Transient Torque Control of a Diesel Hybrid Powertrain for NOx Limitation

2012 Workshop on Engine and Powertrain Control, Simulation and Modeling The International Federation of Automatic Control Rueil-Malmaison, France, October 23-25, 2012

Transient Torque Control of a Diesel Hybrid Powertrain for NOx Limitation O. Grondin ∗ L. Thibault ∗ C. Qu´ erel ∗ ∗ IFP Energies Nouvelles Control, Signal and System Department 1 et 4, avenue de Bois-Pr´eau 92852 Rueil-Malmaison Cedex - France [email protected] - [email protected] [email protected]

Abstract This paper describes a strategy for the reduction of the transient nitrogen oxides (NOx ) emissions in a diesel hybrid electric vehicle (HEV). This strategy limits the dynamics of the engine by using the electric motor to maintain the wheel torque demand. Thus, the split ratio between the motor and the engine, initially computed from a steady-state optimal control strategy, is corrected during transient operations where NOx are produced. The engine torque correction relies on mean value models for the EGR system dynamics and for the NOx formation. The strategy is combined with a static EMS and implemented into a software in the loop platform including a detailed engine model with NOx prediction capabilities. This model based approach for the transient engine torque limitation allows a significant NOx reduction with a limited increase in the fuel consumption. Keywords: Hybrid vehicle, Automotive control, diesel engine, Torque control, NOx emissions. 1. INTRODUCTION The potential of hybrid powertrain to lower CO2 emissions is now recognized. However, the control of diesel hybrid vehicle introduces new issues. Compared to the gasoline engine, the NOx emissions cannot be treated by the catalytic converter since the engine is working in globally lean conditions. As a consequence, these emissions have to be reduced by specific NOx after-treatment systems. A possible alternative is to consider the electric hybridization to lower fuel consumption and NOx at the same time. Then, the NOx emissions must be included in the energy management strategy. In diesel engines, the operating regions of maximun efficiency and minimum NOx emissions are generally not the same. Minimizing a tradeoff between fuel consumption and NOx emissions avoids increasing NOx emission while pure fuel optimal strategy are applied as shown by Thibault et al. (2012). In this context, NOx limitation achievable by using the additional degree of freedom provided by HEV was investigated in the literature by Lin et al. (2003), Musardo et al. (2005) and Grondin et al. (2011). These solutions can be applied for Euro 6 engines but new constraints will arise from the transient nature of the upcoming Euro 7 driving cycle (WLTC). If we consider the current European driving cycle, the transient part of the total NOx emissions can clearly be neglected. If we consider the upcoming Euro 7 standard, especially with the introduction of a new driving cycle, the transient part of regulated emissions will increase. In this context, the current strategies applying optimal control based on static maps are not relevant. The goal of this paper is to highlight 978-3-902823-16-8/12/$20.00 © 2012 IFAC

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the transient NOx emissions problem in diesel engines and to give a solution for their reduction using the degree of freedom provided by the hybrid vehicle. The vehicle architecture is presented in the second part of the paper (section 2.1) with the static EMS based on the equivalent consumption minimization strategy (section 2.2). The transient NOx emissions issue is briefly analysed and an estimation of the transient part is given for engine driving cycles (section 2.3). The third part is dedicated to the strategy description. First, the key idea of the proposed method is explained through engine simulations (section 3.1). Then, the principle of the engine torque setpoint control and the NOx trajectory definition are detailled in section 3.2 and section 3.3, respectively. The strategy is validated and simulation results are discussed in section 4. The paper closes with conclusions and perspectives in section 5. The appendix A explains the mean value models for the EGR dynamics and the NOx formation. 2. SYSTEM DESCRIPTION AND CONTROL ISSUE 2.1 Powertrain In this paper, we consider the vehicle architecture depicted in figure 1. This is a parallel hybrid architecture that uses a starter generator (SSG) in the pre-transmission side (only allowed to start the engine) and the post-transmission electric machine (EM) allows for power assist, full electric drive, regenerative braking and battery recharge. More details about the hybrid parallel vehicle can be found in Chasse et al. (2009b). The diesel engine is a 1.6 liter, 10.3182/20121023-3-FR-4025.00060

2012 IFAC E-CoSM (E-CoSM'12) Rueil-Malmaison, France, October 23-25, 2012

reduction is possible at the price of a slight increase in fuel consumption. This was demonstrated through experimental tests. These results also confirm the simulations of optimal-control-based power split algorithm performed by Lin et al. (2003) (ECMS) and Musardo et al. (2005) (dynamic programming) few years before.

