Parametric vibration stability and active control of nonlinear beams

The vibration stability and the active control of the parametrically excited nonlinear beam structures are studied by using the piezoelectric material. The velocity feedback control algorithm is used to obtain the active damping. The cubic aonlineax equation of motion with damping is established by employing Hamilton＇s principle. The multiple-scale method is used to solve the equation of motion, and the stable region is obtained. The effects of the control gain and the amplitude of the external force on the stable region and the amplitude-frequency curve axe analyzed numerically. From the numerical results, it is seen that, with the increase in the feedback control gain, the axial force, to which the structure can be subjected, is increased, and in a certain scope, the structural active damping ratio is also increased. With the increase in the control gain, the response amplitude decreases gradually, but the required control voltage exists a peak value.

ACTIVE STRUCTURAL ACOUSTIC CONTROL IN ENCLOSURE USING RADIATION MODES

The problem of active structural acoustic control in an enclosure using radiation mode is investigated. The response of the coupled enclosure is derived in terms of radiation modes. The potential energy in the enclosure can be decomposed into independent parts and the radiation modes contribute to potential energy independently. The control strategy for minimizing first G radiation modes with large radiation efficiency is proposed, and the optimal model of control forces is presented. Finally, a numerical simulation for minimizing sound transmission into a rectangular enclosure using the proposed method is conducted. Simulation results indicate that one control force can control one radiation mode and controlling the first four-order radiation modes with four control forces can achieve significant potential energy reduction at the low frequency range.

Modeling and optimal vibration control of conical shell with piezoelectric actuators

In this paper numerical simulations of active vibration control for conical shell structure with dis-tributed piezoelectric actuators is presented.The dynamic equations of conical shell structure are derivedusing the finite element model (FEM) based on Mindlin's plate theory.The results of modal calculationswith FEM model are accurate enough for engineering applications in comparison with experiment results.The Electromechanical influence of distributed piezoelectric actuators is treated as a boundary conditionfor estimating the control force.The independent modal space control (IMSC) method is adopted and theoptimal linear quadratic state feedback control is implemented so that the best control performance withthe least control cost can be achieved.Optimal control effects are compared with controlled responses withother non-optimal control parameters.Numerical simulation results are given to demonstrate the effective-ness of the control scheme.

Active Flow Control of a Low Reynolds Number S809 Wind Turbine Blade Model under Dynamic Pitching Maneuvers

A low Reynolds number wind turbine blade model based on the S809 airfoil was tested in a subsonic wind tunnel to study the structural vibration of the blade under dynamic pitching maneuvers. Piezoelectric-based synthetic jet actuators were embedded inside the blade and activated with a synthetic jet momentum coefficient, Cμ of 2.30 × 10-3. Structural vibration was quantified for a range of unsteady angles undergoing “pitch up and down” and “sinusoidal pitch” maneuvers at a Reynolds number of 5.28 × 104. The blade tip deflection amplitude and frequency were acquired utilizing a pair of strain gauges mounted at the root of the model. Using active flow control vibration reduction was more effective during the pitch up portion of the blade motion cycle compared to the pitch down portion. This effect is due to dynamic stall, where a leading edge vortex is shed during the pitch up motion and contributes to higher lift compared to static angles of attack and lower lift when the blade is pitched down. Dynamic stall was measured with phase-locked stereoscopic particle image velocimetry (SPIV), where global mean flow measurements reveal a shift in location and reduction in the size of a recirculating flow structure near the suction surface of the blade during the pitch up motion compared to the pitch down.

