Statistical properties of first-order bang-bang Pll with nonzero loop delay

A method to solve the stationary state probability is presented for the first-order bang-bang phase-locked loop (BBPLL) with nonzero loop delay. This is based on a delayed Markov chain model and a state How diagram for tracing the state history due to the loop delay. As a result, an eigenequation is obtained, and its closed form solutions are derived for some cases. After obtaining the state probability, statistical characteristics such as mean gain of the binary phase detector and timing error variance are calculated and demonstrated.

Extended nonlinear analytical models of compliant parallelogram mechanisms: third-order models

This paper proposes extended nonlinear analytical models, third-order models, of compliant parallelogram mechanisms. These models are capable of capturing the accurate effects from the very large axial force within the transverse motion range of 10% of the beam length through incorporating the terms associated with the high-order (up to third-order) axial force. Firstly, the free-body diagram method is employed to derive the nonlinear analytical model for a basic compliant parallelogram mechanism based on load-displacement relations of a single beam, geometry compatibility conditions, and load-equilibrium conditions. The procedures for the forward solutions and inverse solutions are described. Nonlinear analytical models for guided compliant multi-beam parallelogram mechanisms are then obtained. A case study of the compound compliant parallelogram mechanism, composed of two basic compliant parallelogram mechanisms in symmetry, is further implemented. This work intends to estimate the internal axial force change, the transverse force change, and the transverse stiffness change with the transverse motion using the proposed third-order model in comparison with the first-order model proposed in the prior art. In addition, FEA (finite element analysis) results validate the accuracy of the third-order model for a typical example. It is shown that in the case study the slenderness ratio affects the result discrepancy between the third-order model and the first-order model significantly, and the third-order model can illustrate a non-monotonic transverse stiffness curve if the beam is thin enough.

Electrical machine characterisation and analysis for renewable energy applications

There has been an increased use of the Doubly-Fed Induction Machine (DFIM) in ac drive applications in recent times, particularly in the field of renewable energy systems and other high power variable-speed drives. The DFIM is widely regarded as the optimal generation system for both onshore and offshore wind turbines and has also been considered in wave power applications. Wind power generation is the most mature renewable technology. However, wave energy has attracted a large interest recently as the potential for power extraction is very significant. Various wave energy converter (WEC) technologies currently exist with the oscillating water column (OWC) type converter being one of the most advanced. There are fundemental differences in the power profile of the pneumatic power supplied by the OWC WEC and that of a wind turbine and this causes significant challenges in the selection and rating of electrical generators for the OWC devises. The thesis initially aims to provide an accurate per-phase equivalent circuit model of the DFIM by investigating various characterisation testing procedures. Novel testing methodologies based on the series-coupling tests is employed and is found to provide a more accurate representation of the DFIM than the standard IEEE testing methods because the series-coupling tests provide a direct method of determining the equivalent-circuit resistances and inductances of the machine. A second novel method known as the extended short-circuit test is also presented and investigated as an alternative characterisation method. Experimental results on a 1.1 kW DFIM and a 30 kW DFIM utilising the various characterisation procedures are presented in the thesis. The various test methods are analysed and validated through comparison of model predictions and torque-versus-speed curves for each induction machine. Sensitivity analysis is also used as a means of quantifying the effect of experimental error on the results taken from each of the testing procedures and is used to determine the suitability of the test procedures for characterising each of the devices. The series-coupling differential test is demonstrated to be the optimum test. The research then focuses on the OWC WEC and the modelling of this device. A software model is implemented based on data obtained from a scaled prototype device situated at the Irish test site. Test data from the electrical system of the device is analysed and this data is used to develop a performance curve for the air turbine utilised in the WEC. This performance curve was applied in a software model to represent the turbine in the electro-mechanical system and the software results are validated by the measured electrical output data from the prototype test device. Finally, once both the DFIM and OWC WEC power take-off system have been modeled succesfully, an investigation of the application of the DFIM to the OWC WEC model is carried out to determine the electrical machine rating required for the pulsating power derived from OWC WEC device. Thermal analysis of a 30 kW induction machine is carried out using a first-order thermal model. The simulations quantify the limits of operation of the machine and enable thedevelopment of rating requirements for the electrical generation system of the OWC WEC. The thesis can be considered to have three sections. The first section of the thesis contains Chapters 2 and 3 and focuses on the accurate characterisation of the doubly-fed induction machine using various testing procedures. The second section, containing Chapter 4, concentrates on the modelling of the OWC WEC power-takeoff with particular focus on the Wells turbine. Validation of this model is carried out through comparision of simulations and experimental measurements. The third section of the thesis utilises the OWC WEC model from Chapter 4 with a 30 kW induction machine model to determine the optimum device rating for the specified machine. Simulations are carried out to perform thermal analysis of the machine to give a general insight into electrical machine rating for an OWC WEC device.