EM SSG GB ICE

wheel

clutch

Figure 1. Parallel hybrid engine. four-cylinder, direct-injection engine, equipped with low pressure (LP) and high pressure (HP) EGR loops. The LP EGR circuit takes the exhaust gases downstream the after treatment system - composed of a Diesel Oxidation Catalyst (DOC) and a Diesel Particulate Filter (DPF) to upstream the compressor. The HP EGR path is shorter than the LP path and it directly connects the exhaust manifold to the intake manifold. In this paper we consider only the LP EGR operations. In this configuration, the system has a slower burned gas settling time compared to the HP EGR mode. The engine transients are then more drastic according to the NOx emission peaks since they are mostly caused by EGR time lag. This is a fancy case study to develop and validate a transient NOx limitation strategy using the power assist from the electric machine. 2.2 Energy Management Strategy For hybrid electric vehicle, the total power delivered to the wheels comes from two energy sources : the fuel and a battery. The energy management strategy computes the best power split between these two sources. The proposed strategy is based on the ECMS (Equivalent Consumption Minimization Strategy) previously developed (Sciarretta et al. (2004); Sciarretta and Guzzella (2007)). For gasoline HEVs, the ECMS mainly accounts (in warm engine conditions) for the fuel saving (Chasse et al. (2009a)). In that case, the main optimization criterion is the overall fuel consumption. For diesel HEVs, the steady state NOx emissions have to be included because the fuel optimal operating points are usually at high NOx density. As a consequence, the NOx emissions of diesel hybrid engine may increase compared to a pure thermal engine. Then, the optimization criterion is defined to be the integral of the weighted sum of the fuel consumption and the NOx emission over the driving cycle. The principle of the ECMS was kept but the cost function merges the fuel map and the NOx map. Thus, the problem formulation was to determine the engine and motor torque demands that minimizes the cost function

J=

Z

tf



Qlhv (1 − kf c/nox ) m ˙ f + kf c/nox m ˙ N Ox t0



dt (1)

where t0 and tf are the initial and final times of the considered driving cycle. kf c/nox is the weighting factor between the fuel consumption and the NOx emissions. This adaptation of the ECMS for diesel HEV was presented in Grondin et al. (2011). The steady-state NOx emissions rate was implemented as a new degree of freedom into an ECMS and it was shown that a significant NOx

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However, NOx emissions produced during transient operations are not included into the quasi-static map used in cost function defined by equation (1). Depending on the engine architecture, engine mapping, and the severity of the driving condition, the transient NOx emissions can be non-negligible. This is explained in the next section. 2.3 Analysis of the transient NOx emisssions The pollutant emission behaviour of an engine is not purely quasi-static. Thus, the assumption that the emissions can be modeled using static maps can be inadequate. An example of transient NOx emissions for a portion of a NEDC is displayed in figure 2. This test was performed on a high dynamic test bench and the NOx emissions were recorded with a gas analyzer. Figure 2 exhibits several peaks in NOx during the first acceleration of the extraurban part of the driving cycle. At each gear change, the injection cut-off decreases the exhaust equivalence ratio. This limits the availability of burned gas at the engine intake. During the transient, the intake burned gas ratio (BGR) drops dramatically. When the driver reaccelerates, the intake BGR target cannot be reached instantaneously due to burned gas transport from the exhaust to the intake plenum. During this transient, the intake gas composition and thus the cylinder burned gas ratio are not in steady-state operating conditions leading to spikes in measured NOx . The transient part of the pollutant emission may vary according to the engine, its calibration and the driving cycle considered. In the experimental data presented in Figure 2, the instantaneous NOx levels can be twice the steady state values during transients. Table 1 recaps the transient NOx contribution on the engine performances during driving cycles. These results correspond to a NECD and a FTP driving cycles performed in conventional engine-driven operations. For the NEDC, the transient NOx contribution is lower than 9%. However, for the FTP cycle, the transient contribution rises up to 42%. driving cycle NEDC

FTP

bench

map

TP

bench

map

TP

NOx (mg/km)

110

100

9%

170

100

42%

FC (l/100km)

4.5

4.3

3%

4.7

4.4

6%

Table 1. Engine perfomances measured during NEDC and FTP driving cycles. The transient part (TP) contribution of the FC and NOx emissions are computed from the experimental measures and the engine static maps. For the next generation Euro 7 vehicles, a new driving cycle (WLTC) is going to be defined. This latter is more representative of real driving conditions (such as the FTP) and imposes more drastic transient solicitations compared

2012 IFAC E-CoSM (E-CoSM'12) Rueil-Malmaison, France, October 23-25, 2012

machine to limit the internal combustion engine dynamics. Some preliminary solutions of transient emission limitation by means of electric boost are proposed in the literature. The limitation of the transient NOx emissions by an adaptation of the transient torque demand is proposed by Predelli et al. (2007). A similar approach, called phlegmatising, was developed by Lindenkamp et al. (2009).

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setpoint measure min. max.

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3.1 Key idea and principle of the strategy 8

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Figure 3 shows the influence of the torque demand on the amplitude of a NOx peak. These results are obtained on a simulator with NOx prediction capabilities (see Lebas et al. (2009)). This simulator was calibrated to fit with steady-state and transient NOx emissions measured on the experimental engine. The simulation results plotted on figure 3 demonstrate that the NOx emissions are strongly linked with the torque demand and the amplitude of the peak increases with the torque gradient.

