arXiv subjects

Jorn van Kampen

Publications and source records attributed to Jorn van Kampen.

14 recordsLinked to original sources

arXiv2026

Geometric Scaling of Battery Cells and Its Effect on Key Performance Indicators

This paper presents a computationally lightweight scaling model for cylindrical lithium-ion battery cells, intended for early-stage battery design-space exploration. The model maps selected geometric and electrode-level design variables, including cell height, cell diameter, cathode active loading, and cathode porosity, to cell-level performance indicators such as capacity, DC internal resistance, mass, volume, and winding length. The scaling model is validated against available cylindrical cell data by comparing predicted capacity, internal resistance, and winding length. The validated model is subsequently used in a single-cell design-space exploration and global sensitivity analysis to evaluate capacity, internal resistance, gravimetric energy density, and volumetric energy density. The results identify the dominant design variables, favourable parameter directions, and key trade-offs between cell geometry, electrode loading, resistance, and energy density. The proposed model provides a basis for future integration into higher-level battery system and vehicle optimization frameworks.

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arXiv2026

A Decomposition-Based Framework for Joint Optimization and Spatial Packaging of Interconnected Systems with Physical Interactions

This paper presents an approach and application of optimization of spatial packaging of interconnected systems with physical interactions (SPI2) in three-dimensional component placement problems. To enable its application for an automotive use case, SPI2 must support both initial design generation, including component alignment, and robust system-level coordination, requiring improved solution reliability and tractable computational cost. To address these requirements, the proposed methodology improves convergence rate and solution quality by enhancing numerical robustness in gradient-based optimization while reducing computational load. Existing SPI2 approaches are extended through the addition of alignment capabilities, enabling the representation of port-to-port alignments between components. Furthermore, the applicability of SPI2 is expanded by treating component placement locations as design variables, allowing for penalty-based coordination to ensure design feasibility and enabling integration within system-level optimization. The approach is validated using a multi-objective optimization framework based on Nondominated Sorting Genetic Algorithm II (NSGA-II), applied to a combined powertrain optimization and battery chassis integration problem. This demonstrates the effectiveness of the SPI2 in a system-level design context. The results show a twofold application of SPI2 in an automotive use case: first, as a tool for initial design generation, and second, as part of a system-level design coordinator that outperforms a discretized exhaustive search while requiring lower computational cost.

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arXiv2026

Competitor-aware Race Management for Electric Endurance Racing

Electric endurance racing is characterized by severe energy constraints and strong aerodynamic interactions. Determining race-winning policies therefore becomes a fundamentally multi-agent, game-theoretic problem. These policies must jointly govern low-level driver inputs as well as high-level strategic decisions, including energy management and charging. This paper proposes a bi-level framework for competitor-aware race management that combines game-theoretic optimal control with reinforcement learning. At the lower level, a multi-agent game-theoretic optimal control problem is solved to capture aerodynamic effects and asymmetric collision-avoidance constraints inspired by motorsport rules. Using this single-lap problem as the environment, reinforcement learning agents are trained to allocate battery energy and schedule pit stops over an entire race. The framework is demonstrated in a two-agent, 45-lap simulated race. The results show that effective exploitation of aerodynamic interactions is decisive for race outcome, with strategies that prioritize finishing position differing fundamentally from single-agent, minimum-time approaches.

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arXiv2026

A Sequential Convex Programming Approach to Free-trajectory Minimum-lap-time Optimization of Racing Cars

This paper presents a modeling and optimization framework to compute the minimum-lap-time spatial trajectory and powertrain operation of racing cars in a computationally efficient fashion. Specifically, we first derive a quasi-steady-state model of a racing car, whereby the racing line trajectory is jointly optimized. Next, we frame the minimum-lap-time problem and leverage its mostly convex structure by devising a sequential convex programming solution algorithm. We benchmark our method against off-the-shelf nonlinear programming solvers, showing how it can bring computation time down from a few minutes to a few seconds, paving the way for real-time implementations. Moreover, we compare our results to similarly efficient minimum-curvature racing line optimization methods, showing how a minimum-time-based racing line might lead to 4% faster lap-times. Finally, we showcase our framework for optimal powertrain energy management and we validate the common modeling assumption that the racing line is unaffected by energy limitations, showing that this assumption results in marginal lap-time losses of under 0.1%.

