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.     

Plate with decentralised velocity feedback loops: Power absorption and kinetic energy considerations

This paper is focused on the vibration effects produced by an array of decentralised velocity feedback loops that are evenly distributed over a rectangular thin plate to minimise its flexural response. The velocity feedback loops are formed by collocated ideal velocity sensor and point force actuator pairs, which are unconditionally stable and produce ‘sky-hook’ damping on the plate. The study compares how the overall flexural vibration of the plate and the local absorption of vibration power by the feedback loops vary with the control gains. The analysis is carried out both considering a typical frequency-domain formulation based on kinetic energy and structural power physical quantities, which is normally used to study vibration and noise problems, and a time-domain formulation also based on kinetic energy and structural power, which is usually implemented to investigate control problems. The time-domain formulation shows to be much more computationally efficient and robust with reference to truncation errors. Thus it has been used to perform a parametric study to assess if, and under which conditions, the minimum of the kinetic energy and the maximum of the absorbed power cost functions match with reference to: (a) the number of feedback control loops, (b) the structural damping in the plate, (c) the mutual distance of a pair of control loops and (d) the mutual gains implemented in a pair of feedback loops.     

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.     

Comparison of decentralized velocity feedback control for thin homogeneous and stiff sandwich panels using electrodynamic proof-mass actuators

Theoretical and experimental work is presented to compare the effect of decentralised velocity feedback control on thin homogeneous and sandwich panels. The decentralised control system consists of five control units, which are composed of a proof-mass electrodynamic actuator with an accelerometer underneath its footprint and an analogue controller. The stability of the feedback loops is analysed by considering the sensor-actuator open-loop frequency response function of each control unit and the eigenvalues of the fully populated matrix of open-loop frequency response functions between the five sensors and five actuators. The control performance is then analysed in terms of the time-averaged total kinetic energy and total sound power radiated by the two panels. The results show that for a stiff sandwich panel higher stable feedback gains can be implemented than on a thin homogeneous panel of comparable weight per unit area. Moreover the implementation of decentralised velocity feedback can offset some of the undesirable sound transmission properties of lightweight sandwich structures by efficiently reducing structural vibration and sound power radiation in the mid audio frequency range.     

Active vibration control using an inertial actuator with internal damping

Collocated direct velocity feedback with ideal point force actuators mounted on structures is unconditionally stable and generates active damping. When inertial actuators are used to generate the control force, the system can become unstable even for moderate velocity feedback gains due to an additional -180 degree phase lag introduced by the fundamental axial resonant mode of the inertial actuator. In this study a relative velocity sensor is used to implement an inner velocity feedback loop that generates internal damping in a lightweight, electrodynamic, inertial actuator. Simulation results for a model problem with the actuator mounted on a clamped plate show that, when internal relative velocity feedback is used in addition to a conventional external velocity feedback loop, there is an optimum combination of internal and external velocity feedback gains, which, for a given gain margin, maximizes vibration reduction. These predictions are validated in experiments with a specially built lightweight inertial actuator.     

Active damping control unit using a small scale proof mass electrodynamic actuator

This paper presents a study on the design and use of a small scale proof mass electrodynamic actuator, with a low mounting resonance frequency, for velocity feedback control on a thin rectangular panel. A stability-performance formula is derived, which can be effectively used to assess the down scaling effects on the stability and control performance of the feedback loop. The design and tests of a velocity feedback loop with a prototype small scale proof mass actuator are also presented. When a feedback control having a gain margin of about 6 dB is implemented, so that there is little control spillover effect around the fundamental resonance of the actuator, reductions of vibration between 5 dB and 10 dB in the frequency band between 80 Hz and 250 Hz have been measured at the control position.     

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.     

Optimisation of a velocity feedback controller to minimise kinetic energy and maximise power dissipation

In this study the active vibration control of a structure modelled as a single degree of freedom system and excited by a white noise force is considered. The control system consists of an inertial actuator driven with a signal proportional to the velocity of the structure under control measured by an ideal collocated sensor. The optimisation of the physical and control parameters of the control system such as the internal damping of the actuator, its natural frequency and the feedback gain of the controller are considered such that either the kinetic energy of the host structure is minimised or the power dissipated by the control system is maximised. This type of control system is only conditionally stable therefore a stability condition has to be satisfied by the optimisation process. The paper shows that the two optimisation criteria are equivalent.     

Different effects of redundant feedback loops on a bistable switch

Bistable switches have important roles in cellular decision-making processes. Bistability can be the consequence of positive or double-negative feedback loops. Although necessary, such feedback is not sufficient for bistability, which also requires nonlinearity. Nonlinearity can be provided by synergy of multiple feedback loops or by an ultrasensitive response within a single feedback loop. However, these two possibilities are not mutually exclusive; a combination of them is also possible. Here we analyze a biochemical regulatory network that controls a crucial cell cycle transition in all eukaryotic cells and contains multiple redundant feedback loops and nonlinearity. We show in this realistic biological example that two redundant feedback loops have different effects on the position of one of the saddle-node bifurcations of the system, which determines where the system switches. This illustrates that even though the roles of positive and double-negative feedbacks have been regarded as equivalent, the difference in their architectures can lead to differences in their effects on the system. We speculate that this conclusion could be general for other bistable systems with redundant feedback loops.     