Interaction of additive and quantization noises in digital PLLs

Phase-locked loops (PLLs) are a crucial component in modern communications systems. Comprising of a phase-detector, linear filter, and controllable oscillator, they are widely used in radio receivers to retrieve the information content from remote signals. As such, they are capable of signal demodulation, phase and carrier recovery, frequency synthesis, and clock synchronization. Continuous-time PLLs are a mature area of study, and have been covered in the literature since the early classical work by Viterbi [1] in the 1950s. With the rise of computing in recent decades, discrete-time digital PLLs (DPLLs) are a more recent discipline; most of the literature published dates from the 1990s onwards. Gardner [2] is a pioneer in this area. It is our aim in this work to address the difficulties encountered by Gardner [3] in his investigation of the DPLL output phase-jitter where additive noise to the input signal is combined with frequency quantization in the local oscillator. The model we use in our novel analysis of the system is also applicable to another of the cases looked at by Gardner, that is the DPLL with a delay element integrated in the loop. This gives us the opportunity to look at this system in more detail, our analysis providing some unique insights into the variance `dip' seen by Gardner in [3]. We initially provide background on the probability theory and stochastic processes. These branches of mathematics are the basis for the study of noisy analogue and digital PLLs. We give an overview of the classical analogue PLL theory as well as the background on both the digital PLL and circle map, referencing the model proposed by Teplinsky et al. [4, 5]. For our novel work, the case of the combined frequency quantization and noisy input from [3] is investigated first numerically, and then analytically as a Markov chain via its Chapman-Kolmogorov equation. The resulting delay equation for the steady-state jitter distribution is treated using two separate asymptotic analyses to obtain approximate solutions. It is shown how the variance obtained in each case matches well to the numerical results. Other properties of the output jitter, such as the mean, are also investigated. In this way, we arrive at a more complete understanding of the interaction between quantization and input noise in the first order DPLL than is possible using simulation alone. We also do an asymptotic analysis of a particular case of the noisy first-order DPLL with delay, previously investigated by Gardner [3]. We show a unique feature of the simulation results, namely the variance `dip' seen for certain levels of input noise, is explained by this analysis. Finally, we look at the second-order DPLL with additive noise, using numerical simulations to see the effects of low levels of noise on the limit cycles. We show how these effects are similar to those seen in the noise-free loop with non-zero initial conditions.

Optical micro- and nanofibres: Higher mode generation and particle manipulation studies

This thesis is centred on two experimental fields of optical micro- and nanofibre research; higher mode generation/excitation and evanescent field optical manipulation. Standard, commercial, single-mode silica fibre is used throughout most of the experiments; this generally produces high-quality, single-mode, micro- or nanofibres when tapered in a flame-heated, pulling rig in the laboratory. Single mode fibre can also support higher transverse modes, when transmitting wavelengths below that of their defined single-mode regime cut-off. To investigate this, a first-order Laguerre-Gaussian beam, LG01 of 1064 nm wavelength and doughnut-shaped intensity profile is generated free space via spatial light modulation. This technique facilitates coupling to the LP11 fibre mode in two-mode fibre, and convenient, fast switching to the fundamental mode via computer-generated hologram modulation. Following LP11 mode loss when exponentially tapering 125μm diameter fibre, two mode fibre with a cladding diameter of 80μm is selected fir testing since it is more suitable for satisfying the adiabatic criteria for fibre tapering. Proving a fruitful endeavour, experiments show a transmission of 55% of the original LP11 mode set (comprising TE01, TM01, HE21e,o true modes) in submicron fibres. Furthermore, by observing pulling dynamics and progressive mode-lass behaviour, it is possible to produce a nanofibre which supports only the TE01 and TM01 modes, while suppressing the HE21e,o elements of the LP11 group. This result provides a basis for experimental studies of atom trapping via mode-interference, and offers a new set of evanescent field geometries for sensing and particle manipulation applications. The thesis highlights the experimental results of the research unit’s Cold Atom subgroup, who successfully integrated one such higher-mode nanofibre into a cloud of cold Rubidium atoms. This led to the detection of stronger signals of resonance fluorescence coupling into the nanofibre and for light absorption by the atoms due to the presence of higher guided modes within the fibre. Theoretical work on the impact of the curved nanofibre surface on the atomic-surface van der Waals interaction is also presented, showing a clear deviation of the potential from the commonly-used flat-surface approximation. Optical micro- and nanofibres are also useful tools for evanescent-field mediated optical manipulation – this includes propulsion, defect-induced trapping, mass migration and size-sorting of micron-scale particles in dispersion. Similar early trapping experiments are described in this thesis, and resulting motivations for developing a targeted, site-specific particle induction method are given. The integration of optical nanofibres into an optical tweezers is presented, facilitating individual and group isolation of selected particles, and their controlled positioning and conveyance in the evanescent field. The effects of particle size and nanofibre diameter on pronounced scattering is experimentally investigated in this systems, as are optical binding effects between adjacent particles in the evanescent field. Such inter-particle interactions lead to regulated self-positioning and particle-chain speed enhancements.