HCCI MVM, RAUSEN ET AL: SUBMITTED TO ASME J-DSMC 1

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1 HCCI MVM, RAUSEN ET AL: SUBMITTED TO ASME J-DSMC A Mean-Value Moel for Control of Homogeneous Charge Compression Ignition (HCCI) Engines D. J. Rausen, A. G. Stefanopoulou The University of Michigan J-M.Kang,J.A.Eng,T-W.Kuo General Motors Corporation Abstract A Mean Value Moel (MVM) for a Homogeneous Charge Compression Ignition (HCCI) engine is presente. The moel is base on ifferential equations that account for manifol filling an air, fuel, an inert gas concentration in the intake an exhaust manifol. Using a phenomenological zero-imensional approach we first moel the effects of the Exhaust Gas Recirculation (EGR) valve, the exhaust Rebreathing Lift (RBL), an the fueling rate on the state of charge in the cyliner at intake valve closing. An Arrhenius integral is then use to moel the start of combustion,. A series of simple algebraic relations that captures the combustion uration an heat release is finally use to moel the state of charge after the HCCI combustion an the Location of Peak Pressure (LPP). The moel is parametrize using steay-state test ata from an experimental engine at the General Motors Corporation. The simple moel captures the temperature, pressure, air-to-fuel ratio, an inert gas fraction of the exhauste mass flow. This characterization is important for the overall HCCI ynamics because the thermoynamic state (pressure, temperature) an concentration (oxygen an inert gas) of the exhauste mass flow affect the next combustion event. The high ilution level in HCCI engines increases the significance of this internal feeback that generally exists to a smaller extent in conventional spark-ignition an compression-ignition internal combustion engines. I. Introuction THE basis of Homogeneous Charge Compression Ignition (HCCI) engines is their fast an flameless combustion after an autoignition process of a homegeneous mixture. HCCI combustion achieves high fuel efficiency [] with low NOx emissions ue to the limite cyliner peak temperature (below 7 K). Col bounary layers typically result in higher CO. However, the absence of iffusionlimite combustion an localize fuel-rich regions iscourages the formation of soot []. HCCI engines might prouce higher HC emission than CI engines [] but the HC prouction ecreases with increase EGR rate [7]. The main ifficulty in HCCI combustion that istinguishes it from other avance gasoline combustion moes (conventional homogeneous or irect injection stratifie) is that ignition cannot be actuate irectly. The timing of HCCI combustion is etermine by mixture conitions, rather than the spark timing or the fuel injection timing that are use to initiate combustion in Otto an Diesel engines, respectively. Instea, controlle autoignition re- Funing is provie by the General Motors Corporation uner contract TCS-96 Corresponing author, annastef@umich.eu, ph:(734) quires regulation of the mixture properties (temperature, pressure, an composition) at the Intake Valve Closing (IVC). After the work in [6] there has been little progress in the evelopment of a simple phenomemological moel that can be use for real-time feeback control algorithms in HCCI combustion. Even the few papers that present experimental results with controlle HCCI combustion through in-cyliner pressure feeback use ecouple (single-input single-output) an heuristic PI control laws. In [7] three ecentralize PI controllers for an inlet heater, fuel charge, an fuel octane ratio are use to regulate inlet temperature to 8 egrees, track IMEP commans, an regulate percent burn timing (CA) to a range of 3-8 egrees ATDC. The last control goal is the harest to achieve. In two recent papers [], [8], PI controllers are use for intake valve closing or negative overlap. The authors anticipate better results with moel-base tuning of the controller gains an coorination of all the available actuators. Inee, coorination of the actuators uring transients will increase the combine actuator authority an can improve the close loop banwith of the mixture control. All observations show that some Variable Valve Timing (VVT) flexibility is necessary for controlling the mixture conitions at IVC [9], []. For example early Exhaust Valve Closing (eevc) an late Intake Valve Opening (livo) enable internal EGR with high temperature trappe resiuals, which also alleviates the preheating nee [4]. Valve lift, mm Crank Angle Degrees, Deg ATDC Fig.. Exhaust, intake an rebreathing valve profiles In this work we concentrate on a relatively inexpensive VVT technique whereby the exhaust valve opens uring the intake stroke. This aitional valve event, also known as rebreathing, is shown in Fig.. The lift of the exhaust valve uring the rebreathing event is the primary mech- rbl=3 rbl= rbl= rbl=4