Smart panel with active damping units. Implementation of decentralized control

This paper contains the second part of a study on a smart panel with five decentralized velocity feedback control units using proof mass electrodynamic actuators [Gonzalez Diaz et al., J. Acoust. Soc. Am. 124, 886 (2008)]. The implementation of five decentralized control loops is analyzed, both theoretically and experimentally. The stability properties of the five decentralized control units have been assessed with the generalized Nyquist criterion by plotting the loci of the eigenvalues of the fully populated matrix of frequency response functions between the five error signals and five input signals to the amplifiers driving the actuators. The control performance properties have been assessed in terms of the spatially averaged response of the panel measured with a scanning laser vibrometer and the total sound power radiated measured in an anechoic room. The two analyses have shown that reductions of up to 10 dB in both vibration response and sound radiation are measured at low audio frequencies, below about 250 Hz.     

Multifunctional design of inertially-actuated velocity feedback controllers

The vibration of a structure can be controlled using either a passive tuned mass damper or using an active vibration control system. In this paper, the design of a multifunctional system is discussed, which uses an inertial actuator as both a tuned mass damper and as an element in a velocity feedback control loop. The natural frequency of the actuator would normally need to be well below that of the structure under control to give a stable velocity feedback controller, whereas it needs to be close to the natural frequency of a dominant structural resonance to act as an effective tuned mass damper. A compensator is used in the feedback controller here to allow stable feedback operation even when the actuator natural frequency is close to that of a structural mode. A practical example of such a compensator is described for a small inertial actuator, which is then used to actively control the vibrations both on a panel and on a beam. The influence of the actuator as a passive tuned mass damper can be clearly seen before the feedback loop is closed, and broadband damping is then additionally achieved by closing the velocity feedback loop.     

Energy harvesting using semi-active control

This paper presents the application of semi-active control for optimising the power harvested by an electro-mechanical energy harvester. A time-periodic damper, defined by a Fourier series, is introduced for energy harvesting in order to increase the performance of the device. An analytical solution for the transmissibility and the average absorbed power is derived based on the method of harmonic balance. The coefficients of the semi-active model are optimised to maximise the harvested power. The harvested power from the optimum periodic time-varying damper at a particular frequency is compared and is shown to be greater than that from an optimum passive damper and a semi-active on–off damper not only at that particular frequency but also at other frequencies. In addition, the performance of the optimised periodic time-varying damper is also compared with an arbitrary semi-active time-periodic damper, which has the same transmissibility at resonance. An optimisation is carried out to maximise the power in a frequency range and the optimum damper is derived as a function of the excitation frequency. The numerical results are validated with the analytical approach.     

Multi-objective control optimization for semi-active vehicle suspensions

In this paper we demonstrate a method for determining the optimality of control algorithms based on multiple performance objectives. While the approach is applicable to a broad range of dynamic systems, this paper focuses on the control of semi-active vehicle suspensions. The two performance objectives considered are ride quality, as measured by absorbed power, and thermal performance, as measured by power dissipated in the suspension damper. A multi-objective genetic algorithm (MOGA) is used to establish the limits of controller performance. To facilitate convergence, the MOGA is initialized with popular algorithms such as skyhook control, feedback linearization, and sliding mode control. The MOGA creates a Pareto frontier of solutions, providing a benchmark for assessing the performance of other controllers in terms of both objectives. Furthermore, the MOGA provides insight into the remaining achievable gains in performance.     

数字光纤陀螺的第二反馈回路实验研究

针对光纤陀螺受外界环境,主要是温度影响,提出了一种控制相位调制器长期漂移的方法。用数字光纤陀螺的第二个反馈回路来控制相位调制通道的增益,尤其是2π复位来控制相位调制器相应的长期漂移。在-40°C～60°C,将标度因子的稳定性控制在0.000 4以内。在陀螺解调电路中采用FPGA进行数字信号处理,实现了两级反馈环路。     

Tuneable vibration absorber using acceleration and displacement feedback

This study is concerned with the analysis and design of a tuneable vibration absorber, which is composed by a flexible beam with a clamping block in the middle and two masses symmetrically mounted at the two ends. The free length of the beam is used to accommodate piezoelectric strain actuators. The two masses at the ends are equipped with inertial accelerometers. This arrangement is used to generate two independent acceleration feedback control loops that produce virtual mass effects, which shift the absorbing frequency of the device. Another arrangement is also studied where the two accelerometer outputs are time-integrated twice in order to implement displacement feedback loops that change the beam stiffness to shift the characteristic frequency of the device. The two feedback approaches are first analysed theoretically, using a mobility-impedance model, and then experimentally on a prototype absorber unit. The stability of the feedback loops is studied using the Nyquist criterion in order to estimate the limits on the tuneable range of frequencies which are set by the maximum stable feedback gains. The study indicates that the stability margins for the acceleration feedback loops substantially depend on the application of an appropriate low-pass filter. On the contrary, the implementation of displacement feedback gives better stability margins.     

