ANÁLISIS PLANES DE ESTUDIO VS DEMANDA COMPETENCIAS SECTOR EMPRESARIAL

The concept of the proposed Extended Eco-CC system (Ext-Eco-CC) based on the

NMPC for theBEVon a hilly road with road curves and traffic speed limits are shown in Figure 5.22.

In this study, the final cost function of the NMPC, Jf is chosen as:

Jf(xN) =

1

2qf(eh− ehref)

2 _(5.1)

where ehref is reference energy consumption and qf is the corresponding weight. The

energy consumption, eh, is only evaluated at the end of the prediction horizon in order

Vehicle and Energy Dynamics Road and Traffic

Information Nonlinear Model Predictive Controller Traction Input Discharging Charging

Figure 5.22: Extended Ecological Cruise Control concept

flexible control actions independent of the cost-per-stage function, Jc, which can be

defined as: Jc(xi, ui) = 1 2qv(vh− vhref) 2₊1 2(ru(u − uref) 2_{− q} slkuslk)

+ exp(qcrv(alat−alat.max))_v2_{+ exp}(qlmt(v−flmt(s)))_{v, (5.2)}

where uref is the reference input, and qv, ru are relative weightings. A small slack

penalty, qslk, is added to avoid the singularity at sslk = 0 and keep the control input away

from the boundary of the feasible set. The lateral acceleration inequality constraint is alat= v2fcrv(δ(s)) and implemented as a soft constraint based on penalty method in the

cost function. An exponential function of the maximum allowable lateral acceleration, alat.max, with the related weight, qcrv is used. In addition, if the reference speed fixed

by the driver is above the speed limit value, the velocity is penalised exponentially with the weight qlmt.

The performance of the NMPCapplied on theSmart-EDis evaluated on the test track located at Centre de Formation pour Conducteurs S.A. Colmar-Berg, Luxembourg with its road geometry model (CFC,2015). The prediction horizon T = 15 s is chosen to cover upcoming road and traffic events. This prediction horizon is discretised into N = 30 steps of size ∆t = 0.5 s based on the approximate vehicle’s actuators maximum delay time. The total-cost function is set as eref = 0, qf = 0.25, vref = 25 m/s, qv = 1,

uref = Fres− M gsin(fslp(s)), ru = 20, qslk = 20, qcrv = 1.2, alat.max = 3.7 m/s2, and

qlmt = 0.1. The maximum speed of the Smart-ED is about vmax = 28 m/s without

activating the boost switch available in the vehicle. The weighting parameters are tuned manually by observing the performance in tracking the reference states considering the road and traffic information, safety and energy consumption.

For the sake of a fair comparison, the proposed ”Ext-Eco-CC” system with the same initial conditions is compared to the ”Ext-CC” system without energy consumption

(a) s (m) 0 200 400 600 800 1000 1200 1400 v (m /s ) 0 10 20 30 40

Ext-Eco-CC Ext-CC SpeedLimit

(b) s (m) 0 200 400 600 800 1000 1200 1400 u (N /k g ) -1 0 1 2 3 Ext-Eco-CC Ext-CC (c) s (m) 0 200 400 600 800 1000 1200 1400 ala t (m/s 2 ) 0 2 4 6

Ext-Eco-CC Ext-CC alat.max

(d) t(s) 0 20 40 60 80 100 120 p (k W ) -10 0 10 20 30 40

Ext-Eco-CC (total consumption e

tot = 0.1682 kWh)

Ext-CC (total consumption e

tot = 0.2328 kWh)

Figure 5.23: Performance of the NMPC with the Smart-ED on the test track in terms of (A) velocity, (B) control input, (C) lateral acceleration, and (D) related power

consumption with total energy consumption.

model (qf = 0). The conventional Eco-CC and CC systems are not considering road

curvature variations and speed limit zones and therefore, these conventional systems may not be comparable with the proposed system. Figure 5.23. shows the optimal driving profile generated by the controller of the Ext-Eco-CC and Ext-CC system. Figure 5.23a. shows the velocity profile at start point with initial standstill state. The controllers increase the velocity of the vehicle during straight downhill road segment

and later reduce the velocity optimally as the vehicle approaches the first and second curves. Next, the vehicle has to stay below the speed limit zone and afterwards does not speed up to reach the reference velocity due to the upcoming sharp third and fourth curves. Comparing to the Ext-CC system, the Ext-Eco-CC system drives the vehicle much slower in the last segment of the road due to the upcoming hilly road and thus saves a considerable amount of energy. Figure5.23b. shows the related control input de- rived from theNMPC. The Ext-Eco-CC controller tries to avoid unnecessary aggressive control inputs namely strong braking and accelerations. Figure5.23c. shows the lateral acceleration of the vehicle in each curve remains below the reference maximum lateral acceleration value. Note that since the driver controls the steering, the actual lateral ac- celeration of the vehicle in the real driving test might be different. Figure5.23d. shows the related power consumptions profile on the test track and the final overall energy consumption, etot, for the whole track. The Ext-Eco-CC takes any advantages of the

road profile and traffic information to save as much energy as possible.

The overall direction of the obtained simulation results showed that the proposed Ext- Eco-CC could be helpful to extend the limited cruising range of the BEV. This was achieved by reducing the driver interventions in velocity control and extending the au- tonomy of the vehicle with respect to road geometric and traffic information. It should be emphasized that with an increase of only 13% of travel time, the Ext-Eco-CC can save 27% of energy compared to the Ext-CC system at the test track. A balanced tradeoff between the energy consumption and travel time can be achieved based on the driver’s preference. It is found that the driver’s high reference velocity was not possible to be achieved with ecological driving style on the test track. However, the lower reference velocity could be tracked by the controller with mentioned assumptions. During sim- ulation, it is found that the control input can be updated approximately every 1 ms on an Intel R _CoreTM

i7 with memory of 7.7 GiB. Hence, this way of the formulation should be a real-time capable controller for the proposed system. For more details about the proposedNMPC for the extended Eco-CCsystem, follow S. Amin Sajadi-Alamdari et al. (2016).

5.3.1.1 Localisation Error

The concept of the proposed Extended Eco-CC system based on the RSNMPC for the

BEVis simulated on a hilly road with road curves without speed limit zone assumption. The localisation of the Smart-ED is based on the GPS signals with a certain degree of accuracy. For instance, the commercialGPS-enable embedded systems are typically accurate to within a 5 m radius approximately. Moreover, if a low-cost GPS receiver is used, the radius of the circle might be as much as 10 m to capture 95% of the points.

Position, (m) 0 200 400 600 800 1000 1200 V el o ci ty , v (m/s ) 0 5 10 15 20 vref Nominal +10 m Position Error −10 m Position Error

Figure 5.24: Performance of the closed-loop step response of the RSNMPC with localisation error on a test track.

Performance of the proposedRSNMPCon the test track is shown in Figure5.24includ- ing the ±10% localisation errors. The 10 m indicates the ten meters more in the actual nominal position and −10 m indicates the ten meters less in the actual nominal position value on the test track.

The Figure5.24shows the velocity profile at start point with initial standstill state. The controllers increase the velocity of the vehicle during straight downhill road segment and later reduce the velocity optimally as the vehicle approaches the first and second curves. Next, the vehicle has to speed up to reach the reference velocity. Afterwards, the velocity of theBEVhas to slow down due to the upcoming sharp third and fourth curves. Finally, theBEVspeeds up to hit the desired velocity. Comparing to the Nominal case, theRSNMPCshows robust state regulation with various constraint and location errors.