Location Of Piezoelectric Actuators Research Articles

Optimization of the location of piezoelectric actuator and sensor in active vibration control using Multi-Verse Optimizer algorithm

In the process of using piezoelectric actuators and sensors to actively control the vibration of flexible structures, the controllability and spillover effect of the system are often the focus of attention, and the location of piezoelectric actuators and sensors is one of the key factors affecting controllability and spillover effect. In this paper, the residual modes are introduced into the location optimization criteria of actuators and sensors, so that the energy can drive as much as possible the eigenmodes that need to be controlled, and avoid driving the residual eigenmodes. At the same time, a modified Multi-Verse Optimizer (MVO) algorithm is used to optimize the location of piezoelectric actuators and sensors. The important results obtained in this paper are compared with the results obtained by the finite element simulation software to verify the accuracy of the relevant derivation results, and the optimization simulation of the position of piezoelectric actuator and the simulation of vibration control are carried out. The simulation results showed that, the MVO algorithm is very suitable for solving the optimization problems that these criteria are non-convex and difficult to derive, and the resulting optimized layout can effectively suppress vibration.

A modified fuzzy-tuned artificial bee algorithm to optimal location of piezoelectric actuators and sensors for active vibration control of isotropic rectangular plates

In this study, an efficient modified artificial bee colony algorithm is presented to find the optimal location of piezoelectric actuators and sensors for active vibration control of plates. An artificial bee algorithm is a population-based approach utilized to search for the optimal solution using swarm intelligence. There are two searching steps in the proposed algorithm, i.e., the random and the local search. These two search types present the main processes of the algorithm, known as exploration and exploitation. Making a balance between these two processes is important in obtaining the best solution. Therefore, a new technique is proposed herein to keep a balance between exploration and exploitation. In this technique, a fuzzy system is utilized as the parameter tuner in the improved artificial bee colony algorithm for providing the balance between global search and local search. Consequently, the solution of the algorithm approaches the optimal object. The presented algorithm is utilized to determine the optimal placement of piezoelectric sensors and actuators on an isotropic rectangular plate. Ensuring good observability and controllability is considered as the optimization criterion. Also, residual modes are considered to limit the spillover effect. The obtained results indicate the superiority of the proposed approach.

Software-in-the-loop optimization of actuator and sensor placement for a smart piezoelectric funnel-shaped inlet of a magnetic resonance imaging tomograph

Performance of smart piezoelectric structures strongly depends on placement of integrated piezoelectric actuators and sensors, which may be implemented in the form of thin film layers on the structure surface or embedded within the structure. In both cases actuator and sensor placement plays an important role, since after applying they remain permanently integrated with structure. In this paper the optimization procedure for piezoelectric structures with curved surfaces is proposed based on the Software-in-the-Loop (SiL) methodology and balanced modal order reduction in combination with H2 and H∞ norms used in placement indices. The optimization procedure is a global one, since it seeks for optima across the entire domain of the structure. A special challenge is tackling the problem of curved surfaces. This problem is solved in this work for a funnel shaped structure – inlet of the magnetic resonance imaging tomopraph. A thorough mesh convergence study with respect to the eigenfrequency analysis is performed in order to obtain a reliable numeric finite element model for further optimization purposes. Material parameter optimization is performed as well. Based on placement indices optimal placement study is performed under consideration of several eigenmodes of interest. The optimization is performed for individual modes as well as for simultaneous consideration of multiple modes. The SiL approach with recurrent communication in each iteration of the optimization between the numerical simulation FE software and optimization tool designed in Python is implemented through the evaluation of the placement indices for candidate locations over the entire curved surface of the structure. Depending on support conditions, optimal locations of piezoelectric actuators and sensors are proposed.

Piezoelectric Actuator Placement Optimization and Active Vibration Control of a Membrane Structure

The placement optimization of piezoelectric actuators and active vibration control of a membrane structure are studied in this paper. The classical linear quadratic regulator controllers are designed to suppress the unwanted vibration. Simulation results indicate that the optimal locations of piezoelectric actuators are affected deeply by the additional mass and stiffness of actuators, the computational efficiency of particle swarm optimizer is higher than that of genetic algorithm for this particular problem, and the control performance of optimally placed actuators is better than that of non-optimally placed actuators.