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= = = = =

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dT dT dT dT dT

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Figure 2. First acceleration of the extra-urban part of the NEDC. From top to bottom : vehicle speed, engine speed (dotted line) and fuel mass flow, BGR and NOx emissions. The steady state NOx value is calculated from a static map depending on engine speed and torque. The measured NOx value is delayed and filtered due to the gas analyzer dynamics. to the actual NEDC. Thus, a higher transient part of the total NOx emissions is expected. This paper addresses this issue and aims at developing a suitable control strategy for diesel HEV. 3. TRANSIENT STRATEGY NOx peaks occurring during engine transients account for an important part of the total NOx emissions. The reduction of the transient part of NOx can be achieved by further improvements of the air system architecture (shorter LP EGR system, combination of HP and LP EGR systems, internal EGR using Variable Valve Actuation (VVA)) or by including a combustion control strategy to adapt injection settings according to air system errors (as proposed by Hillion et al. (2011)). Here, we consider a diesel engine with a LP EGR system and whithout transient combustion control strategy. The goal is to take the advantage of the additional degree of freedom provided by the hybridization only. The idea is to use the electric

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NOx [ g/h ]

0

31 32 Time [ s ]

10

max. max. max. max. max.

5

0 27

28

29

30

31 32 Time [ s ]

35

Figure 3. Simulation of a transient operation representing an engine cut-off followed by a tip-in with a torque gradient limitation. From top to bottom : engine torque and NOx emissions. These results confirm the conclusion drawn by Predelli et al. (2007) and Lindenkamp et al. (2009) who proposed heuristic methods consisting in a limitation of the engine torque setpoint dynamics. In this paper, we apply a similar principle while introducing models of the system to compute the limited engine torque demand. The principle of this strategy is illustrated in figure 4. The transient consists in an increasing engine torque step from point A to point B. In this case, the EMS sp . This choice is the proposes a torque step noted Teng,ss solution of equation (1) computed from purely static maps without any consideration for the diesel engine constraints. The principle of the strategy is to keep the same torque setpoint B requested by the EMS but the trajectory

2012 IFAC E-CoSM (E-CoSM'12) Rueil-Malmaison, France, October 23-25, 2012

point is

sp sp Tmot,t (t) = Tmot,ss (t) + u(t)

(4)

Engine Torque setpoint [ Nm ]

The command u(t) is a portion of the motor torque that compensates for the engine torque during transients. The command u is deduced from equation (3) and (4) and it writes B

B

′

u(t) = sp

Teng,t

A Time [ s ]

cOx N ∆N Ox

sp

N Ox

N Oxss

sp

sp

Teng,t

Teng,ss sp Tpwt

Time [ s ]

Figure 4. Principle of the control strategy to limit the amplitude of the NOx peak during a torque step. followed to reach this value is adapted. The torque setpoint sp control consists in defining a new torque trajectory Teng,t ′ from point A to point B (in red on figure 4) such that the transient NOx peak is avoided or reduced. The sp torque request at wheel, Tpwt , depends on the driving conditions (speed and acceleration) and can be evaluated from driver’s demand (throttle and brake pedal positions). This demand can be satisfied using the engine, the electric motor or any combination of these two torque sources: sp sp sp Tpwt (t) = R1 Tmot,ss (t) + Rgb Teng,ss (t)

(2)

where Rgb is the gear ratio and R1 is the front axle ratio. The torque setpoint can be positive or negative depending on the vehicle operating conditions (traction or braking). sp sp Tmot,ss is the electric motor torque setpoint and Teng,ss is the engine torque setpoint. The steady-state split ratio is chosen by the EMS and the principle of the strategy is to modify its value during the engine transients only. In steady-state, the torque split ratio is maintained. In transient, the equation (2) is not modified but the steadystate engine and motor torques become two trajectories: sp sp sp Tpwt (t) = R1 Tmot,t (t) + Rgb Teng,t (t)

(5)

The command u(t) is directly linked to the static motor and powertrain torque setpoints and the dynamic torque sp setpoint Teng,t . This latter is a key variable and it is computed such that the NOx peak generated during a transient is limited. The computation of the corrected sp engine torque demand Teng,t (or trajectory) is explained in the next section. Following this approach, this strategy is applied in cascade with the EMS displayed in figure 5. The ECMS determines the optimal operating points at some (relatively large) time scale, while a faster controller determines the engine and motor trajectories that minimize the NOx emissions.

sp

Teng,ss

N Oxest

sp sp Tpwt (t) − Rgb Teng,t (t) sp − Tmot,ss (t) R1

(3)

In both cases, the torque request at wheel is not modified. The command u(t) is defined as the motor torque correction u(t) = ∆Tmot . Then, the dynamic motor torque request corresponding to the corrected motor torque set-

289

Energy Management Strategy

sp

Transient Torque Control

Tmot,ss

u(t) = ∆Tmot

sp

Tmot,t

Figure 5. Implementation of the torque control strategy according to the EMS. 3.2 Engine Torque setpoint correction This section explains how to compute the corrected engine torque trajectory. The transient correction of the torque setpoint requested by the EMS relies on a mean value model (MVM) of the engine NOx emissions. This model links the NOx emissions with the engine speed (Ne ), the intake BGR (F1 ) and the maximum cylinder temperab cyl ). These variables are recognized as first order ture (Θ variables of NOx formation in compression-ignition engines. The NOx model, detailed in appendix A, has the general form b cyl , F1 ) N Ox = φ(Ne , Θ

