Recently, thin piezoelectric fibers with diameters between 10 micrometer and 30 micrometer have been manufactured and used as sensor/actuator components of smart composite structures. The paper deals with the mathematical analysis, numerical simulation and optimal design of smart structures controlled by such thin piezoelectric fibers, where two different approaches are investigated. At first a smeared concept is applied. Each active layer consisting of piezoelectric fibers embedded in a matrix material is modeled as an anisotropic coupled electro-mechanical continuum and analyzed by recently developed special finite shell elements. At second a discrete concept is used, where the piezoelectric fibers are modeled as one-dimensional truss like finite elements which are embedded into conventional finite elements by a penalty technique. These two approaches are discussed and compared.

A direct finite element model is developed for the full-scale analysis of electromechanical phenomena involved in SAW devices. The equations of wave propagation in piezoelectric materials are discretized using the Galerkin method, in which an implicit algorithm of the Newmark family with unconditional stability is implemented. The Rayleigh damping coefficients are included in the elements near the boundary to reduce the influence of the reflection of waves. The performance of the model is demonstrated by the analysis of the frequency response of a YZ-lithium niobate filter with two uniform ports, with emphasis on the influence of the number of electrodes. The frequency response of the filter is obtained through the Fourier transform of the impulse response, which is solved directly from the finite element simulation. It shows that the finite element results are in good agreement with the characteristic frequency response of the filter predicted by the simple phase-matching argument. The ability of the method to evaluate the influence of the bulk waves at the high-frequency end of the filter passband and the influence of the number of electrodes on insertion loss is noteworthy. We conclude that the direct finite element analysis of SAW devices can be used as an effective tool for the design of high performance SAW devices. Some practical computational challenges of finite element modeling of SAW devices are discussed.

This paper presents a finite element/boundary element (FE/BE) formulation for modeling and analysis of active-passive noise control system. Finite element method is proposed to model the smart plate with surface bonded piezoelectric patches and the enclosing walls and the dual reciprocity boundary element method is proposed for modeling the acoustic cavity. The use of FE/BE method facilitates us imposing the impedance boundary conditions at the fluid/passive absorber/structure interface. An output feedback optimal controller design procedure is given for the smart plate system with active patches for the low frequency regime.

The design of ultrasonic transducers for high power applications, e.g. in medical therapy or production engineering, asks for effective computer aided design tools to analyze the occurring nonlinear effects. In this paper the finite-element-boundary-element package CAPA is presented that allows to model different types of electromechanical sensors and actuators. These transducers are based on various physical coupling effects, such as piezoelectricity or magneto- mechanical interactions. Their computer modeling requires the numerical solution of a multifield problem, such as coupled electric-mechanical fields or magnetic-mechanical fields as well as coupled mechanical-acoustic fields. With the reported software environment we are able to compute the dynamic behavior of electromechanical sensors and actuators by taking into account geometric nonlinearities, nonlinear wave propagation and ferroelectric as well as magnetic material nonlinearities. After a short introduction to the basic theory of the numerical calculation schemes, two practical examples will demonstrate the applicability of the numerical simulation tool. As a first example an ultrasonic thickness mode transducer consisting of a piezoceramic material used for high power ultrasound production is examined. Due to ferroelectric hysteresis, higher order harmonics can be detected in the actuators input current. Also in case of electrical and mechanical prestressing a resonance frequency shift occurs, caused by ferroelectric hysteresis and nonlinear dependencies of the material coefficients on electric field and mechanical stresses. As a second example, a power ultrasound transducer used in HIFU-therapy (high intensity focused ultrasound) is presented. Due to the compressibility and losses in the propagating fluid a nonlinear shock wave generation can be observed. For both examples a good agreement between numerical simulation and experimental data has been achieved.

A fuzzy finite element based approach is developed for modelling smart structures with vague or imprecise uncertainties. Fuzzy sets are used to represent the uncertainties present in the piezoelectric, mechanical, thermal, and physical properties of the smart structure. In order to facilitate efficient computation, a sensitivity analysis procedure is used to streamline the number of input fuzzy variables, and the vertex fuzzy analysis technique is then used to compute the possibility distributions of the responses of the smart structural system. The methodology has been developed within the framework of the SMARTCOM computational tool for the design/analysis of smart composite structures. The methodology developed is found to be accurate and computationally efficient for solution of practical problems.

A new technique to produce a radial gradient in the refractive index in organic-inorganic nanocomposite materials using sol- gel techniques in combination with electrophoretically induced concentration profiles of oxide nanoparticles is presented. Electric charges of the ZrO₂ nanoparticle surface force the particles to diffuse in the gel state in the presence of an electric field employed by appropriate electrodes. In a previous study is has been shown that there exists a linear relation between the refractive index and the concentration of the oxide particles. In this paper the emphasis is focused to the development of appropriate electrodes through numerical modeling. The underlying time dependent parabolic partial differential equation is solved numerically using implicit methods. For the electric potential, a parametric model is assumed from which the spatial dependent electric field follows by gradient expansion. The parameters of the model are optimized using an iterative modified Levenberg-Marquardt algorithm to match with the prescribed refractive index. The results of this new approach are discussed.

Effective integration of sensors, actuators and controllers with the structures is key to the success of smart structures. This concept has been manifested in numerous applications of smart structures in the areas such as civil, aerospace and automotive engineering. Control systems to be integrated with the structure is of paramount importance for ensuring the performance requirements in the presence of modal parameter variations, modeling errors and control effort constraints. The primary uncertainty associated with smart structural systems use the natural frequency variations. Linear Matrix Inequalities (LMIs) can be utilized to incorporate the real parameter uncertainty due to parameter variations and control input limits in the controller design. One of the challenges in the design of such controllers is the conservatism due to over bounding effect from the multiple constraints. Additional conservatism can also come from the approximation of the real parametric uncertainty due to modal parameter variations as sector bounded nonlinear, time varying or complex valued uncertainty. Using the traditional robustness analysis methods such as small gain theorem in the controller design will result in conservative designs leading to poor performance. In this paper, we present a controller synthesis procedure based on Popov stability results for reducing the conservatism in the design. Robust controllers are designed for real- parametric uncertainty arising from natural frequency variations in the presence of control input limits. Maximum possible attenuation in the structural response due to finite energy disturbances is also achieved. Trade-off between the robustness versus the control input limit is discussed. The design procedure is applied on a smart structural test article and the results are presented.

