Fuel Consumption Optimization of Heavy-Duty Vehicles With Grade, Wind, and Traffic Information

Abstract

In this paper, we establish a mathematical framework that allows us to optimize the speed profile and select the optimal gears for heavy-duty vehicles (HDVs) traveling on highways while varying parameters. The key idea is to solve the analogous boundary value problem (BVP) analytically for a simple scenario (linear damped system with quadratic elevation profile) and use this result to initialize a numerical continuation algorithm. Then, the numerical algorithm is used to investigate how the optimal solution changes with parameters. In particular, we gradually introduce nonlinearities (air resistance and engine saturation), implement different elevation profiles, and incorporate external perturbations (headwind and traffic). This approach enables real-time optimization in dynamic traffic conditions, therefore may be implemented on-board.

Connected cruise control: modelling, delay effects, and nonlinear behaviour

“…These conditions can be checked by using the methods presented in the paper and the corresponding stability diagrams are shown in Figure A1 for the sampling time t = 0.1 [s]. When comparing these with Figures 7(b) and 8(b) made for the average delay σ = 3 t/2 = 0.15 [s] the similarity is remarkable, while the complexity of the formulae (A7), (A8), (A5) is much higher than that of (31).…”

“…We remark that the transfer function of the system with the first-order lag approximation (19) can be obtained by standard analysis of the corresponding ordinary differential equations; see Appendix 3. This corresponds to the approximation e sσ ≈ 1 + σ s in (31). Again, we emphasise that this only provides reliable stability results for small gains and low frequencies as will be shown below.…”

“…Here we investigate the dynamics in the vicinity of the equilibrium (20) at the linear level by using the system (22), (29), and the corresponding transfer function (31). We summarise the results using stability charts in the (K i ,K p )-plane and in the (K v ,K p )-plane for different values of the delay σ .…”

“…The same notation is used as in Figure 6 In Figure 10(c)-(e) the blue curve depicts the amplitude of the tail vehicle v amp T as a function of the excitation frequency ω for different values of the amplitude of the head vehicle v amp H . The nonlinear results are compared with the prediction of the linear model (green curve) that is based on the transfer function (31). For small ω the blue curves are missing since a large number of collocation points were needed to represent the periodic orbit and the continuation tools lead to computational difficulties.…”

“…20), while (iω) is obtained from the transfer function (31). Here | · | and ∠· denote the magnitude and angle of a complex number, respectively.…”