Adaptive Vibration Research Articles

Regressor-free adaptive vibration control of constrained smart beams with axial stretching

This paper proposes an adaptive approximation control AAC technique (or so-called regressor-free adaptive control) for vibration regulation of constrained flexible smart beams with axial stretching. The key idea of the AAC is to control/regulate the target dynamic system while estimating the uncertainty using weighting and basis function terms with guaranteed stability based on Lyapunov theory. Accordingly, the dynamic equation of transverse vibration of the pinned–pinned smart beam is derived considering the effect of axial stretching. Due to the presence of a coupled tension-bending effect, a nonlinearly coupled cubic stiffness term appears in beam modelling making the dynamic system highly nonlinear. The resulted partial differential equation of the vibrating smart beam is discretized into definite N-mode shapes (definite degrees-of-freedom) using the Galerkin approach and a standard multi–input–multi–output ordinary differential equations system is established. Then two decoupled nonlinear control algorithms are designed based on the AAC for vibration attenuation of the nonlinear vibrating beam system. A pinned–pinned piezoelectrically-actuated/sensed flexible beam is simulated and the results show the validity of the proposed control architecture.

Vibration control of a rotor system by shear thickening fluid dampers

This paper presents a study of a novel nonlinear damper on vibration control of rotor system with variable damping by using a smart material- shear thickening fluid (STF), whose viscosity and damping will dramatically increase with shear rate. A STF damper was self-developed and dynamic model of the STF damper-rotor system was established by using the Bouc-Wen model as mechanical model of the smart material damper. The incremental harmonic balance (IHB) method combined with the arc-length method was presented to investigate the dynamic response of rotor system with hysteresis nonlinear damping force theoretically. Experimental study of STF damper on suppressing vibration of rotor system was carried out by using a Bently rotor test rig with two STF dampers. The damping effect under different damper installation direction, vibration frequency and amplitude were investigated theoretically and experimentally. Study shows that the nonlinear damper exhibits larger damping force and fuller hysteresis characteristics, so it has better effect on resonance energy absorption compared with the traditional linear damper; and its output damping force can increase dramatically with the change of frequency and amplitude. It is verified that the unbalance vibration, especially the resonance amplitude of rotor system can be effectively suppressed by nonlinear damping of STF damper. The study shows the feasibility and advantages of using the STF damper for potential applications of adaptive or semi-active vibration control of rotating machinery.

Dynamics Analysis of Active Variable Stiffness Vibration Isolator for Whole-Spacecraft Systems Based on Nonlinear Output Frequency Response Functions

In order to improve the harsh dynamic environment experienced by heavy rockets during different external excitations, this study presents a novel active variable stiffness vibration isolator (AVS-VI) used as the vibration isolation device to reduce excessive vibration of the whole-spacecraft isolation system. The AVS-VI is composed of horizontal stiffness spring, positive stiffness spring, parallelogram linkage mechanism, piezoelectric actuator, acceleration sensor, viscoelastic damping, and PID active controller. Based on the AVS-VI, the generalized vibration transmissibility determined by the nonlinear output frequency response functions and the energy absorption rate is applied to analyze the isolation performance of the whole-spacecraft system with AVS-VI. The AVS-VI can conduct adaptive vibration suppression with variable stiffness to the whole-spacecraft system, and the analysis results indicate that the AVS-VI is effective in reducing the extravagant vibration of the whole-spacecraft system, where the vibration isolation is decreased up to above 65% under different acceleration excitations. Finally, different parameters of AVS-VI are considered to optimize the whole-spacecraft system based on the generalized vibration transmissibility and the energy absorption rate.

Mathematical Modeling and Experimental Evaluation of an Air Spring–Air Damper Dynamic Vibration Absorber

Nowadays, vibration control is one of the limitless and major operating parameters in science and technology. The most promising and adaptive dynamic vibration absorber (DVA) with an air spring–air damper assembly is designed with a facility to change the spring rate and damping in the system to control the vibration. To optimize and effectively controlling the resonant amplitude ratio efficiently, a Maxwell-type air damper mathematical model is formulated for an SDOF vibrating system subjected to sinusoidal base excitation for better performance of DVA. Insight into the physics of such systems was carried out by mathematical modeling, design, and development of an air spring–air damper system for the SDOF vibrating system. Experimental investigation of an air spring–air damper for the primary mass displacement amplitude to optimize and effectively control the vibration. It will provide a compact and right platform for DVA among the current potential market and provide the major attention of the control community as a platform for the development of low-frequency nonlinear devices.

