Negative Velocity Feedback Research Articles

Dynamic analysis and active control of smart doubly curved FGM panels

In this paper, active control and dynamic analysis of shallow doubly curved functionally graded material (FGM) panels integrated with sensor/actuator piezoelectric layers are presented, analytically. Properties of the FGM panel are dictated using a simple power law model across the thickness. Based on the modified Sander’s shell theory combined with first order shear deformation theory, total potential energy of the system is derived. Five mechanical equilibrium equations and two electrical equations are established as the governing equations. The classical negative velocity feedback controller rule is implemented to suppress the vibration response of the panel. For both the active and passive cases, established equations are reduced into new five equations in terms of displacements and rotations. Employing the combined analytical Fourier–Laplace transformation, consistent with the panels with movable simply-supported edges, an accurate closed-form solution is resulted for response of the panel in both active and passive cases in real time domain.

Thermal vibration of magnetostrictive functionally graded material shells

Abstract The functionally graded material (FGM) shell with mounted magnetostrictive layer under thermal vibration was studied by using the generalized differential qradrature (GDQ) method. The FGM shell with/without negative velocity feedback of magnetostrictive position, with different power law index effects subjected to two edges lamped condition was analyzed. With velocity feedback and with suitable control gain value can reduce the amplitudes of displacement and shear stress into a smaller value. The magnetostrictive FGM shell is stable versus the Terfenol-D thickness for all values of FGM power law index. The magnetostrictive FGM shell can stand against the higher heating temperature of environment with some values of power law index.

Active control of geometrically non-linear transient response of sandwich beams with a flexible core using piezoelectric patches

Active control of geometrically non-linear dynamic response of sandwich beams impacted by blast pulses with integrated piezoelectric sensor/actuator patches is addressed. The analysis is based on a higher-order structural model using the first-order shear deformation theory for the face sheets and piezoelectric patches, and the extended high-order sandwich theory for the flexible core. Geometrical non-linearity is considered in the von Karman sense. Hamilton’s principle is employed to introduce a novel smart sandwich beam element which has eighteen physical nodes with mechanical and electric potential degrees of freedom plus two electric nodes for the electric potentials of the electroded surfaces. The presented smart sandwich beam element is used to develop finite element equations of motion. Constant negative velocity feedback algorithm is adapted in the active control. The solution of non-linear equations is sought by Newmark and the modified Newton–Raphson methods for dynamic analysis. Furthermore, the model behavior in free vibrations is assessed by using a direct iteration technique suitably modified for non-linear eigenvalue problems based on the QZ algorithm. A detailed analysis of the influence of geometrical non-linearity, core flexibility and piezoelectric patch arrangement on the dynamic response, frequency and loss factor of active sandwich beams is carried out.

Active structural vibration control: Robust to temperature variations

d-form augmented piezoelectric constitutive equations which take into account temperature dependence of piezoelectric strain coefficient (d31) and permittivity (∈33), are converted into e-form. Using e-form constitutive equations, a finite element model of a smart two dimensional plate instrumented with piezoelectric patches is derived. Equations of motion are derived using Hamilton's variational principle. Coupled equations of motion are uncoupled using modal analysis. Modal state vectors are estimated using the Kalman observer. The first mode of smart cantilevered plate is actively controlled using negative first modal velocity feedback at various temperatures. Total control effort required to do so is calculated using the electro-mechanical impedance method. The temperature dependence of sensor voltage, control voltage, control effort and Kalman observer equations is shown analytically. Simulation results are presented using MATLAB. Variations in (i) peak sensor voltage, (ii) actual and estimated first modal velocities, (iii) peak control voltage, (iv) total control effort and (v) settling time with respect to temperature are presented. Active vibration control performance is not maintained at temperature away from reference temperature when the temperature dependence of piezoelectric stress coefficient ‘e31’ and permittivity ‘∈33’ is not included in piezoelectric constitutive equations. Active control of vibrations becomes robust to temperature variations when the temperature dependence of ‘e31’ and ‘∈33’ is included in piezoelectric constitutive equations.

Improvement of the electrohydraulic power controller of an arc furnace in foundry

Experimental data are used to develop a model for the structure of an adaptive electrohydraulic power controller for an arc furnace, and the introduction of a negative electrode velocity feedback into the electrohydraulic drive of electrode motion is shown to be useful. Model investigations of the operation of the proposed power controller under various conditions are performed, and recommendations are made to choose the parameters in designing power controllers.

