Optimal Trajectories for Vehicles with Energy Recovery Options*

Keulen, T.A.C. van; Jager, Bram de; Steinbuch, M Maarten

doi:10.3182/20110828-6-it-1002.02062

Cited by 19 publications

(11 citation statements)

References 7 publications

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“…For electrified vehicles it is of interest to employ longer prediction horizon, while the computational burden is instead relaxed by simplifying the powertrain model. Batteries and electric machines are commonly approximated by constant efficiencies and engine losses are described by affine relations [10], [35].…”

Section: Convex Relaxation For Forward Simulationmentioning

confidence: 99%

Convex relaxations in the optimal control of electrified vehicles

Murgovski

Johannesson

et al. 2015

2015 American Control Conference (ACC)

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Abstract-When controlling the energy flow among multiple power sources in electrified powertrains, the typically nonconvex set of the original formulation is relaxed to a convex super-set, and the problem is then approached by the means of convex optimization. In this paper we show that when using the backward simulation approach, where vehicle velocity is equal to the reference velocity, the global optimum of the original nonconvex problem can be obtained by solving a relaxed convex problem. When vehicle velocity is kept as a state in the problem, in the so called forward simulation approach, we provide a condition for which, when satisfied, the solution of the relaxed problem will provide the solution of the non-relaxed problem.

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Section: Convex Relaxation For Forward Simulationmentioning

confidence: 99%

Convex relaxations in the optimal control of electrified vehicles

Murgovski

Johannesson

et al. 2015

2015 American Control Conference (ACC)

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“…with τ the thus far unknown switching time. On the first sub-arc, the state equations can be integrated, observing (6) and 7, to give…”

Section: Energy Optimal Control With Velocity Constraintsmentioning

confidence: 99%

“…The solution of these problems usually derives from Pontryagin's Maximum Principle (PMP) [4]. Alternatively, solutions for simplified problems can be derived analytically; see for example [5], [6]. Optimal driving can be split into segments that comprise such things as maximum power acceleration, constant speed, coasting, and limit braking.…”

Section: Introductionmentioning

confidence: 99%

Fuel Consumption Minimization, With Emissions Constraints, for Diesel Powered Cars

Pease

Limebeer

Fussey

2020

IEEE Trans. Contr. Syst. Technol.

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State of the art engine models are used to study the emissions production, and fuel consumption minimisation, of a typical diesel-powered road car operating on a variable-gradient road. The engine models, that have been fitted to measured test cell data, are used to represent both the performance and emissions generation characteristics of a typical diesel-fuelled car engine. Simple example are used to highlight the impact of elevation changes on the main structural features of fuel-optimal control problems (OCP). A typical semi-urban test route, with legislated speed limits and enforced stops, is used for performance evaluation purposes. The optimal functioning of a discretegear automatic transmission system, as opposed to a simple continuously variable transmission, is studied in detail. The main focus of this study is to evaluate the importance of threedimensional (3D) road influences (gradient and camber), preimposed time-of-arrival constraints, enforced stops, and emissions constraints, on the fuel consumption and optimal driving of typical diesel-powered road vehicles. This paper proposes the use of multiple-phase optimal control to elicit a better understanding of 'real' driving situations, and motivates a move away from standardised drive cycles.

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“…With the advent of hybrid electric heavy-duty trucks, this impediment is more restrictive, since the control algorithm has to coordinate both the kinetic and electric energy of the vehicle. To avoid the high computational requirement of a DP algorithm with both kinetic and electric energy as states as in Hellström, Åslund, and Nielsen (2010b), Van Keulen, Foster, de Jager, and Steinbuch (2010) and Van Keulen, de Jager, and Steinbuch (2011) propose the idea of adjoining the system dynamics to the objective, while simplifying the problem by disregarding engine on/off and clutch opening, and approximating the discrete-gear transmission to a continuously variable transmission. The drawback of this strategy is that (1) it is difficult to derive analytical expression when more system dynamics are being considered and (2) analytical solution can be obtained only when buffers are not operated at their energy limits.…”

Section: Introductionmentioning

confidence: 99%