An optimal vibration control logic for minimising fatigue damage in flexible structures

One of the most common applications of active control on flexible structures is the mitigation of vibrations to reduce stresses and consequently increase lifetime. However, except for a few particular cases, the fatigue phenomenon has never been taken into account in the design of the control algorithm. Moreover, since fatigue is mainly a local effect, in some cases active control could even worsen the structure's integrity (e.g. consider local damage close to the actuators caused by control strategies requiring high control forces). For this reason, control is not able to achieve the best performance in terms of damage reduction and lifetime maximisation. This paper proposes an optimal active control designed to minimise fatigue damage on the structure. A model of the fatigue phenomenon is introduced and included in the definition of the control parameters. The solution is firstly described from a theoretical point of view and then tested both numerically and experimentally, showing a significant improvement over state-of-the-art techniques.     

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.     

Suppression of random vibration in flexible structures using a hybrid vibration absorber

A design method is proposed to suppress stationary random vibration in flexible structures using a hybrid vibration absorber (HVA). While the traditional vibration absorber can damp down the vibration mainly at the pre-tuned mode of the primary structure, active damping is generated by the proposed HVA to damp down all resonant modes of interest of the vibrating structure and the spatial average mean square motion of the vibrating structure can be minimized. Only one absorber and one feedback signal are required to achieve global vibration suppression of a flexible structure under stationary random excitation. A special pole-placement controller is designed such that all vibration modes of the flexible structures become critically damped. It is proved analytically that the proposed HVA damps the vibration of the entire structure instead of just the attachment point of the absorber. The proposed optimized HVA is tested on a beam structure and it shows a superior performance on global suppression of broadband vibration in comparison to other published designs of passive and hybrid vibration absorbers.     

Active control of forced harmonic vibration in finite degree of freedom structures with negligible natural damping

Methods of synthesis for vibration controllers are presented for mechanical structures where the number of actuators equals the number of modes to be controlled and for structures where the number of modes exceeds the number of actuators. Provided an observer can be constructed complete isolation from the disturbance will be possible for the first case even when the dynamics of the structure are not well defined. In the second case complete isolation is not in general possible but a considerable reduction of strain energy can still be achieved. Possible practical limitations are discussed.     

A modal disturbance estimator for vibration suppression in nonlinear flexible structures

This paper presents a control strategy for the suppression of vibration due to unknown disturbance forces in large, nonlinear flexible structures. The control action proposed, based on the modal approach, consists of two contributions. The first is the well-known Independent Modal-Space Control, which increases system damping and improves its behavior close to the resonance frequencies. The second is a disturbance estimator, which calculates the modal components of the external forces acting on the system and compensates for them using actuator forces. The system modal coordinates, required by both logics, are estimated through a modal state observer.The proposed control logic is tested on a flexible boom. The paper reports the numerical and experimental results both for the linear and nonlinear (large motion) boom configuration.     

On using moving windows in finite element time domain simulation for long accelerator structures

A finite element moving window technique is developed to simulate the propagation of electromagnetic waves induced by the transit of a charged particle beam inside large and long structures. The window moving along with the beam in the computational domain adopts high-order finite element basis functions through p refinement and/or a high-resolution mesh through h refinement so that a sufficient accuracy is attained with substantially reduced computational costs. Algorithms to transfer discretized fields from one mesh to another, which are the keys to implementing a moving window in a finite element unstructured mesh, are presented. Numerical experiments are carried out using the moving window technique to compute short-range wakefields in long accelerator structures. The results are compared with those obtained from the normal finite element time domain (FETD) method and the advantages of using the moving window technique are discussed.     

Analysis of inplane vibration of box-type structures by a finite element method

Application of the finite element technique in the analysis of box-type structures is described in this paper. The box is developed from plate elements with two degrees of freedom per node and only inplane free vibration is considered.     

Semi-active friction tendons for vibration control of space structures

Semi-active vibration control systems are becoming popular because they offer both the reliability of passive systems and the versatility of active control without high power demands. In this work, a new semi-active control system is proposed and studied numerically. The system consists of variable-friction dampers linked to the structure through cables. Auxiliary soft springs in parallel with these friction dampers allow them to return to their initial pre-tensioned state. Using cables makes the system suitable for deployable, flexible and lightweight structures, such as space structures (spacecraft). A control system with three control laws applied to a single-degree-of-freedom structure is studied. Two of these laws are derived by using Lyapunov theory, whereas the third one is developed heuristically. In order to assess the performance of the control system, a parametric study is carried out through numerical simulations. An application of the proposed method to multi-degree-of-freedom structures is also presented and demonstrated through a numerical example. The system in semi-active mode is more effective than in passive mode and its effectiveness is less sensitive to loss of pre-tension.     

Application of discrete-time variable structure control in the vibration reduction of a flexible structure

This paper studies the application of using the discrete-time variable structure control method to reduce the vibration of the flexible structure. The structure is subjected to arbitrary, unmeasurable disturbance forces. The concept of independent modal space control is adopted, and the system is studied by the discrete-time model. Here, discrete sensors and actuators are used. We choose the modal filters as the state estimator to obtain the modal co-ordinates and modal velocities for the modal space control. A discrete-time variable structure controller with a disturbance force observer is adopted due to its distinguished robustness property of insensitiveness to parameter uncertainties and external disturbances. The included disturbance force observer can observe the unknown disturbance modal forces, which are used in the discrete-time variable structure control law to cancel out the excitations. The upperbound limitations of the unknown disturbances in the variable structure control, therefore, are no longer needed. The switching surface, in the discrete-time variable structure control system, is designed in an optimal sense. That is, along the switching surface, the cost function of the states is minimized. The investigation of this research focuses on the optimal switching surface design and the control performances of the discrete-time variable structure controller. The performance of estimating the disturbance modal forces and the robustness property of the control law are also discussed.     

