This paper summarizes the development of a homogenized free energy model which characterizes the temper- ature-dependent hysteresis and constitutive nonlinearities inherent to relaxor ferroelectric materials. A kernel for the model is developed through mesoscopic energy analysis and extended to provide macroscopic constitutive relations through stochastic homogenization techniques based on the assumption that certain underlying parameters are manifestations of underlying densities rather than constants. Mechanisms characterizing the decrease in hysteresis and saturation polarization polarization as temperatures are increased are constructed using asymptotic properties of the kernel which is derived from statistical mechanics tenets. Attributes of the model are illustrated through comparison with PMN-PT-BT data.

Constitutive and finite element models of a piezoceramic laminated plate are derived using shear deformation (Mindlin plate) theory for each layer, where constraints are added to ensure the elastic deformation continuity at the interface. The major difference of this study compared to previous studies is that the finite element formulation is applicable to both thin and thick laminated plates with thick PZT wafers where electro-mechanical coupling occurs due to either electrical or mechanical input. This formulation allows the cross section of each layer to rotate individually, which increases the accuracy compared to conventional formulations in the literature. An experimental study is conducted to identify the piezoelectric constants of the PZT wafer in 31 and 32 directions and the effect of the directional piezoelectric actuation (g31 ≠ g32) is embedded in the formulation where the PZT layer is formulated as an orthotropic structure. A combination of Lagrange bilinear and Serendipity quadratic elements with 4 and 8 nodes, respectively, are used for approximating the degrees of freedom of the system and to apply the finite element procedure in MATLAB. The proposed FE solution with directional actuation that accounts for orthotropic properties is compared to an FE solution based on thin plate theory with isotropic piezoelectric actuation (g31 = g32) and isotropic material properties. Modeling accuracy is evaluated by comparison with experimental measurements along with a passive control application.

A ferroelastic switching model for single crystal piezoceramic compounds is developed. The model is based on a phenomenological Landau-Devonshire type thermodynamic theory for the materials. The model incorporates externally applied electric fields and compressive stress inputs to the crystals and models the 90° and 180° ferroelastic and ferroelectric switching induced by the inputs. Properties of the ferroelastic model are qualitatively similar to experimental PLZT data.

Traditional piezoelectric actuators have been a mainstay in numerous applications such as precision positioning systems, sonar and medical ultrasound imaging. More recently, new types of piezoelectric actuators have been developed, including transverse mode actuators such as THUNDER and flexible actuators like Micro-fiber composites (MFC). Yet, many aspects of these actuators are still not well understood and have not been adequately modeled. We will present some Finite Element models that represent the manufacturing process of THUNDER actuators as well as their response to DC electric fields and compare the model to experimental results. In addition, we will present experimental results of THUNDER response to AC fields at or near the fundamental resonance frequency. We will compare the results to a nonlinear theory originally developed for piezodriven cantilevers for atomic force microscopes (AFM). Finally, we will briefly mention an aeronautical application of MFC actuators.

Piezoelectric materials (PZT) are commonly used as actuators and sensors for vibration suppression in flexible metal or composite substrates. There are well-established techniques for modeling the actuation of PZTs when they are bonded to these structures. However, if the substrate material is much softer than the piezoelectric actuator/sensor, a higher level of modeling is needed to predict the local deformations at the interface. In this research, a finite-length piezoelectric element bonded perfectly to an infinite elastic strip is modeled. The specific goal was to quantify the actuation and sensing mechanics of piezoelectric devices on substrates potentially much softer than the piezoelectric element. Previous works have addressed membranes or plates bonded to an elastic half-space subjected to mechanical or thermal loads. Euler-Bernoulli beam theory is used to derive equations of equilibrium for the piezoelectric beam. These equations are then recast as integral equations for the interface displacement gradients and equated to the equivalent quantities for an elastic layer subject to distributed shear and normal tractions. The resulting singular integral equations are solved by expanding the interface tractions using a series of Chebyshev polynomials. First, certain sanity checks are performed to confirm the validity of the model by choosing a stiff substrate for which Euler-Bernoulli beam-assumptions holds good. For certain combinations of geometrical and material parameters, the substrate has a positive curvature, whereas the piezoelectric has a negative curvature and vice versa. After analyzing the forces acting on both piezoelectric and the substrate, the reasons for this behavior in soft substrates are justified here. Finally, the range of geometric parameters where the reversal of bending occurs in the piezoelectric is given.

In this paper, concepts associated with the Preisach model and nonlinear mapping functions (neural networks) are coupled to model the hysteretic behavior of piezoceramic actuators. Preisach concepts are utilized in choosing the initial data points and calculating the final displacements having nonlocal memory. In a traditional Preisach model generalization is typically handled by interpolation functions. These functions can lead to significant errors unless the number of data points is considerably high. In this study the generalization of all first order reversal curves is provided by a single neural network. The goal of this work was to enable real-time implementation and learning with a "limited" number of variables. Finally, a novel on-line training approach was developed to account for errors caused by frequency dependency and large variations of the input of the actuator. Results show excellent agreement between simulated and experimental results.