Dynamic Modeling and Analysis of a Rotating Piezoelectric Smart Beam

In active vibration control study, piezoelectric actuators and sensors are bonded on the surface of a beam. They can change the frequency and modal characteristics of the system. This paper presents an analysis of the frequency response to a rotating piezoelectric smart beam. Hamilton’s principle along with the assumed mode method are employed to derive the governing equations of the first-order approximate coupling model for the piezoelectric smart beam. The coupling is taken into account as the second-order coupling effect of the axial elongation caused by the transverse displacement of the beam. Then, the equations are transformed into a dimensionless form after identifying the necessary parameters. The dimensionless natural frequencies of the piezoelectric smart beam corresponding to the bending and stretching vibrations are obtained through a numerical simulation, with comparison made of those of the beam with no actuator or sensor. Furthermore, the implication is investigated of the structural parameters and bond location on the piezoelectric actuators and sensors. Besides, the common case of a smart beam bonded with multiple pairs of piezoelectric actuators and sensors is studied, and the effects of the first natural frequency and tip deformation are analyzed. The research provides a theoretical reference for the optimization of structural parameters and location of piezoelectric actuators and sensors, thereby preventing the resonance when the excitation frequency is approximately equal to the natural frequency of the beam.

A novel method to specify pattern recognition of actuators for stress reduction based on Particle swarm optimization method

This paper is focused on stiffness ratio effect and a new method to specify the best pattern of piezoelectric patches placement around a hole in a plate under tension to reduce the stress concentration factor. To investigate the stiffness ratio effect, some different values greater and less than unity are considered. Then a python code is developed by using particle swarm optimization algorithm to specify the best locations of piezoelectric actuators around the hole for each stiffness ratio. The results show that, there is a line called "reference line" for each plate with a hole under tension, which can guide the location of actuator patches in plate to have the maximum stress concentration reduction. The reference line also specifies that actuators should be located horizontally or vertically. This reference line is located at an angle of about 65 degrees from the stress line in plate. Finally two experimental tests for two different locations of the patches with various voltages are carried out for validation of the results.

Optimal location of piezoelectric actuators for active vibration control of thin axially functionally graded beams

Up to now, optimal location for active control studies concern principally multilayers or homogeneous structures. In the case of functionally graded materials, very few papers exist and they only concern cross section variations. In this way, this paper deals with the optimization of piezoelectric actuators locations on axially functionally graded beams for active vibration control. For this kind of structures, the free vibration problem is more complicated as the governing equations have variable coefficients. Here, the eigenproblem is solved using Fredholm integral equations. The optimal locations of actuators are determined using an optimization criterion, ensuring good controllability of each eigenmode of the structure. The linear quadratic regulator, including a state observer, is used for active control simulations. Two numerical examples are presented for two kinds of boundary conditions.

Control of free-edge interlaminar stresses in composite laminates using piezoelectric actuators

The control of free-edge interlaminar stresses in laminated composite structures using a stress function-based approach is proposed. The assumed stress fields satisfy pointwise traction and free boundary conditions at surfaces. Governing equations are derived using the principle of complementary virtual work. A general eigenvalue solution procedure was adopted to obtain accurate stress states of the laminated composite structure. The results obtained from the proposed method were compared with those obtained by three-dimensional finite element analyses. It was found that interlaminar stresses generated by mechanical loadings could be significantly reduced by applying proper electric fields to piezoelectric actuators, which were surface bonded or embedded in composite laminates. Locations of piezoelectric actuators also influenced the distributions of interlaminar stresses. The results provided that piezoelectric actuators have potential in the application to actively control interlaminar stresses in composite laminates.

Optimal locations of piezoelectric actuators and sensors for supersonic flutter control of composite laminated panels

The optimal active flutter control of supersonic composite laminated panels is studied using the distributed piezoelectric actuators/sensors pairs. The supersonic piston theory is used to calculate the unsteady aerodynamic pressure, and Hamilton’s principle with the assumed mode method is employed to develop the equation of motion of the structural system. The controllers are designed by the proportional feedback control method and the linear quadratic Gauss (LQG) algorithm. The optimal locations of the actuator/sensor pairs are determined by the genetic algorithm (GA). The aeroelastic properties of the structural system are mainly analyzed using the frequency-domain method. The time-domain responses of the structure are also computed using the Runge–Kutta method. The influences of ply angle on the flutter bound of the laminated panel with different length–width ratios are analyzed. The optimal design for the locations for different numbers of piezoelectric patches used in the proportional feedback control is carried out through the GA. Meanwhile, the control effects using different numbers of actuator/sensor pairs are investigated. The flutter suppression by the LQG algorithm is also carried out. The control effects using the two different controllers are compared. Numerical simulations show that the optimal locations obtained by the GA can increase the critical flutter aerodynamic pressure significantly, and the LQG algorithm is more effective in flutter suppression for supersonic structures than the proportional feedback controller.