(6)

b ss , F ss ) N Oxss = φ(Ne , Θ cyl 1

(7)

The steady-state NOx level is

The BGR sepoint F1ss is computed from a static map (A.6). b ss is also mapped according to Temperature setpoint, Θ cyl engine speed and torque (figure 6) 

sp F1ss = ϑ(Ne , Teng,ss ) ss sp b Θcyl = ψ1 (Ne , Teng,ss )

(8)

During a transient, the BGR is not equal to its setpoint due to the EGR system lag (as displayed in figure 2). For the engine control, an online estimation of the BGR is

2012 IFAC E-CoSM (E-CoSM'12) Rueil-Malmaison, France, October 23-25, 2012

used (Grondin et al. (2009)). This estimation is valid for the actual BGR value, however, we need to determine the expected BGR value before the transient has occurred. Then, this estimation cannot be used for the high level torque control strategy. Here, the burned gas transport delay from exhaust manifold to intake manifold is modeled using the MVM detailed in appendix A. This model provides the estimated BGR (F1est ) assuming a first order dynamics and a pure delay applied to the BGR map as described in equation (A.3). The function φ appearing in equation (6) is invertible and a cylinder temperature setpoint can be computed from this BGR estimation and from the target N Oxsp (figure 4): b sp = φ−1 (Ne , N Oxsp , F1est ) Θ cyl

(9)

definition is purely heuristic and relies on a tunable reduction factor of the maximum NOx peak amplitude. The achievable NOx target N Oxsp (figure 4) is supposed to be included between the actual (or estimated) value and the steady-state value: N Oxest ≥ N Oxsp ≥ N Oxss

(12)

The target NOx is tuned empirically with a reduction factor ξ such that:   ξ N Oxsp = N Oxss + ∆N Ox 1 − 100

(13)

where ∆N Ox is the amplitude of the NOx peak referred as the steady NOx value as shown in figure 4 d ∆N Ox = N Ox − N Oxss

1800

This method is simple and allows to flexibly tune the level of NOx reduction. However, the ability for the system to achieve this target is not guaranteed because the system saturation is not considered. Moreover, the reduction factor ξ value is constant for each transient. Including the system saturation to define what can be the reachable NOx target is a necessary improvement to make the transient torque controller more generic and easy to tune. This will lead to define a limiting factor ξ according to a feasible NOx target instead of an empirical one. This is the main perspective of this work.

b cyl [ K ] Θ

1600 1400

1200 1000 800 100 50 Teng [ Nm ]

0

1000

1500

2000

(14)

2500

Ne [ rpm ]

Figure 6. Maximum cylinder temperature map. The NOx target computation is explained in the next subb sp , the cylinder temperature map ψ1 section. Knowing Θ cyl can be inverted in order to find the corrected value of the engine torque (or torque trajectory): t b sp ) Teng = ψ1−1 (Ne , Θ cyl

(10)

For sake of simplicity, we assume that the static maximum temperature map ψ1 , established for the nominal BGR setpoint, is representative of the actual BGR condition. A dependency of the temperature map according to the actual BGR would provides acceptable results. For that, the cylinder temperature map ψ1 can be modified as follows: b cyl = ψ −1 (Ne , Teng , F1 ) Θ (11) 2 Adding this dependency into a modified function ψ2 will increase the calibration part of the strategy. We are currently investigating a model-based approach to reduce the experimental tests needed for the calibration of the maximum temperature function ψ2 . This work is not the purpose of this paper and will be reported in a further paper with the justification for the BGR dependency simplification in map ψ1 .

3.4 Actuator limitation and system saturation The torque control strategy must account for the actuator limitation that depends on the maximum motor max and the static motor torque defined by torque Tmot sp Tmot,ss (t) =

sp sp Tpwt (t) − Rgb Teng,ss (t) R1

Then the command u(t) is bounded such that   sp max u(t) ∈ 0 (Tmot − Tmot,ss (t))

This section explains how to compute the NOx trajectory used for torque trajectory computation. The NOx target

290

(16)

From equations (5), (15) and (16), the minimum and maximun engine torque values write   

sp max Tpwt − R1 Tmot Rgb sp = Teng,ss

sp,min Teng = sp,max Teng

(17)

The transient engine torque setpoint is obtained by saturating the engine torque trajectory (10) sp t f sp,min sp,max Teng,t = sat min(Teng , Teng ), Teng , Teng

3.3 NOx target definition

(15)




(18)

The notation sat(u, um , uM ) is used for the function defined by

2012 IFAC E-CoSM (E-CoSM'12) Rueil-Malmaison, France, October 23-25, 2012

4.2 Results and discussion (19)

f Teng is the feasible torque trajectory that defines the achievable transient NOx emissions. This latter corresponds to the existing minimum value of the NOx emissions that can be realized during transient conditions where the cylinder oxygen content (i.e. BGR) is not in steady-state condition. The system saturation is not included in this paper and is an ongoing work at IFPEN. Thus, the transient engine torque setpoint writes: sp t sp,min sp,max Teng,t = sat Teng , Teng , Teng