The ability to model, investigate and control the behavior of dynamic systems in a simulation environment is highly desirable due to time and cost benefits. A new technique has been developed allowing finite element models to be integrated with Simulink for dynamic simulation and control. The technique is presented by the modeling of a fixed-free cantilever beam with bonded piezoelectric patches. A description of the modeling technique is presented detailing the process of model creation, including input and output variable determination, and exportation to Simulink as a state-space model. A comparison of simulated and experimental open-loop behavior is provided. Furthermore the free and forced system behavior both observed, and simulated with velocity feedback controllers (VFB) is presented. Conclusions are drawn regarding the capabilities and restrictions of the developed technique in comparison to modeling using a system identification technique. The author's views on the techniques application to non-linear system modeling and potential for optimizing sensor and actuator locations are presented.

Piezoelectric ceramic materials are widely used in solid state actuators and sensors. For piezoceramic elements, the use of the d15-effect is of particular interest since the shear piezoelectric coefficient is much higher than the other piezoelectric coefficients d31 or d33. Although this fact is widely known, the application of shear actuators is somewhat rare. Shear induced vibrations are more complex to describe mathematically and there is not an adequate understanding of nonlinear shear induced vibration behavior. At weak electric fields, piezoceramics are described by linearized constitutive relations around an operating point. However, in near resonance frequency excitation of the flexural vibration of piezoceramic beam using d15-effect, even at weak electric field, typical nonlinear vibration behavior is observed. This vibration behavior can not be adequately defined by the linear theories. In this paper, authors have attempted to model this nonlinear behavior using higher order cubic conservative and nonconservative terms in the constitutive equations. The linear eigenfunctions are used to discretize the nonlinear equation of motion obtained by Hamilton's principle. Perturbation methods are used to solve approximately the nonlinear equation of motion. Using this solution, nonlinear parameters are identified by comparing the theoretical and experimental results. The nonlinear effects and the modeling described herein may have strong influence on the design of existing applications and on the development of new applications based on the d15-effect.

The shape control of flexible mirrors has been studied mainly for edge-supported thin-plate configurations. For applications such as optical reflectors, corner-supported configurations, which allow for paraboloidal geometries, prove more applicable. Moreover, the use of corner supports enables more flexibility and larger achievable deflections than with edge supports. This paper discusses a corner-supported thin rectangular plate actuated by a two-dimensional array of segmented piezoelectric laminated actuators. First, a model determining the deflected shape of a laminate for a given distribution of voltages over the actuator array is derived. Second, the results of the model are shown to agree well with a finite element simulation of the structure. Finally, paraboloidal deflection of a rectangular PVDF laminate is investigated.

A thermomechanical model for shape memory alloy (SMA) actuators and SMA hybrid composite (SMAHC) structures has been recently implemented in the commercial finite element codes MSC.Nastran and ABAQUS. The model may be easily implemented in any code that has the capability for analysis of laminated composite structures with temperature dependent material properties. The model is also relatively easy to use and requires input of only fundamental engineering properties. A brief description of the model is presented, followed by discussion of implementation and usage in the commercial codes. Results are presented from static and dynamic analysis of SMAHC beams of two types; a beam clamped at each end and a cantilevered beam. Nonlinear static (post-buckling) and random response analyses are demonstrated for the first specimen. Static deflection (shape) control is demonstrated for the cantilevered beam. Approaches for modeling SMAHC material systems with embedded SMA in ribbon and small round wire product forms are demonstrated and compared. The results from the commercial codes are compared to those from a research code as validation of the commercial implementations; excellent correlation is achieved in all cases.

In this paper, we conduct a feasibility study to investigate the future potential of textile composites with shape memory alloys. Two different types of SMA-based textile composites are presented. First, a composite plate with embedded woven SMA layer is fabricated, and the stiffness tuning capability is evaluated by impact vibration tests. The results are not favorable, but may be improved by increasing the volume fraction of SMA, and by controlling the prestrain more accurately during the lamination process. The modeling and analysis methodology for woven SMA-based composites are briefly discussed. Then, the possibility of textile composites with SMA stitching is discussed, that is expected to give the composites multi-functions such as tunable stiffness, shape control and sensing capability, selectively distributed on demand.

In this paper, we conduct finite element analysis of a pseudoelastic SMA wire with curved shape, which is designed as a spring component in the base isolation devices. A simplified constitutive equation is implemented with the finite beam elements based on the updated Lagrangian formulation to deal with the geometric and material nonlinearities of the SMA wires. The simulated deformation shapes and the force-displacement characteristics are compared with the measured results.

A simple yet accurate specimen-based macroscopic constitutive model of shape memory alloys (SMA) was derived from a grain-based micromechanical model, to understand the complicated thermo-mechanical behavior of SMA and to design structural elements with SMA components optimally. This model was composed of a phase transformation energy criterion, a strain equation, and a heat and energy flow equation. New features are that (1) a partial transformation cycle model was proposed, which is called the shift-skip model, and that (2) required energy for phase transformation was found to be well approximated by a sum of two exponential functions in terms of martensite volume fraction. In the shift-skip model, the energy required for the partial transformation was obtained by shifting and skipping the energy required for the complete transformation, based on a microscopic transformation rule. Comparison of the calculated stress-strain loops for the complete and partial transformation cycles with experimental data and with other often used models was carried out. Result showed that the proposed model could capture the measured stress-strain loops well and much better than the other models.

It has recently been theorized that the initial fast electro-mechanical response of ionic-polymer-metal composites (IPMCs) may be due to a polarization mechanism, while transport dominates the relaxation response. In order to investigate this hypothesis, a computational micromechanics model has been developed to model polarization response in these ionomeric transducers. Assuming a constant solvated state, the model tracks the rotation of individual dipoles within a given cluster in response to dipole-dipole interaction, mechanical stiffness of the pendant chain, and external electrical field loading. Once the system of dipoles reaches equilibrium in response to loading, net polarization/distortion response is recorded. Actuation predictions using the polarization model are consistent with the experimentally observed fast response of these materials.

