A Mixed Mean-Value and Crank-Based Model of a Dual-Stage Turbocharged SI Engine for Hardware-In-the-Loop Simulation

Transcription

1 00 Aerican Control Conference Marriott Waterfront, Baltiore, MD, USA June 30-July 0, 00 hb9. A Mixe Mean-Value an Crank-Base Moel of a Dual-Stage urbocharge SI Engine for Harware-In-the-Loop Siulation Xiaojian Yang an Guoing G. Zhu Abstract: Close loop cobustion control of internal cobustion s becoes a necessity to eet toay s fuel econoy an eission requireents. Harware-In-the-Loop (HIL) siulation of systes plays an iportant role in eveloping an valiating real-tie control systes. raitionally the oels use for the HIL siulation are so-calle ean value ones that siulate average operational behaviors, while the evelopent an valiation of close loop cobustion control require crank-base (or event base) feeback signals, such as in-cyliner pressure signals, in an HIL siulator. In this paper, a ixe ean valve an crank-base oel was evelope for a ual-stage charge. his oel contains both cycle-to-cycle cobustion inforation an average ynaics such as air flow, spee, torque, etc. G-ower oel was evelope to obtain calibrations for the Siulink real-tie oel built for the real-tie HIL siulator. I I. INRODUCION N orer to iprove fuel econoy an reuce eissions of internal cobustion (IC) s, any new technologies have been evelope an use in the past ecae that increase IC syste lexity. Aong these technologies, ownsizing using single or ual-stage chargers was propose in [] an [] for its faster transient response an ability to cover wie range of operating conitions []. Increasing ression ratio has also been use to increase theral efficiency [3]. In reference [4], a higher level of coole EGR (exhaust gas recirculation) approach is use to reuce puping loss an, especially to suppress s tenency to knock as a result of higher ression ratio. Close loop cobustion control (CLCC) using in-cyliner pressure or ionization current signals has also been use for MB (Minial avance for the Best orque) tiing control ([4] an [5]), knock etection an control [6], an cobustion stability control ([7] an [8]). here are two types of control oriente oels, ean value (MV) an crank base (CB) oels (e.g., these oels evelope using G-ower an WAVE). MV oels are wiely use in control syste research ([], [9], [0], [], an []) ue to their siplicity with low siulation throughput. he isavantage of the MV Manuscript receive Septeber 5, 009. his work was supporte in part by the U.S. Departent of Energy uner Grant DE-FC6-07N4375. X. Yang, an G. Zhu are with the Michigan State University, East Lansing, MI 4884, USA (yangxia@egr.su.eu an zhug@egr.su.eu, respectively). oel is that it oes not provie cycle-to-cycle characteristics such as in-cyliner pressure an ionization signals that have been wiely use for close loop cobustion control. On the other han, the CB oels are often of high lexity an not suitable for real-tie siulation. In orer to evelop an valiate the close loop cobustion control strategies for IC s, there is a nee for real-tie CB oels. In this paper, a ixe control oriente oeling schee is propose to eet the requireent of real-tie HIL siulations, where the flow ynaics is oele using ean value approach an cobustion characteristics are oele in a crank base fashion. he propose oeling schee is eonstrate for a.l three-cyliner with ual-stage chargers. For this oel, the air flow ynaics was oele using ean value technique; the fueling an torque were upate after the corresponing cyliner top ea center (DC); an the crank base in-cyliner pressure an ionization signals were upate every crank egree, where both in-cyliner teperature an pressure are generate base upon Wiebe function [9] an the ionization signal is generate base upon the Wiebe function an the generate pressure signal. he evelope real-tie oel was ipleente in a SACE base HIL siulator for eveloping an valiation of close loop cobustion control strategies that optiize fuel econoy with reuce eissions. In orer to generate calibrations for the evelope real-tie ixe MV an CB oel, a G-ower oel was also evelope an use to siulate various operational conitions. his paper is organize as follows. Engine configuration an paraeters of the target ual-stage charger are iscusse in section II. Sections III an IV present the atheatical equations of the MV an CB oels respectively. Integration of both MV an CB oels is escribe in section V. Steay state siulation results are valiate with G-ower ones an transient siulations are also conucte in section VI. Finally, conclusions an recoenations are inclue in section VII. II. ENGINE SRUCURE AND G-OWER MODELING Fig. shows our ownsize three-cyliner with coole EGR an ual-stage chargers. he H (high pressure) charger, connecte to the intake an /0/$ AACC 379