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arXiv2025

Two-dimensional Spatial Optimization for Electric Motorcycle Powertrain Elements using Mixed-integer Programming

This study presents a framework for optimizing the two-dimensional (2D) placement of electric motorcycle powertrain elements, accounting for the position, the orientation and geometric irregularities. Specifically, we construct a 2D placement model at the component level in which we include near-continuous rotation of components and allow for irregular subsystem geometries to make optimal use of the limited design space. Second, we introduce linearization techniques for the trigonometric constraints and formulate the placement problem as a mixed-integer quadratic program (MIQP). Finally, we demonstrate our framework on two electric motorcycle powertrain topologies and study the influence of the geometry complexity on the placement solutions. The results show that gradually increasing complexity leads to more manageable computation times and higher the complexity solution improves handling performance by 2.5% compared to the benchmark placement found in existing electric motorcycles.

math.OC↗

arXiv2024

Human-in-the-loop Energy and Thermal Management for Electric Racing Cars through Optimization-based Control

This paper presents an energy and thermal management system for electric race cars, where we tune a lift-off-throttle signal for the driver in real-time to respect energy budgets and thermal constraints. First, we compute the globally optimal state trajectories in a real-time capable solving time, optimizing a 47-kilometer horizon in 2.5 seconds. Next, for safe operation with a human driver, we simplify it to a maximum-power-or-coast operation in full-throttle regions (straights). Thereby, both the positions from which the vehicle should start coasting and the optimal throttle map are subject to tuning. To this end, we define the coasting sections with a threshold on the co-state trajectory of the kinetic energy from the optimal solution. We devise an online implementable bisection algorithm to tune this threshold and adapt it using PI feedback. Finally, we validate the proposed approach for an electric endurance race car and compare three variants with varying implementation challenges: one re-optimizing and updating the kinetic co-state trajectory online, one applying only the bisection algorithm online, and one relying exclusively on feedback control. Our results show that, under typical racing disturbances, our energy management can achieve stint times ranging from less than 0.056\% to 0.22\% slower compared to offline optimization with a priori knowledge of disturbances, paving the way for on-board implementations and testing.

math.OC↗

arXiv2024

A Human-optimized Model Predictive Control Scheme and Extremum Seeking Parameter Estimator for Slip Control of Electric Race Cars

This paper presents a longitudinal slip control system for a rear-wheel-driven electric endurance race car. The control system integrates Model Predictive Control (MPC) with Extremum Seeking Control (ESC) to optimize the traction and regenerative braking performance of the powertrain. The MPC contains an analytical solution which results in a negligible computation time, whilst providing an optimal solution to a multi-objective optimization problem. The ESC algorithm allows continuous estimation of the optimal slip reference without assuming any prior knowledge of the tire dynamics. Finally, the control parameters are determined using a human-driven preference-based optimization algorithm in order to obtain the desired response. Simulation results and comparisons with other methods demonstrate the system's capability to automatically determine and track the optimal slip values, showing stability and performance under varying conditions.

eess.SY↗

arXiv2024

System-level thermal and electrical modeling of battery systems for electric aircraft design

This work introduces a framework for simulating the electrical power consumption of an 8-seater electric aircraft equipped with high-energy-density NMC Lithium-ion cells. We propose an equivalent circuit model (ECM) to capture the thermal and electrical battery behavior. Furthermore, we assess the need for a battery thermal management system (BTMS) by determining heat generation at the cell level and optimize BTMS design to minimize energy consumption over a predefined flight regime. The proposed baseline battery design includes a 304-kWh battery system with BTMS, ensuring failure redundancy through two parallel switched battery banks. Simulation results explore the theoretical flight range without BTMS and reveal advantages in increasing battery capacity under specific conditions. Optimization efforts focus on BTMS design, highlighting the superior performance of water cooling over air cooling. However, the addition of a 9.9 kW water-cooled BTMS results in a 16.5% weight increase (387 kg) compared to no BTMS, reducing the simulated range of the aircraft from 480 km to 410 km. Lastly, we address a heating-induced thermal runaway scenario, demonstrating the robustness of the proposed battery design in preventing thermal runaway.

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arXiv2024

Multi-layer optimisation of hybrid energy storage systems for electric vehicles

This research presents a multi-layer optimization framework for hybrid energy storage systems (HESS) for passenger electric vehicles to increase the battery system's performance by combining multiple cell chemistries. Specifically, we devise a battery model capturing voltage dynamics, temperature and lifetime degradation solely using data from manufacturer datasheets, and jointly optimize the capacity distribution between the two batteries and the power split, for a given drive cycle and HESS topology. The results show that the lowest energy consumption is obtained with a hybrid solution consisting of a NCA-NMC combination, since this provides the best trade-off between efficiency and added weight.

