Time-optimal Control Strategies for a Hybrid Electric Race Car

Ebbesen, Soren; Salazar, Mauro; Elbert, Philipp; Bussi, Carlo; Onder, Christopher H.

doi:10.1109/tcst.2017.2661824

Cited by 84 publications

(129 citation statements)

References 43 publications

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“…4) Convex optimization: There are several approaches to relax an OCP of electric vehicles to a convex optimization problem [14], [15]. The main advantage of these reformulations is the almost negligible calculation time needed to solve the defined problem.…”

Section: State Of the Artmentioning

confidence: 99%

“…On the other hand, these problem formulations suffer from subsequent extension, since any additional equality or inequality constraint must also be formulated to fit into the existing framework. Furthermore, [15] and [16] assume a fixed driving path as well as a point mass to reduce the complexity of the optimization problem. This in turn enables calculation of a time-optimal velocity profile exploiting the convexity of the problem formulation.…”

Section: State Of the Artmentioning

confidence: 99%

See 1 more Smart Citation

Energy Management Strategy for an Autonomous Electric Racecar using Optimal Control

Herrmann

Christ

Betz

et al. 2019

2019 IEEE Intelligent Transportation Systems Conference (ITSC)

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The automation of passenger vehicles is becoming more and more widespread, leading to full autonomy of cars within the next years. Furthermore, sustainable electric mobility is gaining in importance. As racecars have been a development platform for technology that has later also been transferred to passenger vehicles, a race format for autonomous electric racecars called Roborace has been created. As electric racecars only store a limited amount of energy, an Energy Management Strategy (EMS) is needed to work out the time as well as the minimum energy trajectories for the track. At the same time, the technical limitations and component behavior in the electric powertrain must be taken into account when calculating the race trajectories. In this paper, we present a concept for a special type of EMS. This is based on the Optimal Control Problem (OCP) of generating a time-minimal global trajectory which is solved by the transcription via direct orthogonal collocation to a Nonlinear Programming Problem (NLPP). We extend this minimum lap time problem by adding our ideas for a holistic EMS. This approach proves the fundamental feasibility of the stated ideas, e.g. varying racepaths and velocities due to energy limitations, covered by the EMS. Also, the presented concept forms the basis for future work on meta-models of the powertrain's components that can be fed into the OCP to increase the validity of the control output of the EMS.

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Section: State Of the Artmentioning

confidence: 99%

Section: State Of the Artmentioning

confidence: 99%

Energy Management Strategy for an Autonomous Electric Racecar using Optimal Control

Herrmann

Christ

Betz

et al. 2019

2019 IEEE Intelligent Transportation Systems Conference (ITSC)

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“…2. Detailed information is to be found in [33]. We represent the car as a point with mass m at the longitudinal position s and moving with speed v. Its kinetic energy E kin = m 2 · v 2 is subject to propulsive power P p and drag power P d as…”

Section: A Longitudinal Dynamics and Powertrain Modelmentioning

confidence: 99%

“…In our previous work, we assumed that the driving path cannot be influenced by the energy management, but is rather determined by the driver's steering input and is therefore fixed. We solved the optimal energy management problem numerically and analytically using convex optimization and PMP [33], [34]. Doing so, we provide an effective way to implement the globally optimal control strategies on the car in a feedforward fashion that can be easily tuned [35].…”

Section: Introductionmentioning

confidence: 99%

Equivalent Lap Time Minimization Strategies for a Hybrid Electric Race Car

Salazar

Balerna

Chisari

et al. 2018

2018 IEEE Conference on Decision and Control (CDC)

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The powertrain of the Formula 1 car is composed of an electrically turbocharged internal combustion engine and an electric motor used for boosting and regenerative braking. The energy management system that controls this hybrid electric power unit strongly influences the achievable lap time, as well as the fuel and battery consumption. Therefore, it is important to design robust feedback control algorithms that can run on the ECU in compliance with the sporting regulations, and are able to follow lap time optimal strategies while properly reacting to external disturbances. In this paper, we design feedback control algorithms inspired by equivalent consumption minimization strategies (ECMS) that adapt the optimal control policy implemented on the car in real-time. This way, we are able to track energy management strategies computed offline in a lap time optimal way using three PID controllers. We validate the presented control structure with numerical simulations and compare it to a previously designed model predictive control scheme.

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“…Several approaches such as convex programming [8], [15], [16] or deterministic Dynamic Programming (DP) [17], [18] have been investigated to solve the OCP. Pontryagin's Minimum Principle provides the necessary conditions for solution optimality enabling the initial optimization problem to be reduced to a boundary value problem.…”

Section:  mentioning

confidence: 99%

Hybrid Vehicle Energy Management: Singular Optimal Control

Delprat

Hofman

Paganelli

2017

IEEE Trans. Veh. Technol.

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Abstract-Hybrid vehicle energy management is often studied in simulation as an optimal control problem. Under strict convexity assumptions, a solution can be developed using Pontryagin's Minimum Principle. In practice, however, many engineers do not formally check these assumptions resulting in the possible occurrence of so-called unexplained "numerical issues". The present work intends to explain and solve these issues. Due to the binary controlled-state variable considered (e.g., switching on/off an internal combustion engine) and the use of a lookup table with linear interpolation (e.g., engine fuel consumption map), the corresponding Hamiltonian function can have multiple minima. Optimal control is not unique. Moreover, it is defined as being singular. Consequently, an infinite number of optimal state trajectories can be obtained. In this work, a control law is proposed to easily construct a few of them.

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Time-optimal Control Strategies for a Hybrid Electric Race Car

Cited by 84 publications

References 43 publications

Energy Management Strategy for an Autonomous Electric Racecar using Optimal Control

Energy Management Strategy for an Autonomous Electric Racecar using Optimal Control

Equivalent Lap Time Minimization Strategies for a Hybrid Electric Race Car

Hybrid Vehicle Energy Management: Singular Optimal Control

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