June 19-23, 2016. Norrköping, Sweden ScienceDirect(11) = − ˛ ˝ = + +.. (• • ()=) √ ˙ () · = + + · = + +. ·

IFAC-PapersOnLine 49-11 (2016) 461–468

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2405-8963 © 2016, 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.2016.08.068

© 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

Simultaneous Estimation of Intake andResidual Mass Using In-Cylinder Pressurein an Engine with Negative Valve Overlap

C. Guardiola ∗ V. Triantopoulos ∗∗ P. Bares ∗ S. Bohac ∗∗

A. Stefanopoulou ∗∗

∗ CMT–Motores Termicos, Universitat Politecnica de Valencia,Valencia, Spain (e-mail: {carguaga,pabamo}@mot.upv.es).

∗∗ Department of Mechanical Engineering, University of Michigan, AnnArbor, Michigan, USA (e-mail: {vtrianto,sbohac,annastef}@umich.edu)

Abstract:This work presents a new method for the simultaneous estimation of the intake and residual massin an engine operating with negative valve overlap. The method exclusively uses the in-cylinderpressure information and no additional measurement is needed. It is based on the determinationof the total mass through the pressure resonance in the cylinder and the assumption of apolytropic expansion of the gas during the exhaust stroke for determining the residual gases.The method has been demonstrated on an engine with negative valve overlap operating in SI,SACI and HCCI combustion. The results show that the proposed method can provide goodmass estimations in most cycles in HCCI and SACI combustion, and in lightly knocking cycleswhile operating in SI combustion.

Keywords: In-cylinder pressure, residual mass, air mass, estimation, negative valve overlap,HCCI, SACI, SI

1. INTRODUCTION

Cylinder charge determination in internal combustion en-gines is a difficult task, which is usually achieved throughthe combination of different measurement and modellingtechniques for the individual determination of the externalflows (air, fuel, recirculated gas) and the residual gases.Most of the standard techniques rely on sensors that areslower than the characteristic engine cycle time, and thencannot provide a proper description in the case of fasttransients or significant cycle-to-cycle variability, as is acommon situation in low temperature combustion (LTC)modes.

LTC modes, such as homogeneous charge compressionignition (HCCI) and spark assisted compression ignition(SACI) combustion, have shown potential in increasing thethermal efficiency of the conventional spark ignited (SI)engine, while maintaining low or easily treatable engine-out emissions (Zhao et al., 2002; Manofsky et al., 2011).For the practical implementation of these LTC modes, anexhaust gas recompression strategy is often employed us-ing negative valve overlap (NVO), as this strategy providesfast control of the gas charge composition and tempera-ture, which directly impacts combustion phasing (Cairnsand Blaxill, 2005; Wheeler et al., 2013). In NVO engines,the exhaust valve closes well before top dead center of theexhaust stroke, as shown in Figure 1, thereby trappinghigh levels of residual exhaust gas necessary to promoteautoignition of the charge in the following cycle. However,the temperature and composition of the charge have to bewell controlled to achieve the appropriate top dead center

-1.25 -1 -0.75 -0.5 -0.25 0

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Fig. 1. Unfiltered pressure trace of a given cycle operatingwith NVO; EVO and EVC have been marked. Leftbottom plot is a zoom of the 0 to 80 CAD regionshowing pressure resonance phenomenon. Right plotis the spectrogram of that section in the region from4 to 7 kHz; power spectral density is expressed inlogarithmic scale (dB/rad/sample).

Preprints, 8th IFAC International Symposium onAdvances in Automotive ControlJune 19-23, 2016. Norrköping, Sweden

Copyright © 2016 IFAC 471








1. INTRODUCTION



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462 C. Guardiola et al. / IFAC-PapersOnLine 49-11 (2016) 461–468

(TDC) conditions for optimal combustion characteristics(Lavoie et al., 2010).

For the case of an HCCI engine with NVO, Hellstrom et al.(2013) developed a two-state deterministic model able topredict the mean combustion phasing behavior via theevolution of recycled thermal and chemical energy carriedfrom cycle-to-cycle through the trapped residuals. Theglobal characteristics of the cyclic variability at variousoperating points were also captured in Hellstrom et al.(2013) by introducing a small random perturbation on topof the predicted mean residual mass. The prediction ofthe cyclic dispersion patterns led to cycle-to-cycle controlof fuel injection for reducing the combustion variability(Hellstrom et al., 2014). Analysis of various model-basedcontrol techniques in Hellstrom et al. (2014) showed highsensitivity away from the nominal operating conditions,hence an improved calculation of the residual mass couldaugment the modeled residuals and improve the controlrobustness.

A number of residual estimation methods based on in-cylinder pressure information for engines operating withNVO are available in the literature, as summarized andcompared by Ortiz-Soto et al. (2012):

• State Equation method, where the exhaust tempera-ture is propagated from the exhaust manifold to thecylinder and the residual mass is calculated throughthe application of the state equation at the exhaustvalve closing (EVC):

mres =pEV CVEV C

RTexh(1)

• Yun and Mirsky (1974) method, where the gas mix-ture is assumed to evolve according to a polytropicand the measured intake mass flow is compared withthe state equation evaluated at both exhaust valveopening (EVO) and EVC:

mres =(ma +mf +megr)

VEV C

VEV O

(pEV C

pEV O

) 1γ

1− VEV C

VEV O

(pEV C

pEV O

) 1γ

(2)

• Fitzgerald method (Fitzgerald et al., 2010), whichalso uses the measured intake mass flow for solvingthe mass difference between EVO and EVC, butthe in-cylinder temperature evolution during the ex-haust stroke is modeled combining the convectiveheat transfer equation with the assumption of Texh

to be representative of the mean temperature insidethe cylinder. Woschni correlation (Woschni, 1967) isused for the heat transfer coefficients.

Despite the fact that in-cylinder pressure measurement isfast enough to provide cycle-to-cycle information, in allmethods presented above in-cylinder pressure informationis combined with another variable to estimate residualmass. Exhaust temperature, Texh, is used as an approx-imation of in-cylinder temperature during the exhaustprocess in the State Equation and Fitzgerald methods, andintake mass flow in the Yun and Mirsky and Fitzgeraldmethods. However, such assumptions present significantdrawbacks with the most important being the difficulty toproperly represent transient or cycle-to-cycle variabilitysince the method is hampered by the slow response of

both exhaust temperature and mass flow sensors. Evenif fast sensors are available in a laboratory setting, theirtime constants for a durable on-board application is notsufficient to provide cycle-to-cycle information, hence theexisting method assumptions are not fulfilled.