Optimal vibration control of smart composite beams with optimal size and location of piezoelectric sensing and actuation

Control performances of smart structures depend on the size and location of the piezoelectric actuators and sensors as well as on the applied control algorithm. This article presents optimal vibration control of a thin-walled composite beam by using the fuzzy optimization strategy based on the particle swarm optimization algorithm. The optimization of the size and location of the conventionally collocated piezoelectric actuators and sensors, and optimization of the controller parameters are performed separately. The optimization criteria for optimal size and location of piezoelectric actuators and sensors are based on eigenvalues of the controllability Grammian matrix. The optimization procedure implies constraint of the original dynamic properties change and limitation of the beam mass increase. The particle swarm optimization-based linear quadratic regulator has been implemented for optimal vibration control in order to maximize the modal closed-loop damping ratios and minimize the control voltages required for actuation while keeping them below breakdown voltage for the used piezoelectric actuator. A pseudo-goal function, derived from the fuzzy set theory, gives an expression for global objective functions eliminating the use of weighting coefficients and penalty functions. The problem is formulated using the finite element method based on the third-order shear deformation theory. Several numerical examples are presented for the cantilever beam.

Optimal design of piezolaminated structures using B-spline strip finite element models

A package of B-spline finite strip models is developed for the linear analysis of piezolaminated plates and shells. This package is associated to a global optimization technique in order to enhance the performance of these types of structures, subjected to various types of objective functions and/or constraints, with discrete and continuous design variables. The models considered are based on a higher-order displacement field and one can apply them to the static, free vibration and buckling analyses of laminated adaptive structures with arbitrary lay-ups, loading and boundary conditions. Genetic algorithms, with either binary or floating point encoding of design variables, were considered to find optimal locations of piezoelectric actuators as well as to determine the best voltages applied to them in order to obtain a desired structure shape. These models provide an overall economy of computing effort for static and vibration problems.

A novel technique for optimal placement of piezoelectric actuators on smart structures

The problem of positioning of actuators and sensors on smart materials has been a point of interest in recent years. This is due to the fact that in many practical applications there are limitations in space, weight, etc. of the smart structures, which make the problem of positioning more complex. In addition, it is required that the actuators/sensors have the best possible performance. The development of smart structures technology in recent years has provided numerous opportunities for vibration control applications. The use of piezoelectric ceramics or polymers has shown great promise in the development of this technology. The employment of piezoelectric material as actuators in vibration control is beneficial because these actuators only excite the elastic modes of the structures without exciting the rigid-body modes. This is important since very often only elastic motions of the structures are needed to be controlled. The purpose of this paper is to introduce a novel approach developed for optimizing the location of piezoelectric actuators for vibration suppression of flexible structures. A flexible fin with bonded piezoelectric actuators is considered in this study. The frequency response function (FRF) of the system is then recorded and maximization of the FRF peaks is considered as the objective function of the optimization algorithm to find the optimal placement of the piezoelectric actuators on the smart fin. Three multi-layer perceptron neural networks are employed to perform surface fitting to the discrete data generated by the finite element method (FEM). Invasive weed optimization (IWO), a novel numerical stochastic optimization algorithm, is then employed to maximize the weighted summation of FRF peaks. Results indicate an accurate surface fitting for the FRF peak data and an optimal placement of the piezoelectric actuators for vibration suppression is achieved.