2 exhaust anifols, is saller than that of the L (low pressure) charger. Accoringly, the H ressor has a saller capacity of air ass flow rate than the L one. A bypass valve is parallel connecte to the H ressor to atch the air ass flow rate of both ressors. wo ines are equippe with solenoi controlle continuously ajustable waste-gates. An intake cooler is connecte between H ressor an intake anifol. Unlike traitional s, this utilizes intake throttles locate close to the three intake runners between the intake anifol an intake ports for iprove transient responses. he also features ual intake an exhaust valves with ual intake an exhaust variable valve tiing (VV) control. Both ca phases are ajustable in the range of 0 crank egrees. he is also equippe with ual fuel injection systes: port fuel injection (FI) an irect injection (DI), an can be operate with any blen of ethanol an gasoline. Fig. : Downsize configuration he geoetry iensions are liste below in able. he is still uner evelopent an a G-ower oel has been evelope. he siulation results are use as baseline for the HIL siulation of the evelope real-tie oel in this paper. able : Engine Specification araeter Moel value bore/stroke/con-ro length 83/73.9/3 ression ratio 3.5: intake valve/exhaust valve iaeter 3.4/.5 throttle iaeter 3 48 intake anifol/exhaust anifol volue.0l/0.57l inertia of H-stage charger shaft 3.807E-6kg. inertia of L-stage charger shaft.7e-5kg. III. MEAN VALUE ENGINE MODELING his section escribes atheatical subsyste oels for those subsystes whose average ynaic behaviors are to be use for control, even though these subsyste ynaics are functions of reciprocating phenoenon. All paraeters an variables use in these oels escribe in this section are functions of tie t. A. Valve Moel he valve oel, escribe below, is use for intake throttle, H waste-gate, L waste-gate, an EGR valve since these actuators share sae physical characteristic. Assuing that the spatial effects of the connecting pipes before an after these valves are neglecte an their theroynaic characteristics are isentropic expansion, the governing equations of the valve oel are: valve C ( ) A( ) up R x( x), if x x, if x () where C is the valve ischarge coefficient; θ is the valve opening angle; R is the gas constant; A is the valve open area; up an up are the valve upstrea pressure an teperature; own is the valve ownstrea pressure; an valve is the ass flow rate across the valve. Note that both C an A are functions of θ. B. Manifol Filling Dynaic Moel his oel is ainly use for the intake an exhaust anifol subsystes, inter-ressor an inter-ine pipes. he receiving behavior is assue to be an aiabatic process in these anifols; their theroynaic states are unifor over the entire anifol volue; an the anifol teperature is average over one cycle for this ean-value oel. hen the governing equation for the anifol filling ynaics is: t R ( t) (0) 0 V where is the anifol pressure; is the anifol teperature; V represents the anifol volue; an are the an air ass flow rates, respectively. C. Engine Respiration Moel A typical respiration forulation [9] is use, see below: R V N 30 Vc V Vc V V (5) where an are the ean pressure an teperature at intake anifol; is the ean pressure at exhaust anifol; V an V c are the isplaceent an the cyliner clearance volue, respectively; N is the spee in rp; κ is heat capacity ratio of the gas charge in cyliners; an is the air ass flow rate across cyliners. D. Crankshaft Dynaic Moel Base upon Newton s theory, assuing a rigi crankshaft, it can be erive as: brake loa N 60 J (6) where J is the rotational inertia of the crankshaft; up own up ( N t ) () (3) (4) 379

