The generation, transmission and distribution of electricity underpins modern technology and constitutes a necessary element for our development and economic functionality. In the recent years, as a result of environmental concerns and technological advances, private and public investment have been steadily turning towards renewable sources of energy, resulting in a growing penetration of those in the power network. This poses additional challenges in the control of power networks, since renewable generation is in general intermittent, and a large penetration may cause frequent deviations between generation and demand, which can harm power quality and even cause blackouts. Load side participation in the power grid is considered by many a means to counterbalance intermittent generation, due to its ability to provide fast response at urgencies. Industrial loads as well as household appliances, may respond to frequency deviations by adjusting their demand in order to support the network. This is backed by the development of relevant sensing and computation technologies. The increasing numbers of local renewable sources of generation along the introduction of controllable loads dramatically increases the number of active elements in the power network, making traditionally implemented, centralised control dicult and costly. This demonstrates the need for the employment of highly distributed schemes in the control of generation and demand. Such schemes need to ensure the smooth and stable operation of the network. Furthermore, an issue of fairness among controllable loads needs to be considered, such that it is ensured that all loads share the burden to support the network evenly and with minimum disruption. We study the dynamic behaviour of power networks within the primary and secondary frequency control timeframes. Using tools from non-linear control and optimisation, we present methods to design distributed control schemes for generation and demand that guarantee stability and fairness in power allocation. Our analysis provides relaxed stability conditions in comparison with current literature and allows the inclusion of practically relevant classes of generation and demand dynamics that have not been considered within this setting, such as of higher order dynamics. Furthermore, fairness in the power allocation between loads is guaranteed by ensuring that the equilibria of the system are solutions to appropriately constructed optimisation problems. It is evident that a synchronising variable is required for optimality to be achieved and frequency is used as such in primary control schemes whereas for secondary frequency control a dierent synchronising variable is adopted. For the latter case, the requirements of the synchronising feedback scheme have been relaxed with the use of an appropriate observer, showing that stability and optimality guarantees are retained. The problem of secondary frequency regulation where ancillary services are provided from switching loads is also considered. Such loads switch on and off when some prescribed frequency threshold is reached in order to support the power network at urgencies. We show that the presence of switching loads does not compromise the stability of the power network and reduces the frequency overshoot, potentially saving the network from collapsing. Furthermore, we explain that when the on and o switching frequencies are equivalent, then arbitrarily fast switching phenomena might occur, something undesirable in practical implementations. As a solution to this problem, hysteresis schemes where the switch on and off frequencies differ are proposed and stability guarantees are provided within this setting.

Currently process industry faces a paradoxical situation. On the one hand there is the urgent need to optimise the performance of processes by increasing throughput, decreasing operating costs while increasing the product quality. On the other hand there are only few specialists in industry who are able to develop and apply appropriate control strategies for the increasingly complex processes in the process industry. Generally, these specialists work in research and development departments necessitating a considerable amount of time to develop sophisticated solutions for specific processes. However, in the process industry control design and fine-tuning are mostly done by practitioners more than by specialists, directly at the process and in a minimum of time. Within this commissioning phase the process is assembled and set into operation, often with suboptimally turned controllers. Efforts have been undertaken to support these commissioners doing their tasks, and for single variable processes practically applicable methods have been developed. Nevertheless, for more complex processes the generation of mathematical process models as an appropriate base for control system design still is a major problem in practice. The subject of this work is the development of a structured approach to identification techniques for the analysis of industrial processes that enables industrial users with limited control engineering knowledge to design process models suitable for the design of industrial controllers. This latter aspect has been addressed within the collaborative research project between the University of Glamorgan and the Fachhochschule Hannover, of which the work presented in this thesis is a substantial part. Therefore, an industrially suitable scheme for computer aided control system design (CACSD) has firstly been developed in agreement with industrial users in order to set the frame for the research project. This scheme has been based on simple block-oriented model structures composed from nonlinear static and linear dynamic characteristics. The scheme is simple in use and intuitive to understand and follow. Therefore, it can be directly applied also by inexperienced engineers, who look for quick and efficient solutions as a basis even for nonlinear controller design. Beyond this a standardised identification procedure for nonlinear processes has been elaborated in order to provide process models fitting to the CACSD scheme. This standardised identification procedure has been equipped with two improved algorithms. For the approximation of even multidimensional static characteristics a capable method has been developed necessitating neither apriori information nor user interaction. For the identification of discrete-time linear dynamic models a two-step identification method has been improved by a numerically efficient least squares estimator that allows the parallel estimation of a set of model structures, which is evaluated automatically. For the validation of the proposed approach and the developed methods a prototype identification tool has been programmed, which also lays the ground for the integration of the whole CACSD scheme into a block-oriented simulation environment.