Topic of the presentation is a procedure to determine controller parameters using principles from Internal Model Control (IMC) in combination with Quantitative Feedback Theory (QFT) for robust vibration control of flexible mechanical structures. IMC design is based on a parameterization of all controllers that stabilize a given nominal plant, called the Q-parameter or Youla-parameter. It will be shown that it is possible to choose the controller structure and the Q- parameter in a very straightforward manner, so that a low order controller results, which stabilizes the given nominal model. Additional constraints can be implemented, so that the method allows for a direct and transparent trade-off between control performance and controller complexity and facilitates the inclusion of low-pass filters. In order to test (and if necessary augment) the inherent robust performance of the resulting controllers, boundaries based on the work of Kidron and Yaniv are calculated in the Nichols-Charts of the open loop and the complementary sensitivity function. The application of these boundaries is presented. Very simple uncertainty models for resonant modes are used to assess the robustness of the design. Using a simply structured plant as illustrative example we will demonstrate the design process. This will illuminate several important features of the design process, e.g. trade-off between conflicting objectives, trade- off between controller complexity and achievable performance.

The optimal control algorithm is one of the feasible feedback algorithms for vibration suppression of flexible structures. One of the commonly encountered problems of the optimal control implementation is the spillover problem. The spillover generally occurs when modeling a continuous structure that has infinite number of resonance modes as a nominal model with finite modes for controller design. This paper presents a design of an optimal controller that is low order and can prevent the spillover problem when the unmodeled resonance modes perturb the feedback control loop. For low order controller design, this paper proposes modal Hankel singular values (MHSV) for efficient nominal model reduction. Low order controller can be derived from the reduced nominal model. For design of more stable controller, this paper applies frequency dependent weight functions to the cost function. The weight functions prevent the spillover by making optimal controller not to excite the resonance modes that are not included in nominal model. The optimal controller is derived from the nominal model. This weight function approach optimizes the control performance and control stability by smoothening the discrepancy between the weights of on the modeled modes to be controlled and unmodeled modes to be stabilized. A finite element model is exploited to develop the controller and to test its control performance and stability against high resonance mode spillover.

In this paper, noise reduction performance of piezoelectric smart panels is experimentally studied. Piezoelectric smart panel is comprised of plate structure on which piezoelectric sensor/actuators are bonded and sound absorbing materials. The concept of piezoelectric smart panels is to combine passive and active strategies such that the noise reduction can be effectively achieved over a broad frequency range. The noise reduction performance is tested on an acoustic tunnel. The tunnel is made of a guided tube having a square cross section and loud speaker is installed at one end as a sound source while nonreflection terminator is attached at the other end. The panels can be mounted in the middle of the tunnel and the transmission as well as reflection of panels can be measured. Noise reduction performance of a single plate with absorbing material shows a good result at mid frequency region but little effect in the resonance frequencies. When the active control scheme is activated, a remarkable noise reduction is observed at the resonance. The combined use of absorbing materials and piezoelectric active devices brings the simultaneous noise reduction in mid and low frequency regions. It can be concluded that piezoelectric smart panels incorporating passive absorbing material and active piezoelectric devices, is a promising technology for noise reduction in a wide band frequency.

The influence of piezoceramic actuator nonlinearities on the response of a panel-enclosure system is examined. As an extension of our earlier work, hysteresis effect is also included in the nonlinear relationship between the free strain experienced by a piezoceramic patch and the applied electric field. The responses of the system with the hysteretic effect are discussed and compared with experimental results.

We consider the problem of reducing the noise radiation from a thick-walled cylindrical shell by actively controlling the motion of the shell's outer surface. Because the shell is very stiff, it is difficult to directly control the shell deflections. Instead, the proposed approach is to cover the shell's outer surface with curved active composite panels. Each panel contains several embedded accelerometers mounted to its outer and inner surfaces, which can sense both the motion of the panel base (i.e., the outer motion of the shell) and the outer surface of the panel (i.e., the radiating surface). The accelerometers are used in both feedback and feedforward architectures, in which the accelerometer signals are used to command the panel displacement, in order to reduce the motion of the panel outer surface, reducing the radiated noise. Experimental results show that, in the best case, 10 - 30 dB of surface vibration reduction can be achieved in the frequency range of interest, which is 250 - 2000 Hz.

The possibilities of using dynamic feedback of piezoelectric layers for controlling the acoustic properties of a surface are investigated. The investigation shows that in principle it is possible to achieve desired properties (e.g. no reflection, artificial transparency or simultaneous transmission and reception of information) using a single piezo-electric layer. The layer then operates both as a sensor and as an actuator. This approach can be described as controlling the boundary conditions of the acoustic field. The study shows that this will work well, also in practice, if the material has an electromechanic coupling factor that is large enough. Explicit controllers for these cases are given. However, for the values of electro-mechanic coupling factors of available materials, the above construction is not suitable for practical purposes, due to non-robustness. Therefore, the possibility of using multiple layers is also investigated. It turns out that a two layer construction can achieve the properties of a single layer with large electro-mechanic coupling factor. For the specific problem of achieving no reflection, an explicit construction of a realistic controller is given. Requirements of robust stability and limited voltage amplitudes imply that low reflection cannot be achieved at low and high frequencies. However for a large frequency interval, it is possible to obtain low reflection. It is shown that both the gain and phase margins are infinite with this controller. Our work makes extensive use of the Redheffer star-product for systematic modeling, analysis and synthesis of the system and the regulator.

