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Optimal cooling that minimises thermal gradients and the average temperature is essential for enhanced battery safety and health. This work presents a new modelling approach for battery cells of different shapes by integrating Chebyshev spectral-Galerkin method and model component decomposition. As a result, a library of reduced-order computationally efficient battery thermal models is obtained, characterised by different numbers of states. These models are validated against a high-fidelity finite element model and are compared with a thermal equivalent circuit (TEC) model under real-world vehicle driving and battery cooling scenarios. Illustrative results demonstrate that the proposed model with four states can faithfully capture the two-dimensional thermal dynamics, while the model with only one state significantly outperforms the widely-used two-state TEC model in both accuracy and computational efficiency, reducing computation time by 28.7\%. Furthermore, our developed models allow for independent control of tab and surface cooling channels, enabling effective thermal performance optimisation. Additionally, the proposed model's versatility and effectiveness are demonstrated through various applications, including the evaluation of different cooling scenarios, closed-loop temperature control, and cell design optimisation., Comment: 13 pages

Final written examination is the most important part of summative assessment in automatic control courses. Preparation of the examinations with a given number of points according to the concept of Constructive Alignment (which could be the main concept in future automatic control education) takes significant amount of time of the educator and motivates development of a toolkit for automatic compilation of examination problems. A decision support Matlab-LATEX toolkit based on random number generators for selection of examination problems is described in this report to facilitate the alignment. The toolkit allows application of Stepwise Constructive Alignment (a new method described in this report), where the alignment is achieved by a number of software runs associated with random trials. In each step the educator manually selects suitable problems before each run based on evaluation of the random choice from the previous run. Automatic generation of the examination together with solutions for the course 'Process control and measurement techniques' is presented as an example.

Lithium-ion battery packs demand effective active equalization systems to enhance their usable capacity and lifetime. Despite numerous topologies and control schemes proposed in the literature, conducting quantitative analyses, comprehensive comparisons, and systematic optimization of their performance remains challenging due to the absence of a unified mathematical model at the pack level. To address this gap, we introduce a novel, hypergraph-based approach to establish the first unified model for various active battery equalization systems. This model reveals the intrinsic relationship between battery cells and equalizers by representing them as the vertices and hyperedges of hypergraphs, respectively. With the developed model, we identify the necessary condition for all equalization systems to achieve balance through controllability analysis, offering valuable insights for selecting the number of equalizers. Moreover, we prove that the battery equalization time is inversely correlated with the second smallest eigenvalue of the hypergraph's Laplacian matrix of each equalization system. This significantly simplifies the selection and optimized design of equalization systems, obviating the need for extensive experiments or simulations to derive the equalization time. Illustrative results demonstrate the efficiency of the proposed model and validate our findings.

Growing demands for electrification result in increasingly larger battery packs. Due to factors such as cell position in the pack and variations in the manufacturing process, the packs exhibit variations in the performance of their constituent cells. Moreover, due to the fixed cell configuration, the weakest cell renders the pack highly susceptible to these variations. Reconfigurable battery pack systems, which have increased control flexibility due to additional power electronics, present a promising solution for these issues. Nevertheless, to what extent they can prolong the battery lifetime has not been investigated. This simulation study analyzes the potential of dynamic reconfiguration for extending battery lifetime w.r.t. several parameters. Results indicate that the lifetime extension is larger for series than for parallel configurations. For the latter, the dominant factor is equivalent full cycles spread at the end of life, but resistance increase with age and the number of cells in parallel are also influential. Finally, for the former, the number of series-connected elements amplifies these effects., Comment: Accepted to the 25th European Conference on Power Electronics and Applications (EPE 2023 ECCE Europe)

The concept of integrating physics-based and data-driven approaches has become popular for modeling sustainable energy systems. However, the existing literature mainly focuses on the data-driven surrogates generated to replace physics-based models. These models often trade accuracy for speed but lack the generalisability, adaptability, and interpretability inherent in physics-based models, which are often indispensable in the modeling of real-world dynamic systems for optimization and control purposes. In this work, we propose a novel architecture for generating model-integrated neural networks (MINN) to allow integration on the level of learning physics-based dynamics of the system. The obtained hybrid model solves an unsettled research problem in control-oriented modeling, i.e., how to obtain an optimally simplified model that is physically insightful, numerically accurate, and computationally tractable simultaneously. We apply the proposed neural network architecture to model the electrochemical dynamics of lithium-ion batteries and show that MINN is extremely data-efficient to train while being sufficiently generalizable to previously unseen input data, owing to its underlying physical invariants. The MINN battery model has an accuracy comparable to the first principle-based model in predicting both the system outputs and any locally distributed electrochemical behaviors but achieves two orders of magnitude reduction in the solution time.