A new, and thus far only, method to overcome a selectivity barrier in parametrically pumped quantum pulse gates is proposed and experimentally demonstrated for the first time, using frequency conversion of optical temporal modes in second-order nonlinear waveguides. Temporal modes and quantum pulse gates are defined and their utilities are explored. Pulsed operation of three-field and four-field, parametric, optical processes are modeled and numerically investigated. A maximum limit to achievable selectivity for quantum pulse gating in uniform media is discovered and theoretically explained. An interferometric means of overcoming said limit and asymptotically approaching unit selectivity is proposed. The principle is experimentally verified by double-passing specifically shaped optical pulses derived from an ultrafast Ti:sapphire laser through a periodically-poled lithium niobate waveguide phasematched for sum-frequency generation. Further improvements and future implications for quantum technologies are discussed.

This work presents photophysical and nonlinear optical properties of a novel Cd 2,3-[octakis{4-tert-butylphenoxyphthalocyanine}] (CdOtBPPc) and compared with those of Pb 2,3-[octakis{4-tert-butylphenoxyphthalocyanine}] (PbOtBPPc). For both the CdOtBPPc and PbOtBPPc, third order imaginary susceptibility and second order hyperpolarizability values were found to be within the limit set for good optical limiters. The Pcs were embedded in poly (methyl methacrylate) (PMMA) and poly(bisphenol A carbonate) (PBC) as thin films. The optical limiting values of the Pcs once embedded in film were found to be greatly improved and the limiting intensity of each film was well below the maximum threshold. Both PbOtBPPc and CdOtBPPc showed better optical limiting when embedded in PBC compared to PMMA. CdOtBPPc shows better nonlinear optical behaviour than PbOtBPPc in solution and as thin films, even though the former is aggregated in solution. Novel phosphorus triazatetrabenzcorroles (TBC) tetrasubstituted at the α- and β- and octa substituted at the β- positions of the peripheral fused benzene rings with t-butylphenoxy substituents were prepared and characterized. The effects of the substituents and the missing aza-nitrogen on the electronic structures and optical spectroscopy are investigated with TD-DFT calculations and MCD spectroscopy. The optical limiting properties were investigated to examine whether the lower symmetry that results from the direct pyrrole-pyrrole bond and hence the permanent dipole moment that is introduced result in higher safety thresholds, relative to the values that have been reported for phthalocyanines. The suitability of the compounds for singlet oxygen applications has also been examined. Novel phosphorus phthalocyanines, analogous to the triazatetrabenzcorroles were also investigated. Due to their high photodegradation quantum yield however, only the fluorescence quantum yields and lifetimes were able to be determined.

The physical processes shaping laser plasma dynamics take place on length scales ranging from the microscopic (1 ångström) to the macroscopic realms (µm). Microscopic field fluctuations due to the motions of individual plasma charges evolve on an atomic scale. Collisional effects influencing thermalization and ionization processes depend on the plasma fields on an atomic level. Simultaneously, collective processes such as plasma oscillations take place on a mesoscopic length scale of many-nm. The macroscopic realm is ultimately determined by the laser which typically spans hundreds of nm to a few µm. Consequently, ab-initio modelling of laser plasma dynamics requires the resolution of length scales from 1Å to multiple µm. As such, in order to bridge the microscopic and macroscopic length scales of light-matter interaction, in is necessary to account for the individual motions of up to ~10^11 particles. This is a not an insignificant undertaking. Until recently, approaches to numerical modelling of light-matter interactions were limited to MD and PIC, each with their own limitations. MicPIC has been developed to fill the gap left by MD and PIC but so far has not been adapted for scalable parallel processing on large distributed memory machines. Thus, its full potential was not able to be fully realized until now. This thesis presents the massively parallel MicPIC method capable of bridging the micro- and macroscopic realms. A wide range of applications that have heretofore not been accessible to theory or, at best, had limited applicability are now open for thorough investigation. Among these are nonlinear nanophotonics, quantum nanophotonics, laser machining, ab-initio dynamics of strongly coupled plasmas, high-harmonic generation, electron and x-ray sources, and optical switching. Two of the first applications of parallel MicPIC to a selection of such problems are shown and discussed below, demonstrating the applicability of the method to a wide variety of newly accessible strong field laser-plasma physics phenomena.