In this paper we develop a mathematical model to simulate the actuation of a multilayer metallic strip. In the first step of the model development, we employ previous theory to quantify the radius of curvature in the unimorph due to differing thermal coefficients in the constituent materials. The resulting radius of curvature is subsequently used to compute the voltage required to uncurl the actuator. Numerical experiments were performed with the model and the trends were found to be in agreement with experimental data.

Ionic polymers are a class of electromechanically coupled materials that can be used as flexible transducers. When set up in the cantilever configuration, the actuators exhibit a large bending deflection when an electric field is applied across their thickness. Being a relatively new research topic, the governing physical and chemical mechanisms are not yet fully understood. Experimental results have demonstrated nonlinear dynamic behavior. The nonlinear dynamics can be seen in the response of current, displacement, and velocity of the actuator. This work presents results for the nonlinear identification of ionic polymer actuator systems driven at a specific frequency. Identification results using a 5th-degree Volterra expansion show that the nonlinear distortion can be accurately modeled. Using such a high power in the series expansion is necessary to capture the most dominant harmonics, as evidenced when examining the power spectral density of the response. An investigation of how nonlinearities enter into the response is also performed. By analyzing both the actuation current and tip velocity, results show that both the voltage to current and current to velocity stages influence the nonlinear response, but the voltage to current stage is more dominantly nonlinear.

This paper focuses on the development of parameter estimation techniques for models quantifying hysteresis and constitutive nonlinearities in ferroelectric materials. These models are formulated as integral equations with known kernels and unknown densities to be identified through least squares fit to data. Due to the compactness of the integral operators, the resulting discretized models inherit ill-posedness which often must be accommodated through regularization. The accuracy of regularized finite-dimensional models is illustrated through comparison with experimental data.

In previous works, we have obtained several results on the numerical analysis of magnetostrictive materials at microscopic scale. These studies, based on the minimization of the total energy functional of the system, include the existence and the approximation of solutions and the associated numerical experiments on two-dimensional samples. Next, we have considered the numerical analysis of two-dimensional cubic crystals of ferromagnetic materials with emphasis on the thickness of the walls and their evolution under an incremental magnetic field and the effect of nonmagnetic inclusions. This contribution discusses more specifically two extensions i) to three dimensional ferromagnetic materials (computation and representation of magnetic domains and Bloch walls) and ii) to the case of two-dimensional polycrystals, in particular, the magnetic domains for adjacent rectangular crystals whose easy lines of magnetization have different orientations.

Smart structures typically consist of many interacting components, which result in a closed loop formed by an actuator, structure, sensors, controller, and drive circuit components. Despite the recognition of component interactions, much of the traditional design approach for such systems is highly compartmentalized and sequential. The primary objective of the present work is to develop a basic understanding of the energy flow and dynamic interaction between the electrical and mechanical subsystems of smart actuators. When operating from portable power sources, a crucial factor in determining the performance of such a smart system is the battery capacity required for the actuator to operate through a given time span along with its life time. The real and reactive power in such a system will determine the battery life and size separately. While the real power is dissipated only in the drive circuit, the reactive power of the circuit and the actuator cannot be calculated individually, where the interaction arises. Multi-objective function optimization problem, which combines the real and reactive power by different weights, will result in a better balanced solution than optimizing either one of them separately. Genetic algorithm is applied for discrete component selection to generate more realistic designs. The optimization result is illustrated in the paper, as well as their relationship with multi-objective functions.

Actuators based on smart materials generally exhibit a tradeoff between force and stroke. Researchers have surrounded piezoelectric materials (PZT's) with compliant structures to magnify either their geometric or mechanical advantage. Most of these designs are literally built around a particular piezoelectric device, so the design space consists of only the compliant mechanism. Materials scientists researchers have demonstrated the ability to pole a PZT in an arbitrary direction, and some engineers have taken advantage of this to build "shear mode" actuators. The goal of this work is to determine if the performance of compliant mechanisms improves by the inclusion of the piezoelectric polarization as a design variable. The polarization vector is varied via transformation matrixes, and the compliant actuator is modeled using the SIMP (Solid Isotropic Material with Penalization) or "power-law method." The concept of mutual potential energy is used to form an objective function to measure the piezoelectric actuator's performance. The optimal topology of the compliant mechanism and orientation of the polarization method are determined using a sequential linear programming algorithm. This paper presents a demonstration problem that shows small changes in the polarization vector have a marginal effect on the optimum topology of the mechanism, but improves actuation.

A systematic design method is proposed for the selecting of actuators and sensors in the structural control in order to minimize the instrumental cost. With actuators and sensors placed at all the admissible locations initially, an iterative minimization algorithm is carried out to identify the sensor/actuator that requires the least precision. By deleting the roughest sensor/actuator each time till loss of feasibility, one can conclude simultaneously the necessary number and type of sensor/actuator, and the location and precision for each sensor/actuator. A tensegrity structure example has been solved as an application of the proposed algorithm.

