The geometry of optimal control problems on some six dimensional lie groups

This paper examines optimal solutions of control systems with drift defined on the orthonormal frame bundle of particular Riemannian manifolds of constant curvature. The manifolds considered here are the space forms Euclidean space E3 , the spheres S3 and the hyperboloids H3 with the corresponding frame bundles equal to the Euclidean group of motions SE(3), the rotation group SO(4) and the Lorentz group SO(1,3). The optimal controls of these systems are solved explicitly in terms of elliptic functions. In this paper, a geometric interpretation of the extremal solutions is given with particular emphasis to a singularity in the explicit solutions. Using a reduced form of the Casimir functions the geometry of these solutions are illustrated

Sub-agent elements for control methods in multi-agent energy management system

Increased penetration of generation and decentralised control are considered to be feasible and effective solution for reducing cost and emissions and hence efficiency associated with power generation and distribution. Distributed generation in combination with the multi-agent technology are perfect candidates for this solution. Pro-active and autonomous nature of multi-agent systems can provide an effective platform for decentralised control whilst improving reliability and flexibility of the grid

Closed form solution for p-curves in SO(4)

This paper describes the solution for p-curves in SO(4) and gives its closed form. The rotational symmetry was exploited in order to simplify the algebra. The relationship between the Casimir invariant functions and Lax operator is provided, along with its use as part of a Lax pair. The double cover by SU(2) SU(2) enables two simpler problems to be found and integrated using Philip Hall coordinates and the solutions are then projected onto SO (4). The methodology is generic and can be applied to other problems

Rigid body trajectories in different 6D spaces

The objective of this paper is to show that the group SE(3) with an imposed Lie-Poisson structure can be used to determine the trajectory in a spatial frame of a rigid body in Euclidean space. Identical results for the trajectory are obtained in spherical and hyperbolic space by scaling the linear displacements appropriately, since the influence of the moments of inertia on the trajectories tend to zero as the scaling factor increases. The semi-direct product of the linear and rotational motions gives the trajectory from a body frame perspective. It is shown that this cannot be used to determine the trajectory in the spatial frame. The body frame trajectory is thus independent of the velocity coupling. In addition, it is shown that the analysis can be greatly simplified by aligning the axes of the spatial frame with the axis of symmetry which is unchanging for a natural system with no forces and rotation about an axis of symmetry

Control of Energy Storage

Energy storage can provide numerous beneficial services and cost savings within the electricity grid, especially when facing future challenges like renewable and electric vehicle (EV) integration. Public bodies, private companies and individuals are deploying storage facilities for several purposes, including arbitrage, grid support, renewable generation, and demand-side management. Storage deployment can therefore yield benefits like reduced frequency fluctuation, better asset utilisation and more predictable power profiles. Such uses of energy storage can reduce the cost of energy, reduce the strain on the grid, reduce the environmental impact of energy use, and prepare the network for future challenges. This Special Issue of Energies explore the latest developments in the control of energy storage in support of the wider energy network, and focus on the control of storage rather than the storage technology itself

A study on the wireless power transfer efficiency of electrically small, perfectly conducting electric and magnetic dipoles

This paper presents a general theoretical analysis of the Wireless Power Transfer (WPT) efficiency that exists between electrically short, Perfect Electric Conductor (PEC) electric and magnetic dipoles, with particular relevance to near-field applications. The figure of merit for the dipoles is derived in closed-form, and used to study the WPT efficiency as the criteria of interest. The analysis reveals novel results regarding the WPT efficiency for both sets of dipoles, and describes how electrically short perfectly conducting dipoles can achieve efficient WPT over distances that are considerably greater than their size

Bond graph models of DC-DC converters operating in both CCM and DCM

In this paper, Bond Graphs are employed to develop a novel mathematical model of conventional switched-mode DC-DC converters valid for both continuous and discontinuous conduction modes. A unique causality bond graph model of hybrid models is suggested with the operation of the switch and the diode to be represented by a Modulated Transformer with a binary input and a resistor with fixed conductance causality. The operation of the diode is controlled using an if-then function within the model. The extracted hybrid model is implemented on a Boost and Buck converter with their operations to change from CCM to DCM and to return to CCM. The vector fields of the models show validity in a wide operation area and comparison with the simulation of the converters using PSPICE reveals high accuracy of the proposed model, with the Normalised Root Means Square Error and the Maximum Absolute Error remaining adequately low. The model is also experimentally tested on a Buck topology

Investigation of High-Efficiency Wireless Power Transfer Criteria of Resonantly-Coupled Loops and Dipoles through Analysis of the Figure of Merit

The efficiency of a Wireless Power Transfer (WPT) system is greatly dependent on both the geometry and operating frequency of the transmitting and receiving structures. By using Coupled Mode Theory (CMT), the figure of merit is calculated for resonantly-coupled loop and dipole systems. An in-depth analysis of the figure of merit is performed with respect to the key geometric parameters of the loops and dipoles, along with the resonant frequency, in order to identify the key relationships leading to high-efficiency WPT. For systems consisting of two identical single-turn loops, it is shown that the choice of both the loop radius and resonant frequency are essential in achieving high-efficiency WPT. For the dipole geometries studied, it is shown that the choice of length is largely irrelevant and that as a result of their capacitive nature, low-MHz frequency dipoles are able to produce significantly higher figures of merit than those of the loops considered. The results of the figure of merit analysis are used to propose and subsequently compare two mid-range loop and dipole WPT systems of equal size and operating frequency, where it is shown that the dipole system is able to achieve higher efficiencies than the loop system of the distance range examine

Modeling Power Flow in a Hoist Motor of a Rubber-Tired Gantry Crane

A method for calculating the power demand of the hoist motor in rubber-tired gantry (RTG) cranes with nonparallel cables has been developed to measure the energy consumption in a typical lift cycle. From measurements taken at the Port of Felixstowe, it has been observed that the peculiar geometrical characteristics of the hoisting mechanism cause the power demand to increase with the container height in constant rotor speed conditions. The change in the angle of the hoisting ropes causes an increase in torque load and power consumption. By using information extracted from the crane's geometry, it has been possible to calculate the potential energy increase given the weight and vertical position of the container. The load torque on the hoist motor and the vertical speed of the mass have also been calculated, allowing for the modeling of the hoist motor power consumption when lifting containers with constant rotational speed. The proposed model has been compared to a constant power demand approximation, showing a higher accuracy for masses below 40 t

Control of Energy Storage

In the attempt to tackle the issue of climate change, governments across the world have agreed to set global carbon reduction targets. [...