Residual estimation in an HCCI engine operating withsignificant cyclic variability has been addressed by sev-eral authors. Larimore et al. (2013) developed an onlineestimator of the residual gas fraction, where blowdowntemperature is modeled in order to consider the effect ofthe residual temperature on the next cycle. In Larimoreet al. (2015) a real time implementation of Fitzgerald’smethod was presented and the effect of errors in thedetermination of Texh was analyzed, concluding that thereis a low sensitivity of the residual mass estimation to errorsin Texh. Once again, and as pointed out by the authors,the main limitation of the algorithm is that it requires atransient air mass as an input.

With the aim of overcoming these difficulties, this paperpresents a new method which exclusively relies on thein-cylinder pressure signal for simultaneously providingan estimation of the mass flow entering the cylinderand the residual gas mass. The method takes benefit ofthe excitation of resonant modes in the cylinder by thecombustion, which produces pressure oscillations followingthe combustion as depicted in the lower left plot inFigure 1, for deriving the mix temperature during theexpansion stroke and determining the total cylinder mass(Guardiola et al., 2014). This total mass estimate is thencombined with the assumption of an adiabatic expansionduring the exhaust phase, as in Yun and Mirsky method,for discerning between external and residual mass for thecase of NVO engines. Since only pressure information isused and no temperature or flow measurement is needed,the method is expected to have a better time responsethan the existent methods in the literature.

2. EXPERIMENTAL SETUP

In this study, experiments were performed on a modified2010 GM LNF Ecotec I4 spark-ignited engine. The en-gine has been modified to enable multi-mode combustion,including conventional SI, SACI and HCCI combustion.The compression ratio of the engine has been increasedfrom 9.2:1 to 11.25:1, with custom pistons and head ma-chining. The main characteristics of the engine are shownin Table 1.

Number of cylinders 4Bore (B) 86 mmStroke (S) 86 mmConrod length (L) 145.5 mmCompression ratio (cr) 11.25

Table 1. Engine main characteristics.

The engine is equipped with DOHC, dual variable valvetiming (VVT) with 50 degrees of crank angle degreephasing authority. A negative valve overlap camshaft setwas used in this work with maximum lift of 3.5 mm and 154crank angle degrees duration, defined at 0 mm opening. Ahigh-pressure cooled EGR system has been added to theengine with associated flow control, which is connecteddownstream of a 58 mm throttle body. The throttle and

IFAC AAC 2016June 19-23, 2016. Norrköping, Sweden

472

C. Guardiola et al. / IFAC-PapersOnLine 49-11 (2016) 461–468 463

(TDC) conditions for optimal combustion characteristics(Lavoie et al., 2010).

For the case of an HCCI engine with NVO, Hellstrom et al.(2013) developed a two-state deterministic model able topredict the mean combustion phasing behavior via theevolution of recycled thermal and chemical energy carriedfrom cycle-to-cycle through the trapped residuals. Theglobal characteristics of the cyclic variability at variousoperating points were also captured in Hellstrom et al.(2013) by introducing a small random perturbation on topof the predicted mean residual mass. The prediction ofthe cyclic dispersion patterns led to cycle-to-cycle controlof fuel injection for reducing the combustion variability(Hellstrom et al., 2014). Analysis of various model-basedcontrol techniques in Hellstrom et al. (2014) showed highsensitivity away from the nominal operating conditions,hence an improved calculation of the residual mass couldaugment the modeled residuals and improve the controlrobustness.

A number of residual estimation methods based on in-cylinder pressure information for engines operating withNVO are available in the literature, as summarized andcompared by Ortiz-Soto et al. (2012):

• State Equation method, where the exhaust tempera-ture is propagated from the exhaust manifold to thecylinder and the residual mass is calculated throughthe application of the state equation at the exhaustvalve closing (EVC):

mres =pEV CVEV C

RTexh(1)

• Yun and Mirsky (1974) method, where the gas mix-ture is assumed to evolve according to a polytropicand the measured intake mass flow is compared withthe state equation evaluated at both exhaust valveopening (EVO) and EVC:

mres =(ma +mf +megr)

VEV C

VEV O

(pEV C

pEV O

) 1γ

1− VEV C

VEV O

(pEV C

pEV O

) 1γ

(2)

• Fitzgerald method (Fitzgerald et al., 2010), whichalso uses the measured intake mass flow for solvingthe mass difference between EVO and EVC, butthe in-cylinder temperature evolution during the ex-haust stroke is modeled combining the convectiveheat transfer equation with the assumption of Texh

to be representative of the mean temperature insidethe cylinder. Woschni correlation (Woschni, 1967) isused for the heat transfer coefficients.

Despite the fact that in-cylinder pressure measurement isfast enough to provide cycle-to-cycle information, in allmethods presented above in-cylinder pressure informationis combined with another variable to estimate residualmass. Exhaust temperature, Texh, is used as an approx-imation of in-cylinder temperature during the exhaustprocess in the State Equation and Fitzgerald methods, andintake mass flow in the Yun and Mirsky and Fitzgeraldmethods. However, such assumptions present significantdrawbacks with the most important being the difficulty toproperly represent transient or cycle-to-cycle variabilitysince the method is hampered by the slow response of

both exhaust temperature and mass flow sensors. Evenif fast sensors are available in a laboratory setting, theirtime constants for a durable on-board application is notsufficient to provide cycle-to-cycle information, hence theexisting method assumptions are not fulfilled.

Residual estimation in an HCCI engine operating withsignificant cyclic variability has been addressed by sev-eral authors. Larimore et al. (2013) developed an onlineestimator of the residual gas fraction, where blowdowntemperature is modeled in order to consider the effect ofthe residual temperature on the next cycle. In Larimoreet al. (2015) a real time implementation of Fitzgerald’smethod was presented and the effect of errors in thedetermination of Texh was analyzed, concluding that thereis a low sensitivity of the residual mass estimation to errorsin Texh. Once again, and as pointed out by the authors,the main limitation of the algorithm is that it requires atransient air mass as an input.