We describe structural-acoustic control experiments on a model fuselage test-bed, using collocated pairs of piezoelectric sensors and actuators. The test-bed is a hybrid-scaled model fuselage designed to be representative of complex aircraft structures with rib and stringer construction, which results in a structure with high modal density and complex behavior. The sensor/actuator pairs consist of PVDF film and PZT ceramic sheets bonded to the surface of the model fuselage. Closed- loop control of the fuselage skin was carried out with 30 collocated sensor/actuator pairs, covering approximately 10% of the surface area of the test-bed. The disturbance source is a PZT patch bonded to an adjacent panel. Rate feedback was applied to each collocated pair simultaneously (independent loop closure). Accelerometers attached to the panels and microphones located inside the test-bed were used as performance sensors. The experimental results show a reduction of as much as 20 dB in structural acceleration and up to 10 dB of attenuation in the interior acoustic pressure levels at resonant peaks, over the frequency range of 100 - 2000 Hz.

Previous research has demonstrated that rigorous modeling and identification theory can be derived for structural dynamical models that incorporate control influence operators that are static Krasnoselskii-Pokrovskii integral hysteresis operators. Experimental evidence likewise has shown that some dynamic hysteresis models provide more accurate representations of a class of structural systems actuated by some active materials including shape memory alloys and piezoceramics. In this paper, we show that the representation of control influence operators via static hysteresis operators can be interpreted in terms of a homogeneous Young's measure. Within this framework, we subsequently derive dynamic hysteresis operators represented in terms of Young's measures that are parameterized in time. We show that the resulting integrodifferential equations are similar to the class of relaxed controls discussed by Warga¹⁰, Gamkrelidze²⁴, and Roubicek²⁵. The formulation presented here differs from that studied in ¹⁰, ²⁴ and ²⁵ in that the kernel of the hysteresis operator is a history dependent functional, as opposed to Caratheodory integral satisfying a growth condition. The theory presented provides representations of dynamic hysteresis operators that have provided good agrement with experimental behavior in some active materials. The convergence of finite dimensional approximations of the governing equations is also proven.

Computational micromagnetics plays an important role in design and control of magnetostrictive actuators. A systematic approach to calculate magnetic dynamics and magnetostriction is presented. A finite difference method is developed to solve the coupled Landau-Lifshitz-Gilbert (LLG) equation for dynamics of magnetization and a one dimensional elastic motion equation. The effective field in the LLG equation consists of the external field, the demagnetizing field, the exchange field, and the anisotropy field. A hierarchical algorithm using multipole approximation speeds up to the evaluation of the demagnetizing field, reducing computational cost from O(N²) to O(NlogN). A hybrid 3D/1D rod model is adopted to compute the magnetostriction: a 3D model is used in solving the LLG equation for the dynamics of magnetization; then assuming that the rod is along z-direction, we take all cells with same z-coordinate as a new cell. The values of the magnetization and the effective field of the new cell are obtained from averaging those of the original cells that the new cell contains. Each new cell is represented as a mass- spring in solving the motion equation. Numerical results include: (1) domain wall dynamics, including domain wall formation and motion; (2) effects of physical parameters, grid geometry, grid refinement and field step on H - M hysteresis curves; (3) magnetostriction curve.

The optimal motion control of an asymmetric rotor-magnetic bearing system based on the linear quadratic regulator theory (LQR) is addressed in this paper. To this end, and as a basic prerequisite, a rigorous modeling of the rotor-magnetic bearing system that includes also the unbalance effect is considered. The derivation of the equations of motion is based upon the application of the Hamilton's variational principle. New schemes related to the selection of the state weighting matrix Q and the control weighting matrix R involved in the quadratic functional to be minimized are proposed. The obtained results are compared with those reported in the available literature and the benefices of the selected weighting matrices are revealed.

A robust tracking control architecture is proposed for a class of continuous-time nonlinear dynamic systems actuated by piezoelectric actuators. Generally, hysteresis nonlinearity exists in the piezoelectric actuator, which may cause undesirable inaccuracy. Based on solutions of a general hysteresis model, an approximation function is introduced to compensate for effects of the hysteresis nonlinearities. This approximation function is implemented by fuzzy logic method, which is expressed as a series expansion of basis functions. Combining this approximation function with adaptive control techniques, a robust control algorithm is developed. As a result, global asymptotic stability of the system is established in the Lyapunov sense.

Computational micromagnetics in three dimensions is of increasing interest with the development of magnetostrictive sensors and actuators. In solving the Landau-Lifshitz-Gilbert (LLG) equation, the governing equation of magnetic dynamics for ferromagnetic materials, we need to evaluate the effective field. The effective field consists of several terms, among which the demagnetizing field is of long-range nature. Evaluating the demagnetizing field directly requires work of O(N²) for a grid of N cells and thus it is the bottleneck in computational micromagnetics. A fast hierarchical algorithm using multipole approximation is developed to evaluate the demagnetizing field. We first construct a mesh hierarchy and divide the grid into boxes of different levels. The lowest level box is the whole grid while the highest level boxes are just cells. The approximate field contribution from the cells contained in a box is characterized by the box attributes, which are obtained via multipole approximation. The algorithm computes field contributions from remote cells using attributes of appropriate boxes containing those cells, and it computes contributions from adjacent cells directly. Numerical results have shown that the algorithm requires work of O(NlogN) and at the same time it achieves high accuracy. It makes micromagnetic simulation in three dimensions feasible.

