The accurate control of a positioning system that exhibits scalar hysteresis requires a control strategy that incorporates compensation for the hysteresis. One approach is to develop a compensator based on an inverse hysteresis operator. This method uses an open loop control in which the inverse operation adjusts the actuator input to compensate for the hysteresis in the system. When this is accomplished, the composite operation produces a linear relationship between a reference input and the system output. The difficulty of this method lies in developing an accurate model of the hysteresis for which an inverse operator can be obtained. In this work, a system with hysteresis is modeled by a generic model based on a Preisach type operator. First, it is shown that the operator has an inverse and that both have approximations that are convergent. Then, simulation and experimental data are used to demonstrate the ability of the operator to accurately model a hysteresis relationship. This lays the foundation for then demonstrating the concept of inverse compensation. / Ph. D.

Piezoelectric materials find applications in number of devices requiring inter-conversion of mechanical and electrical energy.  These devices include different types of sensors, actuators and energy harvesting devices. A number of lead-based perovskite compositions (PZT, PMN-PT, PZN-PT etc.) have dominated the field in last few decades owing to their giant piezoresponse and convenient application relevant tunability. With increasing environmental concerns, in the last one decade, focus has been shifted towards developing a better understanding of lead-free piezoelectric compositions in order to achieve an improved application relevant performance.  Sodium potassium niobate (KxNa1-xNbO3, abbreviated as KNN) is one of the most interesting candidates in the class of lead-free piezoelectrics. Absence of any poisonous element makes it unique among all the other lead-free candidates having presence of bismuth. Curie temperature of 400"C, even higher than that of PZT is another advantage from the point of view of device applications. Present work focuses on the development of fundamental understanding of the crystallographic nature, domain structure and domain dynamics of KNN. Since compositions close to x = 0.5 are of primary interest because of their superior piezoelectric activity among other compositions (0 < x < 1), crystallographic and domain structure studies are focused on this region of the phase diagram. KNN random ceramic, textured ceramic and single crystals were synthesized, which in complement to each other help in understanding the behavior of KNN. K0.5Na0.5NbO3 single crystals grown by the flux method were characterized for their ferroelectric and piezoelectric behavior and dynamical scaling analysis was performed to reveal the origin of their moderate piezoelectric performance. Optical birefringence technique used to reveal the macro level crystallographic nature of x = 0.4, 0.5 and 0.6 crystals suggested them to have monoclinic Mc, monoclinic MA/B and orthorhombic structures respectively. Contrary to that, pair distribution function analysis performed on same composition crystals implies them to belonging to monoclinic Mc structure at local scale. Linear birefringence and piezoresponse force microscopy (PFM) were used to reveal the domain structure at macro and micros scales respectively. A noble sintering technique was developed to achieve > 99% density for KNN ceramics. These high density ceramics were characterized for their dielectric, ferroelectric and piezoelectric properties. A significant improvement in different piezoelectric coefficients of these ceramics validates the advantages of this sintering technique. Also lower defect levels in these high density ceramics lead to the superior ferroelectric fatigue behavior as well. To understand the role of seed crystals in switching behavior of textured ceramic, highly textured KNN ceramics (Lotgering factor ~ 88 %) were synthesized using TGG method. A sintering technique similar to one employed for random ceramics, was used to sinter textured KNN ceramics as well. Piezoresponse force microscopy (PFM) study suggested these textured ceramics to have about 6¼m domains as compared to 2¼m domain size for random ceramics.  Local switching behavior studied using switching spectroscopy (SS-PFM) revealed about two and half time improvement of local piezoresponse as compared to random counterpart. / Ph. D.

This thesis introduces the ‘tunable’ piezoelectric transformers (TPT) which provide an extra control terminal, used in this case, to regulate the output voltage. A detailed mathematical analysis is done on the electrical equivalent circuit of the TPT to understand the effect of control terminal loading on the circuit performance. Based on this analysis, a variable capacitor connected across the control terminal is proposed to regulate the output voltage for line and load variations is suggested. The concept of ‘tunability’ in a TPT is introduced and mathematical conditions are derived to achieve the required ‘tunability’. This analysis can help a TPT designer to design the TPT for a specific application and predict the load and line regulations limits for a given design. A circuit implementation of the variable capacitor, intended for control, is presented. With the proposed control circuit design, the effective value of a fixe capacitor can be controlled by controlling the duty cycle of a switch. Hence, this enables pulse width modulated (PWM) control for the TPT based converter operating at a constant frequency. Fixed frequency operation enables a high efficiency operation of TPT near its resonant frequency and the complete secondary control requires no isolation in the voltage feedback and control circuit. This prevents any ‘cross-talk’ between primary and secondary terminals and reduces the component count. The design of series input inductor for achieving zero voltage switching (ZVS) in the inverter switches for the new control is also discussed. Experimental results for two different TPT designs are presented. Their differences in structure and its effect on the circuit performance has been discussed to support the mathematical analysis. / Master of Science

