Microcontroller-based peak current mode control using digital slope compensation

Microcontroller-based peak current mode control of a buck converter is investigated. The new solution uses a discrete time controller with digital slope compensation. This is implemented using only a single-chip microcontroller to achieve desirable cycle-by-cycle peak current limiting. The digital controller is implemented as a two-pole, two-zero linear difference equation designed using a continuous time model of the buck converter and a discrete time transform. Subharmonic oscillations are removed with digital slope compensation using a discrete staircase ramp. A 16 W hardware implementation directly compares analog and digital control. Frequency response measurements are taken and it is shown that the crossover frequency and expected phase margin of the digital control system match that of its analog counterpart.

Choosing the most suitable analogue redesign method for forward-type digital power converters

This work proposes a method to objectively determine the most suitable analogue redesign method for forward type converters under digital voltage mode control. Particular emphasis is placed on determining the method which allows the highest phase margin at the particular switching and crossover frequencies chosen by the designer. It is shown that at high crossover frequencies with respect to switching frequency, controllers designed using backward integration have the largest phase margin; whereas at low crossover frequencies with respect to switching frequency, controllers designed using bilinear integration have the largest phase margins. An accurate model of the power stage is used for simulation, and experimental results from a Buck converter are collected. The performance of the digital controllers is compared to that of the equivalent analogue controller both in simulation and experiment. Excellent correlation between the simulation and experimental results is presented. This work will allow designers to confidently choose the analogue redesign method which yields the greater phase margin for their application.

Optical characterization of the growth and spatial structure of a substorm onset arc

We present a detailed case study of the characteristics of auroral forms that constitute the first ionospheric signatures of substorm expansion phase onset. Analysis of the optical frequency and along-arc (azimuthal) wave number spectra provides the strongest constraint to date on the potential mechanisms and instabilities in the near-Earth magnetosphere that accompany auroral onset and which precede poleward arc expansion and auroral breakup. We evaluate the frequency and growth rates of the auroral forms as a function of azimuthal wave number to determine whether these wave characteristics are consistent with current models of the substorm onset mechanism. We find that the frequency, spatial scales, and growth rates of the auroral forms are most consistent with the cross-field current instability or a ballooning instability, most likely triggered close to the inner edge of the ion plasma sheet. This result is supportive of a near-Earth plasma sheet initiation of the substorm expansion phase. We also present evidence that the frequency and phase characteristics of the auroral undulations may be generated via resonant processes operating along the geomagnetic field. Our observations provide the most powerful constraint to date on the ionospheric manifestation of the physical processes operating during the first few minutes around auroral substorm onset.

Averaging, slaving and balance dynamics in a simple atmospheric model

We report numerical results from a study of balance dynamics using a simple model of atmospheric motion that is designed to help address the question of why balance dynamics is so stable. The non-autonomous Hamiltonian model has a chaotic slow degree of freedom (representing vortical modes) coupled to one or two linear fast oscillators (representing inertia-gravity waves). The system is said to be balanced when the fast and slow degrees of freedom are separated. We find adiabatic invariants that drift slowly in time. This drift is consistent with a random-walk behaviour at a speed which qualitatively scales, even for modest time scale separations, as the upper bound given by Neishtadt’s and Nekhoroshev’s theorems. Moreover, a similar type of scaling is observed for solutions obtained using a singular perturbation (‘slaving’) technique in resonant cases where Nekhoroshev’s theorem does not apply. We present evidence that the smaller Lyapunov exponents of the system scale exponentially as well. The results suggest that the observed stability of nearly-slow motion is a consequence of the approximate adiabatic invariance of the fast motion.