Nonlinear vibration and active control of functionally graded beams with piezoelectric sensors and actuators

Employing higher order shear deformation theory, geometric nonlinear theory, and Hamilton’s principle, a set of nonlinear governing equations for the functionally graded beams with surface-bonded piezoelectric layers is derived. Then, the negative velocity feedback algorithm coupling the direct and inverse piezoelectric effect is used to control the piezoelectric functionally graded beams actively. Using the finite difference method and Newmark method synthetically, the numerical solutions for the nonlinear dynamic equations of functionally graded beams with piezoelectric patches are obtained iteratively. In the numerical examples, the effects of the volume fraction exponent on the nonlinear dynamic responses and amplitude–frequency curves are investigated, and the active control responses of the functionally graded beams with piezoelectric layers under different control gains and volume fraction exponents are analyzed. Some meaningful solutions have been presented.

Vibration Control of a Cylindrical Shell Structure Using Macro Fiber Composite Actuators

We studied the vibration suppression of an end-capped cylindrical shell structure with surface bonded macro fiber composite actuators. The dynamic characteristics of the cylindrical shell structure were first analyzed, and then a negative velocity feedback algorithm was applied to suppress the structural vibration at resonance and nonresonance vibration frequencies. The modal mass and stiffness matrix of the smart cylindrical shell structure were extracted for the controller design. An active controller was designed to suppress vibration of the smart structure, and the control performance was evaluated in resonance and nonresonance regimes. It was found that structural vibration was reduced by adopting a proper negative velocity feedback control algorithm in both resonance and nonresonance regimes.

Active vibration control of a smart plate using a piezoelectric sensor–actuator pair atelevated temperatures

A new scheme for active structural vibration control using piezoelectric patchesat elevated temperatures is analytically derived and experimentally verified. Acontrol law is derived using augmented piezoelectric constitutive equationswhich include the temperature dependence of piezoelectric stress coefficient(e31) and permittivity . Since the temperature dependence of ‘e31’ and ‘’ is not analytically known, their experimental values measured at elevatedtemperatures are used. Using augmented constitutive equations, a finite elementmodel of a smart two-dimensional isotropic plate instrumented with a collocatedpiezoelectric sensor–actuator pair is derived. A control law for active vibrationcontrol of the first mode of the smart cantilevered plate is derived using negativevelocity feedback. Active vibration control of the first mode of a smart cantileveredplate is experimentally achieved at elevated temperatures ranging from 25 to75 °C under two cases: (i) using a control law which ignores the temperature dependence of ‘e31’ and ‘’ and (ii) using a control law which includes the temperature dependence of ‘e31’ and ‘’. A comparison between these two control laws shows that: (i) active vibrationcontrol (AVC) performance is not maintained at elevated temperaturesusing a control law which ignores the temperature dependence of ‘e31’ and ‘’ and (ii) AVC performance is maintained at elevated temperatures whenwe use a control law which includes the temperature dependence of ‘e31’ and ‘’.

Nonlinear Dynamic Response and Active Control of Piezoelastic Laminated Shallow Spherical Shells with Damage

Based on Talreja’s damage model with tensor valued internal state variables and geometric nonlinear theory, the constitutive relations for a moderately thick shallow spherical shell with damage are derived. The distribution of electric potential along the thickness direction in the piezoelectric layer is simulated by a sinusoidal function, and accordingly the dynamic analytical model for the cross-ply laminated moderately thick piezoelectric shallow spherical shell is established. Using the negative velocity feedback control algorithm, an analytical model for active vibration control of the piezoelectric laminated moderately thick piezoelectric shallow spherical shell is built when the damage effect is considered. And the solutions to the whole problem are obtained with synthetical utilization of the orthogonal collocation point method and the Newark method. In numerical examples, the effects of damage, piezoelectric effect, and the structure’s geometrical parameters on the dynamic response and vibration control of the piezoelastic laminated shallow spherical shells with damage are investigated.

Design of a piezostack-based inertial actuator and application to vibration control: experimental investigation

In this work, an inertial actuator featuring a piezoceramic stack is proposed and applied to vibration control of a flexible beam structure. After identifying the field-dependent displacement of the piezoceramic stack, an inertial actuator consisting of the stack and an inertial mass is constructed and its actuating force is evaluated experimentally with respect to the applied voltage. Subsequently, an active mount featuring the inertial actuator and a rubber element is devised and incorporated into a flexible beam structure for vibration control. A negative velocity feedback controller which does not require an accurate system model is then implemented experimentally through the digital signal processor and high-voltage amplifier. In order to demonstrate the effectiveness of the proposed control system, control responses such as beam acceleration and transmitted force are evaluated and presented in both time and frequency domains.