Adaptive neural torsional vibration suppression of the rolling mill main drive system subject to state and input constraints with sensor errors

Torsional vibration often occurs in rolling mill drive system, which seriously affects the product quality accuracy and the service life of transmission equipment. This paper studies the adaptive neural torsional vibration suppression control problem for the rolling mill main drive system with state and input constraints subject to unknown measurement sensitivities. Firstly, considering the nonlinear friction between the work roll and strip, nonlinear damping at the motor and the load and unknown uncertainties on system parameters, a new torsional vibration model of the main drive system of rolling mill is established. Then, by selecting the proper asymmetric tangent barrier Lyapunov function, the motor torque control law is proposed based on backstepping algorithm. The adaptive neural networks are introduced to solve the unknown uncertainties and the unknown measurement errors and a continuous differentiable Gaussian error function is employed to deal with actuator saturation. It is strictly proved that the designed main drive torsional vibration system is stable and the performances of the transformed states are preserved. Finally, simulation shows the validity and the advantages of the proposed algorithm.

Adaptive vibration control for flexible satellite with output constraint and unknown control direction

The focus of this study is the output constraint and unknown control direction problem in flexible satellites. The satellite investigated here is composed of two symmetrical flexible solar panels and a centrebody. The system is described as a distributed parameter system modelled as partial differential equations (PDEs) due to the elastic displacements it contains. Furthermore, to make the actuator more stable, barrier Lyapunov function (BLF) is used to realize the output constraint on the centrebody. A Nussbaum function is introduced to establish a control scheme that stabilizes the system with unknown control direction, where all the signals of the closed-loop system can be proved to be uniformly bounded. A radial basis function neural network is employed to approximate the uncertain disturbance acting on the centrebody. The proposed control laws are validated by a series of simulations.

Design of Variable Auxiliary Noise Influence Ratio for Adaptive Active Vibration Control

Active vibration control (AVC) is an effective way to reduce low-frequency vibration. Accurate secondary path modeling (SPM) is crucial for the implementation of AVC system based on filtered-x least mean square (FXLMS) algorithm. The FXLMS algorithm with online SPM comprises two filters, i.e., an active control filter and an online SPM filter. Mutual interference between them is the key factor that restricts the performance of AVC system with online SPM. This paper designs a novel approach based on variable auxiliary noise influence (ANI) ratio to measure the contrastive relationship of convergence status between the active control filter and the online SPM filter. Based on the proposed variable ANI ratio, the proportion of auxiliary noise component in residual vibration is scheduled. Furthermore, a variable step-size strategy is derived to realize fast and stable online SPM. Comparative simulations with the competing methods are carried out in the case of secondary path sudden change and broadband vibration control. The simulation results indicate that the proposed method gives better performance than the other competing methods.

Disturbance Observer-Based Active Vibration Suppression and Attitude Control for Flexible Spacecraft

In this article, active vibration suppression and attitude control for flexible spacecraft under model uncertainty and external disturbance are investigated. First, an adaptive disturbance observer (ADO) and flexible vibration observer (FVO) are proposed to estimate the lumped uncertainty and flexible vibration. It is shown that the proposed ADO is nonoverestimated and the first derivative upper bound of disturbance is unknown. Then, based on the proposed observers, a novel controller is designed to suppress flexible vibration and realize attitude control. The remarkable feature of the designed algorithm is that flexible vibration is suppressed and attitude tracking is guaranteed simultaneously without intelligent materials which are used to suppress flexible vibration in the previous work. In addition, high-precision attitude control can be achieved. The rigorous proof of closed-loop system stability is presented using Lyapunov techniques. Finally, numerical simulations are given to illustrate the efficiency of the proposed algorithm.

Adaptive feedforward vibration compensation control strategy of bearingless induction motor

In order to solve the unbalanced vibration problem of bearingless induction motor caused by the rotor mass eccentricity, an adaptive feedforward vibration compensation control strategy is researched. Firstly, the inverse dynamic decoupling control me

Dead Zone Compensation and Adaptive Vibration Control of Uncertain Spatial Flexible Riser Systems

This article provides a framework of dead zone compensation and robust adaptive vibration control for uncertain spatial flexible riser systems. First, nonsymmetric dead zone nonlinearity is represented in the form of the desired control input with the addition of an extra nonlinear input error. Second, by visualizing those input errors and extrinsic disturbances as an unknown “disturbance-like” term, a new robust adaptive vibration control technology and online updating laws can be constructed for riser systems to guarantee the oscillation reduction and compensation of uncertainties and dead zone. Third, the constructed control ensures and achieves bounded Lyapunov stability in the controlled system. Ultimately, control performances are demonstrated with appropriate design parameters.

