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This thesis discusses various properties of a number of differential equations which we will term "integrable". There are many definitions of this word, but we will confine ourselves to two possible characterisations — either an equation can be transformed by a suitable change of variables to a linear equation, or there exists an infinite number of conserved quantities associated with the equation that commute with each other via some Hamiltonian structure. Both of these definitions rely heavily on the concept of the symmetry of a differential equation, and so Chapters 1 and 2 introduce and explain this idea, based on a geometrical theory of p.d.e.s, and describe the interaction of such methods with variational calculus and Hamiltonian systems. Chapter 3 discusses a somewhat ad hoc method for solving evolution equations involving a series ansatz that reproduces well-known solutions. The method seems to be related to symmetry methods, although the precise connection is unclear. The rest of the thesis is dedicated to the so-called Universal Field Equations and related models. In Chapter 4 we look at the simplest two-dimensional cases, the Bateman and Born-lnfeld equations. By looking at their generalised symmetries and Hamiltonian structures, we can prove that these equations satisfy both the definitions of integrability mentioned above. Chapter Five contains the general argument which demonstrates the linearisability of the Bateman Universal equation by calculation of its generalised symmetries. These symmetries are helpful in analysing and generalising the Lagrangian structure of Universal equations. An example of a linearisable analogue of the Born-lnfeld equation is also included. The chapter concludes with some speculation on Hamiltoian properties.

Some basic concepts and principles of optical dielectric slab waveguiding and experimental methodology involving characterisation of waveguide films are introduced, Results from the characterisation of thin polymeric waveguide films and measurements of refractive indices of the films are presented. The birefringence of some polymer films is analysed and discussed. The photostabilities of several dopants (DEMI, Ultra-DEMI, Dicyclohexyl-DEMI, Mor2, Morpip and DCM) are investigated in a polymer matrix (PMMA), and their measured photostabilities are presented. These organic chromophores change their properties in the course of photodegradation. Degradation experiments are carried out by exposing the doped waveguide films to light in air, vacuum and nitrogen environments. The degradation mechanisms of these chromophores are discussed. It is found that the degradation of the DEMI, Ultra-DEMI, Dicyclohexyl-DEMI and DCM are due to photooxidation, their photostabilities are much higher in vacuum than in air. The Mor2 and Morpip degrade by direct photodecomposition, their photostabilities are in the same order when exposed to light in their main absorption bands. The oxygen free environment (e.g. vacuum) is essential to increase their photostabilities. A beam branching effect in DCM doped waveguide film is observed. Stacked multi-layer waveguides are investigated as possible humidity sensors. Symmetric structure (PMMA/P-4VP/PMMA/P-4VP/PMMA) (P4VP-I) and unsymmetric structure (Si02/P-4VP/Zeonex/P-4VP/Air) (P4VP-II) are studied. Special procedures and process have been developed to fabricate multi-layer waveguide structures in experiments. It is found that both structures have good reversibilities and show reasonable stabilities. 30 ppm concentrations of water vapour can be detected by the P4VP-II structure. The experimental results show that the overall response of P4VP-II structure exhibits good linearity with increase of the concentration of water vapour. The structures can not only measure the phase shift of interference, but also can measure the direction of fringe movement. The sensitivity of the structure can be further improved by using different combinations of polymers in the structure.

This thesis proposes a distributed observer design for a class of nonlinear systems that arise in the application of model reduction techniques. Distributed observer design techniques have been proposed in the literature to address estimation problems over sensor networks. In large complex sensor networks, an efficient technique that minimizes the extent of the required communication is highly desirable. This is especially true when sensors have problems caused by physical limitations that result in incorrect information at the local level affecting the estimation of states globally. To address this problem, scalable algorithms for a suitable distributed observer have been developed. Most algorithms are focussed on large linear dynamical systems and they are not directly generalizable to nonlinear systems. In this thesis, scalable algorithms for distributed observers are proposed for a class of large scale observable nonlinear system. Distributed systems models multi-agent systems in which each agents attempts to accomplish local tasks. In order to achieve global objectives, there should be agreement regarding some commonly known variables that depend on the state of all agents. These variables are called consensus states. Once identified, such consensus states can be exploited in the development of distributed consensus algorithms. Consensus algorithms are used to develop information exchange protocols between agents such that global objectives are met through local action. In this thesis, a higher order observer is applied in the distributed sensor network system to design a distributed observer for a class nonlinear systems. Fusion of measurement and covariance information is applied to the higher order filter as the first method. The consensus filter is embedded in the local nonlinear observer for fusion of data. The second method is based on the communication of state estimates between neighbouring sensors rather than fusion of data measurement and covariance. The second method is found to reduce disagreement of the states estimation between each sensor. The performance of these new algorithms is demonstrated by simulation, and the second method is effectively applied over the first method. / Thesis (Master, Chemical Engineering) -- Queen's University, 2012-12-12 11:22:49.113

This thesis presents control methods to improve the efficiency and dynamic response of wind turbines that use a permanent magnet synchronous generator operating under a wide input and load range. Two new nonlinear controllers are developed and tested. These controllers are designed to overcome the limitations of the conventional vector control methods which exhibit slow performance and uncertain stability. The first controller is based on a control Lyapunov function (CLF) which increases performance and guarantees stability under all operating conditions but is limited by its dependence on system parameters. A novel adaptive passivity based controller (APBC) is designed to overcome the parameter dependence of the CLF controller while, again, increasing performance and guaranteeing stability under all operating conditions. These controllers are simulated and their performance is compared to that of the conventional controller. The APBC controller exhibits the best performance of the three followed closely by the CLF based controller. / Thesis (Master, Electrical & Computer Engineering) -- Queen's University, 2013-03-28 12:22:19.931