2 HCCI MVM, RAUSEN ET AL: SUBMITTED TO ASME J-DSMC anism for control of the hot resiuals (iegr). A conventional EGR valve allows control of the external Exhaust Gas Recirculation (eegr) an thus the col fraction of the inert mass trappe at IVC. We also consier the potential use of spark to allow for seamless transition from HCCI to SI moe. The performance variables are the air-to-fuel ratio (AFR) at the exhaust tailpipe an the Location of Peak Pressure (LPP). We assume a wie range, heate, an fast Exhaust Gas Oxygen (EGO) sensor for AFR measurements, AF R EGO, in the exhaust manifol. We also assume that an in-cyliner pressure sensor an appropriate signal processing [] is reaily available that can supply accurate measurements of the start of combustion timing θsoc m an the timing of the location of peak pressure θlp m P that typically correspons to the crank-angle egrees of % burnt gas (θ CA ). In summary, we assume that accurate measurements of our performance variables will be available for control implementation. Exogenous Inputs Actuator Signals N w f σ u egr u rbl intake manifol Cyl exhaust manifol AFR SOC LPP or θca Performance Variables an Measurements Fig.. Definition of input output HCCI engine signals The control problem that this moel aresses is as follows. For a given engine spee N an uring step changes in fuel W f, coorinate the rebreathing valve lift u rbl,an the EGR valve u egr for air-to-fuel ratio (AFR), timing of start of combustion (SOC) an location of Peak Pressure (LPP) (or θ CA ) control. Exogenous Inputs w =[W f,n] Actuator signals u =[u egr,u rbl,σ] Performance variables z =[AF R, SOC, LP P ] Measurements y =[AF R EGO,θSOC m,θm CA ] () The input output signals are shown in Fig.. Note here that we consier engine spee as a system parameter that can be potentially treate as another exogenous signal. Engine spee, ue to its effects on EGR amount an available uration for combustion [4], shoul also be taken into account in the HCCI moel. Publishe experimental results [], [], [7] show large eviations of combustion timing uring changes in spee even uring close loop control. Moreover, prior analytical work in [4] has shown unstable behavior in the spee ynamics of an unthrottle VVT engine. Thus, we anticipate substantial challenges associate with spee changes in the future. II. Moel Structure This paper presents a physics-base parametrization of the HCCI behavior. The MVM ynamical behavior is associate with (i) states representing the mass composition an pressures (or temperature through the ieal gas law) in the intake an exhaust manifol volumes an (ii) the elay between cyliner intake an exhaust processes. The cyliner is moelle as a pump (see Fig. 3 as compare to Fig. ) base on (a) cycle-average cyliner flows an (b) temperature out of the cyliner (cycle-sample exhaust runner temperature) T er. The main parameters of the MVM are epicte in the schematic iagram of Fig. 3. The intake manifol is referre to as volume, the exhaust manifol volume as volume an the cyliner as volume c. Variables associate with ambient conitions are enote with subscript. States or variables associate with masses at volume x are calle m x an those associate with pressures are calle p x. To inclue the relevant ynamics ue to changes in mixture compositions, inert gas fraction i x at volume x is efine as i x = mass of inert gas in x total mass in x = mi x m x () where m i x is the mass of inert gas at volume x. The term inert gas refers to the proucts of combustion (other than air) that are in the volumes ue to EGR (external EGR, eegr) or resiuals (internal EGR, iegr). Since the HCCI engine operates lean, both the flow through the EGR valve an the rebreathe resiuals contain air. Note that the lean combustion allows us to assume that all fuel injecte is burne uring combustion, an thus we can keep track of the mixture composition by