(20)

4. SIMULATION & RESULTS 4.1 Simulation platform and method This section presents the simulation results of the transient torque control strategy. The objective is to determine whether limiting the transient part (TP) of the total NOx emissions is possible or not. We also would like to characterize the influence of the strategy on the steadystate part (SSP) of the total NOx emissions as well as the fuel consumption (FC). A simulation platform modeling the complete hybrid vehicle has been developed to simulate driving cycles. In this paper, we consider the FTP. The idea is to simulate the system for several values of the NOx reduction factor ξ ranging from 0% (baseline case) to 100%. This latter case corresponds to a limitation of all the NOx emissions TP. In order to compare these simulations, the equivalence factor is adapted (dotted line on figure 5). The value of the equivalence factor was found by dichotomy in order to satisfy the constraint on the final battery state of charge soc(t0 ) = soc(tf ) = 50%

(21)

t0 and tf are the initial and final times of the considered driving cycle. The simulations are made for three hybridization levels defined by the power of the electric motor Pmot = {8kW ; 14kW ; 20kW}

(22)

To be realistic, the battery capacity and vehicle mass are adapted to the electric motor power as described in Grondin et al. (2011). Pure electric driving is only enabled in the 20kW case. The EMS finds the steadystate optimal torque split repartition which minimizes a trade-off between quasi-static NOx and fuel consumption. The results displayed are obtained for a constant value of the parameter kf c/nox = 0.4 in equation (1). The impact of the hybridization level and this setting variable on NOx emissions and fuel consumption for a diesel HEV is not the purpose of this paper since it affects only the static balance between NOx and FC. A sensitivity analysis was done by Thibault et al. (2012).

291

The strategy acts on transient phases involving increasing BGR setpoint. Figure 8 illustrates its action on two torque transients belonging to the FTP (figure 7). ξ = 0% corresponds to the reference case, without transient strategy; the two others cases (50% and 90%) illustrate the impact of the adjustable transient NOx reduction parameter. For the second torque transient (t = 203 s), the NOx peak can be completely avoided and the tuning parameter allows a flexible reduction of the peak’s amplitude. This reduction is made by limiting the maximal cylinder temperature until enough burned gas is available. In the first torque transient (t = 199 s), a saturation on NOx reduction is observed between the 50% and 90% cases. This saturation can be easily explained looking at the motor torque setmax ) point which has already reached its maximal value (Tmot for ξ = 50%. As a consequence, NOx abatment is not achievable without increasing the electric motor maximum torque (ie. the motor size). We can notice that the strategy does not affect the steady-state engine and motor torque setpoints as claimed in the previous section. They are equal to the one chosen by the EMS once the transient is over sp sp sp sp (Tmot,ss = Tmot,t and Teng,ss = Teng,t ). 100 Vehicle speed [ km/h ]

 umin if u(t) ≤ um     if um ≤ u(t) ≤ uM sat(u, um , uM ) = u     umax if uM ≤ u(t)

80 60 40 20 0

0

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Figure 7. FTP vehicle speed profile. The impact of the transient strategy on the battery state of charge during a complete FTP is illustrated in figure 9. When the strategy is enabled, the state of charge decreases progressively because of the electric energy spent to cut NOx peaks during each transient phase. The missing energy must be recuperated in order to complete the driving cycle with a final state of charge constraint respected. This was done by adjusting the equivalence factor in the energy management strategy which slightly modifies the static operating point choice. The effect of the strategy on the cumulated NOx emissions and fuel consumption is illustrated in figure 10. Due to transient peak reduction, the total NOx emissions significantly drop at the price of a slight increase of fuel consumption. This demonstrates the interest of choosing a partial NOx reduction instead of a total elimination. Indeed in this case, the most interesting case is ξ = 50% since it allows a global NOx reduction of 17% with a fuel penalty of only 2%. The transient part of NOx emissions can be controlled with the damping factor ξ as illustrated in figure 11. The TP of NOx emissions are defined as the difference between total and steady-state emissions. The total emissions are computed from the model (6)

2012 IFAC E-CoSM (E-CoSM'12) Rueil-Malmaison, France, October 23-25, 2012

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Figure 9. Impact of the transient strategy on the Battery State of Charge - FTP Full Hybrid 20kW.

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(24)

They represent what the emissions would be if the exhaust gas recirculation loop had an instantaneous settling time. Even if the static part of the cumulated NOx emissions increases slightly with ξ due to the slight modification of static operating points, the total NOx emissions are decreasing. The strategy allows to divide the transient part by two (from 49% to 24%) while the cumulated NOx emissions are reduced by 26%. For ξ = 90%, the remaining transient part corresponds to the saturation of the electric motor which is not able to provide enough torque.

0.35

ξ ξ ξ ξ

4.05

sp sp N Oxss = φ(Ne , ψ1 (Ne , Teng,t ), ϑ(Ne , Teng,t ))

210

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0.15

4

Figure 10. Impact of the transient strategy parameter ξ on the trade-off between NOx emissions and fuel consumption - FTP Full Hybrid 20kW.

