Base impedance of velocity feedback control units with proof-mass electrodynamic actuators

Control units comprising a proof-mass electrodynamic actuator and accelerometer-sensor pair with a time integrator and fixed gain controller are an effective way to implement velocity feedback control on thin flexible structures. These control units produce active damping provided the fundamental resonance frequency of the actuators is well below that of the structure under control. Control stability limits arise from the actuators fundamental resonances which introduce a 180° phase lag in the sensor-actuator frequency response functions, thus causing the feedback loops to be only conditionally stable. In contrast to previous studies, this paper discusses the response of a control unit with electrodynamic proof-mass actuator in terms of the open- and closed-loop base impedance that it exerts on the structure. This allows for a straight-forward physical interpretation of both stability and control performance. Experimental and simulation results show that the base impedance can be described as the sum of passive and active frequency response functions, where the active part of the control unit response depends on the actuator electromechanical response and also on the response function of the analogue controller circuit. The results show that the base impedance formulation can be effectively used to investigate new designs of both the actuator and electronic controller in order to optimise the stability and performance properties of the control unit.     

Feedback compensator for control units with proof-mass electrodynamic actuators

This paper presents theoretical and experimental work on a velocity feedback control unit with an electrodynamic proof-mass actuator. The study shows that the stability and performance of the feedback control loop can be substantially improved by implementing an appropriate compensation filter, which detunes the passive and active responses of the actuator. The control unit is analysed in terms of the open- and closed-loop base impedance it presents to the structure under control. In this way the analytical expression for the proposed compensator is derived directly from known actuator parameters. The compensation filter provides significant improvement over the uncompensated case, even for considerable variations in the actuator response. One drawback of the compensator is the enhancement of the feedback signal at low frequencies, which may lead to stroke/force saturation effects in the actuator. In this respect the study shows that it can be beneficial to implement an additional high pass filter, which however produces a loss in the phase and gain margins.     

Rectangular plate with velocity feedback loops using triangularly shaped piezoceramic actuators: experimental control performance

This paper presents experimental results on the implementation of decentralized velocity feedback control on a new smart panel in order to produce active damping. The panel is equipped with 16 triangularly shaped piezoceramic patch actuators along its border and accelerometer sensors located at the top vertex of the triangular actuators. The primary objective of this paper is to demonstrate the vibration and sound radiation control using the new smart panel. Narrow frequency band experimental results highlight that the 16 control units can produce reductions up to 15 dB at resonance frequencies between 100 and 700 Hz in terms of both structural vibration and sound power radiation.     

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.     

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.     

Self-tuning control systems of decentralised velocity feedback

This paper is concerned with decentralised velocity feedback for the control of vibration on a flexible structure. Previous studies have shown that a direct velocity feedback loop with a collocated force actuator produces a damping action. Multiple velocity feedback control loops thus reduce the vibration and sound radiation of structures at low frequency resonances, where the response is controlled by damping. However, if the control gains are too high, so that the response of the structure at the control point is close to zero, the feedback control loops will pin the panel at the control positions and thus no damping action is generated. Therefore, in order to maximise the active damping effect, the feedback gains have optimum values and the loops need to be properly tuned.In this paper, a numerical investigation is performed to investigate the possibility of self-tuning the feedback control gains to maximise the power absorbed by the control loops and hence maximise the active damping. The tuning principle is first examined for a single feedback loop for different excitation signals. The tuning of multiple control loops is then considered and the implementation of a practical tuning algorithm is discussed.     

Development of high bandwidth powered resonance tube actuators with feedback control

A high bandwidth powered resonance tube (PRT) actuator potentially useful for noise and flow control applications was developed. High bandwidth allows use of the same actuator at various locations on an aircraft and over a range of flight speeds. The actuator selected for bandwidth enhancement was the PRT actuator, which is an adaptation of the Hartmann whistle. The device is capable of producing high-frequency and high-amplitude pressure and velocity perturbations for active flow control applications. Our detailed experiments aimed at understanding the PRT phenomenon are complemented by an improved analytical model and direct numerical simulations. We provide a detailed characterization of the unsteady pressures in the nearfield of the actuator using phase averaged pressure measurements. The measurements revealed that propagating fluctuations at 9 kHz were biased towards the upstream direction (relative to the supply jet). A complementary computational study validated by our experiments was useful in simulating the details in the region between the supply jet and the resonance tube where it was difficult to gather experimental data. High bandwidth was obtained by varying the depth of the resonance tube that determines the frequency produced by the device. Our actuator could produce frequencies ranging from 1600 to 15,000 Hz at amplitudes as high as 160 dB near the source. The frequency variation with depth is predicted well by the quarter wavelength formula for deep tubes but the formula becomes increasingly inaccurate as the tube depth is decreased. An improved analytical model was developed, in which the compliance and mass of the fluid in the integration slot is incorporated into the prediction of resonance frequencies of the system. Finally a feedback controller that varied both the resonance tube depth and spacing to converge on a desired frequency was developed and demonstrated. We are optimistic that numerous potential applications exist for such high bandwidth high dynamic range actuators.     