accounting for three components, namely: air, fuel, an inert gas. intake manifol m W u egr W u rbl i W c W c W W W f W c T er c (conitions in (elay) exhaust runner) i er exhaust manifol Fig. 3. Schematic iagram an notation for the mean value moel. A escription of the moel s eight ynamic equations, represente by five state equations an three elays, is presente in section IV. The five moel states efine by ifferential equations are shown in rectangular boxes. Flows use to calculate the state equations are also epicte in this figure accoring to the notation W xy where x is the source of the flow an y is the sink. The exhaust flow, W c, from cyliner to exhaust is consiere as a elaye sum of the flows into the cyliner. The other two elaye states correspon to the exhaust runner gas temperature an inert gas fraction (T er an i er, respectively). The MVM is evelope an parameterize using steaystate test ata collecte from a single-cyliner engine at

3 HCCI MVM, RAUSEN ET AL: SUBMITTED TO ASME J-DSMC 3 the General Motors (GM) Corporation. The experimental set-up is escribe in the next Section. Rather than consiering the combustion process as ynamic on a crankangle-resolve timescale, it is instea consiere as a series of causal relations between the conitions at Intake Valve Closing (IVC) an Exhaust Valve Opening (EVO). The combustion moel then provies the composition an temperature of the gas that is exhauste an fe back to the cyliner through eegr an iegr. This recirculation of exhaust gas from cycle to cycle constitutes an internal feeback from the Manifol Filling Dynamics (MFD) through the HCCI combustion an back to the MFD. The integrate moel, shown in Fig. 4 captures both the steaystate relations between the inputs an outputs an their ynamical evolution. The moel is accurate for ynamics slower than the cycle perio, or those below ω v ra/sec where N is in rev/min. u rbl u egr Wf x o Manifol Filling Dynamics MFD (states, x) W c (t-τ), T er, i er AFR c, p ivc, T ivc, m c, i c, p W c (t) Engine Cycle Delay HCCI Combustion Moel T b, i b AFR & AFR EGO θ CA = Nπ Fig. 4. The integrate mean value moel, consisting of Manifol Filling Dynamics (MFD) an HCCI combustion moel. III. Experimental Set-up The experimental ata use to evelop the mean value moel was collecte at steay state operating conitions over a range of spees an loas. The experiments were performe on a single-cyliner engine connecte to a ynamometer. The engine has an 86 mm bore an a 94.6 mm stroke. The isplacement volume is. liters. The cyliner hea has four valves an a pent-roof combustion chamber. A spark plug was mounte in the cyliner hea but was not activate uring these experiments. A flat-top piston was use with valve cutouts esigne for spin-free operation of both intake an exhaust valves as long as the maximum valve lift is kept below 4 mm. This was necessary for the fully flexible valve actuation system use in this work. The compression ratio use in the experiments was 4. Air flow to the engine was measure with sonic nozzles an two large plenums were use to amp the pressure pulsations in the intake. The plenums were equippe with heaters so that the air coul be pre-heate as require to 9 o C. Fuel flow was measure with a Pierburg PLU 3B flow meter. Exhaust gas recirculation (EGR) was mixe with the fresh air an fuel mixture upstream of the engine in the first intake plenum. The EGR mass flow rate was controlle manually with a ball valve. The oil an water temperatures were controlle with external heat exchangers an maintaine at 9 o C for all of the experiments. Cyliner pressure was measure with a Kistler 6 pressure transucer. The transucer was locate at the rear of the combustion chamber along the axis of the pent-roof. The pressure transucer signal was amplifie with a Kistler 4E charge amplifier. Crankshaft position was measure with a Dynapar crankshaft encoer, an a one pulse per cycle signal was obtaine with a hall-effect sensor to etect camshaft location. Intake manifol pressure was measure with a Sensotec strain gage absolute pressure transucer, an the cyliner pressure was pegge to the intake manifol pressure at the bottom of the intake stroke. Cyliner pressure ata was recore using the MTS-DSP Avance Combustion Analysis Program (ACAP) that calculates performance parameters such as Peak Pressure an location of peak pressure in