LINEAR ACTIVE STRUCTURES AND MODES (Ⅱ) —DISCRETE SYSTEMS AND BEAMS

The basic concepts about the active structures and some attributes of the modes were presented in paper “Liner Active Structures and Modes]( I) ". The characteristics of the active discrete systems and active beams were discussed, especially, the stability of the active structures and the orthogonality of the eigenvectors. The notes about modes were portrayed by a model of a seven-storeyed building with sensors and actuators. The concept of the adjoint active structure was extended from the discrete systems to the beams that were the representations of the continuous structures. Two types of beams with different placements of the measuring and actuating systems were discussed in detail. One is the beam with the discrete sensors and actuators, and the other is the beam with distributed sensor and actuator function. The orthogonality conditions were derived with the modal shapes of the active beam and its adjoint active beam. An example shows that the variation of eigenvalues with feedback amplitude for the homo-configuration and non-homo-configuration active structures.

Decentralized Sliding Mode Control for a Spacecraft Flexible Appendage Based on Finite Element Method

This paper is devoted to study the application of the decentralized sliding mode control method, which is used to reduce the vibration of large spacecraft flexible appendage. In the process of control design, the sliding surface of sliding mode control is determined by minimizing the optimal cost function, and the controller is the saturation controller. The controlled structure is subject to arbitrary, unmeasurable and uncertainty disturbance forces and initial displacement. The decentralized control method and the centralized control method are used to control vibration of the structure respectively. When the system is subjected to the initial displacement or external disturbance, the computer simulation shows that both of these control methods perform effectively, but the number of Riccati equation of the decentralized method is far smaller than that of centralized control method, especially in a large system.

Active control of an aircraft tail subject to harmonic excitation

Vibration of structures is often an undesirable phenomena and should be avoided or controlled. There are two techniques to control the vibration of a system, that is, active and passive control techniques. In this paper, a negative feedback velocity is applied to a dynamical system, which is represented by two coupled second order nonlinear differential equations having both quadratic and cubic nonlinearties. The system describes the vibration of an aircraft tail. The system is subjected to multi-external excitation forces. The method of multiple time scale perturbation is applied to solve the nonlinear differential equations and obtain approximate solutions up to third order of accuracy. The stability of the system is investigated applying frequency response equations. The effects of the different parameters are studied numerically. Various resonance cases are investigated. A comparison is made with the available published work.

ACTIVE CONTROL OF FLEXIBLE BEAMS SUBJECTED TO MULTI-DISTURBANCE USING ONE CONTROLLER

The active control of vibration for a beam subjected to multi-disturbances is investigated based on wave propagating suppression. In this control system, there are the same numbers of the sensors, the signal inputting to the controller and the disturbances, but there is only one controller. It is a local control system, the system parameters depend only on the characteristics of the structure bounded by the sensors and the controller, and we need not take into account. the boundary conditions and the properties of structures outside of this held. The system is efficient when a structure vibrates in middle and high frequency regions. Some control design rules are developed from the calculation results.

LINEAR ACTIVE STRUCTURES AND MODES (Ⅰ) —BASIC CONCEPTS AND PROPERTIES

Some basic concepts about the active structures were firstly explained, and the main subjects to study in the field of active structure dynamics were synthesized. For the linear active structures, the annotations on the modes were done in detail. The physical meanings of the right and left eigenvectors were explained. The right eigenvectors are the modal shapes and the modal responses of an active structure depend on the left ones. The adjoint structure of an active structure was defined and the reciprocity theorem was interpreted. For two active structures, which are adjoint to each other and with the reciprocal gain-matrices, the right and left eigenvector are reciprocal. The relationship between an active structure and the corresponding passive structure is expressed with the transfer functions, which is employed to resolve the estimation problems.

Vibration and stability of an aircraft tail under simultaneous primary-combined and internal resonance

This paper adds a negative velocity feedback to the dynamical system of twin-tail aircraft to suppress the vibration.The system is represented by two coupled second-order nonlinear differential equations having both quadratic and cubic nonlinearities.The system describes the vibration of an aircraft tail subjected to both multi-harmonic and multi-tuned excitations.The method of multiple time scale perturbation is adopted to solve the nonlinear differential equations and obtain approximate solutions up to the third order approximations.The stability of the proposed analytic solution near the simultaneous primary,combined and internal resonance is studied and its conditions are determined.The effect of different parameters on the steady state response of the vibrating system is studied and discussed by using frequency response equations.Some different resonance cases are investigated numerically.