Orographic drag associated with lee waves trapped at an inversion

The drag produced by 2D orographic gravity waves trapped at a temperature inversion and waves propagating in the stably stratified layer existing above are explicitly calculated using linear theory, for a two-layer atmosphere with neutral static stability near the surface, mimicking a well-mixed boundary layer. For realistic values of the flow parameters, trapped lee wave drag, which is given by a closed analytical expression, is comparable to propagating wave drag, especially in moderately to strongly non-hydrostatic conditions. In resonant flow, both drag components substantially exceed the single-layer hydrostatic drag estimate used in most parametrization schemes. Both drag components are optimally amplified for a relatively low-level inversion and Froude numbers Fr ≈ 1. While propagating wave drag is maximized for approximately hydrostatic flow, trapped lee wave drag is maximized for l_2 a = O(1) (where l_2 is the Scorer parameter in the stable layer and a is the mountain width). This roughly happens when the horizontal scale of trapped lee waves matches that of the mountain slope. The drag behavior as a function of Fr for l_2 H = 0.5 (where H is the inversion height) and different values of l2a shows good agreement with numerical simulations. Regions of parameter space with high trapped lee wave drag correlate reasonably well with those where lee wave rotors were found to occur in previous nonlinear numerical simulations including frictional effects. This suggests that trapped lee wave drag, besides giving a relevant contribution to low-level drag exerted on the atmosphere, may also be useful to diagnose lee rotor formation.

An exact local conservation theorem for finite-amplitude disturbances to non-parallel shear flows, with remarks on Hamiltonian structure and on Arnol'd's stability theorems

Disturbances of arbitrary amplitude are superposed on a basic flow which is assumed to be steady and either (a) two-dimensional, homogeneous, and incompressible (rotating or non-rotating) or (b) stably stratified and quasi-geostrophic. Flow over shallow topography is allowed in either case. The basic flow, as well as the disturbance, is assumed to be subject neither to external forcing nor to dissipative processes like viscosity. An exact, local ‘wave-activity conservation theorem’ is derived in which the density A and flux F are second-order ‘wave properties’ or ‘disturbance properties’, meaning that they are O(a2) in magnitude as disturbance amplitude a [rightward arrow] 0, and that they are evaluable correct to O(a2) from linear theory, to O(a3) from second-order theory, and so on to higher orders in a. For a disturbance in the form of a single, slowly varying, non-stationary Rossby wavetrain, $\overline{F}/\overline{A}$ reduces approximately to the Rossby-wave group velocity, where (${}^{-}$) is an appropriate averaging operator. F and A have the formal appearance of Eulerian quantities, but generally involve a multivalued function the correct branch of which requires a certain amount of Lagrangian information for its determination. It is shown that, in a certain sense, the construction of conservable, quasi-Eulerian wave properties like A is unique and that the multivaluedness is inescapable in general. The connection with the concepts of pseudoenergy (quasi-energy), pseudomomentum (quasi-momentum), and ‘Eliassen-Palm wave activity’ is noted. The relationship of this and similar conservation theorems to dynamical fundamentals and to Arnol'd's nonlinear stability theorems is discussed in the light of recent advances in Hamiltonian dynamics. These show where such conservation theorems come from and how to construct them in other cases. An elementary proof of the Hamiltonian structure of two-dimensional Eulerian vortex dynamics is put on record, with explicit attention to the boundary conditions. The connection between Arnol'd's second stability theorem and the suppression of shear and self-tuning resonant instabilities by boundary constraints is discussed, and a finite-amplitude counterpart to Rayleigh's inflection-point theorem noted

Representativity error for temperature and humidity using the Met Office high-resolution model

The observation-error covariance matrix used in data assimilation contains contributions from instrument errors, representativity errors and errors introduced by the approximated observation operator. Forward model errors arise when the observation operator does not correctly model the observations or when observations can resolve spatial scales that the model cannot. Previous work to estimate the observation-error covariance matrix for particular observing instruments has shown that it contains signifcant correlations. In particular, correlations for humidity data are more significant than those for temperature. However it is not known what proportion of these correlations can be attributed to the representativity errors. In this article we apply an existing method for calculating representativity error, previously applied to an idealised system, to NWP data. We calculate horizontal errors of representativity for temperature and humidity using data from the Met Office high-resolution UK variable resolution model. Our results show that errors of representativity are correlated and more significant for specific humidity than temperature. We also find that representativity error varies with height. This suggests that the assimilation scheme may be improved if these errors are explicitly included in a data assimilation scheme. This article is published with the permission of the Controller of HMSO and the Queen's Printer for Scotland.