Active Vibration Isolation Demonstration System Using the Piezoelectric Unimorph with Mechanically Pre-stressed Substrate

In this article, a pre-stressed piezoelectric actuator made at room temperature using a mechanically pre-stressed substrate is applied as an actuator for an active vibration isolation system. The fabricated piezoelectric actuator, called PUMPS (piezoelectric unimorph with mechanically pre-stressed substrate), is a kind of unimorph actuators in which actuation stroke level is enhanced by displacement amplification mechanism that converts longitudinal piezoelectric in-plane deformation to large bending/pumping motion. Despite its much simpler fabrication process, PUMPS actuation performance is comparable to that of conventional pre-stressed piezoelectric unimorphs due to its special pre-stress level inside piezoelectric layer. In applying PUMPS as an actuator for active vibration control, multilayer stack configuration using three PUMPS actuators was adapted in order to obtain higher actuation force because unimorph actuators are displacement amplified actuators in which displacement amplification is attained with a sacrifice of the actuation force. Preliminary vibration tests were performed to check the performance of PUMPS as actuators for active vibration control in a lab environment. Two feedback control schemes, the positive position feedback and negative velocity feedback, were applied for active vibration control and about 10 dB vibration reduction was achieved near the resonant frequency region. With the promising results obtained in the preliminary vibration test, PUMPS actuators in multilayer stack configuration were used to develop an integrated active vibration isolation demonstration system. The purpose of the developed system is to demonstrate the need for vibration isolation system to remove degrading effects of jitter and improve the performance of optical payloads in satellites such as its observation and image acquisition abilities. The test results with the demonstration system show that severe blur observed in the image taken without the vibration control is reduced visibly in the image taken during the operation of the active vibration isolation system.

Active modal control simulation of vibro-acoustic response of a fluid-loaded plate

Active modal control simulation of vibro-acoustic response of a fluid-loaded plate is presented. The active modal control of the vibro-acoustic response is implemented using piezoelectric actuators/sensors. The active modal damping is added to the coupled system via negative velocity feedback. The feedback gain between the piezoelectric actuators/sensors for the modal control is obtained using the in-vacuo modal matrix and the incompressible fluid-loaded modal matrix. The modal control performance of structural vibration and acoustic radiation of a baffled plate is numerically studied. It is shown that the proposed method increases the modal damping ratio and achieves reduction in the mean square velocity and the sound power for given modes of the fluid-loaded plate.

Active Control of Geometrically Non-linear Transient Response of Smart Laminated Composite Plate Integrated with AFC Actuator and PVDF Sensor

A coupled electromechanical finite element formulation for active control of geometrically non-linear transient response of laminated composite plate is studied. First-order shear deformation theory and von Karman type non-linear strain displacements are used. The plate is discritized using eight-noded quadratic isoparametric elements with five mechanical degrees of freedom and one electrical degree of freedom per node. Newton-Raphson iterative method in association with Newmark time integration method is used to solve the non-linear finite element equilibrium equation. Negative velocity feedback control algorithm is used to control the dynamic response of the smart laminated composite plate. AFC layer poled in fiber direction acting as distributed actuator and PVDF layer poled in thickness direction acting as sensor are considered. This study involves two types of actuator sensor arrangements: (1) the substrate is sandwiched between AFC actuator and PVDF sensor, called non-collocated arrangement and (2) AFC actuator and PVDF sensor are placed on top of the substrate, called collocated arrangement. The effect of piezoelectric fiber orientation in actuator layer on vibration control for both cross-ply and angle-ply laminates are examined.

Active aeroelastic flutter analysis and vibration control of supersonic beams using thepiezoelectric actuator/sensor pairs

The active vibration control of all kinds of structures by using the piezoelectric materialhas been extensively investigated. In this paper, the active aeroelastic flutter characteristicsand vibration control of supersonic beams applying the piezoelectric material are studiedfurther. The piezoelectric materials are bonded on the top and bottom surfaces of thebeams to act as the actuator and sensor so that the active aeroelastic flutter suppressionfor the supersonic beams can be conducted. The supersonic piston theory is adopted toevaluate the aerodynamic pressure. Hamilton’s principle with the assumed modemethod is used to develop the dynamical model of the structural systems. By usingthe standard eigenvalue methodology, the solutions for the complex eigenvalueproblem are obtained. A negative velocity feedback control strategy is used toobtain active damping. The aeroelastic flutter bounds are calculated and the activeaeroelastic flutter characteristics are analyzed. The impulse responses of the structuralsystem are obtained by using the Houbolt numerical algorithm to study the activeaeroelastic vibration control. The influences of the non-dimensional aerodynamicpressure on the active flutter control are analyzed. From the numerical results it isobserved that the aeroelastic flutter characteristics of the supersonic beams canbe significantly improved and that the aeroelastic vibration amplitudes can beremarkably reduced, especially at the flutter points, by using the piezoelectricactuator/sensor pairs which can provide an active damping. Within a certain value of thefeedback control gain, with the increase of it, the flutter aerodynamic pressure(or flutter velocity) can be increased and the control results are also improved.

