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2405-8963 © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.Peer review under responsibility of International Federation of Automatic Control.10.1016/j.ifacol.2015.10.023

Sandro P. Nüesch et al. / IFAC-PapersOnLine 48-15 (2015) 159–166

© 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

On Beneficial Mode Switch Decisions basedon Short-term Engine Load Prediction �

Sandro P. Nuesch ∗ Jeff Sterniak ∗∗ Li Jiang ∗∗

Anna G. Stefanopoulou ∗

∗ Dept. of Mechanical Engineering, University of Michigan,Ann Arbor, MI 48109 USA (e-mail: [email protected]).∗∗ Robert Bosch LLC, Farmington Hills, MI 48331 USA.

Abstract: Multimode combustion in automotive engines have the potential to increase fuelefficiency by choosing the best combustion mode at each operating condition. When switchesamong the combustion modes are neither instantaneous nor lossless, a mode switch can only bebeneficial if the associated residence time in the target mode is long enough to compensate for thefuel penalty of the switch. An accurate engine load prediction over a short-term horizon is thusnecessary for deciding on a beneficial mode switch. This paper addresses this. In the applicationof spark ignited (SI) and homogeneous charge compression ignition (HCCI) combustion modes,prior work quantified fuel efficiency benefits and mode switch penalties. In this paper, it isestimated that, to result in a fuel economy benefit, the residence time in HCCI mode is requiredto be longer than 1.2 s. If it is possible to accurately predict engine load over such a time horizon,an optimal mode switch decision could be made. To this end, five receding horizon predictionmethods, based on artificial neural networks and polynomial extrapolation, are tested withvehicle measurement data and compared in terms of their accuracy in predicting engine load aswell as HCCI entry and exit events. It is shown that although the prediction accuracy is verylow for visitations of the HCCI regime around 1.2 s, all the methods are able to determine ifan immediate entry of exit will occur, and if a HCCI visitation is going to be very short. Thisfinding is applied in a basic mode switch decision structure.

Keywords: Advanced combustion, Engine control, Supervisory control, Combustion modeswitches, Prediction methods, Artificial neural networks

1. INTRODUCTION

Advanced combustion modes such as homogeneous chargecompression ignition (HCCI) have significant benefits infuel efficiency and engine-out NOx emissions, as shown byZhao et al. (2003). However, they have a limited operatingrange and are not able to fulfill all the drivers demands,see Thring (1989). For that reason they are combined withspark ignition (SI) combustion in a multimode combustionengine, which switches the mode based on operating con-dition, as suggested by Kulzer et al. (2007). SI and HCCIcombustion are radically different, and the mode switchfrom one to the other is a difficult control task, shown byGorzelic et al. (2014) and Zhang and Zhu (2014). Thosemode switches require a certain duration and, as shownin Matsuda et al. (2008), incur a fuel penalty. Based onNuesch et al. (2014) it can be seen that during a conven-tional drive cycle some residence times in the HCCI modeare very short and due to the switching penalty in factharmful for overall fuel economy. A supervisory control

� This material is based upon work supported by the Departmentof Energy [National Energy Technology Laboratory] under AwardNumber(s) DE-EE0003533. This work is performed as a part of theACCESS project consortium (Robert Bosch LLC, AVL Inc., EmitecInc., Stanford University, University of Michigan) under the directionof PI Hakan Yilmaz and Co-PI Oliver Miersch-Wiemers, RobertBosch LLC.

strategy is required to decide when a mode switch shouldbe performed. Such a strategy could be based on theprediction of future operating conditions, thereby makingan optimum decision in terms of fuel economy.

In Sun et al. (2014) several methods to predict vehiclespeed are compared in the context of hybrid electric ve-hicles (HEV). By applying model predictive control thepredictions are used to determine the optimal power splitwhile obeying constraints on battery state-of-charge. Eventhough the problem of optimal HEV power managementshows similarities to the one of optimal combustion modeswitching, there are significant differences. First, the im-pact of non-optimal decisions are different. In the HEVproblem a prediction error might lead to a temporarilywrong power split. However, the supervisory controller will

High-Low Lift Cam Switchp3=1.15, dc,3=1

Low-High Lift Cam Switchp4=1.4, dc,4=1

HCCI

SIPre 1

p1=1.02, ds,1=0.25sPost 2

p6=1.03, dc,6=0.25s

SI→

HC

CIH

CC

I→SI

Pre 2p2=1, dc,2=1

Post 1p5=1.08, dc,5=2

Fig. 1. Reduced representation of the combustion modeswitch model from Nuesch et al. (2015). Shown arethe values for fuel penalties pi, and durations ds,i anddc,i in seconds and engine cycles, respectively.

4th IFAC Workshop onEngine and Powertrain Control, Simulation and ModelingAugust 23-26, 2015. Columbus, OH, USA

Copyright © 2015 IFAC 159







1. INTRODUCTION







HCCI

SIPre 1

p1=1.02, ds,1=0.25sPost 2

p6=1.03, dc,6=0.25s

SI→

HC

CIH

CC

I→SI

Pre 2p2=1, dc,2=1

Post 1p5=1.08, dc,5=2










1. INTRODUCTION







HCCI

SIPre 1

p1=1.02, ds,1=0.25sPost 2

p6=1.03, dc,6=0.25s

SI→

HC

CIH

CC

I→SI

Pre 2p2=1, dc,2=1

Post 1p5=1.08, dc,5=2










1. INTRODUCTION







HCCI

SIPre 1

p1=1.02, ds,1=0.25sPost 2

p6=1.03, dc,6=0.25s

SI→

HC

CIH

CC

I→SI

Pre 2p2=1, dc,2=1

Post 1p5=1.08, dc,5=2




160 Sandro P. Nüesch et al. / IFAC-PapersOnLine 48-15 (2015) 159–166

generally get the opportunity to compensate for the mis-take later, thereby limiting the impact of a wrong decision.In case of the multimode combustion problem this is notpossible. If a mode switch decision is wrong, the associatedopportunity for fuel economy benefits has passed. Second,in the power split case a trend-wise correct predictionis enough to achieve satisfactory controller performance.However, in the case of mode switches, precise predictionof the direction and magnitude of the operating conditionsis necessary to achieve the optimal switching decision. InNuesch et al. (2015) it is shown that the majority of modeswitches are due to the dynamics in engine load ratherthan engine speed. For that reason in this paper it isfocused on methods of predicting engine load, and perfectknowledge of future engine speed is assumed. Even ifelevation changes are taken into account, it can be assumedthat the fast dynamics in engine load are mainly causedby the driver. It can be expected that a model might notbe able to perfectly mimic a human driver and comparedto the more erratic human behavior, a model might bemore predictable. Therefore, the assessment in this paperis done from actual measurements from a drive cycle witha human driver rather than a driver model.