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arXiv2024

Model Predictive Control Strategies for Electric Endurance Race Cars Accounting for Competitors Interactions

This paper presents model predictive control strategies for battery electric endurance race cars accounting for interactions with the competitors. In particular, we devise an optimization framework capturing the impact of the actions of the ego vehicle when interacting with competitors in a probabilistic fashion, jointly accounting for the optimal pit stop decision making, the charge times and the driving style in the course of the race. We showcase our method for a simulated 1h endurance race at the Zandvoort circuit, using real-life data of internal combustion engine race cars from a previous event. Our results show that optimizing both the race strategy as well as the decision making during the race is very important, resulting in a significant 21s advantage over an always overtake approach, whilst revealing the competitiveness of e-race cars w.r.t. conventional ones.

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arXiv2023

Optimal Endurance Race Strategies for a Fully Electric Race Car under Thermal Constraints

This paper presents a bi-level optimization framework to compute the maximum-distance race strategies for a fully electric endurance race car, whilst accounting for the low-level vehicle dynamics and the thermal limitations of the powertrain components. Thereby, the lower level computes the minimum-stint-time for a given charge time and stint length, whilst the upper level leverages that information to jointly optimize the stint length, charge time and number of pit stops, in order to maximize the driven distance in the course of a fixed-time endurance race. Specifically, we first extend a convex lap time optimization framework to capture low-level vehicle dynamics and thermal models, and use it to create a map linking the charge time and stint length to the achievable stint time. Second, we leverage the map to frame the maximum-race-distance problem as a mixed-integer second order conic program that can be efficiently solved in a few seconds to the global optimum with off-the-shelf optimization algorithms. Finally, we showcase our framework for a simulated 6h race around the Zandvoort circuit. Our results show that the optimal race strategy can involve partially charging the battery, and that, compared to the case where the stints are optimized for a fixed number of pit stops, jointly optimizing the stints and number of pit stops can significantly increase the driven distance and hence race performance by several laps.

math.OC↗

arXiv2023

A Two-dimensional Spatial Optimization Framework for Vehicle Powertrain Systems

This paper presents a modeling framework to optimize the two-dimensional placement of powertrain elements inside the vehicle, explicitly accounting for the rotation, relative placement and alignment. Specifically, we first capture the multi-level nature of the system mathematically, and construct a model that captures different powertrain component orientations. Second, we include the relative element placement as variables in the model and derive alignment constraints for both child components and parent subsystems to automatically connect mechanical ports. Finally, we showcase our framework on a four-wheel driven electric vehicle. Our results demonstrate that our framework is capable of efficiently generating system design solutions in a fully automated manner, only using basic component properties.

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arXiv2022

Maximum-distance Race Strategies for a Fully Electric Endurance Race Car

This paper presents a bi-level optimization framework to compute the maximum-distance stint and charging strategies for a fully electric endurance race car. Thereby, the lower level computes the minimum-stint-time Powertrain Operation (PO) for a given battery energy budget and stint length, whilst the upper level leverages that information to jointly optimize the stint length, charge time and number of pit stops, in order to maximize the driven distance in the course of a fixed-time endurance race. Specifically, we first extend a convex lap time optimization framework to capture multiple laps and force-based electric motor models, and use it to create a map linking the charge time and stint length to the achievable stint time. Second, we leverage the map to frame the maximum-race-distance problem as a mixed-integer second order conic program that can be efficiently solved to the global optimum with off-the-shelf optimization algorithms. Finally, we showcase our framework on a 6 h race around the Zandvoort circuit. Our results show that a flat-out strategy can be extremely detrimental, and that, compared to when the stints are optimized for a fixed number of pit stops, jointly optimizing the stints and number of pit stops can increase the driven distance of several laps.

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arXiv2022

Minimum-lap-time Control Strategies for All-wheel Drive Electric Race Cars via Convex Optimization

This paper presents a convex optimization framework to compute the minimum-lap-time control strategies of all-wheel drive (AWD) battery electric race cars, accounting for the grip limitations of the individual tyres. Specifically, we first derive the equations of motion (EOM) of the race car and simplify them to a convex form. Second, we leverage convex models of the electric motors (EMs) and battery, and frame the time-optimal final-drives design and EMs control problem in space domain. The resulting optimization problem is fully convex and can be efficiently solved with global optimality guarantees using second-order conic programming algorithms. Finally, we validate our modeling assumptions via the original non-convex EOM, and simulate our framework on the Formula Student Netherlands endurance race track. Thereby, we compare a torque vectoring with a fixed power split configuration, showing that via torque vectoring we can make a better use of the individual tyre grip, and significantly improve the achievable lap time by more than 4%. Finally, we present a design study investigating the respective impact of the front and rear EM size on lap time, revealing that the rear motor sizing is predominant due to the higher vertical rear tyre load caused by the center of pressure position and rearwards load transfer under acceleration.

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