With the aim of overcoming these difficulties, this paperpresents a new method which exclusively relies on thein-cylinder pressure signal for simultaneously providingan estimation of the mass flow entering the cylinderand the residual gas mass. The method takes benefit ofthe excitation of resonant modes in the cylinder by thecombustion, which produces pressure oscillations followingthe combustion as depicted in the lower left plot inFigure 1, for deriving the mix temperature during theexpansion stroke and determining the total cylinder mass(Guardiola et al., 2014). This total mass estimate is thencombined with the assumption of an adiabatic expansionduring the exhaust phase, as in Yun and Mirsky method,for discerning between external and residual mass for thecase of NVO engines. Since only pressure information isused and no temperature or flow measurement is needed,the method is expected to have a better time responsethan the existent methods in the literature.

2. EXPERIMENTAL SETUP

In this study, experiments were performed on a modified2010 GM LNF Ecotec I4 spark-ignited engine. The en-gine has been modified to enable multi-mode combustion,including conventional SI, SACI and HCCI combustion.The compression ratio of the engine has been increasedfrom 9.2:1 to 11.25:1, with custom pistons and head ma-chining. The main characteristics of the engine are shownin Table 1.

Number of cylinders 4Bore (B) 86 mmStroke (S) 86 mmConrod length (L) 145.5 mmCompression ratio (cr) 11.25

Table 1. Engine main characteristics.

The engine is equipped with DOHC, dual variable valvetiming (VVT) with 50 degrees of crank angle degreephasing authority. A negative valve overlap camshaft setwas used in this work with maximum lift of 3.5 mm and 154crank angle degrees duration, defined at 0 mm opening. Ahigh-pressure cooled EGR system has been added to theengine with associated flow control, which is connecteddownstream of a 58 mm throttle body. The throttle and


472

EGR entry location have been moved further upstream inthe air path to allow for better EGR mixing. An Eaton R-410 supercharger has been added to the air path to provideintake boost, along with the stock twin scroll, waste-gatedModel K04 BorgWarner turbocharger. A back pressurevalve has been installed downstream of the turbochargerto better control the external EGR rate. The fuel used isUTG-96 Federal Certification Gasoline with a RON = 96.0and MON = 88.6.

Cylinder pressure from all 4 cylinders was sampled at0.1 crank angle degrees using Kistler 6125A piezoelectricpressure transducers. Cylinder 1 was additionally instru-mented with Kistler piezoresistive absolute pressure sen-sors near the exhaust and intake ports, the latter used forcylinder pressure pegging. The analysis presented in thiswork uses cylinder pressure data from cylinder 1.

Fuel mass mf was measured using a Pierburg PLU 103positive displacement volumetric flowmeter. Fresh air massma in steady operation was determined from mf andequivalence ratio provided by a Horiba MEXA 7500 DEGRexhaust analyzer, sampling from exhaust runner of cylin-der 1. For the tests running with external EGR, intakeCO2 concentration was measured from the intake manifoldand used, together with ma and exhaust CO2 concentra-tion, to determine the EGR mass megr.

According to the definitions used in the present work, totalmass inside the cylinder would be:

mcyl = ma +mf +megr +mres (3)

where mres is the residual mass to be determined. Theexhaust mass leaving the cylinder for a given cycle k wouldbe:

mexh (k) = mcyl (k)−mres (k) (4)

considering mres (k) the residuals from cycle k to cyclek + 1. Note that the expected average value for mexh isthe measured ma +mf +megr.

3. METHOD DESCRIPTION

The proposed method is based on the determination of thein-cylinder mass and temperature of the mixture duringthe expansion stroke by taking advantage of the existenceof resonant modes in the in-cylinder pressure, which areexcited as a result of the combustion event. The lower leftplot in Figure 1 shows a zoom of the 20 to 80 CAD segmentof the in-cylinder pressure trace, while the lower right plotshows a spectrogram for this section and the frequencyrange from 4 to 7 kHz. It can be clearly seen that thefrequency varies as the expansion stroke takes place.

As shown in Draper (1935), resonance frequency dependson cylinder geometry and the speed of sound, following:

fcyl =aB

πD(5)

where fcyl is the resonance frequency, B is the Besselcoefficient for the first radial mode, D is the cylinder bore,and a =

√γRT =

√γpV/m is the speed of sound.

The variation of fcyl along the expansion stroke shownin the spectrogram in Figure 1 is a consequence, on onehand, of the decrease of the gas temperature and, on theother hand, of the modification of the Bessel coefficient,B. B remains constant only when the radial section doesnot change, which is not true in most internal combustionengines. When a combustion chamber with a bowl isconsidered, B varies with the engine angular position (α).Nevertheless, B (α) results in an engine characteristic andstands invariable for a given engine for every operationcondition.

The first application of (5) to estimate in-cylinder condi-tions was done by Hickling et al. (1983) for temperatureestimation in internal combustion engines, while the ap-proach was later systematized by Guardiola et al. (2014)for inferring the trapped mass. The core of the lattermethod is determining fcyl(α) through the short timeFourier transform (STFT) applied over a crank angle win-dow after the end of the combustion, once the in-cylindertemperature may be considered homogeneous (Broatchet al., 2015a). The trapped mass is then determined by:

mcyl (α) =

(B (α)

√γp (α)V (α)

πDfcyl (α)

)2

(6)

where p is the in-cylinder pressure, V the cylinder volumeand γ the specific heat ratio of the mix. In this expression,a zero-phase low pass filter with cut-off frequency belowthe resonance frequency range (e.g. 2 kHz) is applied tothe in-cylinder pressure in order to avoid the propagationof its oscillations to the mass estimation.

Note that (6) provides an estimate of the mass for eachposition of the crankshaft, so it is possible to derive errormetrics for a given cycle:

mcyl = median (mcyl (α))σmcyl

= std (mcyl (α))(7)

For the present application, median value has been pre-ferred over mean value for the final implementation dueits higher robustness for outlier rejection. An alternativeformulation in Broatch et al. (2015b) compacts the time-frequency analysis, (6) and (7) in a direct transform thatprovides cylinder mass from pressure.