The Smart Disc project at the Drebbel Institute of the University of Twente is aimed at the development of active structural elements for high-precision machines. The active elements consist of a piezoelectric position actuator and a collocated piezoelectric force sensor. As the actuators and sensors are collocated, the elements are especially suited for implementing robust active damping. The decision whether or not to incorporate active damping elements in a high-precision machine should ideally be made in an early design stage, i.e., at a time at which only limited knowledge of the vibration problem is available. Despite the uncertainties that may exist at that stage, one would like to be able to roughly predict the amount of damping that could possibly be obtained. For that reason, the present paper is concerned with the development of an analysis tool that may help in predicting the applicability of active damping elements in a mechanical structure of which only a rough model is available. Based on extensive simulations, several practical rules of thumb are given for the requirements for the mechanical structure and the active elements, in order to enable the realisation of relative damping values as high as 10%.

Actuators based on smart materials generally exhibit a tradeoff between force and stroke. Researchers have surrounded piezoelectric materials (PZT’s) with complaint structures to magnify either their geometric or mechanical advantage. Most of these designs are literally built around a particular piezoelectric device, so the design space consists of only the compliant mechanism. Materials scientists researchers have demonstrated the ability to pole a PZT in an arbitrary direction, and some engineers have taken advantage of this to build “shear mode” actuators. The goal of this work is to determine if the performance of compliant mechanisms improves by the inclusion of the piezoelectric polarization as a design variable. The polarization vector is varied via transformation matrixes, and the compliant actuator is modeled using the SIMP (Solid Isotropic Material with Penalization) or “power-law method.” The concept of mutual potential energy is used to form an objective function to measure the piezoelectric actuator’s performance. The optimal topology of the compliant mechanism and orientation of the polarization method are determined using a sequential linear programming algorithm. This paper presents a demonstration problem that shows small changes in the polarization vector have a marginal effect on the optimum topology of the mechanism, but improves actuation.

The control of the shape of a sub - region of a structure has many important practical applications; for instance the control of the shape of a conformal antenna that is mounted to the surface of a sub - region of a structure. Given the desired shape of the sub - region one can use self - stress actuators, which only act in the sub - region itself, to implement the required control. However, if the structure is disturbed by external excitations, the actuators have to compensate the additional vibrations too; therefore, also sensors have to be designed. A proper sensor design requires the sensor to be an integrated part of the structure and to be located in the sub - region only. Using self - stress sensors is near at hand; moreover, one may even use the actuators as sensors, resulting in so - called self - sensing actuator / sensor pairs. Clearly, this procedure provides collocation between actuator and sensor automatically, which, from a control point of view, is highly desirable. In the present paper we summarize the design of actuators for the sub - region control of a structure. Then we discuss the design of collocated sensors, their output signal and the application of a PD - control law. We show that the output signal is the natural output of the system and that the closed loop system is stable. Finally, we present numerical results for a beam type structure.

The paper introduces a new design method for the synthesis of compliant mechanisms. This method is based on the optimization of the distribution of compliant building blocks within a given design domain. Building blocks are modeled by elementary frame ground structures. The topology, dimensions, material, contacts, fixed frame and actuators of the optimal compliant mechanism are generated automatically using a multi objective genetic algorithm such that the force/motion ratio is maximized. The set of optimal solutions is explored by using the notion of Pareto optimality. An application of this design method is tested on an actuated compliant mechanism with two output degrees of freedom.

This paper presents an advanced strategy to determine the optimal configuration of piezoelectric actuators embedded in an adaptive circular composite plate (ACCP) with one central support and three simply supports on the edges for active vibration suppression. The modeling strategy combines the Finite Element Analysis (FEA) and the transfer function estimation technique taking into account the effects of piezoelectric patches on the dynamics of the structures. To obtain the optimal actuator locations coupled with the control law, the linear quadric regulator (LQR) is chosen as a controller to achieve maximum structural vibration suppression with minimum control energy consumption, where the norm-2 of the LQR optimal feedback gain vector is set as the objective function of the optimization strategy. Due to their effectiveness in searching optimal design parameters and obtaining globally optimal solution, the Genetic Algorithms (GAs) are applied to fmd the optimal actuator configuration and placement among 8 possible configurations. Finally, several simulations are performed using the LQR with five typical actuators configurations including the optimal configuration given by the GAs. The results show that a substantial saving in the objective function as well as a significant vibration reduction can be obtained when the optimal configuration of the actuators is adopted.

Plate and shell laminates that include piezoelectric layers have found increasing use in the field of smart structures. The present work focuses on the design of plate and shell piezoelectric actuators such as bimorph and C-block actuators. In this work, a method for designing piezoelectric plate and shell actuators is proposed which uses topology optimization. The approach is based on the SIMP (Solid Isotropic Material with Penalization) material model, which was extended to piezoelectric materials allowing the change of sign of the polarization of the piezoelectric material. This new material model is called PEMAP-P (Piezoelectric Material with Penalization and Polarization). The design problem consists in finding an optimal distribution of piezoelectric material in a multi-layer plate or shell structure to accomplish the maximum displacement in a given direction at a given point of the domain, when an electric charge is applied. Different and novel types of plate and shell actuators can be obtained for a desired application. For the modelling of the piezoelectric layers, newly developed piezoelectric plate and shell elements are employed, which are free of locking and allow an accurate modeling of thin piezoelectric actuators of arbitrary geometry and number of layers. To illustrate the potential of the proposed method, the optimal distributions of piezoceramics in different layered piezoelectric plates and shells actuators are shown.

