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.     

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 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.     

Global optimization of distributed output feedback controllers

When the frequency range over which a reduction in vibration is desired is limited to a particular structural mode of vibration, for example, it is shown that a centralized velocity feedback controller can perform better than a decentralized controller for a given level of control effort. The decentralized controller, however, has the desirable properties of scalability and ease of implementation. A number of strategies for clustering the control locations have been proposed to exploit both the performance of the centralized controller and the scalability of decentralized controllers but these have previously been only locally optimal. This paper describes methods by which these distributed controllers may be designed to be globally optimal and gives examples of simulated results of these optimal distributed controllers.     

A comparison of decentralized, distributed, and centralized vibro-acoustic control

Direct velocity feedback control of structures is well known to increase structural damping and thus reduce vibration. In multi-channel systems the way in which the velocity signals are used to inform the actuators ranges from decentralized control, through distributed or clustered control to fully centralized control. The objective of distributed controllers is to exploit the anticipated performance advantage of the centralized control while maintaining the scalability, ease of implementation, and robustness of decentralized control. However, and in seeming contradiction, some investigations have concluded that decentralized control performs as well as distributed and centralized control, while other results have indicated that distributed control has significant performance advantages over decentralized control. The purpose of this work is to explain this seeming contradiction in results, to explore the effectiveness of decentralized, distributed, and centralized vibro-acoustic control, and to expand the concept of distributed control to include the distribution of the optimization process and the cost function employed.     

Pole assignment of friction-induced vibration for stabilisation through state-feedback control

Friction-induced self-excited linear vibration is often governed by a second-order matrix differential equation of motion with an asymmetric stiffness matrix. The asymmetric terms are product of friction coefficient and the normal stiffness at the contact interface. When the friction coefficient becomes high enough, the resultant vibration becomes unstable as frequencies of two conjugate pairs of complex eigenvalues (poles) coalesce (when viscous damping is low).This short paper presents a receptance-based inverse method for assigning complex poles to second-order asymmetric systems through (active) state-feedback control of a combination of active stiffness, active damping and active mass, which is capable of assigning negative real parts to stabilise an unstable system.     

Finite time decentralized event-triggered communication scheme for neutral-type Markovian jump neural networks with time varying delays

The objective of this paper is to analyze the finite time problem of a class of neutral-type Markovian jump neural networks with time varying delays and parametric uncertainties using decentralized event-triggered communication scheme. We present a methodology for designing decentralized event-triggered, which utilize only locally available information, for determining the time instants of transmission from the sensors to the central controller. Based on the Lyapunov function with inequality techniques like reciprocal convex combination method, some sufficient conditions are derived to guarantee the finite-time stability of the considered neural networks. Furthermore, the decentralized event-triggered scheme combined with state feedback controller and is designed to solve the finite time stability. The obtained stability criteria are stated in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Finally, numerical examples are given to illustrate the effectiveness and reduced conservatism of the proposed results over the existing ones.     

Taming instabilities in power grid networks by decentralized control

Renewables will soon dominate energy production in our electric power system. And yet, how to integrate renewable energy into the grid and the market is still a subject of major debate. Decentral Smart Grid Control (DSGC) was recently proposed as a robust and decentralized approach to balance supply and demand and to guarantee a grid operation that is both economically and dynamically feasible. Here, we analyze the impact of network topology by assessing the stability of essential network motifs using both linear stability analysis and basin volume for delay systems. Our results indicate that if frequency measurements are averaged over sufficiently large time intervals, DSGC enhances the stability of extended power grid systems. We further investigate whether DSGC supports centralized and/or decentralized power production and find it to be applicable to both. However, our results on cycle-like systems suggest that DSGC favors systems with decentralized production. Here, lower line capacities and lower averaging times are required compared to those with centralized production.     

Synchronization analysis of coloured delayed networks under decentralized pinning intermittent control

This paper investigates synchronization of coloured delayed networks under decentralized pinning intermittent control. To begin with, the time delays are taken into account in the coloured networks. In addition, we propose a decentralized pinning intermittent control are method, which is different from that most of pinning intermittent controls are only applied to the nodes from 1 to l or centralized nodes. Moreover, sufficient conditions are derived to guarantee the synchronization of coloured delayed networks based on Lyapunov stability theorem. Finally, numerical simulations are provided to verify the validity of the obtained results.     

Decentralized control of sound radiation using iterative loop recovery

A decentralized model-based control strategy is designed to reduce low-frequency sound radiation from periodically stiffened panels. While decentralized control systems tend to be scalable, performance can be limited due to modeling error introduced by the unmodeled interaction between neighboring control units. Since bounds on modeling error are not known in advance, it is difficult to ensure the decentralized control system will be robust without making the controller overly conservative. Therefore an iterative approach is suggested, which utilizes frequency-shaped loop recovery. The approach accounts for modeling error introduced by neighboring control loops, requires no communication between subsystems, and is relatively simple. The control strategy is evaluated numerically using a model of a stiffened aluminum panel that is representative of the sidewall of an aircraft. Simulations demonstrate that the iterative approach can achieve significant reductions in radiated sound power from the stiffened panel without destabilizing neighboring control units.     

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.     