real time. Since the engine is operate with exhaust rebreathing, the amount of resiual gas within the cyliner has to be estimate to provie the steay-state ata for the total-mass an the resiual trappe in the cyliner. A simple filling moel was use base on the partial pressure of the intake mass an the exhaust gas temperature in the exhaust runners to estimate the resiual mass within the cyliner. Temperatures throughout the cycle are calculate using the ieal gas law an the estimate trappe mass. These temperatures are estimate to be accurate to within +/- %. Stanar heat release analysis was use to etermine burn locations uring combustion. IV. Manifol Filling Dynamics (MFD) Base on the assumption of an isothermal intake manifol with T = 9 egrees C (363 K), two states are sufficient to characterize the intake manifol: the total intake manifol mass, m, an inert gas fraction, i : t m = W + W W c t i = W i + W (i i ). m The ieal gas law is use to relate the intake manifol pressure p to the mass by p = m V RT where V is the intake manifol volume. The thermoynamic constants use here, in (4) below, an later are the ifference of specific heats at constant pressure an constant volume (R, kj/(kg K)) an the ratio of these specific heats (γ). The epenence of these variables on the inert gas fraction has been neglecte. The irection of all the flows W in an out of the intake manifol are shown in Fig. 3. We assume here that (p <p <p ) so that all the flows through the valves an orifices are ue to the pressure ifference between the volumes an the flow from the intake manifol to the cyliner W c is a force flow ue to the cyliner pumping characteristics (crank rotation an piston motion). Three states are introuce to represent the gas filling ynamics in the exhaust manifol: mass, m, pressure, p, an inert gas fraction, i. The evolution of the gas properties in the exhaust manifol is represente by the (3)

4 HCCI MVM, RAUSEN ET AL: SUBMITTED TO ASME J-DSMC 4 following equations: t m = t i = t p = W c W W W c W c (i er i ) m γr ( ) W c Ter (W + W + W c )T, V where V is the volume of the exhaust manifol. The temperature of the gas entering the exhaust manifol is given by T er = T er T er where T er is a temperature rop of 7 C, base on test ata, from the exhaust runner temperature (T er ). The ieal gas law is use again to relate the temperature to the pressure an mass values: T = p V /(Rm ). W c is the average mass flow rate from the cyliner to the exhaust manifol which is the elaye cycle-sample (implemente as cycle-triggere) total flow into the cyliner: (4) W c (t + τ) =W c (t)+w f (t)+w c (t). () Since gas exhauste from one cycle is rawn back into the cyliner uring the rebreathing process, thereby affecting the subsequent cycle, elays are introuce to account for the temperature T er, an inert gas fraction, i er, of the mass flow through the exhaust runner: T er (t + τ) =T b (t) (6) i er (t + τ) =i b (t) (7) where T b an i b are the temperature an inert gas fraction, respectively, of the exhaust gas as it unergoes a blowown process from the cyliner into the exhaust runner. These quantities are calculate in the last phase of the combustion moel, presente in Sec. VII-C. Again, τ represents the cycle elay impose by the engine s cyclic behavior. Note here that the ifferential equations (3)-(4) can be iscretize using the Euler s metho on an interval equal to the engine cycle. For higher fielity we leave the manifol filing ynamics of Eq. (3)-(4) in the continuous-in-time omain an interface with the iscrete-in-time cyliner elay ylamics of Eq. ()-(7) with a sample an zero-orer hol (ZOH). The flows W xy from volume x to volume y are base on an orifice flow equation ([], Appenix C). The EGR flow W an in particular the effective flow area C A egr (u egr ) is a function for the EGR valve angle u egr. The flows associate with the cyliner are efine in the next section. V. Cycle-Average Cyliner Flow The mean flows into the cyliner, W c an W c are calculate W c = n c( x r ) m c W f τ W c = n cx r (8) m c τ where n c = is the number of cyliners, m c is the trappe cyliner mass at IVC (erive in the next section), W f is the mean fuel flow rate into all of the cyliners an x r is the mass fraction of internal (higher temperature) resiual gases at θ ivc ([] p. ). For the system s fixe intake valve closing angle, θ ivc, an constant