Robustness of the bistable behavior of a biological signaling feedback loop

Biological signaling networks comprised of cellular components including signaling proteins and small molecule messengers control the many cell function in responses to various extracellular and intracellular signals including hormone and neurotransmitter inputs, and genetic events. Many signaling pathways have motifs familiar to electronics and control theory design. Feedback loops are among the most common of these. Using experimentally derived parameters, we modeled a positive feedback loop in signaling pathways used by growth factors to trigger cell proliferation. This feedback loop is bistable under physiological conditions, although the system can move to a monostable state as well. We find that bistability persists under a wide range of regulatory conditions, even when core enzymes in the feedback loop deviate from physiological values. We did not observe any other phenomena in the core feedback loop, but the addition of a delayed inhibitory feedback was able to generate oscillations under rather extreme parameter conditions. Such oscillations may not be of physiological relevance. We propose that the kinetic properties of this feedback loop have evolved to support bistability and flexibility in going between bistable and monostable modes, while simultaneously being very refractory to oscillatory states. (c) 2001 American Institute of Physics.     

The role of auditory feedback in sustaining vocal vibrato

Vocal vibrato and tremor are characterized by oscillations in voice fundamental frequency (F0). These oscillations may be sustained by a control loop within the auditory system. One component of the control loop is the pitch-shift reflex (PSR). The PSR is a closed loop negative feedback reflex that is triggered in response to discrepancies between intended and perceived pitch with a latency of approximately 100 ms. Consecutive compensatory reflexive responses lead to oscillations in pitch every approximately 200 ms, resulting in approximately 5-Hz modulation of F0. Pitch-shift reflexes were elicited experimentally in six subjects while they sustained /u/ vowels at a comfortable pitch and loudness. Auditory feedback was sinusoidally modulated at discrete integer frequencies (1 to 10 Hz) with +/- 25 cents amplitude. Modulated auditory feedback induced oscillations in voice F0 output of all subjects at rates consistent with vocal vibrato and tremor. Transfer functions revealed peak gains at 4 to 7 Hz in all subjects, with an average peak gain at 5 Hz. These gains occurred in the modulation frequency region where the voice output and auditory feedback signals were in phase. A control loop in the auditory system may sustain vocal vibrato and tremorlike oscillations in voice F0.     

Characteristics of an active feedback system for the control of plate vibrations

In the interests of improving airborne insulation of panels and of controlling room reverberation, a technique is studied for establishing control of the transverse vibrations of a thin plate by the application of active energy feedback. A localized point control force is derived from the sensed motion of some point on the plate surface. The superposition principle is applied in the form of a mobility analysis which shows that open loop gain conditions cannot result in a specific motion, including that of complete damping, of any arbitrary point on the plate surface but can be effective for particular points and for control of resonant modal motions under conditions of light damping. With velocity sensing, the characteristics for stable operation under the convenient condition of constant gain depend on maintenance of like symmetry, in the sense of an identity of velocity magnitude and sign, in the relative motion of sensing and control-force points. Bandwidth limitations are avoidable only by closure of the loop between these points. Two varieties of control force generator are involved: namely, where the generator mass is rigidly mounted and again where a spring mounting on the plate provides a self-supporting role.This is the first of two companion papers on active control of plate vibrations. Systems in which an array of multiple control units is used will be described in the second paper.     

Global damping of noise or vibration fields with locally synthesized controllers

A locally synthesized controller (LSC) is one that uses a local feedback signal in a noise or vibration field (VF) to synthesize the actuation signal. The global damping of a VF by available LSCs requires sensor-actuator collocation. This study presents a LSC for the global damping of a VF without requiring sensor-actuator collocation, which is important to noise control applications where a sensor may be placed away from an actuator to avoid the near field effects. It is proven that the LSC damps the entire VF instead of just a local feedback loop. This is different from other LSCs that may control local feedback loops without damping the VFs. A decentralized control law is presented here to extend the LSC to a decentralized damping system using multiple actuators.     

Kinetic Instability of Anisotropic Drift Wave Accompanied by Field Aligned Currents in Solar Coronal Loop

Solar coronal loops are frequently accompanied by the field-aligned currents, which drive instabilities if the drift velocity u₀> v_A the Alfvén velocity. For our choice of parameters, the critical threshold value of u₀/v_A is~3.0 for growth and the corresponding current filling factor~10^-3-10^-4. Below this value we are no longer in the kinetic regime. The coronal loops also have short-scale density gradients within each loop. The electron resonance in the presence of density gradient causes the drift mode to grow. We study the effect of these two free energy sources, the electron drift and the density gradient, in the presence of temperature anisotropy T_⊥α > T_||α. These effects simultaneously exist in the coronae. Using gyrokinetic theory, we investigate the influence of these effects, examine how they interplay with each other and study the consequent growth of the magnetosonic wave. We observe that kinetic instability driven by density gradient can be suppressed by field-aligned currents. The temperature anisotropy with chosen signatures causes further stabilizing effect. The results may prove useful to study the heating mechanism of solar coronal loops, acceleration of particles and confinement of particles in the thermonuclear reactors.