A finite element was developed to model the dielectric property of the medium that fills the crack cavity in a piezoelectric material. The element was interfaced with the commercial code ABAQUS which provides the piezoelectric element to model the cracked piezoelectric body. The crack cavity permeability effects on the near tip stresses and electric fields in a compact tension specimen were investigated and discussed. The domain switching zones corresponding to various loads and crack surface electric boundary conditions were obtained. As expected, an increased permeability in the crack cavity decreased the size of domain switching zone. It was found that the outcome of domain switching depends on the loading sequence.

We investigated the use of positive position feedback (PPF) to suppress high-amplitude vibrations of a structural dynamic model of a twin-tail assembly of the F-15 fighter when subjected to primary resonance excitations. We developed the nonlinear differential equations of motion and obtained an approximate solution using the method of multiple scales. Then, we conducted bifurcation analyses for the open- and closed-loop response of the system and investigated theoretically the performance of the control strategy. The theoretical findings indicate that the control law leads to an effective vibration suppression and bifurcation control. We conducted experiments to verify the theoretical analysis. We built a digital control system that consists of the SIMULINK modeling software and a dSPACE controller installed in a personal computer, and we used actuators made of piezoelectric ceramic material. The experimental results show that PPF is effective in suppressing the steady-state vibrations.

For nonlinear and adaptive control of smart structures direct and indirect neural network control strategies have been suggested. In indirect neural network control the identified plant models are usually implemented as black-box neural networks using no a priori knowledge. Designing a neural network for system identification using dimensional analysis results in neural networks, where in contrary to black-box solutions no dimensionally inhomogeneous states can occur. Furthermore, the generalization and learning properties of neural networks designed using dimensional analysis are usually improved compared to conventional black-box networks. This work describes a technique of using neural networks for system identification and control, where the neural network has been constructed according to a dimensional analysis of the governing equations.

A neural network-based control system is developed for self- adapting vibration control of laminated plates with piezoelectric sensors and actuators. The conventional vibration control approaches are limited by the requirement of an explicit and often accurate identification of the system dynamics and subsequent 'offline' design of an optimal controller. The present study utilizes the powerful learning capabilities of neural networks to capture the structural dynamics and to evolve optimal control dynamics. A hybrid control system developed in this paper is comprised of a feed- forward neural network identifier and a dynamic diagonal recurrent neural network (DRNN) controller. Sensing and actuation are achieved using piezoelectric sensors and actuators. The performance of hybrid control system is tested by numerical simulation of composite plate with embedded piezoelectric actuators and sensors. Finite element equations of motion are developed based on shear deformation theory and implemented for a plate element. The dynamic effects of the mass and stiffness of the piezoelectric patches are considered in the model. Numerical results are presented for a flat plate. A robustness study including the effects of structural parameter variation and partial loss of sensor and actuator is performed. The hybrid control system is shown to perform effectively in all these cases.

Future High Energy Physics experiments require the use of light and stable structures to support their most precise radiation detection elements. These large structures must be light, highly stable, stiff and radiation tolerant in an environment where external vibrations, high radiation levels, material aging, temperature and humidity gradients are not negligible. Unforeseen factors and the unknown result of the coupling of environmental conditions, together with external vibrations, may affect the position stability of the detectors and their support structures compromising their physics performance. Careful optimization of static and dynamic behavior must be an essential part of the engineering design. Genetic Algorithms (GA) belong to the group of probabilistic algorithms, combining elements of direct and stochastic search. They are more robust than existing directed search methods with the advantage of maintaining a population of potential solutions. There is a class of optimization problems for which Genetic Algorithms can be effectively applied. Among them are the ones related to shape control and optimal placement of sensors/actuators for active control of vibrations. In this paper these two problems are addressed and numerically investigated. The finite element method is used for the analysis of the dynamic characteristics. For the case of the optimal placement of sensors/actuators a performance index, proportional to the damping of the system in closed- loop, is used. Genetic algorithms prove their efficiency in this kind of optimization problems.

This paper is concerned with the real-time automatic tuning of the multi-input multi-output positive position feedback controllers for smart structures by the genetic algorithms. The genetic algorithms have proven its effectiveness in searching optimal design parameters without falling into local minimums thus rendering globally optimal solutions. The previous real-time algorithm that tunes a single control parameter is extended to tune more parameters of the MIMO PPF controller. We employ the MIMO PPF controller since it can enhance the damping value of a target mode without affecting other modes if tuned properly. Hence, the traditional positive position feedback controller can be used in adaptive fashion in real time. The final form of the MIMO PPF controller results in the centralized control, thus it involves many parameters. The bounds of the control parameters are estimated from the theoretical model to guarantee the stability. As in the previous research, the digital MIMO PPF control law is downloaded to the DSP chip and a main program, which runs genetic algorithms in real time, updates the parameters of the controller in real time. The experimental frequency response results show that the MIMO PPF controller tuned by GA gives better performance than the theoretically designed PPF. The time response also shows that the GA tuned MIMO PPF controller can suppress vibrations very well.

This paper describes development of a motion controller for Shape Memory Alloy (SMA) actuators using a dynamic model generated by a neuro-fuzzy inference system. This kind of smart alloy is known to have a unique characteristic in that its shape can be controlled by temperature that can be varied by passing a current through it. Using SMA actuators, it would be possible to design miniature mechanisms for a variety of applications. Today SMA is used for valves, latches, and locks, which are automatically activated by heat. However it has not been used as a motion control device due to difficulty in the treatment of its highly non-linear strain-stress hysteresis characteristic which is further influenced by its temperature. In this project, a dynamic model of a SMA actuator is developed using ANFIS, a neuro-fuzzy inference system provided in MATLAB environment. Using neuro-fuzzy logic, the system identification of the dynamic system is performed by observing the change of state variables (displacement and velocity) responding to a known input (voltage across the SMA actuator). Then, using the dynamic model, the estimated input voltage required to follow a desired trajectory is calculated in an open-loop manner. The actual input voltage supplied to the SMA actuator is the sum of this open-loop input voltage and an input voltage calculated from an ordinary PD control scheme. This neuro- fuzzy logic-based control scheme is a very generalized scheme that can be used for a variety of SMA actuators. Experimental results are provided to demonstrate the potential for this type of controller to control the motion of the SMA actuator.