In Sect. 2 the engine and vehicle data is described, andin Sect. 3 the required minimum duration of a stay inHCCI mode is estimated. Sect. 4 introduces the differentprediction methods, which are assessed in Sect. 5, followedby a brief discussion in Sect. 6.

2. DATA

2.1 Engine Data

In this paper a 2.0 L I4 multimode combustion engine witha stock turbocharger is used. Compared to the productionversion (GM Ecotec LNF) the engine includes increasedcompression ratio, two-step cam profile switching, electriccam phasing for recompression, and stronger reciprocat-ing components. This enables naturally aspirated (NA)HCCI, as well as traditional SI mode. Note that advancedcombustion strategies, such as multi injection and multiignition (MIMI) or boosted HCCI can expand the HCCIoperating regime beyond the NA basic HCCI region usedin this paper. A combustion mode switch model, based ona finite state machine, was introduced in Nuesch et al.(2014) and parameterized with experiments in Nueschet al. (2015). A simplified version of this model, reduced tothe six significant transition states i, is depicted in Fig. 1.The associated parameters are fuel penalties pi as well asdurations ds,i in seconds and dc,i in engine cycles. Enginespeed n in RPM relates the two durations with

ds,i = dc,i ·2 · 60n

. (1)

2.2 Drive Cycle Data

Chassis dynamometer measurements for FTP75, HWFET,and US06 drive cycles were used, acquired with a stockCadillac CTS 2009. The measured velocity data is denotedv, the measured engine torque and speed data are T andn, respectively. The selected gear is g. Note that the drivecycle data does not originate from the multimode enginebut from the larger 3.6 L V6 stock engine. However, it

0

50

100

v(km/h)

FTP75 HWFET US06

0

100

200

300

T(N

m)

0 500 1000 1500 2000 2500 3000SI

HCCI

Time (s)

Fig. 2. Vehicle measurements for FTP75, HWFET, andUS06 drive cycles. Top: Velocity v. Center: Enginetorque T . Bottom: Combustion Regime.

0 1.2 5 10 150

5

10

15

20

25All drive cycles

Duration of visitation ∆tHCCI (s)

Fractionofvisitations(%

)

0 5 10 150

20

40

∆tHCCI (s)Fract.ofvisit.(%

)

All

Only FTP75

0 5 10 15

∆tHCCI (s)

All

Only HWFET

0 5 10 15

∆tHCCI (s)

All

Only US06

Fig. 3. Distribution of visitation durations in the HCCIregime. Large: Combined. Insets: Individual drivecycles.

is assumed that, given vehicle and drive cycle, the loadrequirement from the driver to the downsized engine issimilar to the one seen by the stock one. In any casethe applied prediction methods need to be accurate undervarying driver and engine behavior.

Velocity and engine load for all three drive cycles areshown in Fig. 2. In addition every stay in the HCCIoperating regime is highlighted. It should be noted thatthe cold-start period at the beginning of the FTP75 hasbeen neglected in this study, since it is irrelevant to theproblem of load prediction.

The distribution of durations of visitations in the HCCIoperating regime is shown in Fig. 3. As can be seen, thedistributions strongly depend on the applied drive cycle.The aggressive US06 drive cycle exhibits a significantlylarger fraction of short visitations than both the FTP75and the HWFET cycle.

3. REQUIRED MINIMUM DURATION IN HCCI

Each switch to HCCI and back exhibits a fuel penalty.Therefore the residence time in the HCCI mode ∆tHCCI

needs to be long enough to result in a net benefit infuel economy. This duration is denoted required minimumduration of a visitation ∆tHCCI,min.

By using the durations ds,i, the total mode switch durationds,tot(n) as a function of engine speed is calculated, whichincludes both, the SI-HCCI and the HCCI-SI direction:

IFAC E-COSM 2015August 23-26, 2015. Columbus, OH, USA

160

Sandro P. Nüesch et al. / IFAC-PapersOnLine 48-15 (2015) 159–166 161

generally get the opportunity to compensate for the mis-take later, thereby limiting the impact of a wrong decision.In case of the multimode combustion problem this is notpossible. If a mode switch decision is wrong, the associatedopportunity for fuel economy benefits has passed. Second,in the power split case a trend-wise correct predictionis enough to achieve satisfactory controller performance.However, in the case of mode switches, precise predictionof the direction and magnitude of the operating conditionsis necessary to achieve the optimal switching decision. InNuesch et al. (2015) it is shown that the majority of modeswitches are due to the dynamics in engine load ratherthan engine speed. For that reason in this paper it isfocused on methods of predicting engine load, and perfectknowledge of future engine speed is assumed. Even ifelevation changes are taken into account, it can be assumedthat the fast dynamics in engine load are mainly causedby the driver. It can be expected that a model might notbe able to perfectly mimic a human driver and comparedto the more erratic human behavior, a model might bemore predictable. Therefore, the assessment in this paperis done from actual measurements from a drive cycle witha human driver rather than a driver model.

In Sect. 2 the engine and vehicle data is described, andin Sect. 3 the required minimum duration of a stay inHCCI mode is estimated. Sect. 4 introduces the differentprediction methods, which are assessed in Sect. 5, followedby a brief discussion in Sect. 6.

2. DATA

2.1 Engine Data

In this paper a 2.0 L I4 multimode combustion engine witha stock turbocharger is used. Compared to the productionversion (GM Ecotec LNF) the engine includes increasedcompression ratio, two-step cam profile switching, electriccam phasing for recompression, and stronger reciprocat-ing components. This enables naturally aspirated (NA)HCCI, as well as traditional SI mode. Note that advancedcombustion strategies, such as multi injection and multiignition (MIMI) or boosted HCCI can expand the HCCIoperating regime beyond the NA basic HCCI region usedin this paper. A combustion mode switch model, based ona finite state machine, was introduced in Nuesch et al.(2014) and parameterized with experiments in Nueschet al. (2015). A simplified version of this model, reduced tothe six significant transition states i, is depicted in Fig. 1.The associated parameters are fuel penalties pi as well asdurations ds,i in seconds and dc,i in engine cycles. Enginespeed n in RPM relates the two durations with

ds,i = dc,i ·2 · 60n

. (1)

2.2 Drive Cycle Data

Chassis dynamometer measurements for FTP75, HWFET,and US06 drive cycles were used, acquired with a stockCadillac CTS 2009. The measured velocity data is denotedv, the measured engine torque and speed data are T andn, respectively. The selected gear is g. Note that the drivecycle data does not originate from the multimode enginebut from the larger 3.6 L V6 stock engine. However, it

0

50

100

v(km/h)

FTP75 HWFET US06

0

100

200

300

T(N

m)

0 500 1000 1500 2000 2500 3000SI

HCCI

Time (s)

Fig. 2. Vehicle measurements for FTP75, HWFET, andUS06 drive cycles. Top: Velocity v. Center: Enginetorque T . Bottom: Combustion Regime.