结构振动模态之间耦合对预测结构声功率的影响

以简支矩形板为例,分析结构振动模态之间的耦合对声功率的影响。通过对声功率传递矩阵计算方法的改进,得到计算声功率传递矩阵对角元素和非对角元素(模态耦合项)的解析解,并进行数值计算和分析。所得解析解结果同前人发表的数值解非常吻合。     

OPTIMAL CONTROL METHOD WITH TIME DELAY IN CONTROL

Optimal control method for active vibration control of linear time-delay systems is investigated in this paper. In terms of two cases that time delay is integer and non-integer times of sampling period, motion equation with time delay is transformed as standard discrete forms which contain no time delay by using zero order holder respectively. Discrete quadratic function is used as objective function in design of controller to guarantee good control efficiency on sampling points. In every step of computation of the deduced controller, it contains not only current step of state feedback but also linear combination of some former steps of control. Because the controller is deduced directly from time-delay differential equation, system stability can be guaranteed easily, thus this method is generally applicable to ordinary control systems. The performance of the control method proposed and system stability when using this method are all demonstrated by numerical simulation results. Simulation results demonstrate that the presented method is a viable and attractive control strategy for applications to active vibration control. Instability in responses occurs possibly if the systems with time delay are controlled using controller designed in case of no time delay.     

Free vibration of a conical shell with variable thickness

An analysis is presented for the free vibration of a truncated conical shell with variable thickness by use of the transfer matrix approach. The applicability of the classical thin shell theory is assumed and the governing equations of vibration of a conical shell are written as a coupled set of first order differential equations by using the transfer matrix of the shell. Once the matrix has been determined by quadrature of the equations, the natural frequencies and the mode shapes of vibration are calculated numerically in terms of the elements of the matrix under any combination of boundary conditions at the edges. The method is applied to truncated conical shells with linearly, parabolically or exponentially varying thickness, and the effects of the semi-vertex angle, truncated length and varying thickness on the vibration are studied.     

Actuator saturation control of uncertain structures with input time delay

This paper presents a robust saturation control approach for active vibration attenuation of building structures involving parameter uncertainties and input time delay. The parameter uncertainties are described in both polytopic and norm-bounded forms and represent the variations of floor masses, stiffnesses and damping coefficients. The input time delay can be time-varying within a known bound. In terms of the feasibility of certain delay-dependent linear matrix inequalities (LMIs), a state feedback controller can be designed to guarantee the robust stability and performance of the closed-loop system in the presence of parameter uncertainties, actuator saturation, and input time delay. The effectiveness of the proposed approach is investigated by numerical simulations on the vibration control of a three-storey building structure subject to seismic excitation. It is validated that the designed robust saturation controller can effectively suppress the structural vibration and keep the system stability when there are parameter uncertainties and input time delay.     

非简谐振动对SiC的热膨胀系数数和介电性能的影响

利用抛物型电子能谱模型,考虑到原子的非简谐振动,求出了SiC中原子振动的简谐系数与非简谐系数,用固体物理理论和方法,得到了SiC的热膨胀系数和格林乃森参量以及介电常数随温度变化的解析式,探讨了原子非简谐振动对的影响。结果表明：的格林乃森参量和热膨胀系数均随温度升高而非线性增大,而介电常数随温度升高而非线性减小;原子振动的非简谐项（特别是第二非简谐项）对的热膨胀等热学性质和介电性能有重要影响,温度愈高,非简谐振动项的影响愈大。     

A straightforward method for tuning of Lyapunov-based controllers in semi-active vibration control applications

Lyapunov-based control is an attractive strategy for semi-active vibration control as it has a mathematical basis ensuring stability in the sense of Lyapunov and great flexibility in the design. Unfortunately, that flexibility complicates the controller tuning since it involves the construction of a weighting matrix, which is usually done by trial-and-error.     

Development of panel loudspeaker system: design, evaluation and enhancement.

Panel speakers are investigated in terms of structural vibration and acoustic radiation. A panel speaker primarily consists of a panel and an inertia exciter. Contrary to conventional speakers, flexural resonance is encouraged such that the panel vibrates as randomly as possible. Simulation tools are developed to facilitate system integration of panel speakers. In particular, electro-mechanical analogy, finite element analysis, and fast Fourier transform are employed to predict panel vibration and the acoustic radiation. Design procedures are also summarized. In order to compare the panel speakers with the conventional speakers, experimental investigations were undertaken to evaluate frequency response, directional response, sensitivity, efficiency, and harmonic distortion of both speakers. The results revealed that the panel speakers suffered from a problem of sensitivity and efficiency. To alleviate the problem, a woofer using electronic compensation based on H2 model matching principle is utilized to supplement the bass response. As indicated in the result, significant improvement over the panel speaker alone was achieved by using the combined panel-woofer system.     

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.     

Relationship between Helmholtz-resonance absorption and panel-type absorption in finite flexible microperforated-panel absorbers

Microperforated panels (MPPs) can provide wide-band absorption without fibrous and porous materials and are recognized as next-generation absorption materials. Although the fundamental absorbing mechanism of an MPP absorber is Helmholtz-resonance absorption, sound-induced vibration of an MPP itself can affects the absorption characteristics. There have been some studies considering the effects of the sound-induced vibration and there even is a proposal to widen the absorption bandwidth by positively utilizing the vibration of an MPP itself. On the other hand, in a previous study, the relationship between MPP absorbers and panel-type absorbers was investigated with infinite theory. However, the relationship between Helmholtz-resonance absorption and panel-type absorption in finite flexible MPP absorbers has not been clarified. Herein, from the viewpoint of an absorption-characteristics transition with the perforation ratio, the relationship between Helmholtz-resonance absorption and panel-type absorption including the effects of eigen-mode vibrations of the panel is theoretically and experimentally investigated. The analytical model considers a finite flexible MPP supported in a circular duct, and the predicted data for the absorption coefficient under normal incidence is validated by an experiment using an acoustic tube. From this investigation, it is found that panel-type absorption due to eigen-mode vibrations of the panel occurs independently from Helmholtz-resonance absorption, while panel-type absorption due to a mass-spring resonance of a panel and a back cavity has a trade-off relationship with Helmholtz-resonance absorption with respect to the perforation ratio.