where each actuator is operated independently by feeding back the absolute equipment velocity at the same location. Good control and robust stability have been obtained both theoretically and experimentally for the multichannel control systems. This is to be expected if the base structure is rigid, in which case the actuator and sensor are, in principle, collocated and the control system implements a skyhook damper. With a flexible base structure, however, collocation is lost due to the reactive actuator force acting on the base structure, but the control system is still found to be robustly stable and to perform well. Attenuations of 20 dB are obtained in the sum of squared velocities on the equipment structure at the rigid-body mounted resonance frequencies. In addition, attenuations of up to 15 dB are obtained at the resonance frequencies of both the low order flexible modes of the base structure and the equipment structure.     

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.     

Active vibroacoustic control with multiple local feedback loops

When multiple actuators and sensors are used to control the vibration of a panel, or its sound radiation, they are usually positioned so that they couple into specific modes and are all connected together with a centralized control system. This paper investigates the physical effects of having a regular array of actuator and sensor pairs that are connected only by local feedback loops. An array of 4 x 4 force actuators and velocity sensors is first simulated, for which such a decentralized controller can be shown to be unconditionally stable. Significant reductions in both the kinetic energy of the panel and in its radiated sound power can be obtained for an optimal value of feedback gain, although higher values of feedback gain can induce extra resonances in the system and degrade the performance. A more practical transducer pair, consisting of a piezoelectric actuator and velocity sensor, is also investigated and the simulations suggest that a decentralized controller with this arrangement is also stable over a wide range of feedback gains. The resulting reductions in kinetic energy and sound power are not as great as with the force actuators, due to the extra resonances being more prominent and at lower frequencies, but are still worthwhile. This suggests that an array of independent modular systems, each of which included an actuator, a sensor, and a local feedback control loop, could be a simple and robust method of controlling broadband sound transmission when integrated into a panel.     

存在声反馈的前馈有源噪声控制系统性能分析

在一些应用场合,前馈有源噪声控制系统中次级源产生的声信号会反馈至参考传声器,影响参考信号质量和系统稳定,导致控制性能下降。引入了等效次级路径的概念,并通过等效次级路径与实际路径的相位偏差分析存在声反馈时的收敛性能。若某些频率的相位偏差大于90°,则这些频率附近将较难收敛,降噪性能下降,甚至导致系统不稳定。通过仿真和实验对单指向传声器声学方法、自适应滤波u型最小均方差(FuLMS)算法、反馈中和算法和在线建模算法共4种解决声反馈问题的方法的性能进行了比较。结果表明,4种方法都能提高存在声反馈时的前馈有源噪声控制系统的性能,有效解决声反馈引起的问题,但各有优缺点。单指向传声器方法最为方便,但低频指向性较差。FuLMS算法运算量较低,但不能保证收敛。反馈中和算法性能最好,但当系统时变时鲁棒性较差。在线建模算法不需要额外滤波器,但由于参数调节复杂,降噪性能稍差。      

Nonlinear analysis,design and vibration isolation for a bilinear system with time-delayed cubic velocity feedback

This paper combines cubic nonlinearity and time delay to improve the performance of vibration isolation. Nonlinear dynamics properties, design methodology and isolation performance are studied for a piecewise bilinear vibration isolation system with the time-delayed cubic velocity feedback control. By the multi-scale perturbation method, the equivalent stiffness and damping are first defined to interpret the effect of feedback control loop on dynamics behaviours, such as frequency island phenomenon. Then, a design criterion is proposed to suppress the jump phenomenon induced by the saddle-node bifurcation. With the purpose of obtaining the desirable vibration isolation performance, stability conditions are obtained to find appropriate feedback parameters including gain and time delay. Last, the influence of the feedback parameters on vibration transmissibility is assessed. Results show that the strategy developed in this paper is practicable and feedback parameters are significant factors to alter dynamics behaviours, and more importantly, to improve the isolation effectiveness for the bilinear isolation system.     

Control of a unique active vibration isolator with a phase compensation technique and automatic on/off switching

This work examines the characteristics of a unique active vibration isolator and develops a control strategy for it. The proposed active vibration isolator is introduced and its dynamic model is presented. A characterization study is conducted to identify system parameters. It is shown that with a simple proportional feedback the closed-loop system has a very narrow stability margin due to the inherent dynamics of the actuator. To improve the stability of the closed-loop system and enhance the performance of vibration isolation, a phase compensator is incorporated in the control scheme. An optimization problem is formulated to determine the optimum controller parameters by minimizing the 2nd norm of the displacement transmissibility. Both absolute position feedback and relative position feedback are considered. In real time implementation, an automatic on/off switching strategy is devised to take full advantage of both the active isolator and passive isolator. The experimental results show that with the proposed control scheme, the isolator is capable of suppressing base excitations effectively.     