1100 ξ ξ ξ ξ

3.85 3.9 3.95 FC [ l/100km ]

210

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= 0% = 50% = 70% = 90%

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ξ ξ ξ ξ

80 60 40

60 40 TP SSP

20

20 0 198

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0 200

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Figure 8. Impact of the transient strategy parameter ξ FTP Full Hybrid 20kW. From top to bottom : Engine torque, Motor torque, Maximal cylinder temperature, Burned gas ratio and NOx emissions. sp N Oxest = φ(Ne , ψ1 (Ne , Teng,t ), F1est )

(23)

The steady-state NOx emissions are computed with the NOx model previously detailed using the measured engine speed and cylinder temperature :

292

0

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30

40 50 ξ[%]

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Figure 11. Impact of the transient strategy parameter ξ on the NOx transient part - FTP Full Hybrid 20kW. For lower hybridization levels (14kW and 8kW ), the electric torque available to allow transient NOx reduction is lower and the emissions can not be reduced as much as in the full hybrid case. In the 8kW , the electric motor saturation is quickly reached. As a consequence the transient NOx is limited (figure 12). As a conclusion, the transient strategy allows to control the NOx transient emissions as long as the maximal electric motor torque is not reached. With a 20kW electric

2012 IFAC E-CoSM (E-CoSM'12) Rueil-Malmaison, France, October 23-25, 2012

motor, a spectacular NOx reduction is achievable with a reasonable increase in fuel consumption. The value of the damping factor ξ tunes the trade-off between the NOx TP and the FC.

NOx [ mg/km ]

150

The author would like to thanks Gilles Corde and Philippe Moulin for helpful discussions. REFERENCES

100

50 TP SSP 0

ACKNOWLEDGEMENTS

0

20

40

60

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100

ξ[%]

Figure 12. Impact of the transient strategy parameter ξ on the NOx transient part - FTP Mild Hybrid 8kW.

5. CONCLUSION Model-based (ECMS) or heuristic energy management strategies may include a fuel cost mixed with emissions cost. This was mostly introduced using steady-state maps but these strategies generally do not consider the transient NOx emissions. Instead of combining steady state and transient objectives into the ECMS, this paper proposes an approch where the two objectives are separated. The proposed stategy is cascaded with the EMS in order to correct the electric and motor torque split ratio computed by the ECMS during the transient phases. The electric motor torque assistance focuses on transient NOx emissions and the split ratio is modified only during transient operations where NOx peaks are produced. The strategy tends to smooth the engine torque using the motor torque as torque compensator. Mean value models of the intake manifold burned gas ratio coupled with a NOx production model are introduced into the EMS. Using such models into a vehicle supervision level is the novelty of the approach. The simulation results have shown that the transient part of the NOx emissions can be reduced. It is clear that increasing the motor torque for short-term engine transient has a potential to reduce the NOx emissions. The strategy allows to limit the transient part of the emissions without modifying the steady state part. Also, the use of the electric motor during transients has a price and the transient NOx reduction slightly increases fuel consumption. This trade-off can be tuned with the reduction factor. The proposed strategy can be valuable to deal with driving cycles presenting more transient phases. This will be the case for Euro 7 vehicles with the new worldwide harmonized light-duty transient cycle. The further work will consist in the experimental validation of this transient torque control strategy. Some model assumptions will be verified and the temperature model depedency with the BGR is currently investigated. The main focus for the strategy improvement is to define a feasible NOx trajectory that leads to the engine torque trajectory including the system saturation.

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Bowman, C. (1975). Kinetics of pollutant formation and destruction in combustion. Progress in energy and combustion science, 1(1), 33–45. Chasse, A., Hafidi, G., Pognant-Gros, P., and Sciarretta, A. (2009a). Supervisory control of hybrid powertrains: an experimental benchmark of offline optimization and online energy management. In Proceedings of E-COSM’09 - IFAC Workshop on Engine and Powertrain Control, Simulation and Modeling. RueilMalmaison, France. Chasse, A., Pognant-Gros, P., and Sciarretta, A. (2009b). Online implementation of an optimal supervisory control for a parallel hybrid powertrain. In Proceedings of the SAE Conference, 2009-01-1868. Grondin, O., Moulin, P., and Chauvin, J. (2009). Control of a turbocharged Diesel engine fitted with high pressure and low pressure exhaust gas recirculation systeme. In Proceedings of the 48th IEEE Conference on Decision and Control & Chinese control conference. Shangha¨ı, China. Grondin, O., Thibault, L., Moulin, P., and Chasse, A. (2011). Energy management strategy for Diesel hybrid electric vehicle. In Proceedings of the 7th IEEE Vehicle Power and Propulsion Conference. Chicago, USA. Heywood, J.B. (1988). Internal Combustion Engine Fundamentals. McGraw-Hill, New york. Hillion, M., Chauvin, J., and Petit, N. (2011). Control of highly diluted combustion in Diesel engines. Control Engineering Practice, 19(11), 1274–1286. Lebas, R., Mauviot, G., Le Berr, F., and Albrecht, A. (2009). A phenomenological approach to model Diesel engine combustion and in-cylinder pollutant emissions adapted to control strategy. In Proceedings of ECOSM’09 - IFAC Workshop on Engine and Powertrain Control, Simulation and Modeling. Rueil-Malmaison, France. Lin, C.C., Peng, H., Grizzle, J.W., and Kang, J.M. (2003). Power management strategy for a parallel hybrid electric truck. IEEE Transactions on Control Systems Technology, 11(6), 839–849. Lindenkamp, N., St¨ober-Schmidt, C.P., and Eilts, P. (2009). Strategies for reducing NOx and particulate matter emissions in diesel hybrid electric vehicles. In Proceedings of the SAE Conference, 2009-01-1305. Musardo, C., Rizzoni, G., and Staccia, B. (2005). AECMS: An adaptive algorithm for hybrid electric vehicle energy management. In Proceedings of the 44th IEEE Conference on Decision and Control. Predelli, O., Bunar, F., Manns, J., Buchwald, R., and Sommer, A. (2007). Laying out Diesel-engine control systems in passenger-car hybrid drives. Procedding of the IAV conference on Hybrid Vehicle and Energy Management, 131–151. Qu´erel, C., Grondin, O., and Letellier, C. (2012). State of the art and analysis of control oriented NOx models. In Proceedings of the SAE Conference, 2012-01-0723.

