By combining new robot control systems with piezoelectric motors and micromechanics, we propose creating micromechanical systems which are small, cheap and completely autonomous. We have fabricated small - a few millimeters in diameter - piezoelectric motors using ferroelectric thin films and consisting of two pieces: a stator and a rotor. The stationary stator includes a piezoelectric film in which we induce bending in the form of a traveling wave. Anything which sits atop the stator is propelled by the wave. A small glass lens placed upon the stator becomes the spinning rotor. Using thin films of PZT on silicon nitride memebranes, various types of actuator structures have been fabricated.

We want to build tiny gnat-sized robots, a millimeter or two in diameter. They will be cheap, disposable, totally self-contained autonomous agents able to do useful things in the world. This paper consists of two parts. The first describes why we want to build them. The second is a technical outline of how to go about it. Gnat robots are going to change the world.

Coupling between the electric field, magnetic field, and strain of composite materials is achieved when electro-elastic (piezoelectric) and magneto-elastic (piezomagnetic) particles are joined by an elastic matrix. Although the matrix is neither piezoelectric nor piezomagnetic, the strain field in the matrix couples the E field of the piezoelectric phase to the B field of the piezomagnetic phase. This three-phase electro-magneto-elastic composite should have greater ductility and formability than a two-phase composite in which E and B are coupled by directly bonding two ceramic materials with no compliant matrix. A finite element analysis and homogenization of a representative volume element is performed to determine the effective electric, magnetic, mechanical, and coupled-field properties of an elastic (epoxy) matrix reinforced with piezoelectric and piezomagnetic fibers as functions of the phase volume fractions, the fiber (or particle) shapes, the fiber arrangements in the unit cell, and the fiber material properties with special emphasis on the symmetry properties of the fibers and the poling directions of the piezoelectric and piezomagnetic fibers. The effective magnetoelectric moduli of this three-phase composite are, however, less than the effective magnetoelectric coefficients of a two-phase piezoelectric/piezomagnetic composite, because the epoxy matrix is not stiff enough to transfer significant strains between the piezomagnetic and piezoelectric fibers.

With the ability to generate fine displacements with a resolution down to sub-nanometers, piezoelectric actuators (PEAs) have found wide applications in various nano-positioning systems. However, existence of various effects in PEAs, such as hysteresis and creep, as well as dynamics can seriously degrade the PEA performance or even lead to instability. This raises a great need to model and control PEAs for improved performance, which have drawn remarkable attention in the literature. Sliding mode control (SMC) shows its potential to the control of PEA, by which the hysteresis and other nonlinear effects can be regard as disturbance to the dynamic model and thus rejected or compensated by its switching control. To implement SMC in digital computers, this research is aimed at developing novel discrete models and discrete SMC (DSMC)-based control schemes for PEAs, along with their experimental validation. The first part of this thesis concerns with the modeling and control of one-degree of freedom (DOF) PEA, which can be treated as a single-input-single-output (SISO) system. Specifically, a novel discrete model based on the concept of auto-regressive moving average (ARMA) was developed for the PEA hysteresis; and to compensate for the PEA hysteresis and improve its dynamics, an output tracking integrated discrete proportional-integral-derivative-based SMC (PID-SMC) was developed. On this basis, by making use of the availability of PEA hysteresis models, two control schemes, named “the discrete inversion feedforward based PID-SMC” and “the discrete disturbance observer (DOB)-based PID-SMC”, were further developed. To illustrate the effectiveness of the developed models and control schemes, experiments were designed and conducted on a commercially available one-DOF PEA, as compared with the existing ones. The second part of the thesis presents the extension of the developed modeling and control methods to multi-DOF PEAs. Given the fact that details with regard to the PEA internal configurations is not typically provided by the manufacturer, a state space model based on the black box system identification was developed for the three-DOF PEA. The developed model was then integrated in the output tracking based discrete PID-SMC, with its effectiveness verified through the experiments on a commercially available three-DOF PEA. The superiority of the proposed control method over the conventional PID controller was also experimentally investigated and demonstrated. Finally, by integrating with a DOB in the discrete PID-based SMC, a novel control scheme is resulted to compensate for the nonlinearities of the three-DOF PEA. To verify its effectiveness, the discrete DOB based PID-SMC was applied in the control experiments and compared with the existing SMC. The significance of this research lies in the development of the discrete models and PID-based SMC for PEAs, which is of great help to improve their performance. The successful application of the proposed method in the control of multi-DOF PEA allows the application of SMC to the control of complicated multi-inputs-multi-outputs (MIMO) systems without details regarding the internal configuration. Also, integration of the inversion based feedforward control and the DOB in the SMC design has been proven effective for the tracking control of PEAs.

This thesis is concerned with the modeling of the stator of a piezoelectric traveling wave rotary ultrasonic motor. Existing models for piezoelectric traveling wave rotary ultrasonic motors are either too complicated to be used in motor control or do not reflect the real behavior of the motor and are of limited use in developing a controller for the motor. Finite Element methods have been used in the past to examine the properties of piezoelectric structures however, the Finite Volume Method has always been ruled out without justification. The main goal of this thesis is to provide a Finite Volume modeling approach for the stator of the piezoelectric traveling wave rotary ultrasonic motor taking into account the basic theoretical principles from piezoelectricity and structural mechanics. This model can in future be extended to develop a complete model of the motor in addition to other piezoelectric structures. The Finite Volume Method is shown to have the following specific advantages over the Finite Element Method especially for structures with simple geometries: 1. the Finite Volume Method respects the PDEs conservation law structure due to the fact that the fluxes are conserved between cells/domains/subregions, 2. the Finite Volume Method involves only surface integrals thus making it easier to implement a rotor-stator contact model as the contact mechanism occurs at the boundary of the stator, and 3. the Finite Volume Method yields a system of ODEs that more intuitively map onto circuit simulation software. The Finite Volume Method is initially used to model a simple piezoelectric plate. A corresponding circuit of the piezoelectric plate model, based on the Finite Volume Method, is generated. Two additional but more complex models are considered: one for a unimorph plate and one for the stator of an ultrasonic motor. The modeling results obtained with the Finite Volume Method are validated by comparing them with the results obtained with Finite Element simulations performed with COMSOL. Two test platforms designed to test and validate the Finite Volume and COMSOL results for the simple piezoelectric plates and piezoelectric traveling wave rotary ultrasonic motors are also presented in this thesis.

