MEMS gyroscopes are found across a large range of applications, from low precision low cost applications through to high budget projects that require almost perfect accuracy. MEMS gyroscopes fall into two categories – ‘rate’ and ‘rate integrating’, with the latter offering superior performance. The key advantage that the rate integrating type possesses is that it directly measures angle, eliminating the need for any integration step. This reduces the potential for errors, particularly at high rates. However, the manufacturing precision required is far tighter than that of the rate gyroscope, and this has thus far limited the development of rate integrating gyroscopes. This thesis proposes a method for reducing the effect of structural imperfections on the performance of a rate integrating gyroscope. By taking a conventional rate gyroscope and adjusting its control scheme to operate in rate integrating mode, the thesis shows that it is possible to artificially eliminate the effect of some structural imperfections on the accuracy of angular measurement through the combined use of electrostatic tuning and capacitive forcing. Further, it demonstrates that it is viable to base the designs for rate integrating gyroscopes on existing rate gyroscope architectures, albeit with some modifications. Initially, the control scheme is derived through the method of multiple scales and its potential efficacy demonstrated through computational modelling using Simulink. The control scheme is then implemented onto an existing rate gyroscope architecture, with a series of tests conducted that benchmark the gyroscope performance in comparison to standard performance measures. Experimental work demonstrates the angle measurement capability of the rate integrating control scheme, with the gyroscope shown to be able to measure angle, although not to the precision necessary for commercial implementation. However, the scheme is shown to be viable with some modifications to the gyroscope architecture, and initial tests on an alternative architecture based on these results are presented.

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With the increased use of power electronics in aerospace, automotive, industrial, and energy generation sectors, the demand for highly reliable and power dense solutions has increased. Taking into account the demands for high reliability and high power density, matrix converters become attractive. With their lack of large bulky DC- Link capacitors, high power densities are possible with capability to operate with high ambient temperatures [7]. Demand for high reliability under tight weight and volume constrains, often it is not possible to have an entirely redundant system. Under these conditions it is desirable that the system continue to operate even under faulty conditions, albeit with diminished performance in some regard. Research has been carried out on the continued operation of a matrix converter during an open- circuit switch failure[8][9]. These methods however assume that a fault detection and diagnosis system was already in place. The behavior of matrix converters under fault conditions are more complex than traditional inverter drive systems, as there is no decoupling through the DC-Link and the matrix converter's clamp circuit also complicates matters. This thesis describes the operation of a matrix converter and the clamp circuit during a open-circuit fault condition and presents a number of methods for fault detection and diagnosis in matrix converters.

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Waveguide discontinuities are frequently encountered in modern photonic structures. It is important to characterize the reflection and transmission that occurs at the discontinuous during the design and analysis process of these structures. Significant effort has been focused upon the development of accurate modelling tools, and a variety of modelling techniques have been applied to solve this kind of problem. Throughout this work, a Transmission matrix based Bidirectional Beam Propagation Method (T-Bi-BPM) is proposed and applied on the uncoated facet and the single coating layer reflection problems, including both normal and angled incident situations. The T-Bi-BPM method is developed on the basis of an overview of Finite Difference Beam Propagation Method (FD-BPM) schemes frequently used in photonic modelling including paraxial FD-BPM, Imaginary Distance (ID) BPM, Wide Angle (WA) BPM and existing Bidirectional (Bi) BPM methods. The T-Bi-BPM establishes the connection between the total fields on either side of the coating layer and the incident field at the input of a single layer coated structure by a matrix system on the basis of a transmission matrix equation used in a transmission line approach. The matrix system can be algebraically preconditioned and then solved by sparse matrix multiplications. The attraction of the T-Bi-BPM method is the potential for more rapid evaluation without iterative approach. The accuracy of the T-Bi-BPM is verified by simulations and the factors that affect the accuracy are investigated.

As electronics become more and more miniaturised, there is much interest in increasing knowledge about the electronic and transport properties of nano-systems. In particular, there has been some focus on understanding the physics of nanowires with prescribed properties. Two different groups of systems have been considered that of 1D organic molecular nanowires and 2D interconnects based on graphene. In order to develop a deeper insight of the factors that determine the electronic structure and consequently the electrical transport properties, it is desirable to carry out computer simulation studies of these systems. The work reported in this thesis has focused on studying the porphyrin and DNA molecules as well as investigating the consequences of engineered 2D graphene interconnect. The latter class of systems has included graphene nanoribbons (GNRs), graphene sheets with grain boundaries (GGBs) and graphene nanomeshes (GNMs). The methodology was to use self-consistent extended Hückel theory (SC-EHT) and density functional theory (DFT) in combination with non-equilibrium Green functions (NEGFs) formalism to investigate the electronic and transport properties of these systems. The SC-EHT calculations were performed using an in-house developed C++ code named EHTransport. While the SIESTA package was employed for the DFT. It was found that the SC-EHT approach produced comparable results with that obtained by DFT. This supports the idea that the semi-empirical methods can be as valid as ab-initio approaches. The findings demonstrated that porphyrin, DNA, and graphene based systems are very promising candidates to incorporate in future electronics.