Structural design of a piezoelectric meta-structure with nonlinear electrical Bi-link networks for elastic wave control

This study reports a structural optimization work of a piezoelectric meta-structure with nonlinear electrical switched Bi-link electronic networks for adaptive wave propagation manipulation and vibration control applications. The investigated meta-structure consists in a periodic arrangement of elementary cells shaping the beam substructure, each of these comprising two piezoelectric elements with connected electrical terminals through semi-passive nonlinear electrical interface, which therefore forms the so-called Bi-link electrical connection. In order to optimize the investigated structure for wave propagation control, the effects of adjusting the geometric/material parameters and locations of the two piezoelectric elements in one periodic cell are analyzed and summarized in detail. Four kinds of structural optimization methods including eighteen structural optimization sub-methods for the open circuit condition and the SSDI Bi-link condition are concluded and discussed in this research. Results show that the performance of these new resonant-type band gaps can be manipulated to meet the targeted aim in terms of wave propagation characteristics in different frequency domains by proper tuning of the investigated parameters.

Flexible satellite control via fixed-time prescribed performance control and fully adaptive component synthesis vibration suppression

In this work, the problems of active vibration suppression and high accuracy attitude control for a flexible satellite with piezoelectric actuators are studied. Firstly, the attitude error dynamic equation is developed. By utilizing a novel hyperbolic cosecant function and the error transformation equation, the attitude errors can be transferred into new prescribed performance state variables. In order to further ensure better convergence of the new variables, a fixed-time sliding mode control is proposed. Subsequently, a novel fully adaptive component synthesis vibration suppression method is presented to realize vibration suppression during the attitude maneuver by utilizing piezoelectric actuators. Stability analysis of the proposed prescribed performance control is given. Finally, abundant numerical simulation results demonstrate the excellent performances of the proposed control scheme.

Study on adaptive torsional vibration suppression methods for helicopter/turboshaft engine system with variable rotor speed

AbstractIn order to solve the problem that the low‐order torsional model of the integrated helicopter/turboshaft engine system varies significantly under variable rotor speed, research on adaptive torsional vibration suppression methods is conducted. Meanwhile, two adaptive torsional vibration suppression methods, respectively based on fast Fourier transform (FFT) and the least mean square (LMS), are proposed to suppress the low‐order torsional vibration mixing in power turbine speed. Moreover, these two torsional vibration suppression methods are compared in real‐time performance, suppression effect and robustness of performance. The simulation results show that when and only when the designed frequency of the notch filter is away from the low‐order torsional model, the suppression effect of adaptive torsional vibration filter based on FFT is better than that of constant‐coefficient notch filter, but the real‐time performance is worse. On the contrary, no matter how the low‐order torsional model varies, the adaptive filters based on LMS can suppress the low‐order torsion vibration by more than 82.0% and have more superior real‐time and robustness performance, which can overcome torsional vibration instability of turboshaft engine control system under variable rotor speed effectively with more remarkable adaptive ability.

Adaptive semi-active control of a beam structure subjected to a moving load traversing with time-varying velocity

A novel method for adaptive semi-active vibration control of structures subjected to a moving load is studied. The velocity of the load is assumed to be time-varying. The controller consists of an internal model of the moving load, which is being frequently updated to accommodate changes in the load's velocity. The control method relies on a near-optimal switching control law that is based on the solution to the algebraic Lyapunov equation. The infinite-horizon formulation of the control problem enables us to use efficient numerical algorithms for adaptive recomputing of the control signal. The asymptotic stability of the closed-loop system and performance improvement in comparison to the passive method are analysed and formally proven. The controller is tested by means of numerical experiments involving a flexible beam equipped with a set of semi-active viscous dampers. We investigate three distinct simulation scenarios, which correspond to highly non-uniform motions of the load that consist of acceleration, deceleration and temporary halt phases. The results of the simulations are compared to passive and optimal open-loop strategies.

Multiple model hybrid adaptive vibration control for flexible cantilever beam with varying load

To solve the vibration suppression problem for a piezoelectric flexible cantilever beam with varying load, this study proposes a new type of multiple model hybrid adaptive vibration control method with a new multiple model switching cost index function. It employs a pre-filter consisting of secondary path and positive feedback path model to eliminate the positive feedback between the secondary actuator and reference sensor. By constructing a piezoelectric flexible cantilever beam as the controlled plant, we constructed a real-time control verification experiment platform based on a real-time MATLAB xPC target. We did a real-time control experiment comparison for vibration suppression of single-frequency, narrowband, and broadband disturbances. Experimental results show that the proposed multiple model hybrid adaptive vibration control algorithm is feasible and has good vibration suppression performance with rapid convergence speed.