intake manifol temperature, T,thex r is parameterize with the following expression: x r = α ( + κ p κ p κ Ter )(u rbl + α u rbl + α 3 u 3 rbl) (9) }{{} C A rbl where all the α an κ coefficients have been ientifie using experimental ata an simulations of a GM proprietary engine moel with crankangle-resolve flows as shown in the specific example of Fig. for u rbl = 3 mm. W (g/s) P (kpa) Lift (um) P c AFR Pamb&Pamb: RBL: EGR:. Wf:.9 FLOWS W EVP W c W crank angle egrees, =compression TDC IVP RBP W c W c W c W W P c IVP EVP RBP Fig.. Cyliner flow an other crankangle-resolve variables. A comparison of regresse an experimental cycleaverage test values for the estimate flows is shown in Fig. 6. Increasing rebreathing lift correlates with a larger value of x r, but the sensitivity of x r to u rbl ecreases as the rebreathing lift actuator approaches its maximum value of 4 mm as shown also in Fig. 6. In essence the rebreathing lift acts like vanes that throttle the flow through the pump -like cyliner. Note that resiual gas fraction, x r in the cyliner at IVC, as efine in the preceing paragraphs, is istinct from the inert gas fraction in the cyliner, i c, which is calculate below, in (). These two quantities serve ifferent roles. Resiual gas fraction, x r, efines the effect of the mean value moel states, x, an the rebreathing lift, u rbl, on the relative magnitues of the mass flows, W c an W c, into the cyliner. Inert gas fraction in the cyliner, i c, tracks the aggregate percentage of inert gases from these two sources. VI. Conitions at Intake Valve Closing (IVC) The cyliner pressure at IVC is approximate well as a linear function of p : p ivc = β + β p. () Given x r from (9), the charge temperature at IVC is calculate as the mass-weighte average of the temperatures

5 HCCI MVM, RAUSEN ET AL: SUBMITTED TO ASME J-DSMC W, g/s CArbl test moel urbl W, g/s Fig. 6. Valiation of preicte mean cyliner flows of the flows which contribute to the trappe mass m c : T ivc m c = T ( x r )+T er x r = p ivcv ivc RT ivc. W c W c () The resiual gas fraction, x r, also facilitates straightforwar expressions for the remaining conitions at intake valve closing that will be require by the combustion moel: W c i c =( x r ) i + x r i er () W c + W f AF R c = ( i )W c +( i er )W c W f (3) VII. HCCI Combustion Moel If complete an lean combustion is assume, the equation for i b (4) is unaffecte by the combustion process an epens only on two of the conitions at IVC: i c an AF R c. i b = AF R s + AF R c + ( i c)+i c (4) where AF R s is the stoichiometric air-to-fuel ratio. Similarly, the air-to-fuel ratio, AF R EGO, from an exhaust gas oxygen sensor with time constant τ EGO is calculate from i : t AF R EGO = (AF R AF R EGO ) τ EGO AF R = i + AF R s. i () This expression is equivalent to an algebraic rearrangement of the expression for F e (i here) as a function of r e (AF R here) in []. A simplifie combustion moel provies the remaining unefine variables, namely, the exhaust blowown temperature, T b, an the performance variable, θ CA as a function of T ivc an p ivc. The moel consists of five sequential phases: (i) a polytropic compression that leas to start of combustion (SOC) through autoignition at, (ii) a combustion uration that etermines an effective θ CA, preceing (iii) a simulate instantaneous heat release, (iv) a polytropic expansion, an (v) an aiabatic blowown that yiels T b. These phases are epicte in Fig. 7, where the actual (soli line) an moelle (otte line) pressure an temperature trajectories are shown. Pressure, kpa Temperature, K 4 3 Actual(soli) an Moel(otte) Pressure an Temperature Traces Phase Phase 6 Phase 4 ATDC θ EVO θ IVC θ SOC θ C Phase 4 Phase 3 Fig. 7. Actual (soli) an estimate (otte) pressure an temperature traces in cyliner, from before IVC to after EVO. Calculate moel values are inicate with circles. A. Phase : Intake Valve Closing to Start of Combustion Motivate by [], [], [], the Arrhenius integral [] is a measure of the mixture reactivity an preicts the SOC timing, θ SOC : AR( ) = where AR(θ) = θ θ ivc RR(ϑ)ϑ (6) an RR(ϑ) =Ap n c (ϑ)exp( E a R a T c (ϑ) ) (7) where T c an p c are the cyliner temperature an pressure, respectively, uring compression, A is a scaling constant, E a is the activation energy for the autoignition reaction an n inicates the reaction s sensitivity to pressure. We then efine v ivc (ϑ) =V c (ϑ ivc )/V c (ϑ) with V c (ϑ) the cyliner volume at crankangle ϑ, an assume a polytropic compression process from IVC to SOC with coefficient n c.the Arrhenius integran is thus simplifie RR(ϑ) =Ap n ivcv ncn ivc (ϑ)exp( E av n c ivc (ϑ) ) (8) R a T ivc an the coefficients A, E a an n are selecte using = θ CA. With efine by (6)-(8), the charge temperature at SOC is T soc = T ivc v (nc ) ivc ( ). The resulting preictions of an T soc are shown in Fig. 8. B. Phase : Combustion Duration We efine the HCCI combustion uration θ as the crankangle egrees between % an 9% fuel burnt. The