Once total mass mcyl has been determined, it is possibleto derive the cylinder conditions at EVO:

TEV O =pEV OVEV O

mcylR(8)

This estimate of the temperature at exhaust valve openingreplaces the need to use the exhaust temperature mea-surement, as in the State Equation method. The exhaustprocess is then modeled as an isentropic process and theresidual mass (i.e. cylinder mass at EVC) may be calcu-lated:

mres =pEV CVEV C

TEV CR=

pEV CVEV C

TEV O

(pEV C

pEV O

) γ−1γ

R

(9)


473


praw(k,α) fres(α)

pfilt(α,k)

mcyl(α)mcyl(k)

V(α) B(α)

σm(k)

pEVO(k)

pEVC(k)

VEVO VEVC

(10)mres(k)

+

‐

mint(k)

mexh(k)

z‐1

+‐

repeated for α0≤α≤α1

repeated for every cycle k

^window STFT

pegginglow‐pass filter

(< 2 kHz)pint(k,α)

median & standard deviation

(6)

engine charac.

Fig. 2. Method block diagram.

0 45 90 135 180 225 270 315 3600

0.5

1

α [CAD]

dm/d

α [m

g/C

AD

]

EVO EVC

Fig. 3. Calculated exhaust mass flow for a given enginecycle.

Combining these last two expressions:

mres = mcylVEV C

VEV O

(pEV C

pEV O

) 1γ

(10)

Finally, the intake and exhaust flow during intake andexhaust strokes may be determined by analyzing thesuccession mcyl and mres:

mexh (k) = mcyl (k)−mres (k)mint (k) = mcyl (k)−mres (k − 1)

(11)

where k refers to the pressure cycle used for computingthe mass flows.

It is possible to derive the relationship between mcyl andmexh by the combination of (10) and (11):

mcyl =mexh

1− VEV C

VEV O

(pEV C

pEV O

) 1γ

(12)

Note the similarity between Yun and Mirsky method (2),and the combination of (10) and (12). The only differenceis that Yun and Mirsky method uses mexh = ma +mf +megr for determining mcyl and mres, while in the presentmethod the use of the mass flow measurement is avoidedas mcyl is derived from the pressure resonance.

Figure 2 summarizes in a block diagram the main opera-tions and signal manipulations. As the first mode of theresonance is in the range of 3 to 7 kHz, in-cylinder pressurefrequency contents must be preserved (i.e. non filtered)up to 15 kHz in order to avoid aliasing. This correspondsto a minimum angular resolution of 0.5 CAD/sample at1250 rpm as an indicative value. In addition, if the engine

speed is not sufficiently constant during the cycle, time-based acquisition of the pressure signal is advised in orderto preserve the accuracy in the determination of fcyl.

Furthermore, if (9) is used during the complete evolutionof the exhaust stroke, it is possible to infer the exhaustflow through the valve, as depicted in Figure 3.

3.1 On gas properties and heat transfer during the exhauststroke

In its present formulation the method does not considerthe effect of gas mix composition or in-cylinder heat trans-fer during the exhaust stroke. Both of them could beconsidered, but at the cost of using an iterative imple-mentation.

It should be noted that if only residual and total massesare to be computed (and not T or instantaneous massflow), the method only makes use of γ. In Guardiola et al.(2014) it is quantified that the total error due to the effectof composition on γ is lower than 2%. For the present work,γ = 1.3 has been selected as a characteristic value of thecombustion gases.

3.2 On method calibration

One of the difficulties for deploying the method is thedetermination of the geometry dependent Bessel coefficientB (α) in (6). There are several approaches for finding it:

• Model based approach, as in Broatch et al. (2015a),where the Finite Element Method is used for cal-culating the resonance frequency of the cylinder atdifferent crankshaft positions.

• Data based approaches: in this case real pressuretraces of a single operation point or of a set ofoperation points are used for determining the angularvariation of the Bessel coefficient by inversion of (6):

B (α) =πDfcyl (α)

√mcyl√

γp (α)V (α)(13)

However, determining the actual value of B requiresan estimation of a reference mcyl for the calibrationdataset. Several options are possible:

· Using a combination of external measurementsfor mexh = mf +ma +megr and a residual massmodel as, for example, the emptying-and-fillingmodel described in Payri et al. (2007), or othermodels (e.g. high fidelity one dimensional mod-els) or methods (e.g. the ∆p method in Desanteset al. (2010)) able to provide an estimation of thetotal mass inside the cylinder.

· Deriving the cylinder mass from mexh through(12). In this case the Bessel coefficient is cal-ibrated for matching the exhaust mass mexh

rather than the total cylinder mass. Note howeverthat mexh may be externally measured througha combination of state-of-the-art instruments andmethodologies (mexh = ma +mf +megr), whichis not the case for mres.

· Finally, if not sufficient information is availablefor mcyl or mexh, it can be assumed that thecylinder behaves as a cylinder of bore D andinfinite length when the piston moves away from


474


praw(k,α) fres(α)

pfilt(α,k)

mcyl(α)mcyl(k)

V(α) B(α)

σm(k)

pEVO(k)

pEVC(k)

VEVO VEVC

(10)mres(k)

+

‐

mint(k)

mexh(k)

z‐1

+‐

repeated for α0≤α≤α1

repeated for every cycle k

^window STFT

pegginglow‐pass filter

(< 2 kHz)pint(k,α)

median & standard deviation

(6)

engine charac.

Fig. 2. Method block diagram.

0 45 90 135 180 225 270 315 3600

0.5

1

α [CAD]

dm/d

α [m

g/C

AD

]

EVO EVC

Fig. 3. Calculated exhaust mass flow for a given enginecycle.

Combining these last two expressions:

mres = mcylVEV C

VEV O

(pEV C

pEV O

) 1γ

(10)

Finally, the intake and exhaust flow during intake andexhaust strokes may be determined by analyzing thesuccession mcyl and mres:

mexh (k) = mcyl (k)−mres (k)mint (k) = mcyl (k)−mres (k − 1)

(11)

where k refers to the pressure cycle used for computingthe mass flows.

It is possible to derive the relationship between mcyl andmexh by the combination of (10) and (11):

mcyl =mexh

1− VEV C

VEV O

(pEV C

pEV O

) 1γ

(12)

Note the similarity between Yun and Mirsky method (2),and the combination of (10) and (12). The only differenceis that Yun and Mirsky method uses mexh = ma +mf +megr for determining mcyl and mres, while in the presentmethod the use of the mass flow measurement is avoidedas mcyl is derived from the pressure resonance.