In this paper, the concept of variable structure system (VSS) with sliding mode was used to develop a fuzzy controller for a class of nonlinear system. The proposed sliding mode fuzzy controller (SMFC) preserves the fundamental property of sliding mode control that is stability and robustness in the presence of disturbances and model uncertainties. To reduce the number of design parameters in SMFC, we adopted the concept of parameterization or input-output mapping factor and devised a systematic tool for analyzing and enhancing the performance of SMFC. For demonstration, we applied the SMFC to the inverted pendulum problem. Simulation results indicates that the fuzzy sliding mode control perform well in the presence of disturbances and is insensitive to the parameter variation of the system.

An analysis of the evolution of intelligence and survival strategy of certain materials is presented in this paper. Materials have been further classified in this paper based on their smartness or intelligence. The criteria used in the analysis involve matter, energy, information, and geometry. Also, a novel perspective on the meaning of intelligence is proposed. Thus, a system is considered to be intelligent if it normally possesses a survival strategy with regards to its state of being. Essentially, new definitions for information and hierarchical structures have been added to the classical matter-energy dualism. The influence of geometry has proved to be very important in the evolution and properties of matter. Based on the characteristics of the living systems a correlation between living and non-living systems has been established. It has also been demonstrated that the geometrical shape of a material structure is determined by its survival strategy. Furthermore, hierarchical structures of intelligent materials have been analyzed from geometrical point of view. This has led to the conclusion that geometry represents a complementary factor in the intelligence of materials.

Ionic polymers or solid polyelectrolytes in functionally- graded composite form with a conductive phase such as a metal, conductive polymer or graphite, when swollen and suitably plated by conducting electrodes, display a spontaneous curvature increasing with the applied electric field E. There also exists an inverse effect, where an imposed deformation induces an electric field (in open circuit conditions) in such ionic polymer conductive composites (IPCC). Presented here is a description of these effects in the linear regime, based on linear irreversible thermodynamics, with two driving forces, namely the electric field E and a water pressure gradient (Delta) p and two fluxes, namely the electric current density J and water current density Q. Presented are also some qualitative estimates of the four Onsager coefficients which play important roles in the proposed model.

A metamodel-based presented is developed to optimize the force and displacement performance of a piezoceramic bimorph actuator. A segmented design with a variable piezoceramic layer thickness is proposed, where the thicknesses of discrete piezoceramic segments are used as the design variables. Design of experiments and metamodeling techniques are employed to construct computationally inexpensive approximations of finite element simulations of the PZT bimorph actuator. The metamodels are then used in lieu of the actual FEM for optimization. Design objectives include maximum tip deflection, maximum grasping force, and maximum work available at the tip. The metamodels are also used to rapidly generate the design space and identify the Pareto frontier for the competing design objectives of maximum deflection and maximum force. The accuracy and efficacy of two types of metamodels -- response surfaces and kriging models -- are compared in this study. By optimizing the thickness of the piezoceramic layers, and by allowing the voltage applied to each segment to vary, dramatic improvements in deflection and force are obtained when compared to a standard straight bimorph actuator. The motivation for this design is the need in the field of minimally invasive surgery for improved grasping tools, where a pair of optimized bimorph actuators can be used as a simple grasping device.

The unique thermal and mechanical properties offered by shape memory alloys (SMAs) present exciting possibilities in the field of aerospace engineering. When properly trained, SMA wires act as linear actuators by contracting when heated and returning to their original shape when cooled. It has been shown experimentally that the overall shape of an airfoil can be altered by activating several attached SMA wire actuators. This shape-change can effectively increase the efficiency of a wing in flight at several different flow regimes. To determine the necessary placement of these wire actuators within the wing, an optimization method that incorporates a fully-coupled structural, thermal, and aerodynamic analysis has been utilized. Due to the complexity of the fully-coupled analysis, intelligent optimization methods such as genetic algorithms have been used to efficiently converge to an optimal solution. The genetic algorithm used in this case is a hybrid version with global search and optimization capabilities augmented by the simplex method as a local search technique. For the reconfigurable wing, each chromosome represents a realizable airfoil configuration and its genes are the SMA actuators, described by their location and maximum transformation strain. The genetic algorithm has been used to optimize this design problem to maximize the lift-to-drag ratio for a reconfigured airfoil shape.

An experimental testbed is described that is used to study the feasibility of control of a class of flows that have low Reynolds numbers. The experimental testbed is comprised of a thin airfoil with a backward facing step machined into the upper surface. A thin PZT composite flap is mounted at the edge of the backward facing step to enable modification of the flow. Output measurement sensors consist of MEMs-based shear stress sensors, and conventional pressure taps, located on the surface of the airfoil. This paper derives a control framework for the synthesis of control methodologies for the testbed. A reduced order control model is obtained by employing reduced basis approximations of the two dimensional Navier-Stokes equations. Preliminary open loop experimental results are reported that illustrate the existence of convected large scale structures in the flow.

The first and second moments of response variables for SDOF system with pseudoelastic SMA's are obtained by a direct linearization procedure. This is an adaptation in the implementation of well-known statistical linearization methods, which provides concise, model-independent linearization coefficients. The method can be applied to systems that incorporate any SMA hysteresis model having a differential constitutive equation and can be used for zero and non-zero mean random vibration. The implementation eliminates the effort of deriving linearization coefficients for new SMA hysteresis model. In this work the statistical response of SDOF system containing a mass and a bar made of SMA is obtained via direct linearization procedure. The model considered is a phenomenological one-dimensional constitutive model, originally proposed by Graesser and Cozzarelli, which provides the capability to model both the martensitic twinning hysteresis and martensitic-austenite pseudoelastic behavior typical of SMA's. Response statistics for zero mean random vibration can be obtained. Furthermore, non-zero mean analysis of the system is carried out and comparisons are made with Monte Carlo simulation.