A synchrotron powder X-ray diffraction study of the skutterudite-related phases AB1.5Te1.5 (A=Co, Rh, Ir; B= Ge, Sn)

X-ray resonant scattering has been exploited to investigate the crystal structure of the AB1.5Te1.5 phases (A = Co, Rh, Ir; B = Ge, Sn). Analysis of the diffraction data reveals that CoGe1.5Te1.5 and ASn1.5Te1.5 adopt a rhombohedral skutterudite-related structure, containing diamond-shape B2Te2 rings, in which the B and Te atoms are ordered and trans to each other. Anion ordering is however incomplete, and with increasing the size of both cations and anions, the degree of anion ordering decreases. By contrast, the diffraction data of IrGe1.5Te1.5 are consistent with an almost statistical distribution of the anions over the available sites, although some ordered domains may be present. The thermoelectric properties of these materials are discussed in the light of these results.

Superhumps: confronting theory with observation

We review the theory and observations related to the "superhump" precession of eccentric accretion discs in close binary systems. We agree with earlier work, although for different reasons, that the discrepancy between observation and dynamical theory implies that the effect of pressure in the disc cannot be neglected. We extend earlier work that investigates this effect to include the correct expression for the radius at which resonant orbits occur. Using analytic expressions for the accretion disc structure, we derive a relationship between the period excess and mass ratio with the pressure effects included. This is compared to the observed data, recently derived results for detailed integration of the disc equations and the equivalent empirically derived relations and used to predict values for the mass ratio based on measured values of the period excess for 88 systems.

Superhumps, magnetic fields and the mass ratio in AM Canum Venaticorum

We show that the observed K velocities and periodicities of AM CVn can be reconciled given a mass ratio q~0.22 and a secondary star with a modest magnetic field of surface strength B~1 T. We see that the new mass ratio implies that the secondary is most likely semidegenerate. The effect of the field on the accretion disc structure is examined. The theory of precessing discs and resonant orbits is generalized to encompass higher order resonances than 3:2 and shown to retain consistency with the new mass ratio.

People or machines? Assessing the impacts of smart meters and load controllers in Italian office spaces

Government initiatives in several developed and developing countries to roll-out smart meters call for research on the sustainability impacts of these devices. In principle smart meters bring about higher control over energy theft and lower consumption, but require a high level of engagement by end-users. An alternative consists of load controllers, which control the load according to pre-set parameters. To date, research has focused on the impacts of these two alternatives separately. This study compares the sustainability impacts of smart meters and load controllers in an occupied office building in Italy. The assessment is carried out on three different floors of the same building. Findings show that demand reductions associated with a smart meter device are 5.2% higher than demand reductions associated with the load controller.

An enhanced model for small-signal analysis of the phase-shifted full-bridge converter

This paper presents an in-depth critical discussion and derivation of a detailed small-signal analysis of the Phase-Shifted Full-Bridge (PSFB) converter. Circuit parasitics, resonant inductance and transformer turns ratio have all been taken into account in the evaluation of this topology’s open-loop control-to-output, line-to-output and load-to-output transfer functions. Accordingly, the significant impact of losses and resonant inductance on the converter’s transfer functions is highlighted. The enhanced dynamic model proposed in this paper enables the correct design of the converter compensator, including the effect of parasitics on the dynamic behavior of the PSFB converter. Detailed experimental results for a real-life 36V-to-14V/10A PSFB industrial application show excellent agreement with the predictions from the model proposed herein.1

The real-time optimisation of DNO owned storage devices on the LV network for peak reduction