0 1.2 5 10 150

5

10

15

20

25All drive cycles

Duration of visitation ∆tHCCI (s)

Fractionofvisitations(%

)

0 5 10 150

20

40

∆tHCCI (s)

Fract.ofvisit.(%

)

All

Only FTP75

0 5 10 15

∆tHCCI (s)

All

Only HWFET

0 5 10 15

∆tHCCI (s)

All

Only US06

Fig. 3. Distribution of visitation durations in the HCCIregime. Large: Combined. Insets: Individual drivecycles.

is assumed that, given vehicle and drive cycle, the loadrequirement from the driver to the downsized engine issimilar to the one seen by the stock one. In any casethe applied prediction methods need to be accurate undervarying driver and engine behavior.

Velocity and engine load for all three drive cycles areshown in Fig. 2. In addition every stay in the HCCIoperating regime is highlighted. It should be noted thatthe cold-start period at the beginning of the FTP75 hasbeen neglected in this study, since it is irrelevant to theproblem of load prediction.

The distribution of durations of visitations in the HCCIoperating regime is shown in Fig. 3. As can be seen, thedistributions strongly depend on the applied drive cycle.The aggressive US06 drive cycle exhibits a significantlylarger fraction of short visitations than both the FTP75and the HWFET cycle.

3. REQUIRED MINIMUM DURATION IN HCCI

Each switch to HCCI and back exhibits a fuel penalty.Therefore the residence time in the HCCI mode ∆tHCCI

needs to be long enough to result in a net benefit infuel economy. This duration is denoted required minimumduration of a visitation ∆tHCCI,min.

By using the durations ds,i, the total mode switch durationds,tot(n) as a function of engine speed is calculated, whichincludes both, the SI-HCCI and the HCCI-SI direction:


160

T(N

m)

ds,tot (s)

10

20

30

40

50

0.7

0.8

0.9

T(N

m)

Eff. Improv. (%)

10

20

30

40

50

10

20

30

Engine speed n (RPM)

T(N

m)

∆tHCCI,min(s)

1500 2000 2500 3000 3500

10

20

30

40

50

0.8

1

1.2

Fig. 4. HCCI operating regime. Top: Total mode switchduration ds,tot based on the combustion mode switchmodel. Center: Fuel efficiency improvement of HCCIcompared to SI combustion based on measurements.Bottom: Minimum time spent in HCCI to lead to fueleconomy benefit ∆tHCCI,min.

ds,tot(n) =

6∑i=1

ds,i. (2)

It must be noted that, since as of now only experimentalmode switch data at one operating condition is available,the parameters are constant in terms of n and T , whichleads to the linearly changing ds,tot in Fig. 4-top. Basedon the fuel efficiency map the fuel flows mf,SI(n, T ),mf,HCCI(n, T ) are calculated. The relative improvementof the fuel efficiency in HCCI compared to SI is shownin Fig. 4-center. The minimum duration in HCCI modeto lead to a net fuel economy benefit ∆tHCCI,min(n, T )follows as:

mf,Pen(n, T ) =

(6∑

i=1

pi ·∆ti

)· mf,SI (3)

∆tHCCI,min(n, T ) =mf,Pen

mf,HCCI(4)

In Fig. 4-bottom the map of ∆tHCCI,min(n, T ) is shown.As can be seen at higher engine speeds a visitation ofthe HCCI regime needs to be be at least around 0.8 s tobe beneficial. With decreasing speed this value increasesup to 1.2 s. If a stay in HCCI is predicted to be longerthan 1.2 s it is ensured that the stay will be beneficial.Vice versa if the stay in HCCI is predicted to be shorterthan 0.8 s. Note that these numbers do not include otherfuel penalties, e.g. due to the depletion of the catalyst’soxygen storage. Such additional penalties could increase∆tHCCI,min significantly.

As can be seen in Fig. 3, a large fraction of stays is eitherlonger than 1.2 s or much shorter. Here prediction canresolve the trade-off between switching to HCCI as early aspossible and avoiding very short residences in HCCI mode.For the cases 0.8 s < ∆tHCCI < 1.2 s the fuel consumptionneeds to be predicted to make an optimal decision. It hasto be noted that this analysis assumes constant load andspeed during the entire visitation of HCCI, which does notoccur in reality. Nevertheless it gives a good estimate forthe prediction horizon needed to make an optimal modeswitch decision.

4. ENGINE LOAD HORIZON PREDICTORS

Five receding horizon methods for torque prediction arecompared. Two of them apply Artificial Neural Networks(ANN) and are labeled with A. Neural networks havebeen used successfully to forecast timeseries of nonlinearbehavior. The prediction of an ANN depends on its tuning.However, a set of ANNs based different tuning parametersall resulted in comparable performance with the selectedones being the best. The other three methods use linearleast squares to compute linear and quadratic polynomialfits P1 and P2, respectively. In further distinction, themethods labeled with V are based on the velocity his-tory to predict future velocities and, by using a vehiclemodel, to compute the future engine torque trajectory.Conversely, the methods denoted T are based on using theengine torque history directly to predict future torque. Allthe methods are described in detail below.

Based on the result for ∆tHCCI,min a prediction horizonlength H is chosen for all the methods such that

τ1 ·H = 2 s (5)

with sampling time τ1 = 0.01 s. Velocity and engine torqueat time step k are denoted

vk = v(kτ) ; Tk = T (kτ). (6)

At each time step k the receding horizon of engine torqueTk is calculated

Tk =(T kk+1, T

kk+2, ..., T

kk+H

)T

(7)

with predicted torque T kk+j at j time steps after current

time k.