Local feedback control of light honeycomb panels

This paper summarizes theoretical and experimental work on the feedback control of sound radiation from honeycomb panels using piezoceramic actuators. It is motivated by the problem of sound transmission in aircraft, specifically the active control of trim panels. Trim panels are generally honeycomb structures designed to meet the design requirement of low weight and high stiffness. They are resiliently mounted to the fuselage for the passive reduction of noise transmission. Local coupling of the closely spaced sensor and actuator was observed experimentally and modeled using a single degree of freedom system. The effect of the local coupling was to roll off the response between the actuator and sensor at high frequencies, so that a feedback control system can have high gain margins. Unfortunately, only relatively poor global performance is then achieved because of localization of reduction around the actuator. This localization prompts the investigation of a multichannel active control system. Globalized reduction was predicted using a model of 12-channel direct velocity feedback control. The multichannel system, however, does not appear to yield a significant improvement in the performance because of decreased gain margin.     

Experimental validation of a collocated PVDF volume velocity sensor/actuator pair

The active control of sound transmission through a rectangular panel is experimentally verified. The control system is based on a collocated volume velocity sensor/actuator pair which measures and excites the first radiation mode of the panel. Suppression of the first radiation mode is an efficient strategy to control the low frequency sound radiation from the panel. This configuration leads to a simple single-input single-output control system, to which feedback control can be applied.Two implementations of the volume velocity sensor/actuator pair are tested. First, a polyvinyledene fluoride polymer (PVDF) volume velocity actuator foil with shaped electrodes is used in combination with an identical PVDF volume velocity sensor foil. Due to the mechanical coupling between the PVDF sensor and actuator foil, it is shown that a direct velocity feedback control scheme is not feasible because higher order structural modes will be destabilized. Instead integral force feedback is applied, such that the open-loop transfer function has a roll-off towards higher frequencies. Experiments show that this control strategy results in a reduction of the sound pressure in the receiving room of 10 dB at the first structural resonance without spillover to higher order modes. Due to the roll-off towards high frequencies, the control over higher order modes remains limited. Second, a discrete volume velocity sensor is constructed by summing the signals from 12 point sensors placed on the panel. The volume velocity actuator consists of two PVDF foils, glued on each side of the panel and driven in opposite phase. Direct volume velocity feedback is applied to this system, which is minimum phase. This control system is capable of reducing the sound pressure in the receiving room below 300 Hz by 10-15 dB without spillover to higher order modes.     

光学移相干涉仪抗振系统的鲁棒μ控制器设计

将结构奇异值μ综合鲁棒控制技术应用于主动抗振控制系统中,并用于解决光学移相干涉仪抗振系统的不确定性问题.采用小波分析方法将随机振动信号进行时频分析后得到低频全局信息,随后运用μ综合D-K迭代法设计鲁棒μ控制器对低频振动进行抑制.该方法克服了由模型自身和外部干扰所引起的不确定性,使得控制系统能够有效地抑制抗振模型的不确定性和外部振动的干扰,同时也具有很高的控制准确度和灵敏度.仿真结果表明,该方法使光学移相干涉仪在外部振动的干扰下具有较好的鲁棒稳定性和控制准确度,同时也能较好地抑制低频振动.     

Passive-active vibration isolation systems to produce zero or infinite dynamic modulus: theoretical and conceptual design strategies

The application of mechanical springs connected in parallel and/or in series with active springs can produce dynamical systems characterised by infinite or zero value stiffness. This mathematical model is extended to more general cases by examining the dynamic modulus associated with damping, stiffness and mass effects. This produces a theoretical basis on which to design an isolation system with infinite or zero dynamic modulus, such that stiffness and damping may have infinite or zero values. Several theoretical designs using a mixture of passive and active systems connected in parallel and/or in series are proposed to overcome limitations of feedback gain experienced in practice to achieve an infinite or zero dynamic modulus. It is shown that such systems can be developed to reduce the weight supported by active actuators as demonstrated, for example, by examining suspension systems of very low natural frequency or with a very large supporting stiffness or with a viscous damper or a self-excited vibration oscillator. A more general system is created by combining these individual systems allowing adjustment of the supporting stiffness and damping using both displacement and velocity feedback controls. Frequency response curves show the effects of active feedback control on the dynamical behaviour of these systems. The theoretical design strategies presented can be applied to design feasible hybrid vibration control systems displaying increased control performance.     

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.     

Self-powered active vibration control using a single electric actuator

The authors have proposed self-powered active vibration control systems that achieve active vibration control using regenerated vibration energy. Such systems do not require external energy to produce a control force. This paper presents a self-powered system in which a single actuator realizes active control and energy regeneration.The system proposed needs to regenerate more energy than it consumes. To discuss the feasibility of this system, the authors proposed a method to calculate the balance between regenerated and consumed energies, using the dynamical property of the system, the feedback gain of the active controller, the specifications of the actuator, and the power spectral density of disturbance. A trade-off was found between the performance of the active controller and the energy balance. The feedback gain of the active controller is designed to have good suppression performance under conditions where regenerated energy exceeds consumed energy.A practical system to achieve self-powered active vibration control is proposed. In the system, the actuator is connected to the condenser through relay switches, which decide the direction of the electric current, and a variable resistor, which controls the amount of the electric current. Performance of the self-powered active vibration was examined in experiments; the results showed that the proposed system can produce the desired control force with regenerated energy, and that it had a suppression performance similar to that of an active control system using external energy. It was found that self-powered active control is attainable under conditions obtained through energy balance analysis.