Figure 2 summarizes in a block diagram the main opera-tions and signal manipulations. As the first mode of theresonance is in the range of 3 to 7 kHz, in-cylinder pressurefrequency contents must be preserved (i.e. non filtered)up to 15 kHz in order to avoid aliasing. This correspondsto a minimum angular resolution of 0.5 CAD/sample at1250 rpm as an indicative value. In addition, if the engine

speed is not sufficiently constant during the cycle, time-based acquisition of the pressure signal is advised in orderto preserve the accuracy in the determination of fcyl.

Furthermore, if (9) is used during the complete evolutionof the exhaust stroke, it is possible to infer the exhaustflow through the valve, as depicted in Figure 3.

3.1 On gas properties and heat transfer during the exhauststroke

In its present formulation the method does not considerthe effect of gas mix composition or in-cylinder heat trans-fer during the exhaust stroke. Both of them could beconsidered, but at the cost of using an iterative imple-mentation.

It should be noted that if only residual and total massesare to be computed (and not T or instantaneous massflow), the method only makes use of γ. In Guardiola et al.(2014) it is quantified that the total error due to the effectof composition on γ is lower than 2%. For the present work,γ = 1.3 has been selected as a characteristic value of thecombustion gases.

3.2 On method calibration

One of the difficulties for deploying the method is thedetermination of the geometry dependent Bessel coefficientB (α) in (6). There are several approaches for finding it:

• Model based approach, as in Broatch et al. (2015a),where the Finite Element Method is used for cal-culating the resonance frequency of the cylinder atdifferent crankshaft positions.

• Data based approaches: in this case real pressuretraces of a single operation point or of a set ofoperation points are used for determining the angularvariation of the Bessel coefficient by inversion of (6):

B (α) =πDfcyl (α)

√mcyl√

γp (α)V (α)(13)

However, determining the actual value of B requiresan estimation of a reference mcyl for the calibrationdataset. Several options are possible:

· Using a combination of external measurementsfor mexh = mf +ma +megr and a residual massmodel as, for example, the emptying-and-fillingmodel described in Payri et al. (2007), or othermodels (e.g. high fidelity one dimensional mod-els) or methods (e.g. the ∆p method in Desanteset al. (2010)) able to provide an estimation of thetotal mass inside the cylinder.

· Deriving the cylinder mass from mexh through(12). In this case the Bessel coefficient is cal-ibrated for matching the exhaust mass mexh

rather than the total cylinder mass. Note howeverthat mexh may be externally measured througha combination of state-of-the-art instruments andmethodologies (mexh = ma +mf +megr), whichis not the case for mres.

· Finally, if not sufficient information is availablefor mcyl or mexh, it can be assumed that thecylinder behaves as a cylinder of bore D andinfinite length when the piston moves away from


474

the top dead center. Therefore, B tends towards1.841 (Draper, 1935; Broatch et al., 2015a) andthe reference mcyl can be estimated by:

mcyl =

(1.841

√γp (α∞)V (α∞)

πDfcyl (α∞)

)2

(14)

where α∞ is sufficiently far from the top deadcenter. Oncemcyl reference is estimated, the com-plete function B (α) can be determined through(13).

It should be noted that, with independence of the calibra-tion method used, B (α) is a geometric characteristic andstands invariable for any operation condition. As B (α)only depends on the geometry, it will be the same for anyunit of a given engine model.

4. RESULTS AND DISCUSSION

The engine was tested in different operating conditionsand combustion modes. These included conventional sparkignited (SI), homogeneous charge compression ignition(HCCI) and spark assisted compression ignition (SACI).Figure 4 shows three examples of pressure traces andapparent heat release law (HRL) corresponding to thethree different operating modes. Selected examples wererun at 2000 rpm, with λ=0.9793 and IMEP=2.86 barfor the SI case, λ= 1.0071 and IMEP= 3.75 bar for theSACI case, and λ=1.4334 and IMEP=4.25 bar for theHCCI case; 300 consecutive cycles are shown in the Figure.It can be seen that both combustion speed and cycle-to-cycle variability strongly depend on the combustionmode, which directly affects the excitation of the pressureresonant modes. Since the applicability of the methoddepends on the resonant modes detection, it would beaffected by the combustion mode.

Figure 5 depicts the spectrogram from two individualcycles in SI (top), SACI (center) and HCCI (bottom)combustion. The selected cycles have been marked in black(solid and dashed) in the pressure traces and heat releaselaws in Figure 4. The frequencies with maximum excitationfor a given angular position have been marked with a blackline in the spectrograms. It can be seen that the resonantfrequency is sufficiently excited in most of the analyzedcycles, showing a smooth trajectory from slightly above 6kHz at 20 CAD to near 5 kHz at 80 CAD. However, thelevel of the excitation strongly depends on the cycle andcombustion mode considered.

For the case of SI combustion, the level of excitation issignificantly lower and depending on the individual cycleselected, excitation may be almost inexistent (as in thecase of the example in the top-left plot). As a rule of thethumb, only slightly knocking cycles get a sufficient levelof excitation when operating with SI combustion. In thecase of both SACI and HCCI, combustion is very fast andresonance is clearly excited for most of the cycles.

As expected, pressure waves are damped with the gasexpansion, and in some cases, as in the left cycle for SACIcombustion (center) and the right cycle for SI combustion(top), excitation is not sufficient for a correct fcyl detectionwith α > 60, which causes discontinuities in the fcyl

−90 −45 0 45 900

10

20

30

p [b

ar]

α [CAD]−90 −45 0 45 900

100

200

300

400

500

HR

L [J

]

α [CAD]

−90 −45 0 45 900

20

40

60

p [b

ar]

α [CAD]−90 −45 0 45 900

100

200

300

400

500

HR

L [J

]

α [CAD]

−90 −45 0 45 900

20

40

60

p [b

ar]

α [CAD]−90 −45 0 45 900

100

200

300

400

500

HR

L [J

]

α [CAD]

Fig. 4. Pressure traces and HRL for 300 consecutivecycles in an steady operation point with SI (top),SACI (center) and HCCI (bottom) combustion. Blacklines correspond to the individual cycles analyzed inFigure 5.

trajectory estimation. Such damping of the pressure wavesduring the expansion stroke justify the need of limitingthe range for the sliding detection window, which for thisstudy has been set from α0 = 35 CAD, when combustionis finished, to α1 = 50 CAD, when resonance is stilldetectable in most of the cycles.

