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.     

Sensitivity of friction-induced vibration in idealised systems

Friction-induced vibration occurs in many contexts: vehicle brake squeal in particular remains surprisingly unpredictable and poorly understood. Testing theory against measurements has been hindered by the difficulty in obtaining repeatable results suggesting that the phenomenon is sensitive to small changes in parameters. This paper explores highly idealised cases as a starting point to understanding sensitivity. Using a stability criterion based on the roots of the characteristic equations of the system, the sensitivity of predictions to parameter changes is studied, focussing on a single-mode model. The effects of contact stiffness, non-proportional damping and a velocity-dependent coefficient of friction are considered. It is found that each physical effect can significantly alter predictions; each physical effect can lead to extreme sensitivity; and high sensitivity can sometimes occur when modal amplitudes are small such that they might normally be considered insignificant. With a large body of literature focussing on reduced-order models this study provides an important warning when interpreting their results.     

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.     

Composite adaptive fuzzy control for synchronizing generalized Lorenz systems

This paper presents a methodology of asymptotically synchronizing two uncertain generalized Lorenz systems via a single continuous composite adaptive fuzzy controller (AFC). To facilitate controller design, the synchronization problem is transformed into the stabilization problem by feedback linearization. To achieve asymptotic tracking performance, a key property of the optimal fuzzy approximation error is exploited by the Mean Value Theorem. The composite AFC, which utilizes both tracking and modeling error feedbacks, is constructed by introducing a series-parallel identification model into an indirect AFC. It is proved that the closed-loop system achieves asymptotic stability under a sufficient gain condition. Furthermore, the proposed approach cannot only synchronize two different chaotic systems but also significantly reduce computational complexity and implemented cost. Simulation studies further demonstrate the effectiveness of the proposed approach.     

基于自适应模糊控制的分数阶混沌系统同步

本文主要研究了带有未知外界扰动的分数阶混沌系统的同步问题.基于分数阶Lyapunov稳定性理论,构造了分数阶的参数自适应规则以及模糊自适应同步控制器.在稳定性分析中主要使用了平方Lyapunov函数.该控制方法可以实现两分数阶混沌系统的同步,使得同步误差渐近趋于0.最后,数值仿真结果验证了本文方法的有效性.     

基于磁悬浮作动器的自适应有源振动控制研究

针对周期扰动提出一种基于磁悬浮作动器的非线性前馈自适应有源振动控制算法。算法中将磁悬浮作动器视为具有时变非线性的单输入输出系统,并使用径向基函数神经网络进行控制,分别采用聚类算法和随机梯度算法对其隐层中心点和输出层权值进行自适应调整。该算法摆脱了传统磁悬浮控制对模型的依赖,在正常工作条件下不需对作动器建模。仿真和实验结果表明:在单自由度主动隔振系统中,非线性自适应算法可以显著降低周期振动的能量,同时能对磁悬浮作动器的时变非线性进行有效的补偿。      

The onset of friction-induced vibration and spragging

The minimal dynamic models are used to investigate the influences of geometric coupling on frictionally-excited system. At a certain set of system parameters, spragging can occur where the steady-sliding is indeterminate. It is found that the sprag condition becomes the boundary of the regime for the non-existence of the equilibrium in the parametric space. Equilibrium instability induced by the negative friction-velocity slope and mode-coupling is determined for the regime in which the steady-sliding is defined. Its ensuing nonlinear response is shown to reach the stick-slip limit cycle.     

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 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.     

Robust adaptive fuzzy neural tracking control for a class of unknown chaotic systems

In this paper, an adaptive fuzzy neural controller (AFNC) for a class of unknown chaotic systems is proposed. The proposed AFNC is comprised of a fuzzy neural controller and a robust controller. The fuzzy neural controller including a fuzzy neural network identifier (FNNI) is the principal controller. The FNNI is used for online estimation of the controlled system dynamics by tuning the parameters of fuzzy neural network (FNN). The Gaussian function, a specific example of radial basis function, is adopted here as a membership function. So, the tuning parameters include the weighting factors in the consequent part and the means and variances of the Gaussian membership functions in the antecedent part of fuzzy implications. To tune the parameters online, the back-propagation (BP) algorithm is developed. The robust controller is used to guarantee the stability and to control the performance of the closed-loop adaptive system, which is achieved always. Finally, simulation results show that the AFNC can achieve favourable tracking performances.     