Wave propagations of curvilinear motors driven by partially laminated piezoelectricactuators

A piezoelectric arc stator is the key component delivering driving actions to an ultrasoniccurvilinear motor. The arc stator drives the rotor along the arc structure to any specificangular position. Usually conventional stators in ultrasonic motors are fully bounded withpiezoelectric patch actuators. To reduce production costs while maintaining similar drivingcharacteristics, an arc stator partially bonded with piezoelectric actuators is proposed andits dynamic characteristics are analyzed in this study. The effect of actuator locations onthe wave propagation is investigated. Both analytical and finite element resultsdemonstrate similar dynamic responses. That is, the response of the wave propagationdepends on specific locations of piezoelectric actuators. One of the two configurationsinvestigated shows that the partially laminated piezoelectric actuator patterncan also generate rather steady traveling waves on the stator with consistentwave amplitude. This implies that the partially laminated actuator techniquecould be an alternative actuator pattern to the fully laminated actuators in thedesign of ultrasonic curvilinear motors or other finite-length ultrasonic motors.

Modal-based model reduction and vibration control for uncertain piezoelectric flexible structures

In piezoelectric flexible structures, the contribution of vibration modes to the dynamic response of system may change with the location of piezoelectric actuator patches, which means that the ability of actuators to control vibration modes should be taken into account in the development of modal reduction model. The spatial H2 norm of modes, which serves as a measure of the intensity of modes to system dynamical response, is used to pick up the modes included in the reduction model. Based on the reduction model, the paper develops the state-space representation for uncertain flexible structures with piezoelectric material as non-collocated actuators/sensors in the modal space, taking into account uncertainties due to modal parameters variation and unmodeled residual modes. In order to suppress the vibration of the structure, a dynamic output feedback control law is designed by simultaneously considering the conflicting performance specifications, such as robust stability, transient response requirement, disturbance rejection, actuator saturation constraints. Based on linear matrix inequality, the vibration control design is converted into a linear convex optimization problem. The simulation results show how the influence of vibration modes on the dynamical response of structure varies with the location of piezoelectric actuators, why the uncertainties should be considered in the reductiom model to avoid exciting high-frequency modes in the non-collcated vibration control, and the possiblity that the conflicting performance specifications are dealt with simultaneously.

The optimal location of piezoelectric actuators and sensors for vibration control ofplates

This paper considers the optimal placement of collocated piezoelectric actuator–sensorpairs on a thin plate using a model-based linear quadratic regulator (LQR) controller. LQRperformance is taken as objective for finding the optimal location of sensor–actuator pairs. Theproblem is formulated using the finite element method (FEM) as multi-input–multi-output(MIMO) model control. The discrete optimal sensor and actuator location problem isformulated in the framework of a zero–one optimization problem. A genetic algorithm (GA)is used to solve the zero–one optimization problem. Different classical control strategieslike direct proportional feedback, constant-gain negative velocity feedback andthe LQR optimal control scheme are applied to study the control effectiveness.

Optimal placement and active vibration control for piezoelectric smart flexible cantilever plate

Some flexible appendages of spacecraft are cantilever plate structures, such as sun plate and satellite antenna. Thus, vibration problem will be caused by parameter uncertainties and environmental disturbances. In this paper, piezoelectric ceramics patches are used as sensors and actuators to suppress the vibration of the smart flexible clamped plate. Firstly, modal equations and piezoelectric control equations of cantilever plate are derived. Secondly, an optimal placement method for the locations of piezoelectric actuators and sensors is developed based on the degree of observability and controllability indices for cantilever plate. The bending and torsional modes are decoupled by the proposed method using bandwidth Butterworth filter. Thirdly, an efficient control method by combining positive position feedback and proportional-derivative control is proposed for vibration reduction. The analytical results for modal frequencies, transient responses and control responses are carried out. Finally, an experimental setup of piezoelectric smart plate is designed and built up. The modal frequencies and damping ratios of the plate setup are obtained by identification method. Also, the experimental studies on vibration control of the cantilever plate including bending modes and torsional modes are conducted. The analytical and experimental results demonstrate that the presented control method is feasible, and the optimal placement method is effective.