3 brake an loa are the brake an loa torques, respectively. Note that in future siulations, loa is generate by an ynaoeter oel controlle by a ID feeback control to aintain the esire spee. E. urbine an Copressor Moels he charger is oele using so-calle energy conservative equations base upon its steay state ressor an ine aps, which can be foun in [], [] an []. Notice that the ass flow rate (MFR) an shaft spee in the apping equations given below are in so-calle reuce for to ake the aps applicable for all conitions. Without this conversion, it woul require ifferent aps for each cobination of pressure an teperature, see [3]. Both ine an ressor ynaics are escribe below in equations (7) to (4), where an are either ine or ressor pressure an teperature; an are either ine or ressor pressure an teperature; N is the charger shaft spee in rp; an η enotes theral efficiency. ) urbine Mapping: urbine aps (f an f ) in equations (7) an (8) are use to calculate the reuce MFR an theral efficiency base on pressure ratio across the ine an the reuce shaft spee. he actual MFR can be calculate fro the reuce MFR. N f, (7) N f, (8) ) Copressor Mapping: Copressor aps (f an f ) in equations (9) an (0) are use to calculate the ressor pressure ratio an theral efficiency base on reuce MFR an reuce shaft spee. N f, (9) N f, (0) 3) eperature Calculation: he teperature of ine or ressor can be calculate base upon equation () using its teperature an pressure ratio across. () Notice that equation () assues isentropic gas expansion an the ressing process in either ine or ressor. However, the actual physical process is not isentropic, leaing to ore enthalpy reaining in the gas ue to high theral efficiency, which akes the teperature higher than that given by equation (), but the ifference is relatively sall. Siulation results in section VI confir this, an therefore, the assuption is acceptable. 4) urbine ower Calculation: he power generate by ine, enote as E, is calculate in equation () E C p () 5) Copressor ower Calculation: he power require to rive ressor, enote as E, is given in equation (3). E C p 6) ower Balance on urbocharger Shaft: IV. EVEN AND CRANK BASED MODELING his section iscusses the atheatical oels use to siulate the cycle-to-cycle varying an crank angle base variables of subsystes. All variables an paraeters iscusse in this section are either upate base upon cycle (k) or crank angle θ. hey are inepenent of tie t. A. Event-base Wall Wetting Dynaics he wall wetting phenoena of the FI fuel injection can be escribe in such a way that only part of the injecte fuel (β M inject, 0< β<) enters the cyliner while the rest of the fuel ((-β) M inject ) reains on the surface of the intake port an the back of intake valves [9]. hen the total fuel injecte into the cyliner consists of the fuel irectly injecte into the cyliner an the fuel vapor (α M resiue, 0< α<) fro fuel ass store fro previous injection. Wall wetting phenoenon leas to the ost iportant ynaics in FI fuel ass calculation, which affects transient perforance significantly [4]. he governing equation of the wall wetting ynaics is: M trap k M resiue k M inject k M resiue k M resiuek M k (5) inject where k is the inex representing cycle nuber; M trap is the quantity of fuel ass flowe into the cyliner; M resiue is the quantity of fuel ass left on the port an back of the intake valves; M inject is the aount of fuel injecte by the FI injector for the given cycle; coefficients α an β are functions of coolant teperature, spee, an anifol pressure. B. Event-base Engine Air-to-fuel Ratio he s gas exchange behavior introuces ynaics to the air-to-fuel ratio calculation, since a substantial part of the burne gas reains insie the cyliner, especially at low loa. his gas fraction carries the air-to-fuel ratio of the previous cycle to the current one. herefore, the air-to-fuel ratio is oel cycle-by-cycle below: ~ [ M fresh[ [ k ] M burnt[ [ M [ M [ (6) where ~ is the noralize air-to-fuel ratio efine below: (3) N E E J N t (4) where J is the rotational inertia of the ine shaft. fresh burnt 3793

