Abstract
The paper focuses on fuel and emission minimization of platoon based on multi-criteria control. The proposed control design method is able to consider the velocity regulations and inclinations of the road.
A velocity profile, which results in an optimal solution of the simultaneous minimization of emission, fuel consumption and traveling time for the platoon, can be calculated.
Introduction
Reduction of fuel consumption and emission of vehicles are one of the most significant purpose of automotive researches. A possible direction addresses the joint control of vehicle groups. The term platoon is used to describe several vehicles operated under automatic control as a unit when they are traveling at the same speed with relatively small inter-vehicle spacing. A well-organized platoon control may have advantages in terms of increasing highway capacity and decreasing fuel consumption and emissions. As a part of this research, in the paper a method is presented, in which saving energy, fuel consumption and emissions is developed for the platoon systems.
1. Considering road conditions in velocity control
In this section the relationship between the optimal velocity and the road inclinations is only briefly summarized. The results in a detailed form are found in (Nemeth, 2011). The route of the vehicle can be divided into n sections using n+1 number of points as Figure 1 shows.
The rates of the inclinations of the road and those of the speed limits are assumed to be known at the endpoints of each section, vref2 ,j j∈[1,n]. The velocity of the vehicle at the final point of a section ξ&j can be expressed by using the velocity at the starting point ξ&i, the acceleration and the driven distance sj. It is important to emphasize that the longitudinal force Flj affects only the first section and it is assumed that additional longitudinal forces will not act on the vehicle. The velocities of vehicle are described at each section point of the road, i.e, the velocity of the nth section point is ξ&n2 →vref2 ,n. In the next step a weight Q is applied to the momentary (initial) velocity and weights
γn
γ
γ1, 2,..., are applied to the reference velocities of the road sections in advance.
While the weights γi represent the rate of the road conditions, weight Q determines the tracking requirement of the momentary reference velocity vref,0.
In the final step a control-oriented vehicle model in which reference velocities and prediction weights are taken into consideration is constructed. Taking the weights into consideration the following reference velocity formulas are yielded:
)
Consequently, the predicted road conditions can be considered by velocity tracking:
λ
→
ξ&0 .
(3)
2. Multi-criteria optimization & control of the platoon
The aim of this section is to find an optimal velocityξ&0, which guarantees the minimization of emission, control force (fuel consumption) and traveling time. The fulfillment of these performances individually results in differentQ,γi.
Minimization of control force: By using ξ&0 →λ the longitudinal force (Fl1) can be expressed as the linear function of prediction weights:
n
Minimization of traveling time: Second optimization criteria of vehicle cruise
It means, that this optimization criteria can be fulfilled, if the road inclinations are ignored. The optimal solution of this performance is: Q≡1
(
and γ(i ≡0,i∈[1,n]. Minimization of emission: The emission model (Ntziachristos, 2000), (Csikós, 2011) of platoon is approximated by using second order polynomial function
2
Thus the performance weights, which guarantee a balance between the optimizations tasks, are calculated in the following expressions:
3
The velocity of the leader vehicle must track the required velocity. At the same time the other vehicles in the platoon must meet the string-stable requirement in order to guarantee the safe operation of the platoon. Consequently, two types of controllers must be designed: a velocity tracking controller for the leader vehicle and string stable controllers for each vehicle in the platoon. All the controllers must provide disturbance attenuation and robustness against uncertainties. The designs of controllers are based on robust H∞ methods, see (Zhou, 1996).
3. Numerical results and performance analysis
In this Section the proposed optimal multi-criteria method is illustrated. The platoon
different strategies are illustrated: minimization of Fli, emission (HC , CO, NOX), trip time. In these simulation cases the corresponding performance weight (R1,R2,R3) is tuned. Terrain characteristic of road section is illustrated in Figure 2. Figure 2(b) shows the velocities of the vehicles at the three cases. It shows that minimal emission values can be obtained by higher higher vehicle velocities. Figure 2(c) shows the emission. When the velocity reduces the longitudinal control force also is reduced as Figure 2(d) shows. However, emission increases significantly at the same time.
Consequently, there is a conflict between the minimization of control force and the minimization of emission. In case of the minimization of the traveling time the velocity of the leader vehicle is around vref,i, which results almost the same as a conventional cruise control system. The simulation results illustrates, that it is possible to achieve different performances by an appropriately selected strategy.
The second simulation example illustrates a weighting strategy which provides a balance between the three performance specifications. Figure 3 shows that the preceding vehicles track the leader vehicle of the platoon with an acceptable tracking error. Thus, the designed platoon control is able to perform the tracking of the platoon. The velocity of the vehicle is within the velocity interval, [64km/h...76km/h].
Emission and longitudinal control force are minimized with different values, which mean that the effects of road inclinations are exploited.
a, Terrain characteristics b, Velocity
The paper has proposed the design of a platoon velocity based on a multi-criteria optimization method. The optimization method is able to handle three performances, such as the minimization of control force, traveling time and the emission of the platoon. The operation of the method is illustrated through simulation examples, which show that the method guarantees a balance between energy saving, the minimization of traveling time and emission.
Acknowledgement
The work reported in the paper has been developed in the framework of the project
„Talent care and cultivation in the scientific workshops of BME" project. This project is supported by the grant TÁMOP - 4.2.2.B-10/1--2010-0009
References
Németh, B., Gáspár, P.: „LPV-based control design of vehicle platoon considering road inclinations.” 18th IFAC World Congress, 2011.
Ntziachristos, L., Samaras, Z., Eggleston S.: „Validation of road vehicle and traffic emission models, a review and metaanalysis: Copert IV computer programme to calculate emissions from road transport, methodology and emissions factors.” Technical Report No. 49.
European Environment Agency, 2000.
Csikós, A., Luspay, T., Varga, I.: „Modeling and optimal control of travel times and traffic emission on freeways.”
18th IFAC World Congress, 2011.
Zhou, K., Doyle, J.C., Glover, K.: „Robust and Optimal Control”. Prentice Hall, 1996.
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