Thesis (Ph. D.)--University of Wisconsin--Madison, 1970. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Idaho, November 2006. / Major professor: David Egolf. Abstract. Includes bibliographical references (leaves 100-102). Also available online in PDF format.

Thesis submitted in fulfilment of the requirements for the degree Master of Technology: Electrical Engineering in the Faculty of Engineering at the Cape Peninsula University of Technology / In the past decade, the need for flexibility and reconfigurability in automation has contributed to the rise of the distributed concept in control systems engineering. The IEC 61499 standard is used to define a distributed model for dividing various components of an industrial application in automation process and complicated control of machinery into function blocks. Such function blocks have the flexibility to be distributed and interconnected across a number of controllers. However, this new standard for automation faces two main challenges: the complexity in designs of distributed systems and the lack of utilization of the standard in industry. Most applications of controllers based on functional block programming are for linear systems. As most of industrial processes are nonlinear there is a need to extend the functional block approach for implementation of nonlinear controllers. Design complexity involves the exact modeling of the system in function blocks to obtain its accurate behaviour and the lack of utilization of the standard is understandable because new technologies are not easily accepted in industry due to their high prices and risks of compromising the performance at the production level. The thesis describes a methodology for design and implementation of nonlinear controllers for nonlinear plants in IEC 61499 standard compliant real-time environment of TwinCAT 3 and Beckhoff Programmable Logic Controller (PLC). The first step is to design the nonlinear controllers and simulate the closed-loop system in MATLAB/SIMULINK software. Then the new engineering based concepts to transform the obtained closed-loop system model to an IEC 61499 Function Block Model. This is accomplished by applying one method which involves a complete model transformation between two block-diagram languages: Simulink and TwinCAT 3. The development tools that support the transformation algorithm in the thesis sets the foundation stone of the verification and validation structure for IEC 61499 function blocks approach. The transformed model of the closed-loop system is downloaded to the Beckhoff PLC and is simulated in real-time. The obtained results demonstrate that the developed methodology allows complex nonlinear controllers to be successfully transformed to IEC 61499 standard compliant environment and to be applied for real-time PLC control of complex plants.

Control design for nonlinear systems remains an open problem in control theory despite the recent increase in research attention. This PhD work is motivated by this fact, addressing the constructive observer design approach, the output regulation problem, minimum entropy control, fault tolerant control (FTC), and iterative FTC for nonlinear systems.

Estimation of nonlinear models finds applications in every field of engineering and the sciences. Much work has been done to build solid statistical theories for its use and interpretation. However, there has been little analysis of the tolerance of nonlinear model estimators to deviations from assumptions and normality. We focus on analyzing the robustness properties of M-estimators of nonlinear models by studying the effects of deviations from assumptions and normality on these estimators. We discuss St. Laurent and Cook's Jacobian Leverage and identify the relationship of the technique to the robustness concept of influence. We derive influence functions for M-estimators of nonlinear models and show that influence of position becomes, more generally, influence of model. The result shows that, for M-estimators, we must bound not only influence of residual but also influence of model. Several examples highlight the unique problems of nonlinear model estimation and demonstrate the utility of the influence function. / Master of Science

This research studies two nonlinear differential equations arising in fluid mechanics. Firstly, the Zakharov-Kuznetsov's equation in (3+1) dimensions with an arbitrary power law nonlinearity is considered. The method of Lie symmetry analysis is used to carry out the integration of Zakharov-Kuznetsov's equation. Also, the extended tanh-function method and t he G'/G method are used to integrate the Zakharov-Kuznetsov's equation. The non-topological soliton solution is obtained by the aid of solitary wave ansatz method. Numerical simulation is given to support the analytical development. Secondly. the nonlinear flow problem of an incompressible viscous fluid is considered. The fluid is taken in a channel having two weakly permeable moving porous walls. An incompressible fluid fills the porous space inside the channel. The fluid is magnetohydrodynamic in the presence of a time-dependent magnetic field. Lie group method is applied along with perturbation method in the derivation of analytic solution. The effects of the magnetic field, porous medium, permeation Reynolds number and wall dilation rate on the axial velocity arc shown and discussed. / Thesis (M.Sc.(Applied Mathematics) North-West University, Mafikeng Campus, 2010