This paper presents a new type of an optical pick-up for CD- RIM drive feeding system. The optical pick-up is activated by a pair of bimorph piezoceramic actuators in order to achieve fine motion control of the objective lens. Following the derivation of the governing equation of motion, a control model, which takes into account the hysteresis behavior of the actuator and also parameter variation such as frequency changes, is established in a state space form. A robust controller is then formulated and experimentally realized. Various position trajectories to be followed by the optical pick-up are adopted and tracking control responses are presented in time domain. In addition, control durability is demonstrated in order to provide a practical feasibility.

A technique for deforming a flexible wing to achieve a specified roll rate within a specified time at different Mach Numbers is examined. Rather than using an aileron system for roll, antisymmetric elastic twist and camber is determined to achieve the required rolling moment for a specified roll rate. The elastic twist and camber is achieved by providing a system of actuating elements distributed within the internal substructure of the wing to provide control forces. The modal approach is used to develop the dynamic equilibrium equations which culminates in the steady roll maneuver of a wing subjected to aerodynamic loads and the actuating forces. The distribution of actuating forces to achieve the specified steady flexible roll rate within a specified time was determined by using Independent Modal-Space Control (IMSC) design approach. Here, a full-scale realistic wing is considered for the assessment of the strain energy required to produce the antisymmetric twist and camber deformation to achieve the specified roll performance.

Cross-talk in transducer arrays is an important issue that affects the array performance. For therapeutic arrays and other arrays that are driven in continuous wave (CW) mode, the cross-talk between array elements reduce the acoustic power output and array directivity. This paper is devoted to the minimization of the cross-talk in air-backed arrays by optimizing the inter-element connections in the kerf. The kerf region is the design domain and the induced electric voltage on the passive element at a given operating frequency is the objective function. A density-based topology optimization problem is formulated and solved using the sequential linear programing (SLP). Preliminary optimization results for a three-element array are presented. The effectiveness of the design with respect to the cross-talk, far-field pressure level and directivity is discussed.

A prevalent method of damage detection is based on identifying changes in modal characteristics due to damage induced variations in stiffness or mass along a structure. It is known that modal frequencies can be insensitive to damage, and the open-loop sensitivity itself depends on modal properties and damage location. Here, we develop methods of designing control laws that enhance the sensitivity of modal characteristics to damage. Sensitivity enhancing control exploits the relationship between control gains and closed-loop dynamics in order to increase the observability of damage. The design methods are based on optimization of cost functions that involve the dependence of classic measures of sensitivity on design variables, which include placement of sensors and actuators and state feedback control gains. Due to the size of the design space and the unknown nature of the cost surface, genetic algorithms are used to find control laws that maximize sensitivity to specific damage types subject to control effort and stability constraints. Optimized control laws designed for sensitivity enhancement of stiffness damage in a cantilevered beam are demonstrated by numerical simulation.

In previous work we had proposed a low (6) dimensional model for a thin magnetostrictive actuator that was suitable for real-time control. One of the main results of this modeling effort was the separation of the rate-independent hysteretic effects from the rate-dependent linear effects. The hysteresis phenomenon may also be captured by a (modified) Preisach operator with the magnetic field H as the input. If one can find an inverse for the Preisach operator, then the composite system can be approximately linearized. In this paper, we complete the proof of the existence of an inverse theorem due to Brokate and Sprekels and propose a new algorithm for computation of the inverse. Previous algorithms used linearization of the operating point. As numerical differentiation is involved, this approach can cause divergence. Our algorithm does not linearize the Preisach operator, but makes use of its monotone increasing property. Convergence of the algorithm is proved using the contraction mapping principle.

This paper considers control analysis approaches for systems incorporating large actuator and sensor arrays. Applications of such systems are increasingly common because of the development of micro-systems technology. Many imaging systems have large one-dimensional or two-dimensional arrays of actuators. This includes RF or optical reflectors, display, printing, and other systems. Signal processing for large sensor arrays has well-established theory and applications, especially in imaging. At the same time, approaches to control of large distributed actuator and sensor arrays are much less developed. This paper considers one of the fundamental issues in design and analysis of large actuator and sensor array systems. The key notion in modern feedback control theory is the notion of uncertainty and associated notion of control robustness to this uncertainty. In control of dynamical systems evolving in time, structured uncertainty models are commonly accepted for theoretical analysis (Structured Singular Value or (mu) -analysis) and practical control design. In control of spatially distributed processes, there is a need to establish appropriate models of the uncertainty of the system spatial and dynamical characteristics. This paper discusses an extension of structured uncertainty models towards controlled systems with spatially distributed arrays of actuators and sensors. Unlike a dynamical uncertainty, spatial uncertainty is not casual in the spatial coordinate. This leads to related but different uncertainty models in the two cases. For spatial coordinates, boundary effects also contribute to the modeling error. By using the discussed uncertainty models, the existing methods of robust control design and analysis can be extended towards spatially distributed systems. As an illustrative example, this paper demonstrates an application of the developed approach to a one-dimensional model of a flexible reflector with a distrusted actuator array for shape control.

In general, it is well known that the measures of controllability and observability are variant under a coordinates transformation. In particular, the balanced realization of a system which is useful for reducing the order of a model and for implementing filters has some valuable properties, for example, that a system is equally controllable and observable and has a symmetric relation between a left and the corresponding right eigenvector. In this paper, we present a method for optimal placement of sensors and actuators by using the proposed measures of modal controllability and observability which are defined in a balanced coordinate system. This paper shows that these measures are more pertinent and useful in practical engineering problem such as the selection of the optimal number and location of sensors and actuators, and they are more accurate than the earlier results of Hamdan and Nayfeh in a viewpoint that they can reflect the effects of the norm of eigenvectors on the magnitude of measures. In addition, the optimal placement method using the additional measures is presented. For the vibration suppression of a flexible structure, a state feedback controller is designed by using the left eigenstructure assignment scheme which can take into account for the control effectiveness and the disturbance suppressibility of the closed-loop system simultaneously. These methods are applied to a simply supported flexible beam which is modeled to have six vibration modes, and the results of the simulations for optimal placement of sensors and actuators and vibration control of a flexible structure are presented for the validity of the proposed measures and the optimal placement method.