Many commercial finite element programs support piezoelectric modeling and composite modeling to some extent. The popular program ABAQUS, however, has piezoelectric modeling capabilities only for continuum and one-dimensional truss elements. In situations where aspect ratio constraints and computational inefficiencies become a significant issue, such as modeling very large thin structures, alternate modeling techniques are sometimes required. Much of the focus of this thesis was to introduce equivalent methods for modeling laminated piezoelectric beams and plates. Techniques are derived based on classical beam and plate theory, classical lamination theory, and the linear theory of piezoelectricity. Finite element approximations are used with the principle of minimum potential energy to derive the static equilibrium equations for piezoelectric laminated structures. Equivalent loading techniques are derived based on the constitutive equations of piezoelectricity to simulate actuation forces within the piezoelectric layers. Finite element models using equivalent modeling techniques as well as equivalent loading techniques for piezoelectric laminated structures are developed and compared to ABAQUS models using piezoelectric elements to evaluate the error in theoretical assumptions. The analysis will prove that equivalent structural models and equivalent loading techniques provide excellent means for simplifying the analysis of thin piezoelectric laminated structures. / Master of Science

In a conventional electronic ballast for a fluorescent lamp, inductor-capacitor-transformer tank circuit is used. A Piezoelectric Transformer (PT) can potentially be used to replace such a tank circuit to save space and cost. In the past, ballast design using a PT requires selecting a PT from available samples which are normally not matched to specific application and therefore resulting in poor performance. In this thesis, a design procedure was proposed for designing a PT tailored for a 120-V 32-W electronic ballast with high power factor, high efficiency and Zero-Voltage-Switching (ZVS) of the inverter transistors that drive the lamp. This involves selection of PT materials, determination of geometries and the number of physical layers of the PT. A radial mode piezoelectric transformer prototype based on this design process was fabricated by Face Electronics Inc. and was tested experimentally, the results showed that the ballast using this custom-made PT achieved high power factor, Zero-Voltage-Switching and a 83% overall efficiency. / Master of Science

This study evaluates the application of smart damping materials for reducing structural noise and vibrations. The primary purposes of this study are to: 1. Explore the feasibility of smart damping materials, such as piezoelectric materials, for augmenting and improving the noise and vibration benefits of passive damping materials, and 2. Provide a preliminary evaluation of the noise and vibration benefits, and weight savings of smart damping material as compared to conventional damping treatments. To achieve the objectives of the study, a special test rig, designed to measure both vibrations and structure-borne noise of a test plate, was constructed and validated in the early stages of the study. Upon validating the test rig and the instrumentation that was set up for data collection and processing, a series of tests were performed. The tests were intended to establish a baseline for the test rig and compare the performance of smart damping materials with a number of passive interior automotive treatments. Further, in order to evaluate the effect of smart damping materials on the sound transmission loss, a series of tests were conducted according to the SAE J1400 test specifications. The tests evaluate the transmission loss for smart damping materials for an undamped and a damped plate. The passive damping technique used for this study involved attaching piezoelectric patches with resonant electrical shunts. The vibration modes of the plate were determined both analytically and experimentally, using laser measurement techniques, in order to determine effective placement of the piezoceramic materials. Three piezoceramic patches were applied to control four structural resonance frequencies of the plate. The tests show that smart damping materials have substantial performance benefits in terms of providing effective noise and vibration reduction at a frequency range that is often outside the effective range of passive damping materials. Further, judging by the acceleration and noise reduction per added weight, the test results indicate that smart damping materials can decrease the vibration peak of a steel plate at 151 Hz by up to 16.24 dB with an additional weight of only 0.11 lb. The addition of constrained-layer damping (CLD) can decrease that same peak by 18.65 dB, but it weighs 10 times more. This feature of smart damping materials is particularly useful for solving particular noise or vibration problems at specified frequencies, without adding any weight to the vehicle or changing the vehicle structure. / Master of Science

A new dynamic model is presented for piezoelectric tube actuators commonly used in high-precision instruments. The model captures coupling between motions in all three axes such as bending motion due to a supposedly pure extension of the actuator. Both hysteresis and creep phenomena are included in the overall actuator model permitting modeling nonlinear sensitivity in the voltage to displacement response. Experimental data on hysteresis and creep are presented to support the modeling. Experiments and model predictions show that due to coupling a voltage Vz corresponding to vertical displacement will produce lateral displacement that acts as a disturbance to the main lateral response. The resonance frequency for the lateral dynamics is inherently lower than that of the longitudinal dynamics. Therefore, Vz is expected to contain frequencies that may excite the lateral resonance. Accordingly, this out of bandwidth disturbance will not be well compensated for either in open or closed loop control of the actuator. In order to preserve performance in open loop actuator control and stability and performance in closed loop control, a large reduction in the bandwidth of vertical motion would be required to avoid exciting the first bending mode. / Singapore-MIT Alliance (SMA)

