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.     

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.     

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

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

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.     

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

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

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.     

Line narrowing of a distributed feedback dye laser using external frequency selective feedback

Frequency selective feedback, employing a mirror and etalon, applied to a distributed feedback dye laser has reduced the linewidth of the emitted radiation by a factor of up to twenty. Criteria used for choosing suitable etalons are discussed.     

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.     

Adaptive active control of periodic vibration using maglev actuators

In this paper, active control of periodic vibration is implemented using maglev actuators which exhibit inherent nonlinear behaviors. A multi-channel feedforward control algorithm is proposed to solve these nonlinear problems, in which maglev actuators are treated as single-input–single-output systems with unknown time-varying nonlinearities. A radial basis function network is used by the algorithm as its controller, whose parameters are adapted only with the model of the linear system in the secondary path. Compared with the strategies in the conventional magnetic-levitation system control as well as nonlinear active noise/vibration control, the proposed algorithm has the advantage that the nonlinear modeling procedure of maglev actuators and the usage of displacement sensors could be both avoided. Numerical simulations and real-time experiments are carried out based on a multiple-degree-of-freedom vibration isolation system. The results show that the proposed algorithm not only could efficiently compensate for the actuators’ time-varying nonlinearities, but also has the ability to greatly attenuate the energy of periodic vibration.     

Active control of friction-induced self-excited vibration using adaptive fuzzy systems

Vibration caused by friction is harmful to engineering systems. Understanding the mechanism of such a physical phenomenon and developing some strategies to effectively control the vibration have both theoretical and practical significance. Based on our previous work, this paper deals with a problem of active compensation control of friction-induced self-excited vibration using adaptive fuzzy systems. Comparative studies on control performance are carried out, where a class of adaptive compensation control schemes with various friction models are applied to control a motion dynamics with friction. It is observed that our proposed modeling and control techniques are powerful to eliminate the limit cycle and the steady-state error. Furthermore, robustness of the proposed controller with respect to external disturbances is discussed. Simulation results show that the active controller with adaptive fuzzy friction compensation outperforms other active controllers with compensation terms characterized by three well-known friction models.     

Dynamic vibration absorbers for vibration control within a frequency band

The use of dynamic vibration absorbers to control the vibration of a structure in both narrow and broadbands is discussed in this paper. As a benchmark problem, a plate incorporating multiple vibration absorbers is formulated, leading to an analytical solution when the number of absorbers yields one. Using this analytical solution, control mechanisms of the vibration absorber in different frequency bandwidths are studied; the coupling properties due to the introduction of the absorber into the host structure are analyzed; and the control performance of the absorber in different control bandwidths is examined with respect to its damping and location. It is found that the interaction between the plate and the absorber by means of the reaction force from the absorber plays a dominant role in a narrow band control, while in a relatively broadband control the dissipation by the absorber damping governs the control performance. When control bandwidth further enlarges, the optimal locations of the absorbers are not only affected by the targeted mode, but also by the other plate modes. These locations need to be determined after establishing a trade-off between the targeted mode and other modes involved in the coupling. Finally, numerical findings are assessed based on a simply-supported plate and a fair agreement between the predicted and measured results is obtained.     

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.     

Active control of high-frequency vibration: Optimisation using the hybrid modelling method

This work presents active control of high-frequency vibration using skyhook dampers. The choice of the damper gain and its optimal location is crucial for the effective implementation of active vibration control. In vibration control, certain sensor/actuator locations are preferable for reducing structural vibration while using minimum control effort. In order to perform optimisation on a general built-up structure to control vibration, it is necessary to have a good modelling technique to predict the performance of the controller. The present work exploits the hybrid modelling approach, which combines the finite element method (FEM) and statistical energy analysis (SEA) to provide efficient response predictions at medium to high frequencies. The hybrid method is implemented here for a general network of plates, coupled via springs, to allow study of a variety of generic control design problems. By combining the hybrid method with numerical optimisation using a genetic algorithm, optimal skyhook damper gains and locations are obtained. The optimal controller gain and location found from the hybrid method are compared with results from a deterministic modelling method. Good agreement between the results is observed, whereas results from the hybrid method are found in a significantly reduced amount of time.     

A novel technique for active vibration control,based on optimal tracking control

Determination of concentration of major elements such as Ca, Si, Al, and Fe in cement is very important for quality control during its production, correct classification according to the existing standards, and thus for appropriate use in the construction industry. For this purpose, neutron activation analysis is very suitable. In this preliminary theoretical work, the irradiation and consecutive measurement of the percentage of the constituent elements in different cement samples were done using MCNPX with γ-ray spectra as the output. Specific peaks of Ca, Si, Al, and Fe obtained from these spectra were used as input for artificial neural network (18 of them for training and 8 for testing) resulting in the determination of each element in the given sample. The mean absolute errors of the results are less than 0.4%, which is very promising for the future experimental work where the uncertainties are usually one order higher.     

Free vibration control of smart composite beams using particle swarm optimized self-tuning fuzzy logic controller

This paper deals with active free vibrations control of smart composite beams using particle-swarm optimized self-tuning fuzzy logic controller. In order to improve the performance and robustness of the fuzzy logic controller, this paper proposes integration of self-tuning method, where scaling factors of the input variables in the fuzzy logic controller are adjusted via peak observer, with optimization of membership functions using the particle swarm optimization algorithm. The Mamdani and zero-order Takagi–Sugeno–Kang fuzzy inference methods are employed. In order to overcome stability problem, at the same time keeping advantages of the proposed self-tuning fuzzy logic controller, this controller is combined with the LQR making composite controller. Several numerical studies are provided for the cantilever composite beam for both single mode and multimodal cases. In the multimodal case, a large-scale system is decomposed into smaller subsystems in a parallel structure. In order to represent the efficiency of the proposed controller, obtained results are compared with the corresponding results in the cases of the optimized fuzzy logic controllers with constant scaling factors and linear quadratic regulator.     

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

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

Adaptive tracking control for a class of uncertain chaotic systems

The paper is concerned with adaptive tracking problem for a class of chaotic system with time-varying uncertainty, but bounded by norm polynomial. Based on adaptive technique, it proposes a novel controller to asymptotically track the arbitrary desired bounded trajectory. Simulation on the Rossler chaotic system is performed and the result verifies the effectiveness of the proposed method.     

On utilizing delayed feedback for active-multimode vibration control of cantilever beams

We present a single-input single-output multimode delayed-feedback control methodology to mitigate the free vibrations of a flexible cantilever beam. For the purpose of controller design and stability analysis, we consider a reduced-order model consisting of the first n vibration modes. The temporal variation of these modes is represented by a set of nonlinearly coupled ordinary-differential equations that capture the evolving dynamics of the beam. Considering a linearized version of these equations, we derive a set of analytical conditions that are solved numerically to assess the stability of the closed-loop system. To verify these conditions, we characterize the stability boundaries using the first two vibration modes and compare them to damping contours obtained by long-time integration of the full nonlinear equations of motion. Simulations show excellent agreement between both approaches. We analyze the effect of the size and location of the piezoelectric patch and the location of the sensor on the stability of the response. We show that the stability boundaries are highly dependent on these parameters. Finally, we implement the controller on a cantilever beam for different controller gain-delay combinations and assess the performance using time histories of the beam response. Numerical simulations clearly demonstrate the controller ability to mitigate vibrations emanating from multiple modes simultaneously.