4.1 ANN Torque Predictor (A/T )

The ANN to predict future torque is denoted fA/T , using

historical torque data T as input to compute torquepredictions T . At each time step k the receding horizon

of engine torque TA/Tk is calculated:

TA/Tk = fA/T (Tk−h, ..., Tk−2, Tk−1, Tk) (8)

The history for the torque predictor was chosen h·τ1 = 1 s.The ANN fA/T was trained based on the measured torquedata shown in Fig. 2. The network consist of 15 hiddenlayers. 70% of the dataset, sampled with 0.1 s, was usedfor training, based on the Levenberg-Marquardt method.

4.2 Linear Torque Predictor (P1/T )

The linear least squares methods is used to create a linearfit of engine torque with matrices A1 and W and based onthe history h · τ1 = 0.5 s with weighting factor a = 10:

Thistk =

(Tk−h, ..., Tk−2, Tk−1, Tk

)T(9)

A1 = (−h · τ1,−(h− 1)τ1, . . . ,−τ1, 0 )T

(10)

W =

e−a·h·τ1 0 0 0

0 e−a·(h−1)·τ1 0 0

0 0. . . 0

0 0 0 1

. (11)


161


The polynomial is constrained to the initial engine torque

Tk. The slope of the torque trajectory xP1/Tk at each time

step follows by solving:

(AT1 WA1)x

P1/Tk = AT

1 W(Thistk − Tk). (12)

Finally the receding torque horizon follows as

TP1/Tk = Tk + x

P1/Tk · (0, τ1, . . . , H · τ1)T . (13)

4.3 Quadratic Torque Predictor (P2/T )

The quadratic torque predictor is based on the sameprinciple as the linear one and uses a history h · τ1 = 0.5 swith weighting factor a = 10. However, in addition to the

slope xP2/T,1k the curvature x

P2/T,2k is computed:

A2 =

(−h · τ1,−(h− 1)τ1, . . . ,−τ1, 0

(h · τ1)2, ((h− 1) · τ1)2 , . . . , τ21 , 0

)T

(14)

AT2 WA2

(xP2/T,1k

xP2/T,2k

)= AT

2 W(Thistk − Tk) (15)

TP2/Tk = Tk + x

P2/T,1k · (0, τ1, . . . , H · τ1)T . . . (16)

+ xP2/T,2k ·

(0, τ21 , . . . , (H · τ1)2

)T. (17)

4.4 ANN Velocity Predictor (A/V )

The following predictor is based on the ANN fA/V , trainedwith the measured velocity data shown in Fig. 2. Trainingconditions of the ANN are the same as above for fA/T .The velocity history is chosen to be h · τ1 = 3 s. At eachtime step k, based on current velocity vk and h historical

values, the receding velocity horizon vA/Vk is calculated:

vA/Vk = fA/V (vk−h, ..., vk−2, vk−1, vk) (18)

=(vkk+1, v

kk+2, ..., v

kk+H

)T. (19)

The quasi-static vehicle model fv is used to computeengine torque as a function of velocity and gear:

Tk = fv(vk, gk). (20)

The model fv relies on differentiation of the velocity usingfinite differences to compute acceleration and thereforepropulsion torque. It is compared to measurements inFig. 5. As can be seen the general behavior of T isreproduced well. However, the model filters some of thefast torque dynamics, one reason being a higher samplingfrequency for torque compared to velocity during dataacquisition.

The gear over the receding horizon is assumed to beconstant at the recorded value gk. The difference at k

between computed and actual torque Tk, due to modelingerrors and uncertainties, can be calculated

Tk = Tk − Tk (21)

and therefore the entire prediction can be shifted, finallyleading to

TA/Vk = fv(v

A/Vk , gk) + Tk. (22)

4.5 Quadratic Velocity Predictor (P2/V )

The quadratic velocity predictor is fitted over a historyh · τs = 1 s and the weights are exponentially decayingwith a = 5.

vhistk = ( vk−h, ..., vk−2, vk−1, vk )

T(23)

0

50

100

v(km/h)

0

100

200

T(N

m)

1530 1540 1550 1560 1570 1580 1590 1600 1610

1000

2000

3000

n(R

PM)

Time (s)

Measurement

Model

Fig. 5. Vehicle model results (red) compared with chassisdynamometer measurements (blue).

28

33

38

v(km/h)

Actual

(A/V)

(P2/V)

27 28 29 30 310

50

100

150

200

EnginetorqueT

(Nm)

Time (s)

60

65

70

2660 2661 2662 2663 26640

50

100

150

200

Time (s)

Actual

(A/V)

(A/T)

(P2/V)

(P1/T)

(P2/T)

Fig. 6. Velocity and torque prediction result of the fivepredictors at two example situations.

AT2 WA2

(xP2/V,1k

xP2/V,2k

)= AT

2 W(vhistk − vk) (24)

vP2/Vk = vk + x

P2/V,1k · (0, τs, . . . , H · τs)T . . . (25)

+ xP2/V,2k ·

(0, τ2s , . . . , (H · τs)2

)T(26)

TP2/Vk = fv(v

P2/Vk , gk) + Tk. (27)

4.6 Examples

Two examples of receding horizons for all predictionsmethods are shown in Fig. 6. On the left, during anacceleration, all the load predictions are qualitativelycorrect. Note that (A/V ) predicts the velocity profileperfectly and nevertheless results in a relatively largediscrepancy in the torque trajectory. On the right, duringa coasting phase, none of the methods are able to predictthe sudden decrease in load.

Examples of receding torque horizons over a larger timeframe are shown in Fig. 7. Generally, the two velocitypredictors (A/V ) and (P2/V ) (top) forecast the load to re-main relatively close to the real value. The predictor (A/T )(left center) shows larger discrepancies with increasing pre-diction time. The predictions (P1/T ), (P2/T ) (center andbottom right) sometimes show very large slopes leadingto extremely high torque predictions towards the end ofthe horizon. It can be reasoned that the velocity basedpredictors are able to forecast the general trend in loadrelatively well. However, the application of the quasi-static


162


The polynomial is constrained to the initial engine torque

Tk. The slope of the torque trajectory xP1/Tk at each time

step follows by solving:

(AT1 WA1)x

P1/Tk = AT

1 W(Thistk − Tk). (12)

Finally the receding torque horizon follows as

TP1/Tk = Tk + x

P1/Tk · (0, τ1, . . . , H · τ1)T . (13)

4.3 Quadratic Torque Predictor (P2/T )

The quadratic torque predictor is based on the sameprinciple as the linear one and uses a history h · τ1 = 0.5 swith weighting factor a = 10. However, in addition to the

slope xP2/T,1k the curvature x

P2/T,2k is computed:

A2 =

(−h · τ1,−(h− 1)τ1, . . . ,−τ1, 0

(h · τ1)2, ((h− 1) · τ1)2 , . . . , τ21 , 0

)T

(14)

AT2 WA2

(xP2/T,1k

xP2/T,2k

)= AT

2 W(Thistk − Tk) (15)

TP2/Tk = Tk + x

P2/T,1k · (0, τ1, . . . , H · τ1)T . . . (16)

+ xP2/T,2k ·

(0, τ21 , . . . , (H · τ1)2

)T. (17)

4.4 ANN Velocity Predictor (A/V )

The following predictor is based on the ANN fA/V , trainedwith the measured velocity data shown in Fig. 2. Trainingconditions of the ANN are the same as above for fA/T .The velocity history is chosen to be h · τ1 = 3 s. At eachtime step k, based on current velocity vk and h historical

values, the receding velocity horizon vA/Vk is calculated:

vA/Vk = fA/V (vk−h, ..., vk−2, vk−1, vk) (18)

=(vkk+1, v

kk+2, ..., v

kk+H

)T. (19)

The quasi-static vehicle model fv is used to computeengine torque as a function of velocity and gear:

Tk = fv(vk, gk). (20)

The model fv relies on differentiation of the velocity usingfinite differences to compute acceleration and thereforepropulsion torque. It is compared to measurements inFig. 5. As can be seen the general behavior of T isreproduced well. However, the model filters some of thefast torque dynamics, one reason being a higher samplingfrequency for torque compared to velocity during dataacquisition.

The gear over the receding horizon is assumed to beconstant at the recorded value gk. The difference at k

between computed and actual torque Tk, due to modelingerrors and uncertainties, can be calculated

Tk = Tk − Tk (21)

and therefore the entire prediction can be shifted, finallyleading to

TA/Vk = fv(v

A/Vk , gk) + Tk. (22)

4.5 Quadratic Velocity Predictor (P2/V )

The quadratic velocity predictor is fitted over a historyh · τs = 1 s and the weights are exponentially decayingwith a = 5.

vhistk = ( vk−h, ..., vk−2, vk−1, vk )

T(23)

0

50

100

v(km/h)

0

100

200

T(N

m)

1530 1540 1550 1560 1570 1580 1590 1600 1610

1000

2000

3000

n(R

PM)

Time (s)

Measurement

Model

Fig. 5. Vehicle model results (red) compared with chassisdynamometer measurements (blue).

28

33

38

v(km/h)

Actual

(A/V)

(P2/V)

27 28 29 30 310

50

100

150

200

EnginetorqueT

(Nm)

Time (s)

60

65

70

2660 2661 2662 2663 26640

50

100

150

200

Time (s)

Actual

(A/V)

(A/T)

(P2/V)

(P1/T)

(P2/T)

Fig. 6. Velocity and torque prediction result of the fivepredictors at two example situations.

AT2 WA2

(xP2/V,1k

xP2/V,2k

)= AT

2 W(vhistk − vk) (24)

vP2/Vk = vk + x

P2/V,1k · (0, τs, . . . , H · τs)T . . . (25)

+ xP2/V,2k ·

(0, τ2s , . . . , (H · τs)2

)T(26)

TP2/Vk = fv(v

P2/Vk , gk) + Tk. (27)

4.6 Examples

Two examples of receding horizons for all predictionsmethods are shown in Fig. 6. On the left, during anacceleration, all the load predictions are qualitativelycorrect. Note that (A/V ) predicts the velocity profileperfectly and nevertheless results in a relatively largediscrepancy in the torque trajectory. On the right, duringa coasting phase, none of the methods are able to predictthe sudden decrease in load.

Examples of receding torque horizons over a larger timeframe are shown in Fig. 7. Generally, the two velocitypredictors (A/V ) and (P2/V ) (top) forecast the load to re-main relatively close to the real value. The predictor (A/T )(left center) shows larger discrepancies with increasing pre-diction time. The predictions (P1/T ), (P2/T ) (center andbottom right) sometimes show very large slopes leadingto extremely high torque predictions towards the end ofthe horizon. It can be reasoned that the velocity basedpredictors are able to forecast the general trend in loadrelatively well. However, the application of the quasi-static


162

0

100

200

300

Torq

ue

(Nm

)

(A/V) Actual Torque

Predicted Torque

0

100

200

300

Torq

ue

(Nm

) (P2/V)

0

100

200

300

Torq

ue

(Nm

) (A/T)

0

100

200

300

Torq

ue

(Nm

) (P1/T)

150 200 250 300 350 400 450 5000

50

100

Vel

oci

ty (

km

/h)

Time (s)150 200 250 300 350 400 450 500

0

100

200

300

Torq

ue

(Nm

)

Time (s)

(P2/T)

Fig. 7. Torque prediction result of the five predictors for part of the FTP75. The actual torque in shown in blue. Thepredicted torque is shown in red across the prediction horizon of 2 s at each second. The associated velocity profileis shown in the bottom left plot.

vehicle model as well as the velocity differentiation leadsto large uncertainties in the fast torque dynamics. Even atorque forecast based on perfect vehicle speed predictionshows relatively large deviations from the real trajectory.On the other hand, the torque predictors are more suitedto forecast the fast torque dynamics. Towards the endof the prediction horizon, however, they often show largedeviations from the actual trajectory.

5. COMPARISON OF PREDICTION METHODS

In the following section the five predictors are compared inmore detail, first in terms of their general accuracy over theentire load range, then focused on the HCCI load regimeand their predictions of entry and exit times.