International Telemetering Conference Proceedings / October 21, 2002 / Town & Country Hotel and Conference Center, San Diego, California / To achieve good efficiency in a space-based radio transmitter, its final amplifier must be operated near the saturation point, in its nonlinear region. Because of strict band limitations, this nonlinear operation is combined with the problem of intersymbol interference. Normally, these problems are addressed using a combination of equalization and power back-off, resulting in reduced power efficiency. Many proposed receiver-based methods, such as Volterra equalization, attempt to compensate for the nonlinearity and ISI in a single block before the detector, allowing higher efficiency operation, but introducing a great deal of complexity. We propose a receiver-based method in which the two effects are dealt with in separate blocks, an equalizer and a linearizer, resulting in considerable simplification. We go further and place the detector before the linearizer, achieving improved performance by eliminating the errors introduced by the linearizer. Simulation results compare favorably with the performance of a linear AWGN channel.

As natural chiral materials demonstrate limited circularly dichroic contrasts, enhancement of these polarization dependent signals has long been the focus of chiral metamaterial research. By manipulating the geometric chirality of resonant plasmonic nanostructures, we are capable of enhancing light confinement to amplify chiral modified, nonlinear signals from quantum emitters. The metamaterial demonstrates a linear transmission contrast of 0.5 between left and right circular polarizations and a 20× contrast between second harmonic responses from the two incident polarizations. Nonlinear and linear response images probed with circularly polarized lights show strongly defined contrast. As a second set of experimentation, the chiral center of the metamaterial is opened, providing direct access to place emitters to occupy the most light-confining and chirally sensitive regions. The resulting two-photon emission profiles from circularly polarized excitation displays mirrored symmetry for the two enantiomer structures. The efficiency of the nonlinear signal directly correlates to the chiral resonance of the linear regime. The nonlinear emission signal is enhanced by 40× that of the emitters not embedded in the metamaterial and displays a 3× contrast for the opposite circular polarization. Such manipulations of nonlinear signals with metamaterials open pathways for diverse applications where chiral selective signals are monitored, processed, and analyzed.

published_or_final_version / Mechanical Engineering / Master / Master of Philosophy

Acoustic metamaterials are sub-wavelength structures designed to overcome limitations in the material properties of conventional materials. The present research focuses on the nonlinear acoustic and dynamic response of a specific type of engineered microstructure called a snapping acoustic metamaterial (SAMM). Snapping of these elements is defined as large, rapid deformations induced by infinitesimal perturbations in the time-varying external pressure. Snapping behavior in SAMM elements results from their non-monotonic stress-strain response, which displays regimes of positive and negative stiffness. This work presents a modeling study of the nonlinear behavior of both individual SAMM elements and a heterogeneous material containing a dilute concentration of SAMM elements embedded in a nearly incompressible viscoelastic solid. Two different scenarios are considered: (i) nonlinear wave propagation in the heterogeneous medium, and (ii) forced nonlinear dynamics of inclusions embedded in a viscoelastic medium. The nonlinearity of the SAMM elements is represented by a cubic pressure-volumetric strain relationship based on finite element model results from previous work. The effective nonlinear response of a heterogeneous mixture of SAMM elements embedded in a matrix, characterized by the parameters B/A and C/A, is then determined using both a nonlinear mixture law and a nonlinear Hashin-Shtrikman approach. The former estimate is limited to matrix materials with zero shear modulus, which cannot stabilize SAMM inclusions in regimes of negative stiffness. The augmented Hashin-Shtrikman method, however, includes nonlinear elasticity and the shear modulus of the matrix material. It therefore provides accurate estimates of the homogenized material when SAMM elements display negative stiffness and enhanced acoustical nonlinearity. The distortion of an acoustic wave propagating through the effective medium is studied through numerical solution of a nonlinear evolution equation that includes both quadratic and cubic nonlinearity. Finally, the forced nonlinear dynamic response of both a single SAMM element in a matrix and a domain of effective medium material embedded in matrix is considered. This behavior is of interest for generating enhanced absorption of acoustic wave energy because snapping leads to large hysteresis in the stress-strain response. A generalized Rayleigh-Plesset analysis is adapted to model the large-deformation dynamics associated with the system. / text