Fiber optical parametric amplifiers (OPAs) are based on a highly-efficient four-wave mixing process. Their capability to give very high gain and large bandwidths have made them an attractive candidate for providing higher bandwidths for future telecommunication systems, such as wavelength-division multiplexed (WDM) photonics networks. In dynamic photonic networks a where number of channels are dropped and/or added all the time, the OPA gain for the other channels is affected. In this thesis we employed a well-known gain control technique, all-optical gain clamping (AOGC), and reduced the gain variation of fiber OPAs below 0.5 dB, under varying input conditions. We also showed an improvement in power penalties o at the bit-error rate of 10-8, from 2.5 dB to 0.5 dB for on/off keying modulation. We also investigated fiber optical parametric oscillators (OPOs). Using fiber OPAs as gain medium we realized two different continuous-wave (CW) OPOs, centred at 1561 nm and 1593 nm. One gave us watt-level output power from 1600 nm to 1670 nm, with overall tuning range of 211 nm. The output linewidth of signal and idler was measured to be 0.08 nm and 0.15 nm respectively. The OPO centred at 1593 nm gave us a record tuning range of 254 nm, and with 3 dB output coupling fraction, it gave us large output powers (20-27 dBm) from 1610 nm to 1720 nm. Using a large seed generated by a watt-level fiber OPO in the U-band, and using 3 W of CW pump source in the C-band for Raman amplification, we generated 3 W of CW output power. This gave us nearly 100% conversion efficiency. Launching a high-power CW pump with narrow linewidth into a fiber makes stimulated Brillouin scattering (SBS) a major problem. We investigated an SBS suppressor, based on a common technique of phase dithering of the pump to suppress the SBS. We compared a multitone modulation technique to modulation with a pseudo-random bit sequence (PRBS), and we showed that it can increase the SBS threshold by 4.18 dB, and is less expensive to implement.

The elasto-dynamics of flexible frame structures is of interest in many areas of engineering. In certain structural systems the deflections can be large enough to warrant a nonlinear analysis. For example, offshore structures, long suspension bridges and other relatively slender structures used in space applications require a geometrically nonlinear analysis. In addition, if the structure has deployable elements, as in some space structures, the required analysis becomes even more complex. Typical examples are spacecraft antennae, radio telescopes, solar panels and space-based manipulators with deployable elements. The main objective of the present work is to formulate the problem of sliding beams undergoing large rotations and small strains. Further we aim to develop efficient finite element technique for analysis of such complex systems. Finally we wish to examine the nature of the motion of sliding beams and point out its salient features. We start with two well known approaches in the nonlinear finite element static analysis of highly flexible structures, namely, the updated Lagrangian and the consistent co-rotational methods and extend these techniques to dynamic analysis of geometrically nonlinear beam structures. We analyse several examples by the same methods and compare the performance of each for efficiency and accuracy. Next, using McIver's extension of Hamilton's principle, we formulate the problem of geometrically flexible sliding beams by two different approaches. In the first the beam slides through a fixed rigid channel with a prescribed sliding motion. In this formulation which we refer to as the sliding beam formulation, the material points on the beam slide relative to a fixed channel. In the second formulation the material points on the fixed beam are observed by a moving observer on a sliding channel and the beam is axially at rest. The governing equations of motion for the two formulations describe the same physical problem and by mapping both to a fixed domain, using proper transformations, we show that the two sets of governing equations become identical. It is not, possible to find analytical solutions to our problem and we choose the Galerkin numerical method to obtain the transient response of the problem for the special case axially rigid beam. Next we follow a more elegant approach wherein we use the developed incremental nonlinear finite element approaches (the updated Lagrangian and the consistent co-rotational method) in conjunction with a variable time domain beam finite elements (where the number of elements is fixed and as mass enters the domain of interest, but the sizes of elements change in a prescribed manner in the undeformed configuration). To verify the formulation and its computational implementation we analyse many examples and compare our findings with those reported in the literature when possible. We also use these illustrative examples to identify the importance of various terms such as axial flexibility and foreshortening effects. Finally we look into the problem of parametric resonance for the beam with periodically varying length and we show that the regions of stability obtained in the literature, using a linear analysis, do not hold when a more realistic nonlinear analysis is undertaken. / Graduate