5.1 General Performance

To quantify the accuracy of the different prediction meth-ods, at each time step k the error Ek

j between the load

prediction Tk and the actual value TRealk is calculated,

based on the infinity norm of the deviation:

TRealk =

(Tk+1, Tk+2, ..., Tk+H

)T(28)

ekj = |Tk+j − T kk+j | with j = 1, 2, . . . , H (29)

Ekj = max

(ek1 , . . . , e

kj

). (30)

The entire dataset, shown in Fig. 2, was sampled atτ2 = 0.5 s and a prediction performed for each timestep k at which the velocity is nonzero and the loadis positive. Note that the time step for the predictionsthemselves is still τ1. The distribution of the predictionerrors Ek

j for all k was calculated and is shown in Fig. 8as a function of the receding horizon j · τ1. The contourlines, representing 3Nm, 6Nm, and 9Nm, are plotted inFig. 9 to directly compare the five prediction methods. Inaddition to the five methods the performance of a naivepredictor, which simply assumes constant load over theprediction horizon, is shown as well. At the beginning of

0

50

100(A/V)

(P

2/V)

0 0.5 1 1.5 20

50

100

Fractionofpredictions(%

)

(A/T)

(P1/T)

0Nm ≤ Ekj < 3Nm

3Nm ≤ Ekj < 6Nm

6Nm ≤ Ekj < 9Nm

9Nm ≤ Ekj

0 0.5 1 1.5 20

50

100

Prediction horizon jτ1 (s)

(P2/T)

Fig. 8. Distribution of the prediction error Ekj over the

horizon. The plots show the fraction of predictionswith Ek

j < 3Nm, Ekj < 6Nm, and Ek

j < 9Nm.

the prediction most methods are more accurate than thenaive predictor. However, the accuracy of all the predictorsdrops rapidly with increasing j and are outperformed bythe naive predictor. Beyond jτ1 > 0.5 s less than 40% ofpredictions show Ek

j < 3Nm. At the end of the predictionhorizon at jτ1 = 2 s the number of accurate predictionsis below 5%. The fraction of predictions, that are stillsomewhat accurate with Ek

j < 9Nm, is higher and at best20%. All the methods show comparable and relatively poorperformance, with (A/T ) resulting in the lowest accuracy.

One question is, how the different prediction methodscompare for different driving styles and cycles. The anal-ysis from above was conducted for the three drive cycleindividually and is shown in Fig. 10. The torque responseduring the HWFET seems overall to be easier to predictversus one during the US06 cycle. This includes the naivepredictor, which simply assumes constant load. Those dif-ferences might be due to the characteristics of the drivecycles themselves and their number of fast accelerations,gearshifts, driver behavior, and engine response etc. For


163


0 1 20

20

40

60

80

100

Predict. horizon jτ1 (s)


) 0Nm ≤ Ekj < 3Nm

(A/V)

(A/T)

(P2/V)

(P1/T)

(P2/T)

const

0 1 2


0Nm ≤ Ekj < 6Nm

0 1 2


0Nm ≤ Ekj < 9Nm

Fig. 9. Distribution of the prediction error over the hori-zon. The plots show the fraction of predictions withEk

j < 3Nm (Left), Ekj < 6Nm (Center), and Ek

j <9Nm (Right).

0

20

40

60

80

100

FT

P7

5

0Nm ≤ Ekj < 3Nm

(A/V)

(A/T)

(P2/V)

0Nm ≤ Ekj < 6Nm

(P1/T)

(P2/T)

const.

0Nm ≤ Ekj < 9Nm

0

20

40

60

80

100

HW

FE

T

0 0.5 1 1.5 20

20

40

60

80

100

Pred. horizon jτ1 (s)

US

06

0 0.5 1 1.5 2

Pred. horizon jτ1 (s)0 0.5 1 1.5 2


Fig. 10. Distribution of the prediction error over thehorizon for the three individual drive cycles. The plotsshow the fraction of predictions with Ek

j < 3Nm

(Left), Ekj < 6Nm (Center), and Ek

j < 9Nm (Right).

example, it is reasonable to assume that a linear fit workswell for slow dynamics but poorly for fast ones. In addi-tion, other method-related aspects may play a role. Forexample the weighting factors of the polynomial fits, theapplied training data for the ANNs or the accuracy of themeasurements will have an influence. However, based onthe variety of methods and drive cycles tested here, webelieve the presented trends in terms of short-term loadprediction are representative.

5.2 HCCI Performance

The load predictions from above are tested specificallytowards their application in SI/HCCI mode switches. Theyare used to give an estimate of the next entry and exittimes in the HCCI operating regime and the associatedduration of a stay in the regime. At each time step k, Tk

is used to find the next crossings of either the maximumor the minimum HCCI load boundary. As mentionedabove, perfect knowledge of engine speed n is assumed.If at k the engine operates outside the HCCI regime, theduration until the next crossing of the HCCI limits isdenoted tEntry,Pred. Similarly, the predicted duration untilthe HCCI regime is left again is denoted tExit,Pred. Theannotations are explained in Fig. 11. The subscript Realis used for the associated values derived from the actualtorque trajectory.

1500

2500

3500

n(R

PM)

47 47.2 47.4 47.6 47.8 48 48.2 48.4 48.6 48.8

0

10

20

30

40

tEntry,Pred

tEntry,Real

tExit,Pred

tExit,Real

∆ tReal

∆ tPred

Time (s)

EnginetorqueT

(Nm)

Measurement

(P1/T)

Fig. 11. Annotation for HCCI entry and exit times atexample engine speed and load trajectories.

The prediction based entry and exit durations are com-pared to the actual values in Fig. 12. The durations areseparated into different bins from 0 s to 2 s, the end of thehorizon. If no crossing is detected within the horizon, thebin is called No Entry or No Exit. Note that the probabili-ties for the exit assumes that the prediction is made withinthe HCCI regime. For a given prediction the probability iscalculated at which the prediction lies in the same bin as anactual duration. In case of a perfect prediction the entrieson the diagonal would be 100%. The larger the deviationfrom the diagonal the worse the overall prediction quality.As can be seen in Fig. 12 all the methods show highaccuracies between 60-70% in predicting an entry or exitwithin the next 0.2 s. In addition, the accuracies of no entryand exit predictions are relatively high as well with 77-81%and 50-67%, respectively. However, prediction in-betweenthose two cases show very low accuracy and are throughouttoo pessimistic.

The duration of the next visitation in HCCI ∆t is calcu-lated if at time step k the engine either operates in theHCCI regime or or an entry is predicted to occur shortly:

∆t =

tExit − tEntry tEntry ≤ 0.5 s

tExit in HCCI

No calculation

(31)

The probabilities for a given predicted HCCI visitationduration ∆tPred are shown in the bottom third of Fig. 12.Note that the shown probabilities assume that an entrywithin the next 0.5 s is correctly predicted. It can beseen that short visitations with ∆t < 0.5 s are predictedwith a high accuracy of 66-71%. Also, predictions of longvisitations with ∆t > 1.5 s are relatively accurate. How-ever, again all the prediction in-between show insufficientaccuracies and are in majority too pessimistic. The per-formance of the different predictors is very similar. All themethods are unable to give good predictions, except forthe extreme cases of very short or very long durations. Thevelocity predictors show the lowest accuracies in predictingentries and exits. The linear torque extrapolation showsoverall the highest accuracy.

