The complexity of large industrial engineering systems such as chemical plants has continued to increase over the years. As a result, flexible control systems are required to handle variation in the operating conditions. In the classical approach, first the plant model should be linearized at the nominal operating point and then, a robust controller should be designed for the resulting linear system. However, the performance of a controller designed by this method deteriorates when operation deviates from the nominal point. When the distance between the operating region and the nominal operating point increases, this performance degradation may lead to instability. In the context of traditional linear control, one method to solve this problem is to consider the impact of nonlinearity as “uncertainty” around the nominal model and design a controller such that the desired performance is satisfied for all possible systems in the uncertainty set. As the size of uncertainty increases, conservatism occurs and at some point, it becomes impossible to design a controller that can provide satisfactory performance. One of the methods proposed to overcome the aforementioned shortcomings is the so-called Multiple Model approach. Using Multi-Models, local designs are performed for various operating regions and membership functions or a supervisory switching scheme is used to interpolate or switch among the controllers as the operating point moves among local regions. Since the Multiple Model method is a natural extension of the linear control method, it inherits some benefits of linear control such as simplicity of analysis and implementation. However, all these benefits are valid locally. For example, the multiple model method may be vulnerable when global stability is taken into account. The core objective of this thesis is to develop new tools to study stability of closed-loop nonlinear systems controlled by local controllers in order to improve design of multiple model control systems. For example, one of the aims of this work is to investigate how to determine the region where closed loop system is stable. A secondary objective is to study the effects of the exogenous signals on stability of such systems. / Controls

Thesis (doctoral)--Université de Rennes I, 1984. / "Série: 17. No d'ordre: 386. No de série: 57." Includes bibliographical references.

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.