Micro-tools can have a wide range of application such as cell manipulation, microsurgery, nanotechnology equipment,etc. Micro-tools considered in this work consist of a multiflexible structure actuated by two or more piezoceramics that must generate different output displacements and forces in different specified points of the domain and directions, for different excited piezoceramics. The multiflexible structure acts as a mechanical transform by amplifying and changing the direction of the piezoceramics output displacements. Thus, the development of micro-tools requires to design micromechanisms with many degrees of freedom that perform complex movements without presence of joints and pins, due to manufacturing constraints of MEMS scale. In addition, when many piezoceramics are involved the coupling among movements becomes critical, that is, undesired movements may appear. This makes the design task very complex, which suggests that systematic design method, such as topology optimization, must be applied. Thus, in this work the topology optimization formulation was applied to design micro-tools actuated by many piezoceramics with minimum movement coupling. Essentially, the topology optimization method consists of finding the optimal material distribution in a design domain to extremize some objective function. The topology optimization method implemented is based on the CAMD approach where the pseudo-densities are interpolated in each finite element, providing a continuum material distribution in the domain. The optimization problem is posed as the design of a flexible structure that maximizes different output displacements (or grabbing forces) in different specified directions and points of the domain, for different excited piezoceramics. Different types of micro-tools can be obtained for a desired application. Among the examples, designs of a XY nanopositioner and a micro-gripper are considered.

In this paper, the feasibility of using a magnetorheological (MR) fluid-based system for motion control is studied based on the hysteretic biviscous model of the MR damper. A feedback control system is designed to synchronize the motion of the two masses in a two degree of freedom spring-mass-damper system subject to an unknown disturbance. The controller performance is evaluated numerically. For the derivation of the control law, a quadratic Lyapunov function, which is a function of the relative position and velocity of two masses, is considered. The control input (current) is obtained by minimizing the derivative of the Lyapunov function along the trajectory of the system. In the computer simulation, it is observed that the controller is effective in synchronizing the two body motions.

This paper concerns open-loop control laws for reconfiguration of tensegrity towers. By postulating the control strategy as an equilibrium tracking control, very little control energy is required. Several different reconfiguration scenarios are possible for different string connectivity schemes. This includes unit radius control, twist angle control and truncation parameter control. All these control laws allow a nonuniform distribution of the control parameters among units. By defining a wave--like reference signal and injecting it in the open--loop control law, we demonstrate the concept of self--propelled tensegrity structure that are capable of locomotion.

The recursive generalized predictive control (RGPC), which combines the process of system identification using recursive least-squares (RLS) algorithm and the process of generalized predictive feedback control design, has been presented and successfully implemented on testbeds. In this research, the RGPC algorithm is extended when the disturbance measurement signal is available for feedforward control. First, the feedback and feedforward RGPC design algorithm is presented when the disturbance is stochastic or random, and is applied to an optical jitter suppression testbed. Second, the feedback and feedforward algorithm is further extended when the disturbance is deterministic or periodic. The deterministic disturbance measurement is used to estimate the future disturbance values that are then used in the control design to enhance the performance. The RGPC with future disturbance estimation algorithm is applied to a structural system and an acoustic system.

The generalized predictive control (GPC) concept is extended to an adaptive control algorithm by combining with a least-squares lattice filter. A least-squares lattice (LSL) filter, another class of exact least-squares filters, has a modular structure that is advantageous in the application of on-line system identification. The modular structure passes system information from lower order to higher order in a wave motion. The adaptive GPC algorithm combined with a LSL filter is implemented for a real-time computer algorithm and its performance is experimentally demonstrated to a structural system and an acoustic enclosure. In addition, the adaptive GPC algorithm with a LSL filter is compared with the adaptive GPC algorithm combined with a classical recursive least-squares (RLS) filter in terms of complexity, computational cost and other on-line application concerns. The average task execution time (TET) --- the measured processing time to run the algorithm during each sample interval --- is reduced by over 35 \% by using the adaptive GPC algorithm with a LSL filter.

The objective of this paper is to study the feasibility of using smart material to control the rotation angle of a subsonic projectile fin during flight. The fin produces maneuvering force and moment which are utilized to control the projectile. In this paper a beam model of piezoelectric actuator is used for rotating the projectile fin. The fin, which is assumed to be rigid, is rotated by a cantilever beam-based piezoelectric actuator whose both end are attached to the projectile body and the fin. An analytical model of the beam actuator is obtained by the finite element approach with each element satisfying Euler-Bernoulli's theorem. A feedback linearizing adaptive control system is designed for the trajectory control of the fin angle. The controller consists of an inverse system and a high gain observer. Simulation results are presented which show that fin control is accomplished in spite of uncertainties in the system.

An internal active vibration control system is developed and verified experimentally to suppress gearbox housing vibrations due to gear transmission error excitation. The approach is based on an active shaft transverse vibration control concept. The system contains a piezoelectric stack actuator for applying control forces to the shaft via a rolling element bearing. A modified filtered-x LMS control algorithm with frequency estimation is developed to generate the appropriate control signals. The experimental results show 5-20 dB reduction in the housing vibration at the first two gear mesh harmonics over a wide gear rotation speed range. However, under certain narrow conditions, vibration amplifications at other locations are observed in the experiments, which might be attributed to the system un-modeled dynamics. In spite of this limitation, the approach developed is fairly promising. Studies are being performed to improve the overall performance of the prototype active control system.