5.3 Error Margins

In the following section it is estimated, how accurate aprediction method would need to be to achieve satisfyingresults. The actual torque trajectory TReal

k is perturbedby adding an error which increases linearly with rate ferr


164


0 1 20

20

40

60

80

100



) 0Nm ≤ Ekj < 3Nm

(A/V)

(A/T)

(P2/V)

(P1/T)

(P2/T)

const

0 1 2


0Nm ≤ Ekj < 6Nm

0 1 2


0Nm ≤ Ekj < 9Nm

Fig. 9. Distribution of the prediction error over the hori-zon. The plots show the fraction of predictions withEk

j < 3Nm (Left), Ekj < 6Nm (Center), and Ek

j <9Nm (Right).

0

20

40

60

80

100

FT

P7

5

0Nm ≤ Ekj < 3Nm

(A/V)

(A/T)

(P2/V)

0Nm ≤ Ekj < 6Nm

(P1/T)

(P2/T)

const.

0Nm ≤ Ekj < 9Nm

0

20

40

60

80

100

HW

FE

T

0 0.5 1 1.5 20

20

40

60

80

100


US

06

0 0.5 1 1.5 2

Pred. horizon jτ1 (s)0 0.5 1 1.5 2


Fig. 10. Distribution of the prediction error over thehorizon for the three individual drive cycles. The plotsshow the fraction of predictions with Ek

j < 3Nm

(Left), Ekj < 6Nm (Center), and Ek

j < 9Nm (Right).

example, it is reasonable to assume that a linear fit workswell for slow dynamics but poorly for fast ones. In addi-tion, other method-related aspects may play a role. Forexample the weighting factors of the polynomial fits, theapplied training data for the ANNs or the accuracy of themeasurements will have an influence. However, based onthe variety of methods and drive cycles tested here, webelieve the presented trends in terms of short-term loadprediction are representative.

5.2 HCCI Performance

The load predictions from above are tested specificallytowards their application in SI/HCCI mode switches. Theyare used to give an estimate of the next entry and exittimes in the HCCI operating regime and the associatedduration of a stay in the regime. At each time step k, Tk

is used to find the next crossings of either the maximumor the minimum HCCI load boundary. As mentionedabove, perfect knowledge of engine speed n is assumed.If at k the engine operates outside the HCCI regime, theduration until the next crossing of the HCCI limits isdenoted tEntry,Pred. Similarly, the predicted duration untilthe HCCI regime is left again is denoted tExit,Pred. Theannotations are explained in Fig. 11. The subscript Realis used for the associated values derived from the actualtorque trajectory.

1500

2500

3500

n(R

PM)

47 47.2 47.4 47.6 47.8 48 48.2 48.4 48.6 48.8

0

10

20

30

40

tEntry,Pred

tEntry,Real

tExit,Pred

tExit,Real

∆ tReal

∆ tPred

Time (s)

EnginetorqueT

(Nm)

Measurement

(P1/T)

Fig. 11. Annotation for HCCI entry and exit times atexample engine speed and load trajectories.

The prediction based entry and exit durations are com-pared to the actual values in Fig. 12. The durations areseparated into different bins from 0 s to 2 s, the end of thehorizon. If no crossing is detected within the horizon, thebin is called No Entry or No Exit. Note that the probabili-ties for the exit assumes that the prediction is made withinthe HCCI regime. For a given prediction the probability iscalculated at which the prediction lies in the same bin as anactual duration. In case of a perfect prediction the entrieson the diagonal would be 100%. The larger the deviationfrom the diagonal the worse the overall prediction quality.As can be seen in Fig. 12 all the methods show highaccuracies between 60-70% in predicting an entry or exitwithin the next 0.2 s. In addition, the accuracies of no entryand exit predictions are relatively high as well with 77-81%and 50-67%, respectively. However, prediction in-betweenthose two cases show very low accuracy and are throughouttoo pessimistic.

The duration of the next visitation in HCCI ∆t is calcu-lated if at time step k the engine either operates in theHCCI regime or or an entry is predicted to occur shortly:

∆t =

tExit − tEntry tEntry ≤ 0.5 s

tExit in HCCI

No calculation

(31)

The probabilities for a given predicted HCCI visitationduration ∆tPred are shown in the bottom third of Fig. 12.Note that the shown probabilities assume that an entrywithin the next 0.5 s is correctly predicted. It can beseen that short visitations with ∆t < 0.5 s are predictedwith a high accuracy of 66-71%. Also, predictions of longvisitations with ∆t > 1.5 s are relatively accurate. How-ever, again all the prediction in-between show insufficientaccuracies and are in majority too pessimistic. The per-formance of the different predictors is very similar. All themethods are unable to give good predictions, except forthe extreme cases of very short or very long durations. Thevelocity predictors show the lowest accuracies in predictingentries and exits. The linear torque extrapolation showsoverall the highest accuracy.

5.3 Error Margins

In the following section it is estimated, how accurate aprediction method would need to be to achieve satisfyingresults. The actual torque trajectory TReal

k is perturbedby adding an error which increases linearly with rate ferr


164

0

0.2

0.5

1

2

No Entry

(A/V)

t Entry,R

eal(s)

(P2/V)

0 0.2 0.5 1 2 No Entry 0

0.2

0.5

1

2

No Entry

tEntry ,P red (s)

(A/T)

t Entry,R

eal(s)

(P1/T)

Pro

bab

ilit

y (

%)

0

20

40

60

80

100

0 0.2 0.5 1 2 No Entry 0

0.2

0.5

1

2

No Entry

tEntry ,P red (s)

(P2/T)

t Entry,R

eal(s)

Entry

0

0.2

0.5

1

2

No Exit

(A/V)

tExit,Real(s)

(P2/V)

0 0.2 0.5 1 2 No Exit 0

0.2

0.5

1

2

No Exit

tExit,P red (s)

(A/T)

tExit,Real(s)

(P1/T)

Pro

bab

ilit

y (

%)

0

20

40

60

80

100

0 0.2 0.5 1 2 No Exit 0

0.2

0.5

1

2

No Exit

tExit,P red (s)

(P2/T)

tExit,Real(s)

Exit

0

0.5

1

1.5

2

(A/V)

∆tReal

(s)

(P2/V)

0 0.5 1 1.5 20

0.5

1

1.5

2

∆tP red (s)

(A/T)

∆tReal

(s)

(P1/T)

Pro

bab

ilit

y (

%)

0

20

40

60

80

100

0 0.5 1 1.5 20

0.5

1

1.5

2

∆tP red (s)

(P2/T)

∆tReal(s)

Duration

Fig. 12. Statistical correlation between the predicted andthe actual HCCI entry (top third) and exit (centerthird) times as well as durations of visitations (bottomthird) for the five prediction methods. The times aredivided into bins. For a given prediction, the colorrepresents the probability to end up with a certainactual time.