Abrupt capacity fade can have a significant impact on performance and safety in battery applications. To address concerns arising from possible knee occurrence, this work aims for a better understanding of their cause by introducing a new definition of capacity knees and their onset. A curvature-based identification of a knee and its onset is proposed, which relies on the discovery of a distinctly fluctuating behavior in the transition between an initial and a final stable acceleration of the degradation. The method is validated on experimental degradation data of two different battery chemistries, synthetic degradation data, and is also benchmarked to the state-of-the-art knee identification method in the literature. The results demonstrate that our proposed method could successfully identify capacity knees when the state-of-the-art knee identification method failed. Furthermore, a significantly strong correlation is found between knee and end of life (EoL) and almost equally strong between knee onset and EoL. As the method does not require the full capacity fade curve, this opens up online knee-onset identification as well as knee and EoL prediction.

Battery cycle life prediction using early degradation data has many potential applications throughout the battery product life cycle. For that reason, various data-driven methods have been proposed for point prediction of battery cycle life with minimum knowledge of the battery degradation mechanisms. However, managing the rapidly increasing amounts of batteries at end-of-life with lower economic and technical risk requires prediction of cycle life with quantified uncertainty, which is still lacking. The interpretability (i.e., the reason for high prediction accuracy) of these advanced data-driven methods is also worthy of investigation. Here, a Quantile Regression Forest (QRF) model, having the advantage of not assuming any specific distribution of cycle life, is introduced to make cycle life range prediction with uncertainty quantified as the width of the prediction interval, in addition to point predictions with high accuracy. The hyperparameters of the QRF model are optimized with a proposed alpha-logistic-weighted criterion so that the coverage probabilities associated with the prediction intervals are calibrated. The interpretability of the final QRF model is explored with two global model-agnostic methods, namely permutation importance and partial dependence plot.

In this paper LQG control over unreliable communication links is derived. That is to say, the communication channels between the controller and the actuators and between the sensors and the controller are unreliable. Previous solutions to finite horizon discrete time hold-input LQG control for this case do not fully utilize the available information. Here a new solution is presented which resolves this limitation. The focus is to derive and present a full mathematical proof to derive the optimal control sequence., Comment: 47 Pages

This paper presents an adaptive equivalent consumption minimization strategy (ECMS) and a linear quadratic tracking (LQT) method for optimal power-split control of combustion engine and electric machine in a hybrid electric vehicle (HEV). The objective is to deliver demanded torque and minimize fuel consumption and usage of service brakes, subject to constraints on actuator limits and battery state of charge (SOC). We derive a function for calculating maximum deliverable torque that is as close as possible to demanded torque and propose modeling SOC constraints by tangent or logarithm functions that provide an interior point to both ECMS and LQT. We show that the resulting objective functions are convex and we provide analytic solutions for their second order approximation about a given reference. We also consider robustness of the controllers to measurement noise using a simple model of noise. Simulation results of the two controllers are compared and their effectiveness is discussed.

A key problem in process control is to decide which inputs should control which outputs. There are multiple ways to solve this problem, among them using gramian based measures, which include the Hankel interaction index array, the participation matrix and the $\Sigma_{2}$ method. The gramian based measures however have issues with input and output scaling. Generally, this is resolved by scaling all inputs and outputs to have equal range. However, we demonstrate how this can result in an incorrect pairing and examine alternative methods of scaling the gramian based measures, using either row or column sums, or by utilizing the Sinkhorn-Knopp algorithm. The benefits of these scaling strategies are first illustrated by applying them to the control structure selection for a heat exchanger network. Then, to more systematically analyze the benefits of the scaling schemes, a multiple input multiple output model generator is used to test the different schemes on a large number of systems. This, along with implementation of automatic controller tuning, allows for a statistical comparison of the scaling methods. This assessment shows considerable benefits to be gained from the alternative scaling of the gramian based measures, especially when using the Sinkhorn-Knopp algorithm. The use of this method also has the advantage that the results are completely independent of the original scaling of the inputs and outputs., Comment: 20 pages, 2 figures