This paper addresses the active vibration control of a new smart board designed by mounting piezoelectric fibers with a metal core on the surface of the CFRP composite. These complex fibers function as sensors and actuators in the CFRP board. A finite element model of a cantilever and a reduced order model for controller design were established. The piezoelectric fibers are uneven in the actuator outputs.Therefore, the linear fractional transformation (LFT) is formulated considering the unevenness of the actuator outputs as the perturbation. Next, the controller is designed by using mu synthesis, considering the perturbation and robust stability. The control performance of the proposed method is verified by experiment and demonstrates that piezoelectric fibers can be effectively used in vibration control.

The actuating physical mechanisms utilized in smart materials can be described by eigenstrains. E.g., the converse piezoelectric effect in a piezoelastic body may be understood as an actuating eigenstrain. In the last decades, piezoelectricity has been extensively applied for the sake of actuation and sensing of structural vibrations. An important field of research in this respect has been devoted to the goal of compensating force-induced vibrations by means of eigenstrains. Considering the state-of-the-art in structural control and smart materials, almost no research has been performed on the problem of compensating stresses in force-loaded engineering structures by eigenstrains. It is well-known that stresses can influence the characteristics and the age of structures in various unpleasant ways. The present contribution is concerned with corresponding concepts for stress compensation which may have a highly beneficial influence upon the lifetime and structural integrity of the structure under consideration. We discuss the possibilities offered by displacement compensation to reduce the stresses to their quasi-static parts. As a numerical example, we consider the step response of an irregularly shaped cantilevered elastic plate under the action of an assigned traction at its boundary.

The Euler-Bernoulli model of transverse vibration of a cantilever beam is extended to include strain rate (Kelvin-Voigt) damping to study active vibration control under internal damping. A piezo patch sensor is bonded onto the top of the beam, while an actuator patch is bonded onto the bottom of the beam. Displacement and velocity feedback are considered as the control mechanisms. The resulting partial differential equation is solved using an integral equation approach and investigated for control effectiveness in terms of changes in the natural frequencies and damping ratios for different gains, damping coefficients, and patch locations. Results from the integral equation approach for patch sizes extended to the boundary are compared to results of the boundary control method.

This paper investigates the feasibility of direct model reference adaptive control (MRAC) scheme for the vibration suppression of a smart flexible beam. Direct model reference adaptive controller whose parameters are updated directly from the Lyapunov-based adaptive laws is developed. The adaptive laws for updating the controller parameters are derived and the stability for the closed loop system is proved. The developed MRAC design is numerically verified on a flexible beam model, showing that it has better performance and robustness in vibration suppression with respect to the system parameter variations. Compared with classical active vibration control such as positive position feedback (PPF) control, MRAC can produce more efficient and faster control than PPF control. The satisfactory simulation results show that the MRAC scheme is an effective approach for vibration suppression.

This paper presents a method to change the excitation frequency such that a piezoelectric actuator keeps the levitation height of a floating object suspended on a layer of air at its maximal possible height, despite changes to the system. An ultrasonic actuator capable of injecting ultrasonic vibrations to an air layer is being using as a demonstrator in this work. The high frequency oscillations and the compressibility of air generate an average pressure higher than the ambient one thus causing a flat object to float. Environmental changes and temperature effects render this system inefficient, unless the excitation frequency is constantly varied to maintain the best possible efficiency of energy transfer. An adaptive method with which an optimal excitation frequency is generated is shown to yields the best mechanical efficiency and it thus essential when the available input power is restricted. The proposed method uses a minimal amount of frequency dither to revive an identification process that is otherwise singular. With this identified model, the algorithm seeks the best momentary excitation frequency. The algorithm is validated in a simulation and on a dedicated experimental apparatus.

One of the main requirements of a digital system for the control of interferometric detectors of gravitational waves is the computing power, that is a direct consequence of the increasing complexity of the digital algorithms necessary for the control signals generation. For this specific task many specialised non standard real-time architectures have been developed, often very expensive and difficult to upgrade. On the other hand, such computing power is generally fully available for off-line applications on standard Pc based systems. Therefore, a possible and obvious solution may be provided by the integration of both the the real-time and off-line architecture resulting in a hybrid control system architecture based on standards available components, trying to get both the advantages of the perfect data synchronization provided by the real-time systems and by the large computing power available on Pc based systems. Such integration may be provided by the implementation of the link between the two different architectures through the standard Ethernet network, whose data transfer speed is largely increasing in these years, using the TCP/IP and UDP protocols. In this paper we describe the architecture of an hybrid Ethernet based real-time control system protoype we implemented in Napoli, discussing its characteristics and performances. Finally we discuss a possible application to the real-time control of a suspended mass of the mode cleaner of the 3m prototype optical interferometer for gravitational wave detection (IDGW-3P) operational in Napoli.

This paper presents a model reduction method based on modal coordinates and Modal Hankel Singular Values (MHSV). Model reduction has recently become one of the main topics among many numerical engineers, since a reduced model increases its flexibility and adaptability in synchronizing with other models in many numerical multi-physics applications. On the other hand, a full numerical model from various FEM/BEM tools has pin-point modeling accuracy over their modeling domain. The proposed model reduction method reduces the full size model to a smaller size while maintaining the modeling accuracy. The original model reduction theory is established based on state space model that describes a linear dynamic system as a first order differential matrix equation. The magnitude of each state variable is measured by the Hankel Singular Value (HSV), and the reduced model has state variables with large HSVs. In this paper, the model is described using modal coordinates system instead of state space, since most dynamic system is described as a second order system rather than first order. A modal Hankel singular value for each mode is introduced to measure the magnitude of the mode. A numerical example of coupled acoustic and piezoelectric models is included.

