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.

Optimisation of granola breakfast cereal manufacturing process by wet granulation and pneumatic conveying

This study has considered the optimisation of granola breakfast cereal manufacturing processes by wet granulation and pneumatic conveying. Granola is an aggregated food product used as a breakfast cereal and in cereal bars. Processing of granola involves mixing the dry ingredients (typically oats, nuts, etc.) followed by the addition of a binder which can contain honey, water and/or oil. In this work, the design and operation of two parallel wet granulation processes to produce aggregate granola products were incorporated: a) a high shear mixing granulation process followed by drying/toasting in an oven. b) a continuous fluidised bed followed by drying/toasting in an oven. In high shear granulation the influence of process parameters on key granule aggregate quality attributes such as granule size distribution and textural properties of granola were investigated. The experimental results show that the impeller rotational speed is the single most important process parameter which influences granola physical and textural properties. After that binder addition rate and wet massing time also show significant impacts on granule properties. Increasing the impeller speed and wet massing time increases the median granule size while also presenting a positive correlation with density. The combination of high impeller speed and low binder addition rate resulted in granules with the highest levels of hardness and crispness. In the fluidised bed granulation process the effect of nozzle air pressure and binder spray rate on key aggregate quality attributes were studied. The experimental results show that a decrease in nozzle air pressure leads to larger in mean granule size. The combination of lowest nozzle air pressure and lowest binder spray rate results in granules with the highest levels of hardness and crispness. Overall, the high shear granulation process led to larger, denser, less porous and stronger (less likely to break) aggregates than the fluidised bed process. The study also examined the particle breakage of granola during pneumatic conveying produced by both the high shear granulation and the fluidised bed granulation process. Products were pneumatically conveyed in a purpose built conveying rig designed to mimic product conveying and packaging. Three different conveying rig configurations were employed; a straight pipe, a rig consisting two 45° bends and one with 90° bend. Particle breakage increases with applied pressure drop, and a 90° bend pipe results in more attrition for all conveying velocities relative to other pipe geometry. Additionally for the granules produced in the high shear granulator; those produced at the highest impeller speed, while being the largest also have the lowest levels of proportional breakage while smaller granules produced at the lowest impeller speed have the highest levels of breakage. This effect clearly shows the importance of shear history (during granule production) on breakage during subsequent processing. In terms of the fluidised bed granulation, there was no single operating parameter that was deemed to have a significant effect on breakage during subsequent conveying. Finally, a simple power law breakage model based on process input parameters was developed for both manufacturing processes. It was found suitable for predicting the breakage of granola breakfast cereal at various applied air velocities using a number of pipe configurations, taking into account shear histories.

A facilities maintenance management process based on degradation prediction using sensed data

Energy efficiency and user comfort have recently become priorities in the Facility Management (FM) sector. This has resulted in the use of innovative building components, such as thermal solar panels, heat pumps, etc., as they have potential to provide better performance, energy savings and increased user comfort. However, as the complexity of components increases, the requirement for maintenance management also increases. The standard routine for building maintenance is inspection which results in repairs or replacement when a fault is found. This routine leads to unnecessary inspections which have a cost with respect to downtime of a component and work hours. This research proposes an alternative routine: performing building maintenance at the point in time when the component is degrading and requires maintenance, thus reducing the frequency of unnecessary inspections. This thesis demonstrates that statistical techniques can be used as part of a maintenance management methodology to invoke maintenance before failure occurs. The proposed FM process is presented through a scenario utilising current Building Information Modelling (BIM) technology and innovative contractual and organisational models. This FM scenario supports a Degradation based Maintenance (DbM) scheduling methodology, implemented using two statistical techniques, Particle Filters (PFs) and Gaussian Processes (GPs). DbM consists of extracting and tracking a degradation metric for a component. Limits for the degradation metric are identified based on one of a number of proposed processes. These processes determine the limits based on the maturity of the historical information available. DbM is implemented for three case study components: a heat exchanger; a heat pump; and a set of bearings. The identified degradation points for each case study, from a PF, a GP and a hybrid (PF and GP combined) DbM implementation are assessed against known degradation points. The GP implementations are successful for all components. For the PF implementations, the results presented in this thesis find that the extracted metrics and limits identify degradation occurrences accurately for components which are in continuous operation. For components which have seasonal operational periods, the PF may wrongly identify degradation. The GP performs more robustly than the PF, but the PF, on average, results in fewer false positives. The hybrid implementations, which are a combination of GP and PF results, are successful for 2 of 3 case studies and are not affected by seasonal data. Overall, DbM is effectively applied for the three case study components. The accuracy of the implementations is dependant on the relationships modelled by the PF and GP, and on the type and quantity of data available. This novel maintenance process can improve equipment performance and reduce energy wastage from BSCs operation.

Delivering enhanced efficiency in the synthesis of α-diazosulfoxides by exploiting the process control enabled in flow

Continuous-flow generation of α-diazosulfoxides results in a two- to three-fold increase in yields and decreased reaction times compared to standard batch synthesis methods. These high yielding reactions are enabled by flowing through a bed of polystyrene-supported base (PS-DBU or PS-NMe2) with highly controlled residence times. This engineered solution allows the α-diazosulfoxides to be rapidly synthesized while limiting exposure of the products to basic reaction conditions, which have been found to cause rapid decomposition. In addition to improved yields, this work has the added advantage of ease of processing, increased safety profile, and scale-up potential.

Development of a continuous process for α-thio-β-chloroacrylamide synthesis with enhanced control of a cascade transformation

A continuous process strategy has been developed for the preparation of α-thio-β chloroacrylamides, a class of highly versatile synthetic intermediates. Flow platforms to generate the α-chloroamide and α-thioamide precursors were successfully adopted, progressing from the previously employed batch chemistry, and in both instances afford a readily scalable methodology. The implementation of the key α-thio-β-chloroacrylamide casade as a continuous flow reaction on a multi-gram scale is described, while the tuneable nature of the cascade, facilitated by continuous processing, is highlighted by selective generation of established intermediates and byproducts.