6 HCCI MVM, RAUSEN ET AL: SUBMITTED TO ASME J-DSMC 6 (ml) 4 Moel Accuracy for Preiction of SOC 3 θ CA θ CA θ CA9 θ c fuel sweep k=f(,, ) e=f(,k): θ vs. fuel, mg/cycle 4 T soc θ soc fuel sweep iegr/eegr sweep eegr sweep no eegr high AFR T soc Fig. 8. Plots showing preiction accuracy for an T soc. heat release ue to combustion is consiere to occur instantaneously at θ c [8]: θ c = + θ ( ) where θ = k (T soc ) ( /3) (T m ) /3 Ec exp 3R c T m an T m = T soc + e( i c ) T Q LHV finally T = c v ( + AF R c ). (9) The activation energy, E c, represents an effective threshol at which the combustion reaction occurs an is assume to be 8 kj/mol. The parameter e represents an averaging of the release thermal energy uring combustion. The parameter k relates to the effective uration for combustion, θ, uring which no heat is release. As uration lengthens, a smaller proportion, e, of the release heat contributes to an effective mean temperature, T m uring the combustion. After the combustion uration, instantaneous heat release occurs at the combustion location, θ c. Both of the parameters k an e have been optimize to match the actual burn uration from % to 9%. Then the LPP that we assume here coincies with the crankangle of % burnt fuel is calculate as θ CA = +. θ. Since e is a measure of the average temperature uring combustion, a lower value of k correspons to a shorter combustion, which also correspons to a higher value for e. The combinations of inepenently optimize values of k an e results in a single relation () for which the value for e is uniquely etermine by the value for k: e = a + a k () This yiels a physically-base combustion uration moel whose variations over the operating range can now be capture with a single parameter, k. Optimize values of k are then foun that precisely reprouce the combustion uration for each set of test ata. These optimize values for k can then be parametrize by a function of : k = b + b + b θ soc. () The accuracy of these preictions can also be seen in Fig. 9. ATDC fuel, mg/cycle Fig. 9. Plot showing the impact of the parametrize values for k on the burn uration for the fuel sweep ata. C. Phase 3: Instantaneous Heat Release The charge temperature just before the combustion can be calculate by T bc = T ivc v (nc ) ivc (θ c ) an the corresponing pressure as p bc = p ivc v nc ivc (θ c). Assuming an instantaneous release of all of the fuel s heat, the charge temperature an pressure after the combustion are given by: T ac = T bc +( i c ) T an p ac = p bc T ac /T bc () D. Phase 4: Polytropic Expansion To account for the polytropic expansion with coefficient n e, a volume ratio analogous to v ivc (ϑ) is efine as v c (ϑ) = V c (ϑ c )/V c (ϑ) so that the charge temperature an pressure at EVO is T evo = T ac v c (ne ) (θ evo ) an p evo = p ac vc ne (θ evo ). (3) E. Phase : Exhaust Blowown After the exhaust valve opens, the temperature of the exhaust flow leaving the cyliner can be consiere as T b = T evo p p evo n e n e + T b (4) ue to the aiabatic expansion of the gas own to the exhaust manifol pressure, p. T b represents a temperature ifference between a pure aiabatic blowown temperature an the actual measure temperature in the exhaust runner. The moel provies a minimal mathematical representation of the physical combustion process as well as a basis function base on which the six parameters, namely, A, E a, an n from (8) an k, E c an e from () can be tune to fit all available ata in the future. The an θ CA preictions are shown in Fig.. The T b preictions of the HCCI Combustion moel are shown in Fig.. In the next section, we review the results of integrating the flow-base state equations of Sec. IV with the instantaneous combustion moel presente in this section.