Energy storage is a potential alternative to conventional network reinforcementof the low voltage (LV) distribution network to ensure the grid’s infrastructure remainswithin its operating constraints. This paper presents a study on the control of such storagedevices, owned by distribution network operators. A deterministic model predictive control (MPC) controller and a stochastic receding horizon controller (SRHC) are presented, wherethe objective is to achieve the greatest peak reduction in demand, for a given storagedevice specification, taking into account the high level of uncertainty in the prediction of LV demand. The algorithms presented in this paper are compared to a standard set-pointcontroller and bench marked against a control algorithm with a perfect forecast. A specificcase study, using storage on the LV network, is presented, and the results of each algorithmare compared. A comprehensive analysis is then carried out simulating a large number of LV networks of varying numbers of households. The results show that the performance of each algorithm is dependent on the number of aggregated households. However, on a typical aggregation, the novel SRHC algorithm presented in this paper is shown to outperform each of the comparable storage control techniques.

Impact of non-hydrostatic effects and trapped lee waves on mountain wave drag in directionally sheared flow

The orographic gravity wave drag produced in flow over an axisymmetric mountain when both vertical wind shear and non-hydrostatic effects are important was calculated using a semi-analytical two-layer linear model, including unidirectional or directional constant wind shear in a layer near the surface, above which the wind is constant. The drag behaviour is determined by partial wave reflection at the shear discontinuity, wave absorption at critical levels (both of which exist in hydrostatic flow), and total wave reflection at levels where the waves become evanescent (an intrinsically non-hydrostatic effect), which produces resonant trapped lee wave modes. As a result of constructive or destructive wave interference, the drag oscillates with the thickness of the constant-shear layer and the Richardson number within it (Ri), generally decreasing at low Ri and when the flow is strongly non-hydrostatic. Critical level absorption, which increases with the angle spanned by the wind velocity in the constant-shear layer, shields the surface from reflected waves, keeping the drag closer to its hydrostatic limit. While, for the parameter range considered here, the drag seldom exceeds this limit, a substantial drag fraction may be produced by trapped lee waves, particularly when the flow is strongly non-hydrostatic, the lower layer is thick and Ri is relatively high. In directionally sheared flows with Ri = O(1), the drag may be misaligned with the surface wind in a direction opposite to the shear, a behaviour which is totally due to non-trapped waves. The trapped lee wave drag, whose reaction force on the atmosphere is felt at low levels, may therefore have a distinctly different direction from the drag associated with vertically propagating waves, which acts on the atmosphere at higher levels.

The 'veil' of control: exploring the attitudes and perceptions of UK design controllers

In the UK, architectural design is regulated through a system of design control for the public interest, which aims to secure and promote ‘quality’ in the built environment. Design control is primarily implemented by locally employed planning professionals with political oversight, and independent design review panels, staffed predominantly by design professionals. Design control has a lengthy and complex history, with the concept of ‘design’ offering a range of challenges for a regulatory system of governance. A simultaneously creative and emotive discipline, architectural design is a difficult issue to regulate objectively or consistently, often leading to policy that is regarded highly discretionary and flexible. This makes regulatory outcomes difficult to predict, as approaches undertaken by the ‘agents of control’ can vary according to the individual. The role of the design controller is therefore central, tasked with the responsibility of interpreting design policy and guidance, appraising design quality and passing professional judgment. However, little is really known about what influences the way design controllers approach their task, providing a ‘veil’ over design control, shrouding the basis of their decisions. This research engaged directly with the attitudes and perceptions of design controllers in the UK, lifting this ‘veil’. Using in-depth interviews and Q-Methodology, the thesis explores this hidden element of control, revealing a number of key differences in how controllers approach and implement policy and guidance, conceptualise design quality, and rationalise their evaluations and judgments. The research develops a conceptual framework for agency in design control – this consists of six variables (Regulation; Discretion; Skills; Design Quality; Aesthetics; and Evaluation) and it is suggested that this could act as a ‘heuristic’ instrument for UK controllers, prompting more reflexivity in relation to evaluating their own position, approaches, and attitudes, leading to better practice and increased transparency of control decisions.