Resumo: Na presença de não linearidades, a resposta forçada de estruturas exibe diversos fenômenos físicos que não podem ser descritos através de modelos lineares. Estes fenômenos incluem ressonâncias sub-harmônicas, ressonâncias super-harmônicas, “jumps”, movimentos quasi-periódicos, movimentos de período múltiplo, caos e interações modais. Recentes estudos experimentais indicam que um novo tipo de interação modal pode ocorrer através de mecanismos não ressonantes, decorrente da transferência de energia de modos de alta freqüência e baixa amplitude para modos de baixa freqüência e alta amplitude. Neste trabalho, interações modais não ressonantes são investigadas na resposta planar não linear de vigas cantilever flexíveis sujeitas a excitações externas e paramétricas. As equações diferenciais e as condições de contorno associadas que governam o movimento flexional-flexional não linear de uma viga assumida inextensível, metálica e isotrópica, são apresentadas. O estudo experimental conduzido revelou que a transferência de energia entre modos de alta freqüência para modos de baixa freqüência ocorre via modulação, sendo função do valor da amplitude de excitação e da proximidade entre os valores da freqüência de modulação e da freqüência dos modos ativados. O estudo revelou também que a ativação de modos de baixa freqüência pode ocorrer sob uma variedade de condições de entrada. Em adição, outros fenômenos dinâmicos não lineares classificados como rotas para o movimento caótico são também observados. Em determinadas condições, movimentos quasi-periódicos com amplitudes moduladas caoticamente e moduladas periodicamente são exibidos. Um movimento de resposta de período dois é também observado. / Abstract: Interesting physical phenomena occur in the forced response of structures in the presence of nonlinearities, which cannot be explained by linear models. These phenomena include subharmonic resonances, superharmonic resonances, jumps, period-multiplying motions, quasiperiodic motions, chaos and modal interactions. Recent studies suggest that another type of modal interaction may occur through nonresonant mechanisms, due to the energy transfer from the low-amplitude highfrequency modes to high-amplitude low-frequency modes. In this work, nonresonant modal interactions in the nonlinear planar motions of flexible cantilever beams subjected to transverse and parametric harmonic excitations are investigated. The governing equations of the nonlinear bending-bending motions and the associated boundary conditions for an isotropic metallic inextensional beam are presented. An experimental study revealed that the transfer of energy from high-frequency to lowfrequency modes occurs via modulation and is found to be function of the excitation amplitude and the closeness of the modulation frequency to the frequencies of the low modes activated. The experimental study also revealed that the energy transfer from high-frequency modes to low-frequency modes occurs for a variety of conditions. In addition, others nonlinear dynamic phenomenas routes to the chaotic motions, are also observed. Under certain conditions, quasiperiodic motion with periodically and chaotically modulated amplitudes are exhibited. Period-doubling motion is also observed. / Orientador: Fernando de Azevedo Silva / Coorientador: Mauro Hugo Mathias / Banca: Othon Cabo Winter / Banca: Victor Orlando Gamarra Rosado / Banca: José Juliano de Lima Júnior / Banca: Olivério Moreira de Macedo Silva / Doutor

M.Sc. / In this work we concentrate on two generalizations of Lie symmetries namely conditional symmetries in the form of Q-symmetries and approximate symmetries. The theorems and definitions presented can be used to obtain exact and approximate solutions for nonlinear partial differential equations. These are then applied to various nonlinear heat and wave equations and many interesting solutions are given. Chapters 1 and 2 gives an introduction to the classical Lie approach. Chapters 3, 4 and 5 deals with conditional -, approximate -, and approximate conditional symmetries respectively. In chapter 6 we give a review of symbolic algebra computer packages available to aid in the search for symmetries, as well as useful REDUCE programs which were written to obtain the results given in chapters 2 to 5.

M.Sc. (Mathematical Statistics) / This dissertation deals with the computation of nonlinear control strategies for an autonomous vehicle. The vehicle consists of two wheels attached to an axle. It is assumed that both wheels roll without slipping leading to nonholonomic constraints. A third order nonlinear kinematic model of the vehicle is derived from these constraints. It is further assumed that the vehicle has builtin feedback controllers independently regulating the rotational velocities of the wheels (using electric motors as actuators). Thus, the vehicle is maneuvered by applying a separate rotational velocity reference command to the feedback controller of each wheel. The closed loop system dynamics from the reference command to the wheel rotational velocity is approximately modelled by a first order system. This leads to a fifth order nonlinear state-space model for the vehicle. The above-mentioned reference commands constitute the control input variables of the vehicle model and are subject to amplitude constraints. Firstly, a methodology is developed for computing reference command strategies to drive the autonomous vehicle from a specified initial state to a desired final state in a given time and such that a circular obstacle is avoided. The vehicle performs the required maneuver whilst satisfying all the specifications and constraints. Secondly, feedback reference command laws are developed such that a specified point just ahead of the vehicle asymptotically tracks a given reference trajectory in the horizontal plane. The feedback control law steers the vehicle onto the reference path from any initial position and keeps it moving on the path. Thirdly, the stochastic system performance is evaluated when the above-mentioned tracking control strategy is applied and the initial state of the vehicle is a random vector.