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.     

受扰统一混沌系统的主动自适应模糊积分滑模控制

针对受扰统一混沌系统,提出一种主动白适应模糊积分滑模控制方法．在保持原非线性积分滑模控制暂态性能的同时,设计了一种改进非线性积分滑模控制方法,保证了系统的稳定性．所提出控制方法减小了统一混沌系统的不可控状态和自适应模糊补偿项的逼近精度对系统状态误差的影响．基于Lyapunov稳定性理论分析了系统的稳定性．数值仿真结果表明,在存在参数摄动和外部扰动时,能将统一混沌系统控制到目标点上．数值仿真验证了所提出控制方法的有效性．     

Suppression of maglev vehicle-girder self-excited vibration using a virtual tuned mass damper

The self-excited vibration that occurs between a stationary Electromagnetic Suspension (EMS) maglev vehicle and a girder is a practical problem that greatly degrades the performance of a maglev system. As of today, this problem has not been fully solved. In this article, the principle underlying the self-excited vibration problem is explored, and it is found that the fundamental resonance frequency of the maglev girder plays a vital role in the initiation of the self-excited vibration. To suppress the self-excited vibration, a scheme applying a tuned mass damper (TMD) to the maglev girder is proposed, and the stability of the combined system is analyzed. Furthermore, a novel concept of a virtual TMD is introduced, which uses an electromagnetic force to emulate the force of a real TMD acting on the girder. However, in the presence of the time delay caused by the inductance of the electromagnets, the stability analysis of the levitation system combined with the virtual TMD becomes complex. Analysis of the stability shows that there exist some repeated time delay zones within which the overall system is stable. Based on this rule, time delay control is introduced to stabilize the system with a virtual TMD, and a procedure to determine the optimal time delay and gain is proposed. Numerical simulation indicates that the proposed virtual TMD scheme can significantly suppress the self-excited vibration caused by one unstable vibration mode, and is suitable for application to EMS maglev systems.     

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.     

Generalized projective synchronization of the fractional-order chaotic system using adaptive fuzzy sliding mode control

An adaptive fuzzy sliding mode strategy is developed for the generalized projective synchronization of a fractionalorder chaotic system, where the slave system is not necessarily known in advance. Based on the designed adaptive update laws and the linear feedback method, the adaptive fuzzy sliding controllers are proposed via the fuzzy design, and the strength of the designed controllers can be adaptively adjusted according to the external disturbances. Based on the Lyapunov stability theorem, the stability and the robustness of the controlled system are proved theoretically. Numerical simulations further support the theoretical results of the paper and demonstrate the efficiency of the proposed method. Moreover,it is revealed that the proposed method allows us to manipulate arbitrarily the response dynamics of the slave system by adjusting the desired scaling factor λi and the desired translating factor ηi, which may be used in a channel-independent chaotic secure communication.     

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.     

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.     

主动磁悬浮系统的变论域自适应模糊PID控制

针对主动磁悬浮轴承系统具有强非线性、强耦合、模型不确定等特点,提出了一种变论域自适应模糊PID算法。该方法通过选择合适的伸缩因子,避免了传统模糊PID控制中出现规则爆炸的问题。同时针对传统伸缩因子的函数结构和参数难以确定的特点,设计了基于模糊规则的论域伸缩因子。在SIMULINK环境中对主动磁悬浮轴承系统进行仿真,仿真结果表明,变论域模糊PID算法控制的主动磁悬浮系统具有更好的动静态性能,对外界干扰具有更强的鲁棒性。     

Adaptive active noise and vibration control systems

A review of research concerned with adaptive noise and vibration control systems and performed under the supervision of Corresponding Member of the Russian Academy of Sciences V.A. Zverev at Nizhni Novgorod State University in the 1980s and 1990s is presented. The history of the subject is briefly outlined, and the theoretical foundations of the design of adaptive active control systems for random wave fields are considered. The main experimental studies performed in this area of research at the Department of Bionics and Statistical Radiophysics of Nizhni Novgorod State University are described. Promising lines of research in this area are indicated, and examples of the practical application of adaptive control systems are given.