7 HCCI MVM, RAUSEN ET AL: SUBMITTED TO ASME J-DSMC 7 ATDC 3 θ CA θ CA θ CA9 θ c fuel sweep k=f(, θ,θ ) e=f(,k) fixe Arrh: θ vs. fuel, mg/cycle soc soc fuel, mg/cycle Fig.. Comparison of integrate combustion moel preictions of an resulting preictions of θ CA with test ata for fuel sweep. Preicte T b (K) Accuracy of T b Preiction From Moel Starte at IVC fuel sweep iegr/eegr sweep eegr sweep no eegr high AFR Exhaust Runner Temperature (K) Fig.. Plot showing the accuracy of preicting the exhaust runner blowown temperature by using all five phases of the moel from conitions at intake valve closing. VIII. Valiation The full control-oriente HCCI engine moel is constructe by combining the manifol filling ynamics of Section IV with the simplifie combustion moel presente in section VII as shown in Fig. 4. Although the accuracy of the MFD an the HCCI moel has been emonstrate separately in the previous sections, we assess here the propagation of the iniviual errors ue to the intrinsic feeback structure of the HCCI engine. Specifically, the valiation of the integrate moel is important because the temperature at the en of the combustion (prouct of the HCCI combustion moel) affects the thermoynamic state (pressure, temperature) of the next combustion event through the manifol filling ynamics (MFD moel). The high ilution level in HCCI engines increases the significance of this internal feeback that generally exists to a smaller extent in conventional spark-ignition an compression-ignition internal combustion engines. The moel is valiate after the calibration of the orifices C A, C A,anC A using ambient conition p = kpa. Setting a value of C A is equivalent to setting the appropriate value for the input, u egr. The remaining input, u rbl, an the fueling rate, W f are set irectly accoring to the constant commane values from the tests. Note here that the experimental ata are recore in a ynamometer facility with force inlet flow that effectively ecouples the inlet flow (W ) from the intake manifol gas state (ensity an pressure). Simulations uner these laboratory-like conitions can be achieve by employing unequal atmospheric pressures of p = KPa an p = KPa connecte to the intake an exhaust manifols of the HCCI moel, respectively. These conitions show very goo agreement between the moel an the experimental ata [9]. In the results reporte here we simulate the moel using a single atmospheric supply pressure of p = kpa. Although these conitions preclue vali simulation of the higher fueling rate ata, we report them here because they emonstrate the realistic operating conitions of an actual unthrottle engine. The steay-state flows are shown in Fig.. Due to the light throttle conitions a eviation in p result in a large eviation in W. The maximum error appears in the case of the mg/cycle. Preictions of T ivc show goo accuracy, with the mg point showing the greatest overpreiction, as shown in Fig. 3. System in/out Flows, g/s Internal Flows, g/s. Moel Flow Valiation W. W W W W c. W c W c W c. W W fueling rate, mg/cyc Fig.. Actual an simulate flows for the integrate combustion moel using ambient pressure of KPa connecte to both intake an exhaust manifols. Finally, consistent with the reuce W for the mg/cycle point shown in Fig., the preiction of AF R at this operating point is lower, 9. versus for the actual test ata. This iscrepancy in AF R preiction is shown in Fig. 4. Also, the higher value for T ivc leas to a preiction of earlier an performance variable θ CA. IX. Conclusions We present a simple mean value moel an valiate it in steay-state. Despite some iscrepancies in the integrate moel steay-state preictions, the trens in flows, states, conitions at IVC, an performance parameters are reprouce. Specifically, the moel captures:

8 HCCI MVM, RAUSEN ET AL: SUBMITTED TO ASME J-DSMC 8 T ivc (K) p ivc (KPa) T er (K) T ivc T ivc Moel Conitions at IVC an T er Valiation p ivc p ivc T er T er Fuel (mg/cyc) Fig. 3. Actual an simulate conitions at IVC, T ivc an p ivc an exhaust runner temperature, T er. AFR egrees ATDC 9 Moel Performance Parameter an Measurement Valiation AFR AFR EGO AFR θ soc θ soc θ CA θ CA Fuel Rate (mg/cyc) Fig. 4. Actual an simulate performance parameters an relate measurements. the intake an exhaust manifol flows an the effects of the external EGR (flow from exhaust manifol to intake manifol) an internal EGR (rebreathing of exhaust gases). the moulating effects of the actuators, u egr an