For the present work, the calibration of the Bessel coeffi-cient B (α) was done considering that the cylinder behavesas a cylinder of infinite length when the piston is suffi-ciently far from the top dead center. Thus, only in-cylinderpressure information was used. Since the excitation inHCCI combustion is higher than in the rest of operatingconditions, 3000 consecutive cycles of a single operationpoint with such combustion mode were used. The topplot in Figure 6 shows the traces of B (α)/

√mcyl for the

3000 cycles. The median of the traces (solid line) and theinterval defined by the standard deviation (dashed) is alsoshown. Outliers, marked in gray in the plot and definedas the points out of the 1-σ interval were less than 5% ofthe considered samples, while 79.9% of the cycles has allsamples inside the confidence region. Finally, consideringthat at the end of the expansionB = 1.841, the value of theaverage mcyl for that operating point may be determinedthrough (14); then the complete function B (α) may becomputed by (13), as shown in bottom plot of Figure 6. Inthe latter plot, a detection window from 35 to 50 CAD hasbeen also shown with dashed lines. Outliers for the sameoperation point in this range are less than 2.5%. Once thecalibration for B (α) was obtained, it was kept constant


475


20 40 60 80

, [CAD]

4

5

6

7f [

kHz]

-20

0

20

40

60

20 40 60 80

, [CAD]

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5

6

7

f [kH

z]

-20

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40

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, [CAD]

4

5

6

7

f [kH

z]

-20

0

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20 40 60 80

, [CAD]

4

5

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7

f [kH

z]

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, [CAD]

4

5

6

7

f [kH

z]

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0

20

40

60

20 40 60 80

, [CAD]

4

5

6

7

f [kH

z]

-20

0

20

40

60

Fig. 5. Spectrogram of the in-cylinder pressure for twodifferent cycles, for SI (top), SACI (center) and HCCI(bottom) operation; black line indicates the frequencywith the maximum amplitude for a given angularposition. Left plot corresponds to the dashed linein Figure 4, and right plot to the solid line. Powerspectral density is expressed in logarithmic scale(dB/rad/sample).

for the rest of the work and the method was then appliedto different steady operation points.

Figure 7 shows the results obtained for the operatingpoints in Figure 4, with SI (top), SACI (center) andHCCI (bottom). For each one of the operating conditions,cycle-to-cycle results for residuals (top) and exhaust mass(bottom) are shown, as well as the median for the proposedmethod (solid line) and for the reference method (dashed).The proposed method results (green) for mres and mexh

are compared with the Yun and Mirsky method mres

results (gray) and the measured exhaust flow mexh usingmf +ma +megr values, respectively. The right side plotsshow the histograms of the results of the proposed method(green) and of the Yun and Mirsky method (gray). Thehistogram for the measured exhaust mass is not providedsince the sensors where not fast enough.

It can be seen in Figure 7 that the median results of theproposed method match very well that of the referencemethods in both residual and exhaust mass. However,qualitative differences may be found depending on thecombustion mode considered. For the case of SI combus-tion (top), most of the cycles were rejected due to a value ofσmcyl

> σthr. Only a fraction of the cycles (22.33% for thepresented operating point and selected standard deviationthreshold σthr) provided an estimate of the residual andexhaust masses. In other SI operating conditions it was notpossible to apply the method since most of the cycles had

20 30 40 50 60 70 80

, [CAD]

0.05

0.1

0.15

B/m

0.5 [m

g-0.5

]

20 30 40 50 60 70 80

, [CAD]

1.8

1.9

2

B [-

]

detection window

infinite cylinderself calibrated B

Fig. 6. Calibration of the Bessel coefficient. Top plotrepresents B (α)/

√mcyl for 3000 consecutive cycles at

a given HCCI condition; median is marked as a solidline and 1-σ interval with the dashed lines. Bottomplot uses the median from the top plot with the mcyl

derived from (14) with α∞=80 CAD, thus satisfyingthat the terminal value of B is that of a cylinder ofinfinite length.

not sufficient resonance excitation. In SACI (center) andHCCI (bottom) combustion, most of the cycles yield to anestimate (82.67% and 93.67% respectively for the pointsshown). These results are in line with previous studiesusing the pressure resonance for total mass estimation onRCCI (Guardiola et al., 2014), HCCI (Lujan et al., 2016)and CI (Broatch et al., 2015a) engines.

Another observation from the proposed method results isthat they show a lower cyclic variability in the residualmass when compared to the Yun and Mirsky method. Thiscould be a result of the assumption of constant cycle-to-cycle exhaust mass used in Yun and Mirsky method, whichis not strictly true. In the case of the proposed method, thevariability is divided between the exhaust mass mexh andthe residual mass mres. Part of this variation is expectedto be a random noise, while the rest could be due to cycle-to-cycle variation of the quantities.

To evaluate the linearity of the proposed method, a sweepof engine operating conditions was performed under SACIcombustion. Figure 8 compares the exhaust mass flowresults of the proposed method with the test cell mea-surement (black squares) and the residual mass estimationresults of the proposed method with that provided by theYun and Mirsky method (light green circles). Error barsrepresent the cycle-to-cycle standard deviation. It can beseen that the method exhibits excellent linearity, wherer2 = 0.997 and the mean average error MAE = 2.8mg/str. It must be highlighted that the calibration ofthe method was done without considering any mass mea-surement, so results could be improved by canceling anycalibration bias through the fine tuning of B.

Lastly, the transient potential of the method was checkedby performing sharp changes in cam phasing during ex-periments. Figure 9 shows two examples of steps in valvetiming. The left plots show a step actuation in exhaust


476


20 40 60 80

, [CAD]

4

5

6

7

f [kH

z]

-20

0

20

40

60

20 40 60 80

, [CAD]

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6

7

f [kH

z]

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, [CAD]

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f [kH

z]

-20

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, [CAD]

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7

f [kH

z]

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, [CAD]

4

5

6

7

f [kH

z]

-20

0

20

40

60

20 40 60 80

, [CAD]

4

5

6

7

f [kH

z]

-20

0

20

40

60

Fig. 5. Spectrogram of the in-cylinder pressure for twodifferent cycles, for SI (top), SACI (center) and HCCI(bottom) operation; black line indicates the frequencywith the maximum amplitude for a given angularposition. Left plot corresponds to the dashed linein Figure 4, and right plot to the solid line. Powerspectral density is expressed in logarithmic scale(dB/rad/sample).

for the rest of the work and the method was then appliedto different steady operation points.