Experimental implementation of a self-tuning control system for decentralised velocity feedback

Simulations have previously shown that, for broadband excitation, adjusting the gain of a local velocity feedback loop to maximise their absorbed power also tends to minimise the kinetic energy of the structure under control. This paper describes an experimental implementation of multiple velocity feedback loops on a flat panel, whose gains can be controlled automatically by an algorithm that maximises their local absorbed power. Taking care to remove excessive phase shift in the control loop allows a stable feedback gain that is high enough to experimentally demonstrate the transition in control action between optimum damping and pinning of the structure. A simple search algorithm is then used to adapt the feedback gains of two control loops to maximise their local absorbed powers, thus demonstrating self-tuning. By measuring the power absorbed by each of these loops and also estimation of the kinetic energy of the plate from velocity measurements for a wide range of the two feedback gains, it is shown that not only does the adaptive algorithm converge to a set of feedback gains that maximise total power absorbed by the two feedback loops, but also that this set of feedback gains is very close to those that minimise the measured kinetic energy of the panel.     

A numerical modeling for eigenvibration analysis of honeycomb sandwich panels

The eigenvibration properties of honeycomb sandwich panels are investigated in this paper. A new numerical modeling for eigenvibration analysis of the honeycomb sandwich panels is proposed under the assumption that the orthotropic shell and two kinds of beam elements represent face materials, adhesive layers and honeycomb core, respectively. The shell element is also connected to the beam element through the thickness. The effects of geometry of honeycomb core and thickness of face material on the eigenfrequency are examined through the comparisons between finite element simulation and experimental results. It is shown as a result that the eigenvibration properties depend strongly on the face material rigidity and honeycomb core geometry. The implications of the findings for the design of eigenvibration of honeycomb sandwich panels are discussed from the point of view of overall flexural rigidity.     

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.     

Finite element reduced order model for noise and vibration reduction of double sandwich panels using shunted piezoelectric patches

This work concerns the control of sound transmission through double laminated panels with viscoelastic core using semi-passive piezoelectric shunt technique. More specifically, the system consists of two laminated walls, each one composed of three layers and called sandwich panel with an air cavity in between. The external sandwich panel has a surface-mounted piezoelectric patches. The piezoelectric elements, connected with resonant shunt circuits, are used for the vibration damping of some specific resonance frequencies of the coupled system. Firstly, a finite element formulation of the fully coupled visco-electro-mechanical-acoustic system is presented. This formulation takes into account the frequency dependence of the viscoelastic material. A modal reduction approach is then proposed to solve the problem at a lower cost. In the proposed technique, the coupled system is solved by projecting the mechanical displacement unknown on a truncated basis composed by the first real short-circuit structural normal modes and the pressure unknown on a truncated basis composed by the first acoustic modes with rigid boundaries conditions. The few initial electrical unknowns are kept in the reduced system. A static correction is also introduced in order to take into account the effect of higher modes. Various results are presented in order to validate and illustrate the efficiency of the proposed finite element reduced order formulation.     

Active vibration isolation of a system with a distributed parameter isolator using absolute velocity feedback control

This paper is concerned with the active isolation of a system containing a distributed parameter isolator using absolute velocity feedback control. The main differences between this type of system and one with a massless isolator, is that there are isolator resonances. It is shown that the vibration at these resonance frequencies cannot be suppressed using a simple velocity feedback control strategy. Moreover, it is found that the isolator resonances can cause the control system to become unstable, if the isolated equipment is supported on a flexible base. A stability criterion based on the mode shapes of the system is presented. Two techniques to stabilise the system are investigated and compared. The first involves the addition of mass on the base structure, and the second involves an electronic lead compensator. Experimental results are presented to support the theoretical findings. It is shown that even if the instability due to the isolator resonances and flexibility of the base can be prevented, the instability due to the flexibility of the equipment remains a problem.     