Adaptive inverse backlash boundary vibration control design for an Euler–Bernoulli beam system

In this paper, we address the vibration suppression problem of an Euler–Bernoulli beam structure suffering from the input backlash nonlinearity and the unknown disturbance. Considering the nonlinearity and discontinuity of the backlash with the uncertain parameter, an adaptive inverse backlash dynamics is proposed to handle the nonlinear characteristic and correct the mismatch of the backlash parameter. Further, an adaptive vibration control law is developed to improve the system performance via combining with the proposed inverse backlash dynamics. Meanwhile, a disturbance observer is designed to reject the external boundary disturbance, and we bring a logarithmic barrier function in control design to ensure the end-point displacement of this system be constrained in the desired limitation. At last, we analyze the stability of this flexible system and the effectiveness of the proposed control method with simulation experiments.

Adaptive modal vibration control for smart flexible beam with two piezoelectric actuators by multivariable self-tuning control

It has been popular for decades that the vibrations of space structures are suppressed with smart actuators. However, the higher mode vibrations are often motivated when a control strategy is applied to attenuate the vibration for the smart structures. Moreover, if the multi-mode vibration of a smart structure is suppressed with multi-actuators, a proper multivariable control law will be adopted to solve the coupling problem caused by the multi-actuators of the smart structure. Therefore, in the paper, a decoupling technique for two modal vibrations of a smart flexible beam with two piezoelectric patches is adopted by adaptive control. The proposed control law is designed with a multivariable minimum variance self-tuning control. Considering the first two orders of modal vibrations, two piezoelectric patches are configured on the flexible beam according to the strain of the first two orders of modal vibrations along the longitudinal direction of the beam. A dynamical model for the flexible beam with two piezoelectric actuators is constructed by the mode superposition method. With the dynamical model, simulations are implemented to suppress the free vibration of the flexible beam. Moreover, experiments are carried out to verify the effectiveness of the multivariable minimum variance self-tuning control for vibration suppression of the flexible structure. The control results clearly show that the free vibration amplitude of the cantilevered beam with two control voltages applied to the two piezoelectric patches is less than that with one control voltage applied to the first piezoelectric actuator. Thus, multivariable minimum variance self-tuning control is a more efficient approach for suppressing multimodal vibration for a smart flexible beam with two piezoelectric actuators compared with the conventional velocity feedback control.

Adaptive Fuzzy Vertical Vibration Suppression Control of the Mechanical-Hydraulic Coupling Rolling Mill System With Input Dead-Zone and Output Constraints

This paper investigates the adaptive fuzzy vertical vibration suppression control problem for the six-high rolling mill system. Firstly, a new vibration model is established with the consideration of the coupling of mechanical and hydraulic systems and the unknown uncertainty on nonlinear rolling force. Then, the adaptive active control strategy is proposed to suppress chatter of the rolling mill under the input dead-zone and output constraints. The adaptive fuzzy logic systems are used to deal with the unknown nonlinear functions and the unknown system parameters. Based on the designed controller, the mechanical-hydraulic coupling rolling system is proven to be stable and the performance of the displacement of work roll is preserved. Finally, the simulation comparison shows the validity and the advantages of the proposed algorithm.

Barrier Function-Based Adaptive Neuro Network Sliding Mode Vibration Control for Flexible Double-Clamped Beams With Input Saturation

In this paper, a novel adaptive neuro network nonsingular fast terminal sliding mode control based on barrier Lyapunov functions is proposed for flexible double-clamped beam systems with input saturation and distributed disturbance. First, the Galerkin projection method is employed to reduce the partial differential dynamic equations of the beam into ordinary differential equations. Second, a novel barrier Lyapunov function is employed to design a nonsingular fast terminal sliding mode controller that ensures the closed-loop system is stable with state constraints. In addition, an auxiliary system is proposed to guarantee the stability of the beam system subject to input saturation. Third, an adaptive neural network is used to deal with the possible unknown part of the model parameters. It is proved that the proposed control law can handle input saturation and state constraints simultaneously without knowing the model exactly. Finally, numerical simulations illustrate the effectiveness of the proposed control laws.

Adaptive neural network vibration control of a flexible aircraft wing system with input signal quantization

In this paper, we study a boundary vibration control problem for a flexible aircraft wing system with input signal quantization and unknown input disturbances. The wing system is a distributed parameter system with coupled bending and torsional deformations. The dynamic behavior of the flexible wing is represented by partial differential equations (PDEs) and several ordinary differential equations (ODEs). The control methods that already exist for similar PDE systems, which is suitable for general situations, will reduce the control precision of the system after control input quantization and may generate stability losses in serious cases. To suppress the elastic deformation of the wing after input quantization, an adaptive quantitative control scheme based on a radial basis function (RBF) neural network is proposed. The new controller can restrain the wing vibration deformation successfully and the stability of the closed-loop system is verified via the Lyapunov's direct method. Finally, numerical simulations illustrate the effectiveness and superiority of the control system.