2012 IFAC E-CoSM (E-CoSM'12) Rueil-Malmaison, France, October 23-25, 2012

Schmitt, J.C., Fremovici, M., Grondin, O., and Berr, F.L. (2009). Compression ignition engine model supporting powertrain development. In Proceeding of the E-COSM Symposium, 75–82. Rueil-Malmaison, France. Sciarretta, A., Back, M., and Guzzella, L. (2004). Optimal control of parallel hybrid electric vehicles. IEEE Transactions on Control Systems Technology, 12(3). Sciarretta, A. and Guzzella, L. (2007). Control of hybrid electric vehicles - optimal energy management strategies. IEEE Control Systems Magazine, 60–70. Thibault, L., Grondin, O., Qu´erel, C., and Corde, G. (2012). Energy management strategy and optimal hybridization level for a Diesel HEV. In Proceedings of the SAE Conference, 2012-01-1019.

NOx emissions with a good accuracy over the whole engine operating range as well as for variations of BGR, as shown in Qu´erel et al. (2012). An example of the NOx model sensitivity according to a BGR variation is displayed in figure A.1. MVM model validations in transient are reported in figure A.2 and A.3. Table A.1. NOx model parameters. α1 0.37

α2 3250

α3 -0.56

α4 12.4

α5 0.63

α6 3.06

α7 1.15

1000

experimental data model

900

N Ox = α1



Ne α2

 α3 

α6  b cyl − α5 α4 Θ

600 500 400

200 100

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

F1 [ - ]

Figure A.1. Comparison between the NOx model and experimental data for a BGR variation. 300

measure model

250

NOx [ ppm ]

where θ represents the crank angle, Ne is the engine speed, Θb the temperature in the burned gases and [X]e refers to the equilibrium concentration of the species X. NOx formation is thus promoted by high O2 concentrations and elevated temperatures in the post-combustion gases. Moreover, Heywood (1988) experimentally shows that the critical time period is when burned gas temperatures are at a maximum. The complexity level of the model employed in the present study to predict NOx emissions has to be compatible with its integration in the transient torque control strategy, preventing the use of a crank angle resolved thermodynamical model. As the torque trajectory is determined a priori, the use of measured values as input variables of the model is also banned. A semi-physical mean value model proposed by Schmitt et al. (2009), and inspired by NOx kinetics, has been chosen to estimate NOx emissions. A detailed analysis of this model is proposed by Qu´erel et al. (2012). NOx concentration in the output of the cylinders is expressed as a function of the engine speed Ne , the intake manifold burned gas ratio F1 and the b cyl , according maximum value of in-cylinder temperature Θ to the following expression:

700

300

200 150 100 50 0

580

590

600

610

620

630

640

650

660

670

680

690

Time [ s ]

Figure A.2. Comparison between NOx model and experimental data for a portion of NEDC driving cycle. 4

8

cumulated NOx [ g/h ]

Nitrogen oxides produced by diesel engines mainly consist of nitric oxides (NO) and, to a lesser extent, of nitrogen dioxides (NO2 ). In standard diesel combustion conditions, NO is essentially produced by the extended Zeldovich mechanism. According to Bowman (1975), under the equilibrium asumption, the initial NOx formation rate (in mol.cm−3 .s−1 ) may be written:   1 d[NO] 1 6 · 1016 69090 = [O2 ]e2 [N2 ]e(A.1) exp − 1 dθ 6Ne Θ 2 Θb b

NOx [ ppm ]

800

Appendix A. NOX EMISSION MODEL

x 10

measure model

7 6 5 4 3 2 1 0

0

200

400

600

800

1000

1200

1400

Time [ s ])