Extensive Experiments on Genetic Algorithms for the Optimization of Piezoelectric Actuator Locations

For shape control of smart structures, we have developed a series of micro-genetic-algorithms for optimal placement of a large number of piezoelectric actuators. Here, we investigate the effect on the solution quality of 1) different random seed generators; 2) restart criteria in micro-genetic-algorithms, specifically the two parameters, the number of generations used for the inner loop and the level of diversity in the population; and 3) different numbers of actuators. We also report a comparison of our genetic algorithms with two heuristic integer programming algorithms: worst-out-best-in and exhaustive single point substitution proposed by Haftka and Adelman (Selection of Actuator Locations for Static Shape Control of Large Space Structures by Heuristic Integer Programming, Computers and Structures, Vol. 20, 1985, pp. 572-582). Using current genetic algorithms, we not only get better layouts of actuators than reported in our previous publications, but we also find that the most distinct nature of genetic algorithms is randomness and robustness. The best parameter setting of genetic algorithms is dependent on both the number of evaluations used for termination and the seed generator used. Moreover, the best parameter setting of genetic algorithms varies as the number of actuators changes. To get the highest quality of solutions, multiple runs using different random seed generators are necessary. The time of investigation can be significantly reduced using a coarse grain parallel computing. Comparison of our genetic algorithms with the worst-out-best-in and exhaustive single point substitution shows that for a group of runs our genetic algorithms usually converge faster in the first few thousand evaluations and are more likely to find better solutions than the worst-out-best-in and exhaustive single point substitution algorithms.

Active Control of Nonlinear Panel Flutter Under Yawed Supersonic Flow

A coupled structural-electrical modal finite element formulation for composite panels with embedded piezoelectric sensors and actuators is presented for nonlinear panel flutter suppression under yawed supersonic flow. The first-order shear deformation theory for laminated composite plates, the von Karman nonlinear strain-displacement relations for large deflection response, the linear piezoelectricity constitutive relations, and the first-order piston theory of aerodynamics are employed. Nonlinear equations of motion are derived by extending the three-node triangular Mindlin (MIN3) plate element. Additional electrical degrees of freedom are introduced to model piezoelectric sensors and actuators. The system equations of motion are transformed and reduced to a set of nonlinear equations in modal coordinates. Analysis results for the effect of arbitrary flow yaw angle on nonlinear supersonic panel flutter are presented. The results show that the flow yaw angle has a major effect on the panel limit-cycle oscillation amplitude and deflection shape. Two different control methods are investigated for the suppression of nonlinear panel flutter. The first method is the linear quadratic Gaussian controller. The second method is the nonlinear output controller comprised of a linear quadratic regulator and an extended Kalman filter nonlinear state estimator. Closed-loop criteria based on the norm of feedback control gain and on the norm of Kalman filter estimator gain are used to determine the optimal location of piezoelectric actuators and sensors at different flow yaw angles. Optimal sensor and actuator locations for a range of yaw angles are determined by grouping the optimal locations for different angles within the range. The results demonstrate the effectiveness of piezoelectric materials and of the nonlinear output controller in suppressing nonlinear flutter of isotropic and composite panels at different flow yaw angles.

Buckling optimization of composite laminated adaptive structures

This paper deals with the optimal design of laminated composite plates with integrated piezoelectric actuators. Refined finite element models based on equivalent single layer high-order shear deformation theories are used. These models are combined with simulated annealing, a stochastic global optimization technique, in order to find the optimal location of piezoelectric actuators and also to find the optimal fiber reinforcement angles in both cases having the objective of maximizing the buckling load of the composite adaptive plate structure. To show the performance of the proposed optimization models, two illustrative and simple examples are presented and discussed. In one of these examples a comparison between the simulated annealing technique and a gradient based optimization scheme, is carried out.

Enhancing flutter and buckling capacity of column by piezoelectric layers

This paper illustrates the use of a pair of piezoelectric layers in increasing the flutter and buckling capacity of a column subjected to a follower force. The column is fixed at one end while the other one is free to rotate but constrained transversely by a spring. The mathematical formulation is presented and solved numerically. The effect of the spring stiffness on the capacity and type of instability of the column is first illustrated numerically for the case without any piezoelectric actuators. A transition value for the stiffness can be identified, below which the column fails by flutter and above which the column buckles. Next, an external voltage is applied on the piezoelectric layers bonded on the surfaces of the column, which induces locally a pair of tensile follower force. This has the effect of increasing the capacity of the column as the voltage increases while the transition stiffness remains virtually unchanged for a given size and location of piezoelectric actuators. It is also shown that the capacity of the column increases with longer layers for a fixed voltage. However, the location of the layers along the column determines the transition stiffness and hence has an effect on the type of failure for a fixed spring constant. Positioning towards the fixed end increases the flutter capacity whereas positioning away will result in an increase in buckling capacity.