Figure 7 shows the results obtained for the operatingpoints in Figure 4, with SI (top), SACI (center) andHCCI (bottom). For each one of the operating conditions,cycle-to-cycle results for residuals (top) and exhaust mass(bottom) are shown, as well as the median for the proposedmethod (solid line) and for the reference method (dashed).The proposed method results (green) for mres and mexh

are compared with the Yun and Mirsky method mres

results (gray) and the measured exhaust flow mexh usingmf +ma +megr values, respectively. The right side plotsshow the histograms of the results of the proposed method(green) and of the Yun and Mirsky method (gray). Thehistogram for the measured exhaust mass is not providedsince the sensors where not fast enough.

It can be seen in Figure 7 that the median results of theproposed method match very well that of the referencemethods in both residual and exhaust mass. However,qualitative differences may be found depending on thecombustion mode considered. For the case of SI combus-tion (top), most of the cycles were rejected due to a value ofσmcyl

> σthr. Only a fraction of the cycles (22.33% for thepresented operating point and selected standard deviationthreshold σthr) provided an estimate of the residual andexhaust masses. In other SI operating conditions it was notpossible to apply the method since most of the cycles had

20 30 40 50 60 70 80

, [CAD]

0.05

0.1

0.15

B/m

0.5 [m

g-0.5

]

20 30 40 50 60 70 80

, [CAD]

1.8

1.9

2

B [-

]

detection window

infinite cylinderself calibrated B

Fig. 6. Calibration of the Bessel coefficient. Top plotrepresents B (α)/

√mcyl for 3000 consecutive cycles at

a given HCCI condition; median is marked as a solidline and 1-σ interval with the dashed lines. Bottomplot uses the median from the top plot with the mcyl

derived from (14) with α∞=80 CAD, thus satisfyingthat the terminal value of B is that of a cylinder ofinfinite length.

not sufficient resonance excitation. In SACI (center) andHCCI (bottom) combustion, most of the cycles yield to anestimate (82.67% and 93.67% respectively for the pointsshown). These results are in line with previous studiesusing the pressure resonance for total mass estimation onRCCI (Guardiola et al., 2014), HCCI (Lujan et al., 2016)and CI (Broatch et al., 2015a) engines.

Another observation from the proposed method results isthat they show a lower cyclic variability in the residualmass when compared to the Yun and Mirsky method. Thiscould be a result of the assumption of constant cycle-to-cycle exhaust mass used in Yun and Mirsky method, whichis not strictly true. In the case of the proposed method, thevariability is divided between the exhaust mass mexh andthe residual mass mres. Part of this variation is expectedto be a random noise, while the rest could be due to cycle-to-cycle variation of the quantities.

To evaluate the linearity of the proposed method, a sweepof engine operating conditions was performed under SACIcombustion. Figure 8 compares the exhaust mass flowresults of the proposed method with the test cell mea-surement (black squares) and the residual mass estimationresults of the proposed method with that provided by theYun and Mirsky method (light green circles). Error barsrepresent the cycle-to-cycle standard deviation. It can beseen that the method exhibits excellent linearity, wherer2 = 0.997 and the mean average error MAE = 2.8mg/str. It must be highlighted that the calibration ofthe method was done without considering any mass mea-surement, so results could be improved by canceling anycalibration bias through the fine tuning of B.

Lastly, the transient potential of the method was checkedby performing sharp changes in cam phasing during ex-periments. Figure 9 shows two examples of steps in valvetiming. The left plots show a step actuation in exhaust


476

0 10 20 3050

60

70

80

mre

s [mg/

str]

cycle [−]0 0.5 1

50

60

70

80

frequency [−]

00.51

50

60

70

80

mre

s [m

g/st

r]

60.1±0.941

60.6±2.19

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mex

h [mg/

str]

cycle [−]0 0.5 1

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h [mg/

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s [m

g/st

r]

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h [mg/

str]

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h [mg/

str]

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s [mg/

str]

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frequency [−]

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200

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mre

s [m

g/st

r]

214±2.03

216±2.65

0 10 20 30270

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mex

h [mg/

str]

cycle [−]0 0.5 1

270

280

290

300

frequency [−]

00.51

270

280

290

300

mex

h [mg/

str]

282±3.1

284

Fig. 7. Left: results over 30 consecutive cycles for a steadyoperation point, for SI (top), SACI (center) andHCCI (bottom) operation for both mres and mexh;error bars represent intra-cycle standard deviationaccording to (7); solid line is median value for themethod and dashed line is the mean value of the testcell (for mexh) or Yun and Mirsky method (for mres).Right: histograms for 300 cycles at the same operationconditions for the presented method (left) and theYun and Mirsky method (right).

50 100 150 200 250 30050

100

150

200

250

300

mexh

(measured) and mres

(Yun and Mirsky) [mg/str]

mex

h and

mre

s (m

etho

d re

sult)

[mg/

str]

mres

mexh

Fig. 8. Scatter plot for different operative conditions withSACI combustion, comparing mexh with ma +mf +megr measurement (black squares), and mres withthe estimation provided by Yun and Mirsky method(light green circles). All operating conditions are at2000 rpm and nearly stoichiometric combustion, whileboost pressure varies from 0.87 to 1.40 bar, IMEPfrom 3.5 to 4.3 bar. Error bars correspond to the cycle-to-cycle standard deviation.

cam phaser, thus providing a sharp variation in both EVOand EVC (not shown). Both EVO and EVC timing isshifted at cycle 1000, and back to the original positionat cycle 2000. The central and lower plots shows themethod results for the residual and the exhaust massrespectively. It can be seen that the results provided bythe proposed method change between two probability dis-tributions without significant dynamics, thus illustratingthe ability of the method for transient operation. Rightplots show the results of a similar transient in IVO andIVC timing, with identical conclusion.

5. CONCLUSIONS

The method presented in Guardiola et al. (2014) has beenextended in this work to include the estimation of residualsin an NVO engine. It is based on the analysis of thein-cylinder pressure signal and does not need any flowmeasurement. If sufficient excitation of the resonant modesexists, the method provides a cycle-to-cycle estimation ofboth exhaust (and intake) mass and residual mass. It canbe easily integrated in real time prototyping systems fornext cycle control.

