arXiv subjects

Stephen Duncan

Publications and source records attributed to Stephen Duncan.

6 recordsLinked to original sources

arXiv2026

Current and temperature imbalances in parallel-connected grid storage battery modules

A key challenge with large battery systems is heterogeneous currents and temperatures in modules with parallel-connected cells. Although extreme currents and temperatures are detrimental to the performance and lifetime of battery cells, there is not a consensus on the scale of typical imbalances within grid storage modules. Here, we quantify these imbalances through simulations and experiments on an industrially representative grid storage battery module consisting of prismatic lithium iron phosphate cells, elucidating the evolution of current and temperature imbalances and their dependence on individual cell and module parameter variations. Using a sensitivity analysis, we find that varying contact resistances and cell resistances contribute strongly to temperature differences between cells, from which we define safety thresholds on cell-to-cell variability. Finally, we investigate how these thresholds change for different applications, to outline a set of robustness metrics that show how cycling at lower C-rates and narrower SOC ranges can mitigate failures.

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arXiv2023

Control of Cross-Directional Systems using the Generalised Singular Value Decomposition

Diamond Light Source produces synchrotron radiation by accelerating electrons to relativistic speeds. In order to maximise the intensity of the radiation, vibrations of the electron beam are attenuated by a multi-input multi-output (MIMO) control system actuating hundreds of magnets at kilohertz rates. For future accelerator configurations, in which two separate arrays of magnets with different bandwidths are used in combination, standard accelerator control design methods based on the singular value decomposition (SVD) of the system gain matrix are not suitable. We therefore propose to use the generalised singular value decomposition (GSVD) to decouple a two-array cross-directional (CD) system into sets of two-input single-output (TISO) and single-input single-output (SISO) systems. We demonstrate that the two-array decomposition is linked to a single-array system, which is used to accommodate ill-conditioned systems and compensate for the non-orthogonality of the GSVD. The GSVD-based design is implemented and validated through real-world experiments at Diamond. Our approach provides a natural extension of single-array methods and has potential application in other CD systems, including paper making, steel rolling or battery manufacturing processes.

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arXiv2023

Control of Cross-Directional Systems with Approximate Symmetries

Structural symmetries of linear dynamical systems can be exploited for decoupling the dynamics and reducing the computational complexity of the controller implementation. However, in practical applications, inexact structural symmetries undermine the ability to decouple the system, resulting in the loss of any potential complexity reduction. To address this, we propose substituting an approximation with exact structural symmetries for the original system model, thereby introducing an approximation error. We focus on internal model controllers for cross-directional systems encountered in large-scale and high-speed control problems of synchrotrons or the process industry and characterise the stability, performance, and robustness properties of the resulting closed loop. While existing approaches replace the original system model with one that minimises the Frobenius norm of the approximation error, we show that this can lead to instability or poor performance. Instead, we propose approximations that are obtained from semidefinite programming problems. We show that our proposed approximations can yield stable systems even when the Frobenius norm approximation does not. The paper concludes with numerical examples and a case study of a synchrotron light source with inexact structural symmetries. Exploiting structural symmetries in large-scale and high-speed systems enables faster sampling times and the use of more advanced control techniques, even when the symmetries are approximate.

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arXiv2020

Fast Gradient Method for Model Predictive Control with Input Rate and Amplitude Constraints

This paper is concerned with the computing efficiency of model predictive control (MPC) problems for dynamical systems with both rate and amplitude constraints on the inputs. Instead of augmenting the decision variables of the underlying finite-horizon optimal control problem to accommodate the input rate constraints, we propose to solve this problem using the fast gradient method (FGM), where the projection step is solved using Dykstra's algorithm. We show that, relative to the Alternating Direction of Method Multipliers (ADMM), this approach greatly reduces the computation time while halving the memory usage. Our algorithm is implemented in C and its performance demonstrated using several examples.

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arXiv2019

ADMM for Block Circulant Model Predictive Control

This paper deals with model predictive control problems for large scale dynamical systems with cyclic symmetry. Based on the properties of block circulant matrices, we introduce a complex-valued coordinate transformation that block diagonalizes and truncates the original finite-horizon optimal control problem. Using this coordinate transformation, we develop a modified alternating direction method of multipliers (ADMM) algorithm for general constrained quadratic programs with block circulant blocks. We test our modified algorithm in two different simulated examples and show that our coordinate transformation significantly increases the computation speed.

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arXiv2018

Accelerated Gradient Methods with Memory

A set of accelerated first order algorithms with memory are proposed for minimising strongly convex functions. The algorithms are differentiated by their use of the iterate history for the gradient step. The increased convergence rate of the proposed algorithms comes at the cost of robustness, a problem that is resolved by a switching controller based upon adaptive restarting. Several numerical examples highlight the benefits of the proposed approach over the fast gradient method. For example, it is shown that these gradient based methods can minimise the Rosenbrock banana function to $7.58 \times 10^{-12}$ in 43 iterations from an initial condition of $(-1,1)$.

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