(1−α7 F1 )

(A.2)

The coefficients αi are calibration parameters learnt on experimental data. The values obtained for the diesel engine considered in this paper are given in table A.1. In this model, the temperature in the burned gases has been replaced by the maximum value of the mean temperature in the cylinder for sake of simplicity, as the temperature in the burned gases is not measurable for control applications. In spite of this simplification, the model predicts

294

Figure A.3. Comparison between the cumulated NOx model and experimental data for a FTP driving cycle. During transients, the intake manifold gas composition are not in steady-state operating conditions. The maximum in-cylinder temperature reaches its steady-state values much faster, and as a result, is considered to be quasistatic. A simplified model is used to represent the dynamics of the intake manifold burned gas ratio (equation (A.3)). It consists of a delayed first order filter of the BGR static value:

2012 IFAC E-CoSM (E-CoSM'12) Rueil-Malmaison, France, October 23-25, 2012

τ (t) F˙ 1est (t) + F1est (t) = F1ss (t − td (t))

where the time constant τ and the time delay td are parametrized as a function of the engine speed. τ (t) = and td (t) =

kf Ne (t)

(A.4)

 

kd sp , if Teng (t) > 0 Ne (t)  0, else

(A.5)

The BGR map F1 has the general form: F1 = ϑ(Ne , Teng )

(A.6)

The burned gas ratio dynamic model is compared with experimental results in figure A.4. The model is in good agreement with the observed test data and can be used as a reference EGR system model into the torque control strategy. 0.4 0.35

BGR [ - ]

0.3 0.25 0.2 0.15 0.1

F1ss F1m (experiment) F1est (model)

0.05 0 115

120

125

130

135

140

145

150

Time [ s ]

Figure A.4. Comparison between measured and estimated intake manifold burned gas fraction (top) and NOx emission (bottom) during a gear change. Table A.2 compares the estimated cumulated emissions and the NOx transient contribution on these emissions during driving cycles with the corresponding experimental results given in table 1. The model correctly predicts both the cumulated NOx emissions and the transient part. It is employed to validate the NOx limitation strategy in simulation. driving cycle

bench model

NEDC

FTP

total SSP TP (mg/km) (mg/km) (%)

total SSP TP (mg/km) (mg/km) (%)

110 109

100 94

9 14

170 179

Appendix B. NOMENCLATURE

(A.3)

100 125

42 30

Table A.2. Comparison between measured and estimated NOx emissions during NEDC and FTP driving cycle. The experimental steadystate part (SSP) of the emissions are computed from the static map. The estimated steadystate emissions are calculated from the model using the intake BGR setpoint F1sp .

295

Parameters & Variables αi . . . . . . . . . . . . . . . NOx model parameters F1 . . . . . . . . . . . . . . Intake burned gas ratio kd . . . . . . . . . . . . . . . EGR model time delay kf . . . . . . . . . . . . EGR model time constant kf c/nox . . . . . . Emissions weighting factor Ne . . . . . . . . . . . . . . . . . . . . . . . . Engine speed R1 . . . . . . . . . . . . . . . . . . . . . . Front axle ratio Rgb . . . . . . . . . . . . . . . . . . . . . Gear Box Ratio soc . . . . . . . . . . . . . . Battery state of charge Θb . . . . .Temperature in the burned gases b cyl . . . . Maximum cylinder temperature Θ t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Time T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Torque u . . . . . . . . . . . . . Command (motor torque) ξ . . . . . . . . . . . . . . . . . . NOx reduction factor

s.rpm s.rpm rpm % K K s Nm Nm %

Subscripts & superscripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . engine est . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . estimated f . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . feasible mot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . motor pwt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . powertrain ss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . steady-state sp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . setpoint t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .trajectory eng

Acronyms BGR . . . . . . . . . . . . . . . . . . . . . . . . . . Burned Gas Ratio DPF . . . . . . . . . . . . . . . . . . . . Diesel Particulate Filter ECMS . . . . Equivalent Consumption Minimization Strategy EGR . . . . . . . . . . . . . . . . . . Exhaut Gas Recirculation EM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electric Machine EMS . . . . . . . . . . . . . . .Energy Management Strategy FC . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fuel Consumption FTP . . . . . . . . . . . . . . . . Federal Transient Procedure GB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gear Box HEV . . . . . . . . . . . . . . . . . . . . . Hybrid Electric Vehicle HP . . . . . . . . . . . . . . . . . . . . . . . . .High Pressure (EGR) LP . . . . . . . . . . . . . . . . . . . . . . . . . Low Pressure (EGR) MVM . . . . . . . . . . . . . . . . . . . . . . . . .Mean Value Model NEDC . . . . . . . . . . . . . . . New European Drive Cycle NOx . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nitrogen oxides SSG . . . . . . . . . . . . . . . . .Separated Starter-Generator SSP . . . . . . . . . . . . . . . . . . . . . . . . . . . Steady-State Part TP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Transient Part VVA . . . . . . . . . . . . . . . . . . . Variable Valve Actuation WLTC . . . . . . . . Worldwide harmonized Light-duty Transient Cycle