4 ~ M [ M air fuel [ [ (7) λ is noralize air-to-fuel ratio of gas ixture insie cyliner after intake valve is close; an σ is stoichioetric air-to-fuel ratio of the fuel. Note that M fresh is the ass of fresh gas ixture charge into the cyliner, which is suation of fresh air charge ass M air an fresh fuel charge ass M fuel, an M burnt is burne gas reaining in the cyliner after exhaust valve closing. C. Crank-base In-cyliner eperature an ressure In-cyliner pressure signals are wiely use for close loop cobustion control of internal cobustion s ([5] an [5]), which otivates to generate real-tie in-cyliner pressure signals. Wiebe base MFB (Mass Fraction Burne) function [3], see equation (8), is use to construct the in-cyliner pressure signals. Ign a x b e (8) where θ is crank angle; θ Ign is the spark tiing; Δθ is the cobustion uration in crank angle; an a are calibration paraeters use to fit the shape of the actual MFB; he in-cyliner teperature an pressure are calculate using the following iteration equations when crank position is between intake valve closing (IVC) an exhaust valve opening (EVO) tiings: V( ) QLHV xb ( i ) xb ( ) i i ( i) ( i ) V( i) Cv( ) (9) V( i ) ( i) ( i) ( ) (0) i V( i ) ( i ) where V(θ) is the cyliner volue at crank angle ; η is the cobustion efficiency ue to heat loss across cyliner wall an hea; γ is the inertia gas fraction of the in-cyliner gas ixture; C v is the specific heat of in-cyliner gas ixture; Q LHV is the low heating value of the fuel. For crank position before IVC an after EVO, the intake anifol status an exhaust anifol status are use as the in-cyliner status respectively. Also, the ionization signal can be siulate base on the in-cyliner pressure signal. Ionization signal calculation is oitte ue to liitation of paper length. D. Event-base Engine orque Calculation For each cyliner, the calculations of IME ( IME ) an torque ( ) were ipleente every cycle, see the following equations. 79 i IME i i i v i0 () V V 60 N IME vn where n is cyliner quantity; v is the volue of each cyliner. V. SYSEM INEGRAION FOR HIL SIMULAION In this section, the ynaic equations presente in both () sections III an IV are ipleente into a Siulink oel for a ual-stage charge three cyliner shown in Fig.. he Siulink oel is then ipleente into a SACE siulation syste for HIL siulation. Fig. presents an overall architecture of the HIL siulation syste. Note that for siplicity, not all the signals an subsystes are inclue in the iagra. Fuel pulse Spark tiing hrottle uty Wastegate uty EGR valve uty Control Signal Measuring (DS-003 AD) (DS-500 DI) Fueling Air intake Mfuel[ Mair[ xegr boost boost ECU Ion/pressure generation Dynaoeter Cobustion & torque generation EGR Dual-stage charger Control Oriente Engine Moel (DS-005 CU) DC Crank Angle (θ) Iion(θ) N brake λ exhaust exhaust Fig. : Integrate syste oel in HIL environent Engine Signal Conitioning (DS-03 DA) (DS-400 DO) As shown in Fig., the Siulink oel is execute in real-tie at a fixe step (s for this stuy) in a SACE HIL siulator with a SACE DS-005 CU. Note that the fixe saple step only applies to the ean value subsyste oels. he event base subsyste oels are trigge internally an execute after each DC an the crank base signals, such as in-cyliner pressure an ionization signals, are upate every crank egree. Fig. 3: Siulate signals he outputs of the HIL siulation syste are ivie into both analog an igital ones. he analog signals are generate by a D/A boar (DS 03) of the SACE siulator an the igital signals, such as crank encoer an ca hall-effect position sensor signals, are generate using a SACE igital output boar (DS-400). he generate signals, incluing crank, ca, 3794