Antireflection subwavelength structures analyzed by using the finite difference time domain method

Antireflection subwavelength structures (ASSs) are analyzed by using the finite difference time domain (FDTD) method in the visible light spectrum. Low reflectance can be obtained by both the conical and pyramidal shapes over a broadband range. Comparing the reflectance of different structure shapes and aspect ratios by the FDTD method, it shows that the antireflection efficiencies of the pyramidal structures are better than that of the conical structures when the aspect ratio is up to 0.8. It is found that, for the conical structure surface, the average transmittance increases gradually with the aspect ratio and the average transmittance is about 99.6% with the aspect ratio of 2.0. However, for the pyramidal structure with the aspect ratio ranging from 1.0 to 2.0, the average transmittance is up to 99.7%.     

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.     

Optimization of a hybrid vibration absorber for vibration control of structures under random force excitation

A recently reported design of a hybrid vibration absorber (HVA) which is optimized to suppress resonant vibration of a single degree-of-freedom (SDOF) system is re-optimized for suppressing wide frequency band vibration of the SDOF system under stationary random force excitation. The proposed HVA makes use of the feedback signals from the displacement and velocity of the absorber mass for minimizing the vibration response of the dynamic structure based on the H₂ optimization criterion. The objective of the optimal design is to minimize the mean square vibration amplitude of a dynamic structure under a wideband excitation, i.e., the total area under the vibration response spectrum is minimized in this criterion. One of the inherent limitations of the traditional passive vibration absorber is that its vibration suppression is low if the mass ratio between the absorber mass and the mass of the primary structure is low. The active element of the proposed HVA helps further reduce the vibration of the controlled structure and it can provide significant vibration absorption performance even at a low mass ratio. Both the passive and active elements are optimized together for the minimization of the mean square vibration amplitude of the primary system. The proposed HVA are tested on a SDOF system and continuous vibrating structures with comparisons to the traditional passive vibration absorber.     

Application of the time dependent finite difference theory to the study of sound and vibration interactions in ducts

The time dependent finite difference theory is extended to the solution of the acoustic wave equation in rectangular ducts when acoustic/structural interactions are allowed at a duct wall. The treatment of the boundary condition which describes the coupling is examined, and the stability of the procedure is studied and found to depend on the nature of this coupling. The convergence of solutions is discussed as a function of the discretization of the solution domain, particularly at frequencies approaching resonance.     

Decentralized harmonic active vibration control of a flexible plate using piezoelectric actuator-sensor pairs

We have investigated decentralized active control of periodic panel vibration using multiple pairs combining PZT actuators and PVDF sensors distributed on the panel. By contrast with centralized MIMO controllers used to actively control the vibrations or the sound radiation of extended structures, decentralized control using independent local control loops only requires identification of the diagonal terms in the plant matrix. However, it is difficult to a priori predict the global stability of such decentralized control. In this study, the general situation of noncollocated actuator-sensor pairs was considered. Frequency domain gradient and Newton-Raphson adaptation of decentralized control were analyzed, both in terms of performance and stability conditions. The stability conditions are especially derived in terms of the adaptation coefficient and a control effort weighting coefficient. Simulations and experimental results are presented in the case of a simply supported panel with four PZT-PVDF pairs distributed on it. Decentralized vibration control is shown to be highly dependent on the frequency, but can be as effective as a fully centralized control even when the plant matrix is not diagonal-dominant or is not strictly positive real (not dissipative).     

Disturbance rejection control for vibration suppression of piezoelectric laminated thin-walled structures

Thin-walled piezoelectric integrated smart structures are easily excited to vibrate by unknown disturbances. In order to design and simulate a control strategy, firstly, an electro-mechanically coupled dynamic finite element (FE) model of smart structures is developed based on first-order shear deformation (FOSD) hypothesis. Linear piezoelectric constitutive equations and the assumption of constant electric field through the thickness are considered. Based on the dynamic FE model, a disturbance rejection (DR) control with proportional-integral (PI) observer using step functions as the fictitious model of disturbances is developed for vibration suppression of smart structures. In order to achieve a better dynamic behavior of the fictitious model of disturbances, the PI observer is extended to generalized proportional-integral (GPI) observer, in which sine or polynomial functions can be used to represent disturbances resulting in better dynamics. Therefore the disturbances can be estimated either by PI or GPI observer, and then the estimated signals are fed back to the controller. The DR control is validated by various kinds of unknown disturbances, and compared with linear-quadratic regulator (LQR) control. The results illustrate that the vibrations are better suppressed by the proposed DR control.     

On saturation suppression in adaptive vibration control

An anti-saturation scheme is presented for adaptive vibration control with LMS controllers. A new recursive formula for weight updating is derived from the optimization of certain object functions, which is an extension of the normalized LMS algorithm. The anti-saturation formula is capable of suppressing controller output in case of a large disturbance and expected to improve the performance of the controller. Numerical simulation and experiment have been conducted to demonstrate the performance of the anti-saturation scheme and the results have shown that the scheme is effective in alleviating output saturation and as a result improves performance of the controller in vibration suppression.