Due to the complexity of electro-elastic coupling characteristics in piezoelectric material, some of the elastic, dielectric and piezoelectric parameters are difficult to be measured. Usually, these parameters are determined by assuming that all offer parameters are remained constant during the measurement. However, the interactive effect between material properties makes this assumption be not always true. In this study, the measured natural frequencies of the specified circular piezoelectric plate are used to extract these parameters simultaneously. In other words, all these parameters are determined with considering the interactive electro-elastic coupling effect. The analytic model of free-free circular piezoceramic plate was derived and solved to establish the relationship between natural frequencies and its material parameters, to cover most all the parameters, the out-of-plane(non-symmetric transverse) and in-plane(symmetric extensional) modes are considered. The genetic algorithm is employed to determine most all elastic, dielectric and piezoelectric parameters from a least square error between the calculated and measured natural frequencies. Numerical results derived from the parameters proposed in this work reveal a good agreement with the measured data. In other words, the proposed method to extract the piezoelectric parameters is feasible and effective.

Much recent research has focused on the development lead-free perovskite piezoelectrics as environmentally compatible alternatives to lead zirconate titanate (PZT). Two main categories of lead free perovskite piezoelectric ceramic systems were investigated as potential replacements to lead zirconate titanate (PZT) for actuator devices. First, solid solutions based on Li, Ta, and Sb modified (K���.���Na���.���)NbO��� (KNN) lead-free perovskite systems were created using standard solid state methods. Secondly, Bi-based materials a variety of compositions were explored for (1-x)(Bi���.���Na���.���)TiO���-xBi(Zn���.���Ti���.���)O��� (BNT-BZT) and Bi(Zn���.���Ti���.���)O������(Bi���.���K���.���)TiO������(Bi���.���Na���.���)TiO��� (BZT-BKT-BNT). It was shown that when BNT-BKT is combined with increasing concentrations of Bi(Zn[subscript 1/2]Ti[subscript 1/2])O��� (BZT), a transition from normal ferroelectric behavior to a material with large electric field induced strains was observed. The higher BZT containing compositions are characterized by large hysteretic strains (> 0.3%) with no negative strains that might indicate domain switching. This work summarizes and analyzes the fatigue behavior of the new generation of Pb-free piezoelectric materials. In piezoelectric materials, fatigue is observed as a degradation in the electromechanical properties under the application of a bipolar or unipolar cyclic electrical load. In Pb-based materials such as lead zirconate titanate (PZT), fatigue has been studied in great depth for both bulk and thin film applications. In PZT, fatigue can result from microcracking or electrode effects (especially in thin films). Ultimately, however, it is electronic and ionic point defects that are the most influential mechanism. Therefore, this work also analyzes the fatigue characteristics of bulk polycrystalline ceramics of the modified-KNN and BNT-BKT-BZT compositions developed. The defect chemistry that underpins the fatigue behavior will be examined and the results will be compared to the existing body of work on PZT. It will be demonstrated that while some Pb-free materials show severe property degradation under cyclic loading, other materials such as BNT-BKT-BZT essentially exhibit fatigue-free piezoelectric properties with chemical doping or other modifications. Based on these results, these new Pb-free materials have great potential for use in piezoelectric applications requiring a large number of drive cycles such as MEMS devices or high frequency actuators. / Graduation date: 2013

In recent years, vibration-based energy harvesting technologies have gained great importance because of reduced power requirement of small electronic components. External power source and maintenance requirement can be minimized by employment of mechanical vibration energy harvesters. Power sources that harvest energy from the environment have the main advantages of high safety, long shell life and low cost compared to chemical batteries. Electromagnetic, electrostatic and piezoelectric transduction mechanisms are the three main energy harvesting methods. In this thesis, it is aimed to apply the piezoelectric elements technology to develop means for energy storage in munitions launch. The practical problems encountered in the design of piezoelectric energy harvesters are investigated. The applicability of energy harvesting to high power needs are studied. The experience compiled in the study is to be exploited in designing piezoelectric energy harvesters for munitions applications. Piezoelectric energy harvesters for harmonic and mechanical shock loading conditions with different types of piezoelectric materials are designed and tested. The test results are compared with both responses from analytical models generated in MATLAB&reg / and ORCAD PSPICE&reg / , and finite element method models generated in ATILA&reg / . Optimum energy storage methods are considered.