Fuel efficient driving patterns are well investigated for highway driving, but less so for applications with varying speed requirements, such as urban driving. In this article, the driving mission of a heavy-duty vehicle in urban driving is formulated as an optimal control problem. The velocity of the vehicle is restricted to be within upper and lower constraints referred to as the driving corridor. The driving corridor is constructed from a test cycle with large variations in the speed profile, together with statistics from vehicles in real operation. The optimal control problem is first solved offline using Pontryagin's maximum principle. A sensitivity analysis is performed in order to investigate how variations in the driving corridor influence the energy consumption of the optimal solution. The same problem is also solved using a model predictive controller with a receding horizon approach. Simulations are performed in order to investigate how the length of the control horizon influences the potential energy savings. Simulations on a test cycle with varying speed profile show that 7 % energy can be saved without increasing the trip time nor deviating from a normal driving pattern. A horizon length of 1000 m is sufficient to realize these savings by the model predictive controller. The vehicle model used in these simulations is extended to include regenerative braking in order to investigate its influence on the optimal control policy and the results.
A benchmark problem for fuel efficient control of a truck on a given road profile has been formulated and solved. Six different solution strategies utilizing varying degrees of off-line and on-line computations are described and compared. A vehicle model is used to benchmark the solutions on different driving missions. The vehicle model was presented at the IFAC AAC 2016 symposium and is compiled from model components validated in previous research projects. The driving scenario is provided as a road slope profile and a desired trip time. The problem to solve is a combination of engine-, driveline-and vehicle-control while fulfilling demands on emissions, driving time, legislative speed, and engine protections. The strength of this publication is the collection of all six different solutions in one paper. This paper is intended to provide a starting point for practicing engineers or researchers who work with optimal and/or model based vehicle control.
Controlling the longitudinal movement of heavyduty vehicles based on optimal control can be a cost-efficient way of reducing their fuel consumption. Such controllers today mainly exist for vehicles in haulage applications, in which the velocity is allowed to deviate from a constant set-speed. For distribution vehicles, which is the focus of this paper, the desired and required velocity has large variations, which makes the situation more complex. This paper describes the implementation of an optimal controller in a real heavy-duty distribution vehicle. The optimal control problem is solved offline as a Mixed Integer Quadratic Program, which yields reference trajectories that are tracked online in the vehicle. Some important steps in the procedure of the implementation are, except for designing the controller: developing a positioning system for the test track where the experiments are performed, estimating the parameters of the resistive forces, and setting the velocity constraints. Simulations show a potential of 10% reduction in fuel consumption without increasing the trip time. Experiments are then performed in a Scania truck, with the optimal solution as reference for the existing cruise control functions in the vehicle. It is concluded that in order to verify the fuel savings experimentally, the low-level controllers in the vehicle must be modified such that the tracking error is decreased.
Improving the powertrain control of heavy-duty vehicles can be an efficient way to reduce the fuel consumption and thereby reduce both the operating cost and the environmental impact. One way of doing so is by using information about the upcoming driving conditions, known as look-ahead information, in order to coast with a gear engaged or to use freewheeling. Controllers using such techniques today mainly exist for vehicles in highway driving. This paper therefore targets how such control can be applied to vehicles with more variations in their velocity, such as distribution vehicles. The driving mission of such a vehicle is here formulated as an optimal control problem. The control variables are the tractive force, the braking force, and a Boolean variable representing closed or open powertrain. The problem is solved by a Model Predictive Controller, which at each iteration solves a Mixed Integer Quadratic Program. The fuel consumption is compared for four different control policies: a benchmark following the reference of the driving cycle, look-ahead control without freewheeling, freewheeling with the engine idling, and freewheeling with the engine turned off. Simulations on a driving cycle typically used for testing distribution vehicles show the potential of saving 10 %, 16 %, and 20 % respectively for the control policies compared with the benchmark, in all cases without increasing the trip time.
The fuel consumption of heavy-duty vehicles in urban driving is strongly dependent on the acceleration and braking of the vehicles. In intersections with traffic lights, large amount of fuel can be saved by adapting the velocity to the phases of the lights. In this paper, a heavy-duty vehicle obtains information about the future signals of traffic lights within a specific horizon. In order to minimize the fuel consumption, the driving scenario is formulated as an optimal control problem. The optimal control is found by applying a model predictive controller, solving at each iteration a quadratic program. In such problem formulation, the constraints imposed by the traffic lights are formulated using a linear approximation of time. Since the fuel-optimal velocity can deviate strongly from how vehicles normally drive, constraints on the allowed velocity are imposed. Simulations are performed in order to investigate how the horizon length of the information from the traffic lights influences the fuel consumption. Compared to a benchmark vehicle without knowledge of future light signals, the proposed controller using a control horizon of 1000 m saves 26 % of energy with similar trip time. Increasing the control horizon further does not improve the results. Funding provided by Swedish Governmental Agency for Innovation Systems (VINNOVA) through the FFI program is gratefully acknowledged.
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