Active control of sound reflection on a boundary of acoustic medium is studied based on the electro-acoustic multilayer model and the feedback control. The acoustic medium boundary is made of multiple layers of elastic materials and two electro-acoustic transducer layers that can transform acoustic signal to electric signal and vice versa. When acoustic waves are incident on the boundary, the external control circuit receives the electric signal from the transducer that measures acoustic pressure level on the boundary surface, properly filters the signal band and actuates the other transducer so that actuated acoustic waves can suppress the reflection waves. Advantage of this active approach is in the small thickness of the boundary layer configuration over passive absorption layers and in wider frequency band control over other control algorithms. This paper discusses the controllability of the active boundary layers from the view of time delay caused from the thickness of transducers layers, and its affect on the reflection control performance and stability.

This paper addresses the development of energy-based models and model-based control designs necessary to achieve present and projected applications involving atomic force microscopy. The models are based on a combination of energy analysis at the mesoscopic level with stochastic homogenization techniques to construct low-order macroscopic models. Approximate model inverses are then employed as filters to linearize transducer responses for linear robust control design.

In this paper precise specifications are given for a microgripper based on a polyarticulated micromechanism. This polysilicon gripper actuated by Scratch Drive Actuators (SDA) has dimensions of 1.2mm.x 1.6mm and a thickness of 0.0045mm. The stroke of its jaws is about 0.275mm each, with a stroke ratio of 5. These specifications can be useful to compare such compliant micromechanisms. In particular, we propose an alternative to the polyarticulated mechanism based on a compliant structure. A new conceptual design method, based on compliant building blocks, is introduced. The proposed method, using a genetic algorithm, quickly leads to several compliant solutions. A compromise between these solutions has performances close to the polyarticulated microgripper (about 20% less).

This paper presents a sliding mode controller that uses a state variable estimator for control of a single degree of freedom rotary manipulator actuated by Shape Memory Alloy (SMA) wire. A model for SMA actuated manipulator is presented. The model includes nonlinear dynamics of the manipulator, a constitutive model of the Shape Memory Alloy, and the electrical and heat transfer behavior of SMA wire. The current experimental setup allows for the measurement of only one state variable which is the angular position of the arm. This estimator predicts the state vector at each time step and corrects its prediction based on the angular position measurements. The transformation temperatures of the SMA wire are stress dependent, adding to complexity of the control of the position of the arm for certain angular positions. To overcome thais problem a sliding mode controller is designed to calculate the desired stress of the wire based on the desired angular position of the arm. The stress of the wire is a better set-point for the controller since the transformation temperatures and hence the Martensite fraction are functions of the wire's stress. A feedback controller maintains this desired stress by regulating the input voltage to the wire. The stabilization and tracking performance of this controller is presented and compared with a PID controller.

Unconstrained magnetorheological-elastomers (MRE) experience a stiffness increase and elastomeric deformation in response to an applied magnetic field. An MRE consists of ferromagnetic particles dispersed in a host elastomer matrix. This study considers whether the stiffness change of MRE springs is due to magnetic particle-to-particle interactions or to elastomer deformation. If the stiffening is attributable to magnetic particle interaction, then it should occur even in the absence of the elastomer. To test this hypothesis, a smart fabric consisting of low-carbon steel thread in one direction and nonmagnetic thread in the other was created. Two extension springs were placed in parallel with this smart fabric, and placed in between two iron masses. An electromagnet coil wound about one of the masses provided the source of magnetic field across the smart fabric. The frequency response of the device was measured when the coil was driven by a DC current, at 0.5 Amp increments, from 0 to 4. The device exhibited a 33% increase in stiffness at 4 Amps compared to the stiffness at 0 Amps. While this shift is not as large as shifts observed in MREs, the design was not optimized for iron content, and only had a 0.6% iron content.

In this paper, the authors proposed to study a model and a control strategy of a two-dimensional conveyance system based on the principles of the Autonomous Decentralized Microsystems (ADM). The microconveyance system is based on distributed cooperative MEMS actuators which can produce a force field onto the surface of the device to grip and move a micro-object. The modeling approach proposed here is based on a simple model of a microconveyance system which is represented by a 5 x 5 matrix of cells. Each cell is consisted of a microactuator, a microsensor, and a microprocessor to provide actuation, autonomy and decentralized intelligence to the cell. Thus, each cell is able to identify a micro-object crossing on it and to decide by oneself the appropriate control strategy to convey the micro-object to its destination target. The control strategy could be established through five simple decision rules that the cell itself has to respect at each calculate cycle time. Simulation and FPGA implementation results are given in the end of the paper in order to validate model and control approach of the microconveyance system.

This paper presents novel magnetic actuator and sensor devices with a magnetostrictive/piezoelectric laminate. Both actuator and sensor are based on the conversion of electric and magnetic energies of piezoelectric and magnetostrictive materials via mechanical coupling, thus the advantages of the piezoelectric material, low power consumption and high speed response, are reflected on both functions. Here, several devices, laminations of Tb-Dy-Fe alloys and PZTs with different geometries or properties integrated into a magnetic circuit, are fabricated and their capabilities of magnetic force controlling and displacement sensing are investigated.