5 in-cyliner pressure an ionization signals are shown in Fig. 3 an are reaily to be use by real-tie controllers. he crank signal is generate by a high frequency pulse output port of DS-400 as a function of current spee. he crank signal is feeback to the igital input ports of DS-400 to generate interrupts to trigger a function call that generates the DC an ca positions an calculates in-cyliner pressure an ionization current signals. his crank angle base function has highest priority in the siulation. he igital signals (crank an ca signals), shown in the top of Fig. 3, are position inputs for the real-tie controller for crank position synchronization. VI. SIMULAION RESULS AND VALIDAION A G-ower oel was evelope base upon the configuration shown in Fig.. A series of G-ower oel siulations are perfore with ifferent spees an loas to calibrate the paraeters like a,, Δθ an η. he G-ower oel siulation results were also use as baseline to are with the HIL siulation results. A. G-ower Siulation Results Both full loa an half loa siulations were perfore for spees between 000 an 5000rp with a 500rp increent using the evelope G-ower oel to evaluate the perforance. In the siulations, soe actuation variables were set to be constant to ake siulation siple. hese actuator control variables are EGR flow rate (0%), intake an exhaust valve tiings (00 ADC an 00 BDC respectively). he fuel quantity was controlle in a close loop to aintain stoichioetric air-to-fuel ratio for all G-ower siulations. Engine spark tiing was ajuste to MB tiing for all siulations. he ual-stage charger was set as liste in able. able : Dual-stage charger setting for full/half loa siulation H Waste-gate L Waste-gate Bypass valve Engine spee ( ) ( ) ( ) (rp) Full Half Full Half Full Half he waste-gate an bypass valve positions were selecte to achieve best perforances while aintaining the stability of the ressor an systes. For instance, for the full loa siulations, the L ressor always reains within the surge an over spee liits of its ressor ap to aintain the best stable operation without aaging the associate ressor, see Fig. 4. Note that for this own size, high boost pressure is esire to achieve axiu torque output at full loa, an as a result, the L ressor tens to operate at the region close to its surge liit to have the best perforance possible. ressure Ratio surge liit Reuce Mass Flow Rate (kg/s.k 0.5 /ka) overspee liit Fig. 4: Operating status of L ressor for full loa siulation G-ower siulation is capable of proviing results over entire operational ap. Fig. 4 shows the ressor relate variables. For this paper, only liite paraeters an variables, such as IME (inicate ean effective pressure) an MA (intake anifol air pressure), are presente in next subsection to are with the HIL siulation results. B. Steay State erforance Correlation he steay state siulations of both full an half loa were also perfore using the HIL siulator. he operational conitions an its actuator control paraeters an variables are sae as these use for G-ower siulations, shown in able. he HIL siulation results were are with the corresponing ones of G-ower siulations. Fig. 5 shows the correlations of torque, IME, MA an EM (exhaust anifol pressure). Goo correlations were foun for ost of the siulate conitions over spee an loa ranges. orque of HIL (N.) MA of HIL (bar) orque of G-ower (N.) 4 3 Half loa MA of G-ower (bar) EM of G-ower (bar) Fig. 5: Correlation plots of the HIL an G-ower siulation results IME of HIL (bar) EM of HIL (bar) IME of G-ower (bar) 4 3 Full loa (WO) C. ransient erforance of HIL Siulation wo transient siulation responses were perfore using the HIL siulator, one with feeforwar fuel control an the other without. Both siulations utilize close loop fuel control with a ID (proportional, integral, an erivative) control strategy. he transfer function of the feeforwar controller is: M FF MA s s g N s s (3) 3795

6 where g is a function of spee, ipleente as a lookup table, τ is tie constant of feeforwar fuel control. he control syste block iagra with both feeforwar an close-loop fuel control is shown in Fig. 6. he transient fuel pulse outputs of feeback an feeforwar controls are presente in Fig. 7. Fig. 6: Control architecture for transient response siulation Note that except for the fuel control, all the other control paraeters reaine unchange for both siulations. Engine spee was at 500rp with 0% throttle an MB spark tiing. he control reference of the air-to-fuel ratio was set at stoichioetric ratio when a step throttle input of 90% to WO (wie open throttle) was applie. As a result, the starte switching fro partial