ACTIVE VIBRATION CONTROL OF COMPOSITE PLATE USING AFC ACTUATOR AND PVDF SENSOR

A finite element formulation for active vibration control of laminated composite plate integrated with active fiber composite (AFC) layer acting as distributed actuator and PVDF layer as sensor is presented in this paper. An eight noded quadratic isoparametric element with five mechanical degrees of freedom and one electrical degree of freedom per node of the element is considered. Newmark time integration method is used to calculate the dynamic response and negative velocity feedback control algorithm is used to control the dynamic response of the laminated composite plate. The effect of piezoelectric fiber orientation in actuator layer on the control of vibration is studied.

Driving at Resonance Point of Multi-Degree-of-Freedom System by Decentralized Control

A control method has been developed to always excite a multi-degree-of-freedom system efficiently at a resonance frequency. When an excitation point corresponds to a vibration detection point in the multi-degree-of-freedom system, a phase lag at a resonance frequency and a phase lead at an anti-resonance frequency alternately appear in the vibration characteristics, and the phase lag becomes 90° at all the resonance frequencies. Therefore, if a controller that has a phase lag of 90° and a constant gain in a wide frequency range is used, self-excited vibration is generated at all the resonance frequencies. The self-excited vibration controller can be expressed as the sum of the positive velocity feedback control with a high gain in a high frequency domain and the integral control of the displacement with a high gain in a low frequency domain. A local feedback controller for each actuator consists of a self-excited vibration controller, a saturation element that limits excitation force, and a negative velocity feedback controller that provides damping. A driving at a resonance point system using many actuators with local feedback control, that is, decentralized control, is excellent in its adaptability to the environment, in its extendibility, and in its fault tolerance. In addition, the self-excited vibration mode can be freely switched on by changing the frequency of the sine wave that causes the self-excited vibration.

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

Finite element modelling and experimental study on static deflection and vibration of piezoelectric composite plates

A finite-element model based on the First-Order Shear Deformation Theory is developed for the static flexural shape and vibration control of a glass fibre/polyester composite plate bonded piezoelectric actuator and sensor patches. The piezoelectric's mass and stiffness are taken into account in the present model. A simple negative velocity feedback control algorithm coupling direct and converse piezoelectric effects are used to actively control the dynamic response of an integrated structure through a closed control loop. The static analysis and active vibration suppression control of a cantilever composite plate are performed as a numerical example to validate the proposed model. The Newmark-\(\beta\) method is used in the numerical simulation to calculate the dynamic response of the piezolaminated composite plate. The numerical results are presented with discussion and in good agreement with carried out experiments.

Response and control of functionally graded laminated piezoelectric shells under thermal shock and moving loadings

Abstract Based on the first-order shear deformation theory (FSDT), approximate solution for FG (functionally graded) laminated piezoelectric cylindrical shells under thermal shock and moving mechanical loads is given utilizing Hamilton’s principle. The thin piezoelectric layers embedded on inner and outer surfaces of the functionally graded layer are acted as distributed sensor and actuator to control dynamic characteristics of the FG laminated cylindrical shells. Here, the modal analysis technique and Newmark’s integration method are used to calculate the dynamic response of FG laminated cylindrical shells. Constant-gain negative velocity feedback approach is used for active vibration control. The active vibration control to a single moving concentrated loading, thermal shock loading and a continuous stream of moving concentrated loadings is, respectively, investigated. Results indicate that the control gain and velocity of moving loadings have significant effects on the dynamic response and resonance of the system.

Static behavior and vibration control of piezoelectric cantilever composite plates and comparison with experiments

A finite element (FE) model based on the First-Order Shear Deformation Theory (FSDT) is developed for the static flexural shape and vibration control of a glass fibre/polyester composite plate bonded with piezoelectric actuator and sensor patches. The piezoelectric’s mass and stiffness are taken into account in the present model. A simple negative velocity feedback control algorithm coupling direct and converse piezoelectric effects are used to actively control the transient response of an integrated structure through a closed control loop. The numerical results are presented with discussion and in good agreement with actual experiments.