u rbl. the impact of the system state variables an actuators on the performance variable, conventional AF R (inlet mass air flow rate/fuel flow rate), the tailpipe measure value, AF R EGO, an the actual in-cyliner air-fuel ratio, AF R c. the impact of the system state variables an actuators on the performance variable, θ CA, crank angle of % fuel burne (correspons to location of peak pressure (LPP). The crank angle for start of combustion,, is also calculate. The moel inclues also simple ynamics, namely, 3 continuous manifol states, 3 iscrete cyliner states, sensor lag, but the existing experimental setup oes not allow valiation of transient behavior. The moel can provie the basis for ynamical analysis an feeback control esign of the HCCI engine. X. Acknowlegments We thank Sharon Liu, Jason Chen an Man-Feng Chang of General Motors Corporation, George Lavoie of the University of Michigan, an Paul Ronney of the University of Southern California. References [] Agrell F. Angstrom H.-E., Eriksson B., Linery J., Integrate Simulation an Engine Test of Close Loop HCCI Control by ai of Variable Valve Timing, SAE paper [] Au M. Y., Girar J. W., Dibble R., Aceves S. V., Martinez-Frias J., Smith R., Seibel C., Maas U.,.9-Liter Four-Cyliner Engine Operation with Exhaust Gas Recirculation, SAE paper [3] J. C. Cantor, A Dynamical Instability of Spark-Ignite Engines, Science, Vol 4(464), pp June 4, 984 [4] Daily J.W. Cycle-to-cycle Variations: a chaotic process? Combustion Science an Technology 7, 49-6,988. [] Douau A. M. an Eyzat P., Four-Octane-Number Metho for Preicting the Anti-Knock Behavior of Fuels an Engines, SAE paper 788. [6] Ewars S. P., Frankle G. R., Wirbeleit F., Raab A., The Potential of a Combine Miller Cycle an Internal EGR Engine for Future Heavy Duty Truck Applications, SAE paper 988. [7] Fivelan S. B., Assanis D., A Four Stroke Homogenous Charge Compression Ignition Engine Simulation for Combustion an Performance Stuies, SAE paper [8] C. Ji, P. D. Ronney, Moeling of Engine Cyclic Variations by a Thermoynamic Moel, SAE [9] Martinez-Frias J., Aceves S. M., Flowers D., Smith J. R., Dibble R., HCCI Control by Thermal Management, SAE paper [] Fuerhapter A., Piock W.F., Frail G.K., CSI- Controlle Autoignition the best solution for the fuel consumption versus emission traeoff?, SAE paper [] J. Grizzle, J. Bucklan an J. Sun, Ile spee control of a irect injection spark ignition stratifie charge engine, Int. J. of Robust an Nonlinear Control, ()pp.43-7, Sept. [] Heywoo, J.B., Internal Combustion Engine Funamentals, McGraw-Hill, Inc., 988. [3] Hiltner J., Agama R., Mauss F., Johansson B., HCCI Operation With Natural Gas: Fuel Composition Implications, ASME conference, Sep, Peoria, Illinois, USA [4] Kontarakis G., Collings N., Ma T., Demonstration of HCCI Using a Sinlge Cyliner Four-stroke SI Engine with Moifie Valve Timing, SAE paper [] Livengoo, J.C., Wu, P.C. Correlation of Autoignition Phenomena in Internal Combustion Engines an Rapi Compression Machines, Fifth Symposium on Combustion, 9. [6] Najt P., Foster D., Compression-Ignite Homegeneous Charge Combustion, SAE paper [7] Olsson J. O., Tunestal P., Johansson B., Close Loop Control of an HCCI Engine, SAE paper --3. [8] Olsson J. O., Tunestal P., Johansson B., Fivelan S., Agama R., Willi M., Assanis D., Compression Ratio Influence on Maximum Loa of a Natural Gas Fuele HCCI Engine, SAE paper - -. [9] Rausen, D. J. A Dynamic Low Orer Moel of Homogeneous Charge Compression Ignition Engines, MS Thesis, Mechanical Engineering, The University of Michigan, Sept. 3. [] Ryan III T.W., Callahan T. J., Homogenous Charge Compression Ignition of Diesel Fuel, SAE paper 966. [] Sellnau M. C., Matekunas F. A., Battiston P. A., Chang C.- F., Lancaster D. R., Cyliner-Pressure-Base Engine Control Using Pressure-Ratio-Management an Low-Cost Non-Intrusive Cyliner Pressure Sensors, SAE paper [] Stanglmaier D. S., Roberts E., Homogenous Charge Compression Ignition (HCCI): Benefits, Compromises, an Future Engine Applications, SAE paper [3] Thring R. H., Homegeneous-Charge Compression-Ignition (HCCI) Engines, SAE paper [4] Y. Wang, A. Stefanopoulou an R. Smith, Inherent Limitations an Control Design for Camless Engine Ile Spee Dynamics, Int. J. of Robust Nonlinear Control, ()p.3-4, Sept..

9 HCCI MVM, RAUSEN ET AL: SUBMITTED TO ASME J-DSMC 9 [] Willan J., Niebering R.-G., Vent G., Enerle C., The Knocking Synrome - Its Cure an Its Potential, SAE paper