loa to full loa conition. Engine torque (N.) Relative air-to-fuel ratio Fuel pulse with (s) with feeforwar w/o feeforwar with feeforwar.4 w/o feeforwar total feeback feeforwar ie (s) Fig. 7: ransient perforance of HIL siulation he corresponing ynaic responses are also presente in Fig. 7. Feeforwar fuel control provies aitional fuel output to iprove transient response. With feeforwar fuel control, the air-to-fuel ratio response settles within secon, while without feeforwar fuel control it takes about 4 secons. he corresponing transient torque settling tie ecreases fro. secons without feeforwar to.9 secons with feeforwar, which is significant. In Fig. 7, with feeforwar fuel control, the air-to-fuel ratio is aintaine close to the reference uring the transient tie since the feeforwar fuel control provies aitional fuel base on both MA an spee. Fro Fig. 7 it can be observe that even with feeforwar control, uring the transition operation there exists an ipulse of the relative air-to-fuel ratio, which inicates that lean cobustion occurs right after the step throttle an last for a few cycles. his is ainly ue to the special architecture. As entione in section II, the throttle locates between the intake anifol an hea. he lack of the volue between throttle an intake valve leas to a rapi increent of s voluetric efficiency when the throttle is suenly opene. VII. CONCLUSIONS his paper presents a ual-stage charge oel for HIL siulation using ean value, event an crank base ethos. he steay state HIL (Harware-In-the-Loop) siulation results have been are with the corresponing G-ower ones an eonstrate satisfactory correlations. he transient HIL siulation results are also presente an will be valiate using test ata in future. he real-tie HIL oel provies a tool for eveloping close loop cobustion control strategy evelopent before the actual is available. REFERENCES [] A. Chasse, Double Stage urbocharger Control Strategies Developent, SAE echnical aper , 008. [] S. Saulnier an S. Guiliain, Coputational Stuy of Diesel Engine Downsizing using wo-stage urbocharging, SAE echnical aper , 004. [3] J. B. Heywoo, Internal Cobustion Engine Funaentals, McGraw-Hill, Inc., 988. [4] G. G. Zhu, I. Haskara, an J. Winkelan, (October 004) MB iing Detection an its Close-Loop Control Using In-Cyliner Ionization Signal, SAE owertrain an Flui Systes Conference, apa, Floria, USA. [5] G. G. Zhu, C. Daniels, an J. Winkelan, (October 003) MB iing Detection an Its Close-Loop Control Using In-Cyliner ressure Signal, SAE , SAE owertrain an Flui Systes Conference & Exhibition, ittsburgh, ennsylvania, USA. [6] C. F. Daniels, G. G. Zhu, an J. Winkelan, (003) Inauible Knock an artial Burn Detection Using In-Cyliner Ionization Signal, SAE [7] I. Haskara, G. G. Zhu, an J. Winkelan, (October 004) IC Engine Retar Ignition iing Liit Detection an Control Using In-Cyliner Ionization Signal, SAE owertrain an Flui Systes Conference, apa, Floria, USA. [8] I. Haskara, G. Zhu, C. Daniels, an J. Winkelan, (October 005) Close Loop Maxiu Dilution Liit Control using In-Cyliner Ionization Signal, SAE , SAE owertrain an Flui Systes Conference & Exhibition, San Antonio, exas, USA. [9] L.Guzzella an C.H.Oner, Introuction to Moeling an Control of Internal Cobustion Engine Systes, Springer, Inc., 004. [0] A. Lefebvre an S. Guilain, Moeling an Measureent of the ransient Response of a urbocharge SI Engine, SAE echnical aper [] A. Y. Karnik, J. H. Bucklan, J. S. Freuenberg, Electronic hrottle an Wastegate Control for urbocharge Gasoline Engines, Aerican Control Conf., pp , 005. [] M. Jung, R. G. For, araeterization an ransient Valiation of a Variable Geoetry urbocharger for Mean-Value Moeling at Low an Meiu Spee-Loa oints, SAE echnical aper [3] K. L. Hoag, R. J. rius, Funaentals of Diesel Engine erforance, Cuins Engine Copany, Inc., 99. [4] M. Locatelli, C. H. Oner, an H.. Geering, An Easily unable Wall-Wetting Moel for FI Engines, SAE echnical aper [5] Mark C. Sellnau, Freeric A. Matekunas, aul A. Battiston, Chen-Fang Chang, an Davi R. Lancaster, Cyliner-pressure-base control using pressure-ratio-anageent an low-cost non-intrusive cyliner pressure sensor, SAE ,