This thesis is concerned with the modeling of the stator of a piezoelectric traveling wave rotary ultrasonic motor. Existing models for piezoelectric traveling wave rotary ultrasonic motors are either too complicated to be used in motor control or do not reflect the real behavior of the motor and are of limited use in developing a controller for the motor. Finite Element methods have been used in the past to examine the properties of piezoelectric structures however, the Finite Volume Method has always been ruled out without justification. The main goal of this thesis is to provide a Finite Volume modeling approach for the stator of the piezoelectric traveling wave rotary ultrasonic motor taking into account the basic theoretical principles from piezoelectricity and structural mechanics. This model can in future be extended to develop a complete model of the motor in addition to other piezoelectric structures. The Finite Volume Method is shown to have the following specific advantages over the Finite Element Method especially for structures with simple geometries: 1. the Finite Volume Method respects the PDEs conservation law structure due to the fact that the fluxes are conserved between cells/domains/subregions, 2. the Finite Volume Method involves only surface integrals thus making it easier to implement a rotor-stator contact model as the contact mechanism occurs at the boundary of the stator, and 3. the Finite Volume Method yields a system of ODEs that more intuitively map onto circuit simulation software. The Finite Volume Method is initially used to model a simple piezoelectric plate. A corresponding circuit of the piezoelectric plate model, based on the Finite Volume Method, is generated. Two additional but more complex models are considered: one for a unimorph plate and one for the stator of an ultrasonic motor. The modeling results obtained with the Finite Volume Method are validated by comparing them with the results obtained with Finite Element simulations performed with COMSOL. Two test platforms designed to test and validate the Finite Volume and COMSOL results for the simple piezoelectric plates and piezoelectric traveling wave rotary ultrasonic motors are also presented in this thesis.

No description available.

Piezoelectric actuators are well suited for high precision mechanical and electrical engineering applications. However, its performance in regulator configurations has been limited due to hysteresis. The hysteresis in these actuators means that multiple input states can result in the same output, which introduces a further design variable (initial state) in the regulation problem. It is proposed that certain initial states result in better regulation performance based on the structure of the Preisach model. These initial states are called “neutral states”. In this thesis, hysteresis and piezoelectric actuators are introduced as background information. The Preisach model is used in this work to describe the hysteresis behaviour of a customized shape control unit SS15 due to its convenient general structure and ability to model hysteresis. The representation tests are performed and a Preisach model is subsequently constructed and verified by comparing simulation and experimental results to ensure that the hysteresis inherent in the piezoceramic actuators of the SS15 is suitably described by this model. In order to evaluate the regulation performance for a given desired output, uniformly-distributed noise is injected at the input side of the SS15 in open- and closed-loop tests. It is demonstrated, by both simulation and experimental results, that the system output drifts less when it starts from the neutral state in open-loop tests. A PI regulator is implemented in the closed-loop tests. When the system is driven from the neutral state, both simulation and experimental results demonstrate that the system requires less control effort for closed-loop regulation.

This thesis presents a numerical model for determining piezoelectric and non-linear elastic properties of piezoelectric composites consisting of nanotubes in a polymer matrix. Finite Element Analysis (FEA), in conjunction with the Embedded Fiber Method (EFM), is used, and variable nanotube geometry, alignment, and waviness are taken into account. First, a random morphology of a user-defined volume fraction of nanotubes is generated, and their properties are incorporated into the polymer matrix using the EFM. Next, the system is solved and the values are post-processed to determine the effective elastic and piezoelectric properties of the composite. Finally, incremental FEA approaches are used for the determination of the non-linear properties of the nanocomposite. Monte Carlo Analysis of five hundred random microstructures is performed to capture the stochastic nature of the fiber generation and to derive statistically reliable results. The models are validated by comparison with theoretical and experimental data reported in recent literature.

Piezoelectric actuators are well suited for high precision mechanical and electrical engineering applications. However, its performance in regulator configurations has been limited due to hysteresis. The hysteresis in these actuators means that multiple input states can result in the same output, which introduces a further design variable (initial state) in the regulation problem. It is proposed that certain initial states result in better regulation performance based on the structure of the Preisach model. These initial states are called “neutral states”. In this thesis, hysteresis and piezoelectric actuators are introduced as background information. The Preisach model is used in this work to describe the hysteresis behaviour of a customized shape control unit SS15 due to its convenient general structure and ability to model hysteresis. The representation tests are performed and a Preisach model is subsequently constructed and verified by comparing simulation and experimental results to ensure that the hysteresis inherent in the piezoceramic actuators of the SS15 is suitably described by this model. In order to evaluate the regulation performance for a given desired output, uniformly-distributed noise is injected at the input side of the SS15 in open- and closed-loop tests. It is demonstrated, by both simulation and experimental results, that the system output drifts less when it starts from the neutral state in open-loop tests. A PI regulator is implemented in the closed-loop tests. When the system is driven from the neutral state, both simulation and experimental results demonstrate that the system requires less control effort for closed-loop regulation.