Seismic test of least-input-energy control with ground velocity feedback for variable-stiffness isolation systems

A variable-stiffness isolation system, whose isolation stiffness can be altered instantaneously in response to the seismic load, is able to provide better seismic protection for vibration-sensitive equipment or facilities than a conventional isolation system with a fixed stiffness. To determine its time-variant isolation stiffness, this system usually requires an effective on-line control law. In this study, a control strategy called the least input energy control (LIEC) is proposed for a general variable-stiffness isolation system. With the feedback of the ground velocity, at each time step the LIEC is able to determine the optimal isolation stiffness that minimizes the input seismic energy transmitted onto the isolated object. In order to evaluate its control performance, the LIEC was physically implemented on a leverage-type variable-stiffness isolation system, and tested in a seismic simulation test. The experimental response of the LIEC was then compared to the uncontrolled response, as well as the simulated responses of two semi-active control laws derived from the widely used LQR control and modal control. A comparison of the results demonstrates that, among all the control cases considered, the LIEC transmits the least seismic input energy to the isolated system, and thus has the best isolation performance. In addition, the test data also show that the LIEC requires the least control force and control energy. This indicates that the LIEC is also a very efficient control method for variable-stiffness isolation systems.     

Comparison of feedback control methods for a hyperchaotic Lorenz system

More and more attention has been payed to the hyperchaotic system for the huge potential applications of hyperchaotic system such as secure communication and more complex structure than chaotic system. So at present the controlling of the hyperchaotic system simply and effectively is a frontier topic of nonlinear science. In this Letter, for the latest hyperchaotic Lorenz system, four feedback control methods were studied with analytic solution and necessary numerical simulations. It is found that the enhancing feedback control approach is the best choice of the given four feedback control methods for its relatively simple external inputs and relatively small necessary feedback coefficient after comparison. The conclusion is a helpful for the choice of control methods of any other chaotic and hyperchaotic systems.     

超混沌系统的间歇同步与控制

基于稳定性理论，采用间歇反馈控制研究了四维连续超混沌Rssler和LC振子系统.通过选择恰当的控制周期T_s、自治周期T_a以及反馈系数k来设计控制器.数值计算表明：所设计的控制器使系统经过大约8到35个时间单位达到了稳定点，两个系统之间经过大约15到50个时间单位实现了全局同步.通过求解系统Jacobi矩阵的特征值来确定T_s与T_a的关系，获得间歇控制下控制器稳定的条件.数值计算结果与理论分析一致. 关键词： 超混沌 同步 Jacobi矩阵 稳定性     

Sound transmission loss of foam-filled honeycomb sandwich panels using statistical energy analysis and theoretical and measured dynamic properties

Comparisons between the experimental and predicted sound transmission loss values obtained from statistical energy analysis are presented for two foam-filled honeycomb sandwich panels. Statistical energy analysis (SEA) is a modeling procedure which uses energy flow relationships for the theoretical estimation of the sound transmission through structures in resonant motion. The accuracy of the prediction of the sound transmission loss using SEA greatly depends on accurate estimates of: (1) the modal density, (2) the internal loss factor, and (3) the coupling loss factor parameters of the structures. A theoretical expression for the modal density of sandwich panels is developed from a sixth-order governing equation. Measured modal density estimates of the two foam-filled honeycomb sandwich panels are obtained by using a three-channel spectral method with a spectral mass correction to allow for the mass loading of the impedance head. The effect of mass loading of the accelerometer is corrected in the estimations of both the total loss factor and radiation loss factor of the sandwich panels.     

利用反馈光路的弹光调制器定标及稳定控制

为了实现弹光调制器（photoelastic modulator,PEM）精确定标和长时间稳定工作,提出了一种利用反馈光路的相位延迟幅值定标及控制方案,理论计算并仿真分析了PEM通光孔径上相位延迟幅值的空间分布。在偏离PEM中心的位置设计了集成化的定标反馈光路;结合倍频项比值的相位延迟幅值定标方法,采用数字锁相技术同时提取反馈光路调制光强信号中倍频项,求解出PEM相位延迟幅值。按照上述方案加工制作了PEM实物,并进行了定标及稳定控制实验。实验结果表明,PEM中心相位延迟幅值的定标值与实测值相对偏差不超过0.22%;利用反馈光路控制约100 min,PEM相位延迟幅值标准偏差为0.001 8 rad,最大偏差低于0.42%,实现了PEM相位延迟幅值精确、实时定标,同时实现了PEM长时间稳定控制。     

Stability criterion for synchronization of chaotic systems using linear feedback control

This Letter introduces linear balanced feedback control scheme to design controller for the synchronization of two identical chaotic systems based on Lyapunov stability theory and constrained extreme approach. The technique is applied to synchronizing two identical four-scroll chaotic systems and guiding balanced feedback gains design. In accordance with the result of the analysis, an adaptive control scheme is proposed for chaos synchronization when the parametric variations of the response system are uncertain. The feasibility and effectiveness of the proposed synchronization scheme are verified via numerical simulations.     

A new criterion for chaos and hyperchaos synchronization using linear feedback control

Based on the characteristic of the chaotic or hyperchaotic system and linear feedback control method, synchronization of the two identical chaotic or hyperchaotic systems with different initial conditions is studied. The range of the control parameter for synchronization is derived. Simulation results are provided to show the effectiveness of the proposed synchronization method.