The excitation of the pressure resonance strongly dependson the type of combustion used. While in the case of SIcombustion it is only possible to apply the method if someknocking occurs, SACI and HCCI combustions providesufficient excitation in most of the cycles. The methodhas shown a very good linearity when compared with thetest cell sensors for the mass flow though the engine, andwith Yun and Mirsky method for the residual estimation.In addition, the method predicts a lower cycle-to-cyclevariability of the residual mass, but considers a variabilityin the intake mass.

Lastly, as the proposed method provides insight into thecycle-to-cycle cylinder load and composition, it may be


477


0 1000 2000 3000120

130

140

150

160

EV

O [C

AD

]

0 1000 2000 3000120

140

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180

mre

s [mg/

str]

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0 1000 2000 3000120

140

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180

mex

h [mg/

str]

cycle [−]

0 1000 2000 3000−320

−310

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IVO

[CA

D]

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160

180

mre

s [mg/

str]

cycle [−]

0 1000 2000 3000120

140

160

180

mex

h [mg/

str]

cycle [−]

Fig. 9. Method results for a sharp actuation on exhaust(left) and intake (right) valve timing. Green dots anderror bars indicate the cycle average and the intra-cycle standard deviation respectively, as in (7).

an excellent tool for analyzing the causes of combustionphasing variability.

6. ACKNOWLEDGEMENTS

C. Guardiola research has been partially funded by theFulbright Commission and the Spanish Ministerio de Ed-ucacion, Cultura y Deporte through grant PRX14/00274,and Spanish Ministerio de Economıa y Competitividadthrough project TRA2013-40853-R.

REFERENCES

Broatch, A., Guardiola, C., Bares, P., and Denia, F.D.(2015a). Determination of the resonance response in anengine cylinder with a bowl-in-piston geometry by thefinite element method for inferring the trapped mass.Int. Journal of Engine Research, 1468087415589701.

Broatch, A., Guardiola, C., Pla, B., and Bares, P. (2015b).A direct transform for determining the trapped mass onan internal combustion engine based on the in-cylinderpressure resonance phenomenon. Mech. Syst. SignalProcess., 62, 480–489.

Cairns, A. and Blaxill, H. (2005). The effects of combinedinternal and external exhaust gas recirculation on gaso-line controlled auto-ignition. SAE Tech. Paper 2005-01-0133.

Desantes, J.M., Galindo, J., Guardiola, C., and Dolz,V. (2010). Air mass flow estimation in turbochargeddiesel engines from in-cylinder pressure measurement.Experimental Thermal and Fluid Science, 34(1), 37–47.

Draper, C.S. (1935). The physical effects of detonationin a closed cylindrical chamber. National AdvisoryCommittee for Aeronautics.

Fitzgerald, R.P., Steeper, R., Snyder, J., Hanson, R., andHessel, R. (2010). Determination of cycle temperatures

and residual gas fraction for HCCI negative valve over-lap operation. SAE Tech. Paper 2010-01-0343.

Guardiola, C., Pla, B., Blanco-Rodriguez, D., and Bares,P. (2014). Cycle by cycle trapped mass estimation fordiagnosis and control. SAE Int. Journal of Engines,7(2014-01-1702), 1523–1531.

Hellstrom, E., Larimore, J., Jade, S., Stefanopoulou, A.G.,and Jiang, L. (2014). Reducing cyclic variability whileregulating combustion phasing in a four-cylinder HCCIengine. IEEE Trans. Control Syst. Technol., 22(3),1190–1197.

Hellstrom, E., Stefanopoulou, A.G., and Jiang, L. (2013).Cyclic variability and dynamical instabilities in au-toignition engines with high residuals. IEEE Trans.Control Syst. Technol., 21(5), 1527–1536.

Hickling, R., Feldmaier, D.A., Chen, F.H., and Morel,J.S. (1983). Cavity resonances in engine combustionchambers and some applications. The Journal of theAcoustical Society of America, 73(4), 1170–1178.

Larimore, J., Hellstrom, E., Jade, S., Stefanopoulou, A.,and Jiang, L. (2015). Real-time internal residual massestimation for combustion with high cyclic variability.Int. Journal of Engine Research, 16(3), 474–484.

Larimore, J., Jade, S., Hellstrom, E., Stefanopoulou, A.G.,Vanier, J., and Jiang, L. (2013). Online adaptive resid-ual mass estimation in a multicylinder recompressionHCCI engine. In ASME 2013 Dynamic Systems andControl Conference, V003T41A005–V003T41A005.

Lavoie, G.A., Martz, J., Wooldridge, M., and Assanis, D.(2010). A multi-mode combustion diagram for sparkassisted compression ignition. Combust. Flame, 157(6),1106–1110.

Lujan, J.M., Guardiola, C., Pla, B., and Bares, P. (2016).Estimation of trapped mass by in-cylinder pressureresonance in HCCI engines. Mech. Syst. Signal Process.,66, 862–874.

Manofsky, L., Vavra, J., Assanis, D.N., and Babajimopou-los, A. (2011). Bridging the gap between HCCI and SI:Spark-assisted compression ignition. SAE Tech. Paper2011-01-1179.

Ortiz-Soto, E.A., Vavra, J., and Babajimopoulos, A.(2012). Assessment of residual mass estimation meth-ods for cylinder pressure heat release analysis of HCCIengines with negative valve overlap. J. Eng. Gas Turb.Power, 134(8), 082802.

Payri, F., Galindo, J., Martın, J., and Arnau, F. (2007).A simple model for predicting the trapped mass in a DIdiesel engine. SAE Tech. Paper 2007-01-0494.

Wheeler, J., Polovina, D., Frasinel, V., Miersch-Wiemers,O., Mond, A., Sterniak, J., and Yilmaz, H. (2013).Design of a 4-cylinder GTDI engine with part-loadHCCI capability. SAE Int. Journal of Engines, 6(2013-01-0287), 184–196.

Woschni, G. (1967). A universally applicable equation forthe instantaneous heat transfer coefficient in the internalcombustion engine. SAE Technical Paper 670931.

Yun, H. and Mirsky, W. (1974). Schlieren-streak mea-surements of instantaneous exhaust gas velocities froma spark-ignition engine. SAE Tech. Paper 741015.

Zhao, H., Li, J., Ma, T., and Ladommatos, N. (2002).Performance and analysis of a 4-stroke multi-cylindergasoline engine with CAI combustion. SAE Tech. Paper2002-01-0420.


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