Research on semi-active control method of a building structure based on non-smooth control

This study investigates the effectiveness of the non-smooth semi-active control algorithm on suppressing the vibration performance of a building structure subjected to seismic waves. According to the Lyapunov stability theory, it has bene proven that the non-smooth semi-active control algorithm can achieve a finite-time stability of the vibration relative to the isolation layer of a building structure. Through numerical simulation of two buildings with different parameters subjected to the input of a seismic wave, the vibration conditions of passive control, LQR semi-active control and non-smooth semiactive control are compared and analyzed. The simulation results show that the non-smooth semi-active control algorithm has a better robustness and effectiveness in restraining the impact of earthquakes on the structure.

Finite element modeling and feedback control of piezoelectric smart structures

Presents the general formula derived with a smart beam structure bonded with piezoelectric material using the piezoelectricity theory, elastic mechanism and Hamilton principle for electromechanically coupled piezoelectric finite element and dynamic equations, the second order dynamic model built, and the expression of state space, and the analysis of conventional speed and position feedback and the design of optimum feedback controller for output, the finite element models built for a piezoelectric cantilever beam, and the feedback controller designed eventually, and concludes with simulation results that the vibration suppression obtained is very satisfactory and the algorithms proposed are very useful.

Researches on active structural acoustic control by radiation modes

Based on the radiation modes, an active control strategy is presented for sound radiation from elastic structures with an example of simply supported rectangular panel. The physical characteristics and mathematical meaning of the radiation modes are analyzed. The radiation efficiency of radiation mode falls off very rapidly with the increase of modes order at low frequency. A new control strategy is developed in which by canceling the adjoint coef- ficient of the first k radiation modes, the sound powers of the first k radiation modes is zero theoratically. The numerical calculation is made by using point force actuators as control forces.

A hybrid multi-degree-of-freedom vibration isolation platform for spacecrafts by the linear active disturbance rejection control

The hybrid vibration isolation, which takes advantages of both the passive and active approaches, has been an important solution for space missions. The objective of this paper is to design a vibration isolation platform for payloads on spacecrafts with the robust, wide bandwidth, and multi-degree-of-freedom(MDOF). The proposed solution is based on a parallel mechanism with six voice-coil motors(VCMs) as the actuators. The linear active disturbance resistance control(LADRC) algorithm is used for the active control. Numerical simulation results show that the vibration isolation platform performs effectively over a wide bandwidth, and the resonance introduced by the passive isolation is eliminated. The system robustness to the uncertainties of the structure is also verified by simulation.

VIBRATION CONTROL OF A SPACE TRUSS STRUCTURE WITH A PIEZOELECTRIC ACTIVE MEMBER

Active vibration control is an effective way of increasing robustness of the design to meet the stringent accuracy requirements for space structures. This paper presents the results of active damping realized by a piezoelectric active member to control the vibration of a four-bay four-longern aluminum truss structure with cantilever boundary. The active member, which utilizes a piezoelectric actuating unit and an integrated load cell, is designed for vibration control of the space truss structures. Active damping control is realized using direct velocity feedback around the active member. The placement of the active member as one of the most important factor of affecting the control system performance, is also investigated by modal dissipation energy ratio as indicator. The active damping effectiveness is evaluated by comparing the closed-loop response with the open loop response.

Anti-Dead-Zone Integral Sliding Control and Active Vibration Suppression of a Free-floating Space Robot with Elastic Base and Flexible Links

Under the conditions of joint torque output dead-zone and external disturbance,the trajectory tracking and vibration suppression for a free-floating space robot(FFSR)system with elastic base and flexible links were discussed.First,using the Lagrange equation of the second kind,the dynamic model of the system was derived.Second,utilizing singular perturbation theory,a slow subsystem describing the rigid motion and a fast subsystem corresponding to flexible vibration were obtained.For the slow subsystem,when the width of deadzone is uncertain,a dead-zone pre-compensator was designed to eliminate the impact of joint torque output dead-zone,and an integral sliding mode neural network control was proposed.The integral sliding mode term can reduce the steady state error.For the fast subsystem,an optimal linear quadratic regulator(LQR)controller was adopted to damp out the vibration of the flexible links and elastic base simultaneously.Finally,computer simulations show the effectiveness of the compound control method.