In active Fault Tolerant Control Systems (FTCS), a Fault Detection and Identification (FDI) algorithm is used to monitor system performance, to detect the occurrence of a fault and to estimate system parameters. The natural existence of environmental noises, disturbances, and small modelling uncertainties will force the FDI algorithm to estimate system parameters with some inaccuracies. As a result, the system to be controlled includes parameter uncertainties. In this paper, plant parameter uncertainties are assumed to be time-varying unknown-but-bounded. Exponential stabilization of FTCS for systems with uncertainties is studied, and a stabilization algorithm is constructed. A numerical example is presented to demonstrate the potential of the theoretical developments.

In this paper we discuss an Adaptive Optics (AO) system for the control of geometrical fluctuations in a laser beam based on the interferometric detection of phase front. By comparison with the usual Shack-Hartmann based AO system, we show that this technique is of particular interest when high sensitivity and high band-pass are required for correction of small perturbations like, for instance, the control of the input beam of gravitational waves interferometric detectors. The good results obtained allow us to decide for its application within the mode cleaner system of the 3m prototype optical interferometer on gravitational wave detection (IDGW-3P) developed for R&D and operational in Napoli.

We investigate whether the discrete energy levels and the high peak absorption in quantum dots (QDs) provide an opportunity for increasing the electro-optic and nonlinear optical properties. For this purpose we calculate the electrorefraction spectra of QDs starting from the Luttinger-Kohn Hamiltonian and using a plane-wave expansion for solving the eigenstates of the QD. For a pyramidal InAs/GaAs quantum dot, we find a high peak electrorefraction of 0.35 for TE-polarization, which is 35x larger than in a quantum well. In the tail of the quantum dot absorption spectrum, we find an electrorefraction of 1.3.10-2 at an absorption loss of 0.15 dB/cm. Finally we investigate the refractive index variation due to state filling in InAs/InP cylindrical quantum dots.

In this paper, an adaptive reconfigurable control system based on extended Kalman filter approach and eigenstructure assignments is proposed. System identification is carried out using an extended Kalman filter (EKF) approach. An eigenstructure assignment (EA) technique is applied for reconfigurable feedback control law design to recover the system dynamic performance. The reconfigurable feedforward controllers are designed to achieve the steady-state tracking using input weighting approach. The proposed scheme can identify not only actuator and sensor variations, but also changes in the system structures using the extended Kalman filtering method. The overall design is robust with respect to uncertainties in the state-space matrices of the reconfigured system. To illustrate the effectiveness of the proposed reconfigurable control system design technique, an aircraft longitudinal vertical takeoff and landing (VTOL) control system is used to demonstrate the reconfiguration procedure.

Laser interferometry is one of the most sensitive methods for small displacement displacement. This technique was successfully used in several fields of physics, giving very good performances also due to the large availability of optical components and high quality and relatively low cost laser sources. At the same time this technique is enough flexible to be effectively used in very different applications. In particular, in this paper, we present a laser interferometric system used to read the position of a free mirror to measure the local seismic noise. The performances of the interferometric system were analyzed in comparison with a standard accelerometer. The result are encouraging also if some problem, mainly connected with the sensibility a with the stability of the interferometric system have to be better studied.

Studies have been conducted on the identification of modal parameters including natural frequencies, damping coefficients and mode shapes of the Nottingham Wilford Bridge using ambient excitation. An approach to estimate modal parameters, from only output data (in the time domain) using the wavelet transform, is presented. Displacements responses of this structural system are used in the wavelet transform to identify its dynamic characteristics. To measure real-time displacement of the bridge a global positioning system (GPS) sensor network was designed and installed on the bridge. The modal properties were extracted using a two-step methodology. In the first step, the random decrement method was used to transform random signals in free vibration responses. Finally, the Eigensystem Realization Algorithm and a Wavelets based technique were used to extract natural frequencies and to determine the mode shapes of the structure.

The main purpose of this paper is to describe how standard spectral analysis techniques can provide an efficient and easy to interpret method for the characterisation and identification of semi-active dampers. The paper begins with a brief description of the spectral analysis algorithms, followed by detailed simulation examples to demonstrate their use. The focus throughout is on the techniques ability to provide an intuitive insight into a systems behaviour and the ease with which a priori knowledge and various modelling strategies can be incorporated.

The Preisach operator and its variants have been successfully used in the modeling of a physical system with hysteresis. In an application, one has to determine the density function describing the Preisach operator from measurements. In our earlier work, we described a regularization method to obtain an approximation to the density function with limited measurements. In this paper, we describe methods for recursively computing the approximate density function. These methods can be implemented in real-time controllers for smart actuators.

Aeroelastic control of flutter by means of trailing edge surfaces can be a very effective method, providing that the actuation system is capable of generating suffcient force and displacement over the bandwidth of interest. This effort describes the mechanical design aspects of a flap actuation system using V-stack piezoelectric actuator and Q-parameterization technique for identifying the plant at supercritical speeds. A flap actuation mechanism that takes advantage of the shape of the actuator (V) was designed. In order to validate the actuation concept the actuator was integrated into a NACA 0015 typical section that was tested in the wind tunnel at Duke University. An initial nominal controller was designed to stabilize the typical section for a limited range of speeds above the open-loop flutter boundary. The technique of Q-parameterization was then used to parameterize the unstable system as a function of stable systems, each derived from the nominal controller. Operating in closed loop, flutter was suppressed at the speed it occurred in open loop, and the flutter boundary was extended by more than 50%.