0 0.5 1 1.5 20

0.5

1

1.5

2Error ferr = 2 Nm/s

∆tP red (s)

∆tReal(s)

0 0.5 1 1.5 2

Error ferr = 4 Nm/s

∆tP red (s)0 0.5 1 1.5 2

Error ferr = 8 Nm/s

∆tP red (s)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

10

20

30

40

2 Nm/s

4 Nm/s

8 Nm/s

Mea

nabserrorin

torque(N

m)

Time horizon (s)

(A/V)

(A/T)

(P2/V)

(P1/T)

(P2/T)

const.

Fig. 13. Top: Statistical correlation between the predictedand the actual visitation duration of the HCCI regimefor a prediction based on the actual behavior plus alinearly increasing error. Three different error slopesare compared. Bottom: Mean absolute error of the fivepredictors as a function of prediction time. In additionthe three error slopes (dashed black).

T kerr,j = Tk+j ± ferr · jτs (32)

Terrk =

(T kerr,k+1, T

kerr,k+2, ..., T

kerr,k+H

)T. (33)

Terrk is used as a prediction. This means, almost per-

fect knowledge of future torque with increasingly overor under prediction is assumed. The same analysis ofduration of stay ∆t was done for error rates ferr ={2Nm/s, 4Nm/s, 8Nm/s} and plotted on the top of Fig. 13.It can be seen that for a small error the distribution isstill very close to diagonal. Even with ferr = 4Nm/s aprediction of stays up to 1 s can still be made. However,the case of ferr = 8Nm/s is already very similar to theones in Fig. 12. On the bottom of Fig. 13 those threeslopes are compared with the mean absolute error of thefive prediction methods. As can be seen, all those methodsshow in average significantly larger error rates than 8Nm/s.Note that the two velocity predictors show a decreasingerror rate compared to the torque predictors.

6. DISCUSSION

To make an optimal mode switch decision it would bepreferable to have an accurate torque prediction over ashort horizon. However, the results above suggest thatthis is difficult. It is surprising to see in Fig. 9 howa naive predictor assuming constant load performs inaverage better than all the prediction methods. However,it is impossible to predict HCCI entry and exit times byassuming the load to remain constant.

One large difficulty seems to originate from the strongnonlinearity in the driver’s torque response. In additionmodeling and measurement errors result in less accuratepredictions. Therefore it was deemed important to testprediction methods against actual drive cycle measure-ment and not simulation data, which is generally smootherand more predictable. Maybe a different parameter offersbetter potential for prediction such as commanded torqueby the ECU or the accelerator pedal position. Upcominggenerations of vehicles will offer capabilities for V2X com-munication. Such technologies will provide valuable infor-mation to make predictions of future vehicle and engine


165


states. It must be tested if this data increases predictionaccuracy and enables optimal SI/HCCI mode switchingdecisions.

Until then, based on the comparison of the different pre-dictors above, it can be seen that none of the predictors isaccurate enough to allow an optimal decision for visitationdurations between 0.5 s < ∆t < 1.5 s. Therefore, visita-tions slightly too short to lead to fuel efficiency benefitscannot be predicted. Visitations with ∆t < 0.5 s can,however, be predicted with any of the presented meth-ods. Therefore if constraints posed by mode switch fuelpenalties, drivability, or hardware restrict the use of a sim-ply reactive supervisory control strategy, some predictioncould be used to improve performance.

It can be seen that the prediction shows high accuracy forimmediate HCCI boundary crossings. This would allow forsome time to prepare the mode switch, thereby alleviatingpotential issues concerning drivability. It is also able topredict very short visitations of the HCCI regime rela-tively well. For such a reduced strategy, a linear torqueextrapolation seems to be the preferable choice, due to itssimplicity. Based on the load extrapolation the predictedHCCI entry time tHCCI,Entry and the predicted duration

of a visitation of HCCI ∆tHCCI can be derived. If theentry time is closer than the time required to preparethe mode switch tHCCI,Entry ≤ ds,1 and the predicted

duration of the visitation ∆tHCCI > 0.5s, the mode switchshould be prepared. As soon as HCCI is entered and still∆tHCCI > 0.5s, the cam switch should be conducted. Onthe other hand if ∆tHCCI increases above some thresholdit can be assumed that the prediction was wrong, andit should be returned to standard SI. Vice versa for theHCCI/SI mode switch, if tHCCI,Exit is smaller than thetime requirement then the strategy should be to startpreparing the switch.

7. CONCLUSION

Based on steady-state engine maps and combustion modeswitch experiments the required residence time in HCCIcombustion to lead to a fuel economy benefit was esti-mated to be around 1.2 s. Different receding horizon pre-diction methods were assessed with chassis dynamometerexperiments. The methods based on ANN and polynomialfits were compared in terms of their general accuracy inload prediction as well as their forecast of HCCI entry andexit events. For the given engine data and all the methodscompared, it was seen that the prediction accuracy forvisitations of the HCCI regime with durations around1.2 s is very low. Overall a linear extrapolation of enginetorque showed the best performance. In future work, asupervisory control structure, based on determining animmediate HCCI entry or exit, will be implemented insimulation and tested in terms of fuel economy and driv-ability. Combustion mode switch measurement data willbe used to extend the parameterization of the associatedmodel to other operating conditions.

This report was prepared as an account of work sponsored by anagency of the United States Government. Neither the United StatesGovernment nor any agency thereof, nor any of their employees,makes any warranty, express or implied, or assumes any legal liabilityor responsibility for the accuracy, or usefulness of any information,

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apparatus, product, or process disclosed, or represents that itsuse would not infringe privately owned rights. Reference hereinto any specific commercial product, process, or service by tradename, trademark, manufacturer, or otherwise does not necessarilyconstitute or imply its endorsement, recommendation, or favoringby the United States Government or any agency thereof.


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Documents

4th IFAC Workshop on August 23-26, 2015. Columbus, OH, USA ...annastef/papers_hcci/Nuesch2015IFAC.pdf · Peer review under responsibility of International Federation of Automatic