H∞ Control for Externally Excited Building Structures with Active Mass Damper under Actuator Saturation

This paper investigates the application of active mass dampers to mitigate the vibrations of building structures subjected to unknown external excitations under controller saturation conditions. By utilizing an H∞ control strategy, the optimal state feedback controller is derived by solving the linear matrix inequality problem for controller saturation. Case studies show that the proposed controller is capable of stabilizing the closed-loop system with good control performance and effectively suppressing vibrations in building structures under unknown external excitation. When compared to controllers that do not consider saturation, the proposed controller requires lower gain and results in reduced energy consumption. The research findings provide valuable insights for addressing real-world building structure control problems, contributing to both theoretical significance and practical applications.

Active Vibration Control of Macroscopically Smart Mechanisms

This paper presents an investigation on the active vibration control of flexible linkage mechanisms featuring piezoceramic actuators and strain gauge sensors. The dynamic equation of the macroscopically smart mechanism is decoupled by means of the complex mode theory. The state-space expression of the controlled system is developed, which includes the system noise and the observation noise. Moreover, a discrete linear quadratic Gaussian （LQG） state feedback controller and a discrete Kalman filter are designed separately. Finally, the proposed method is applied to the on-line vibration control of a macroscopically smart mechanism. The experimental results reveal that the strain amplitude of the flexible link ig suppressed by 80% and the dynamic performance of mechanism has been ameliorated significantly.

Research of an Active Tunable Vibration Absorber for Helicopter Vibration Control

Significant structural vibration is an undesirable characteristic in helicopter flight that leads to structural fatigue, poor ride quality for passengers and high acoustic signature. Previous Individual Blade Control (IBC) techniques to reduce these effects have been hindered by electromechanical limitations of piezoelectric actuators. The Smart Spring is an active tunable vibration absorber using IBC approach to adaptively alter the 'structural impedance' at the blade root. In this paper, a mathematical model was developed to predict the response under harmonic excitations. An adaptive notch algorithm was designed and implemented on a TMS320c40 DSP platform. Reference signal synthesis techniques were used to automatically track the shifts in the fundamental vibratory frequency due to variations in flight conditions. Closed-loop tests performed on the proof-of-concept hardware achieved significant vibration suppression at harmonic peaks as well as the broadband reduction in vibration. The investigation verified the capability of the Smart Spring to suppress multiple harmonic components in blade vibration through active impedance control.

Hybrid Passive/Active Vibration Control of a Loosely Connected Spacecraft System

In this paper,a hybrid passive/active vibration(HPAV)controller of a loosely connected spacecraft consisting of a servicing satellite,a target and an X-shape structure isolator is first proposed to suppress vibrations of the system when subjected to the impulsive external excitations during the on-orbit missions.The passive dynamic response of the combined system can be adjusted appropriately to achieve the desired vibration isolation performance by tuning the structural parameters of the bio-inspired X-shape structure.Moreover,the adaptive control design through dynamic scaling technique is selected as the active component to maintain high vibration isolation performance in the presence of parameter uncertainties such as mass of the satellite platform,the damping and rotation friction coefficients of the X-shape structure.Compared with the pure passive system and the traditional spring-mass-damper(SMD)isolator,the HPAV strategy witnesses lower transmissibility,smaller vibration amplitude and higher convergence rate when subjected to the post-capture impact.Numerical simulations demonstrate the feasibility and validity of the proposed hybrid control scheme in suppressing vibrations of the free-floating spacecraft.