A dual approach based on both the structural tailoring and piezoelectric strain actuation, aimed at controlling the free vibration of rotating circular shaft subjected to axial forces is presented in this paper. Due to involvement in these systems of gyroscopic forces and, consequently of the possible occurrence of the divergence and flutter instabilities, implementation of the dual control methodology shows a high degree of efficiency toward postponement of the occurrence of these instabilities. The structural model of the shaft as considered in this paper is based on an advanced thin-walled beam that includes the effects of transverse shear, anisotropy of constituent materials, rotary inertias, etc. The displayed results reveal the synergistic implications of the application of this dual technology toward enhancing the dynamic response characteristics of these systems and expanding the domain of stability.

This paper presents an overview of the principles governing the formation of shape memory alloys (SMA) martensite in thin films SMA/Si composites and some examples. The transformation in these composites is constrained by the compatibility conditions at the martensite/austenite interface and as the martensite. Due to the difference of the thermal expansivities of the bimorph layers and due to the martensitic transformation in the active layer, internal stresses arise upon changing the temperature. These internal stresses together with the dual constraint determine the martensitic microstructure and, with it, the actuation characteristics of the bimorph. For tetragonal martensites bi- and uniaxial tensile and compressive stresses lead to larger or smaller hystereses. Details depend on the sign of the eigenstrain, c/a-1, and the texture of the film.

This study demonstrates that AFM is capable of observing domains of several tens of nanometers in fine grain PZT ceramics. The investigators have also shown that carefully conducted light polishing can result in no significant disturbance to domain patterns in hard PZT ceramics.

Classical Plate Theory (CPT) has been applied successfully in the past to the plates with distributed piezoelectric patch bonded to the surface or embedded within the layers. In all earlier models the mass and stiffness' contributions from sensor and actuator patches were neglected for estimating the natural frequencies of the smart plate. Also the thickness direction electric fields and strain fields inside the patches are assumed to be constant over the entire area of the patch. The validity of these assumptions depends on the size and relative stiffnesses of the patches and is not investigated before. In this paper the CPT is used to estimate the natural frequencies of a plate structure with surface bonded piezoelectric patches without the above-mentioned assumptions. A detailed modeling of the patches is developed by expressing the electric potential inside the patch as a quadratic function of thickness coordinate. The equations of motion are derived for a generally isotropic plate with surface bonded segmented patches. Solution to the dynamic equation of motion are obtained using Fourier series method for a plate with collocated piezoelectric actuator/sensor patches. The effect of the passive and active stiffness' of the surface bonded actuator and sensor patches on the dynamic characteristics of host plate structure is investigated.

An analytical method is given for the determination of the eigenfunctions and eigenfrequencies for one-dimensional structural vibration problems in the presence of patch sensors and patch actuators. The method is based on converting the differential equation formulation of the problem to an integral equation formulation. The conversion is accomplished by introducing an explicit Green's function. The Green's function consists of two parts, one taking account of the stiffness and the other taking account of the control moments induced by the distributed actuators. The control moments involve piezoelectric constants and feedback voltages made up of gains times the sensor signals. Obtaining the eigenvalues and eigenfunctions of this integral equation gives the solution to the piezo-control problem.

The main purpose of this paper is to assess the implications of a number of effects of geometric and physical nature on the vibration control of adaptive cantilevers modeled as composite thin-walled beams and simulating an aircraft wing. It is considered that the cantilevered beam is exposed to a pressure pulse generated, among others, by a blast or sonic-boom. The features on which preponderance will be given in this study are related with the non-uniformity of the beam cross section in the spanwise direction, anisotropy of constituent materials, transverse shear and warping inhibition. In order to control the dynamic response, a dual approach based on structural tailoring and adaptive materials technology will be implemented. The numerical simulations provide a comprehensive picture of the synergistic implications of the application of both the tailoring technique and feedback control upon the vibration response of nonuniform cantilevers exposed to time- dependent external excitations.

A finite-element based analysis for modeling active composite beams with embedded anisotropic actuation is presented. It is derived from three-dimensional electroelasticity, where the original problem is reduced via the variational asymptotic method. The resulting cross-sectional analysis takes into consideration passive and active anisotropic and nonhomogeneous materials, and represents general (thin-walled, thick-walled, solid) cross-sectional geometries. The formulation requires neither the costly use of 3-D finite element discretization nor the loss of accuracy inherent to any simplified representation of the cross section. The developed formulation is numerically implemented in VABS-A, and several numerical and experimental tests cases are used to support validation of the proposed theory. Also, the effect of the presence of a core in originally hallow configurations is presented and counter-intuitive conclusions are discussed. The generality of the method and accuracy of the results increase confidence at the design stage that the active beam structure will perform as expected and, consequently, should lower costs from experimental tests and further adjustments.

A theory for localized vibration control that is based on a partitioned Linear Quadratic Regulator (LQR) synthesis is presented. The present localized control consists of two components: a localized LQR controller that minimizes the control effort to attenuate the disturbances directly applied to each partitioned substructural system, and a controller that mitigates the interface transmission forces. The present theory is applicable both for quasistatic structural shape control and for the attenuation of structural vibrations. The localized controllers can be implemented in terms of strain actuation, proof-mass actuators, and strain rate-type active dampers. The basic features of the present theory are illustrated via numerical experiments as applied to the control of vibrations of a beam.

In this research, a real-time simulation of full state- derivative feedback control using acceleration measurements is presented. A new optimal control design algorithm based on non-standard performance indices in the 'Reciprocal State Space' framework is employed to design controllers and observers. A piezoelectric material (PZT) laminated cantilevered steel beam with an accelerometer is selected as a test bed. The system is modeled utilizing a multi-layered integrated finite element method with four degree of freedom, one-dimensional, bending elements. The resulting model, presented in generalized coordinates, is transformed to real orthogonal modal coordinates and a reduced order model is developed. Simulated results are provided in multiple formats.

Arrays of sensors and actuators designed to provide robust broadband feedback control with high performance and limited modeling are the subject of this paper. The reconfigurable array technique proposed here enables the design of reduced- order controllers for complex structures and offers the potential to improve closed-loop robustness and to broaden the region of good performance even as the plant changes. The weighted summation of sensor signals senses the modes that are relevant to performance while rejecting the remaining modes; therefore reducing the required complexity of the controller. These weights are obtained from the minimization of a cost function and under certain assumptions; it can be shown that a single optimum solution exists. The use of reconfigurable arrays is motivated by the need to control the vibration of complex structures. A thirty element collocated actuator and sensor array was bonded to a cylinder section. Array weights were computed and successfully applied to isolate target modes. Different methods of computing the weights are implemented and compared. The deleterious effects of spatial aliasing and the performance as a function of the array size are experimentally explored.

This paper is to present a numerical program of dynamic control for suppressing external disturbance to variable thickness beam-plates with sensors and actuators of piezoelectric layers on/in the structures using the scaling function transform of the Daubechies wavelet theory for approximation of functions. After the generalized Gaussian integral is applied to the scaling function transform, an explicit expression of identification of deflection configuration of the structures is expressed by the electric charge/current signals measured from the piezoelectric sensors. When a control law of negative feedback of the identified deflection and velocity signals is employed, the wavelet Galerkin method or wavelet weighted residual method is used to determine control voltage applied on the piezoelectric actuators. Due to that the scaling function transform is like a low-pass filter which can automatically filter out high- order signals of vibration or disturbance from the measurement and the controller employed here, this control approach does not lead to the undesired phenomenon of control instability that is often generated in a control system and caused by the spilling over of high-order signals from measurement and controller if no special technique is used in the control system. Some numerical simulations are carried out to show the efficiency of the proposed approach.

Controlled continuous tuning of the stiffness of shape memory alloy (SMA) spring elements of an adaptively tunable vibration absorber (ATVA) is a novel concept for adaptive-passive vibration control. Minimization of the vibration of a primary system is achieved indirectly via stiffness control of the SMA structural elements supporting a secondary mass. Stiffness control is further achieved via the heating of the SMA elements. In this paper a control law to achieve phase- tracking by controlling the heating of the SMA elements is developed and implemented. Successful analytical and experimental results demonstrate the feasibility of continuous control of the SMA ATVA. Performance of the SMA ATVA is compared to the performance of comparable passive tuned vibration absorbers (TVA). The comparison shows that substantial improvements in vibration attenuation can be achieved through the implementation of the SMA ATVA.

In this study, vibration distribution of a thin plate is detected using outputs from a number of long-span piezoelectric films that serve as distributed vibration sensors affixed on the plate. Using long-span piezoelectric films, only the integrated strains along the direction of the sensor span could be obtained. However, in the case that plural sensors were affixed and a kind of transformation was used, the vibration distribution could be obtained. We are considering applying the method for vibration control of space structures, namely antennas and/or solar battery paddles. In this study, basic technology for realizing the applications is presented. The strain distributions and the sensor outputs are predicted and calculated using NASTRAN (Finite Element Method). The strain distributions of a vibrating rectangular thin plate to which a number of long-span PVDF films were affixed are detected by experiment. These PVDF films are cut into several kinds of sinusoidal shapes and the outputs of the films are composed to the vibration distribution. This method is based on the theory that waves of any kind are composed by the sum of trigonometric function series. The usefulness of this approach is confirmed by comparing the calculational and experimental results.

This paper presents the theoretical development and experimental results of an active control system used to create a variable impedance termination on a Timoshenko beam that allows for the arbitrary setting of the reflection and/or transmission coefficients at the active boundary of the beam. A realizable feedforward control configuration with one input and two outputs is derived where a cost function constructed by filtering the response from four closely spaced sensors is minimized. The effectiveness of the system was evaluated experimentally on an aluminum beam with four patches of PVDF piezofilm used as sensors and two pairs of PZT piezoceramic patches used as bending moment actuators.

Results of an experimental study on the performance of a high speed, precision gantry system for application to X-ray stepper systems are presented. In particular a cross coupled control system design was compared to a master-master controller design on a gantry test bed powered by two linear motors. Tests were performed for the case where only inertial loads were present, as well as for the case where static loads were added to simulate gravity loading. The experiments demonstrated that high speed positioning to an accuracy of +/- 3 micron or less could be obtained with both the cross- coupled and the master-master control strategies. Finally, it was observed that the changes in the dynamics of the closed loop gantry system appear to take place during continuous operation, leading to significant variations in the closed loop performance. It was concluded that robust controller design methods or adaptive control methods would be necessary to meet all performance goals for gantry based X-ray steppers.

The free vibrations of a solid 3D piezoelectric cylinder of class 6 mm are investigated. First the equations of motion are reformulated with the help of three scalar potentials. This decouples the SH waves and is done in a way which is coordinate-free in the transverse coordinates. Next the modes in an infinite plate are derived in cylindrical coordinates, and this involves Bessel functions in the radial direction. A superposition of these modes is then used to form the eigenmodes of the cylinder with a finite radius. The remaining lateral boundary conditions give a determinantal condition for the eigenfrequencies. Numerical results are given and are compared with previous published results.