Validation of an Open-Source Mean-Value Heavy-Duty Diesel Engine Model

Transcription

1 Valiation of an Open-Source Mean-Value Heavy-Duty Diesel Engine Moel Kristoffer Ekberg Viktor Leek Lars Eriksson Vehicular Systems, Department of Electrical Engineering, Linköping University, Sween, {kristoffer.ekberg, viktor.leek, Abstract The pursuit for lower fuel consumption an stricter emission legislation has mae a simulation- an optimizationbase evelopment methoology important to the automotive inustry. The keystone in the methoology, is the system moel. But for the results obtaine using a moel to be creible, the moel has to be valiate. The paper valiates an open-source, mean-value engine moel of a 2.7 liters CI inline 6 cyliner heavy-uty engine, an releases it as open-source. Keywors: Mean-value engine moel, 0-D moeling, Simulation, Optimal control Introuction In toay s automotive inustry, there is a rive for lower fuel consumption an better control of emissions. Simulation an numerical optimization are two tools that can be use to achieve that. The keystone in a simulation riven approach, is the system moel. For it an the results obtaine using it) to be creible, it nees to be valiate. This paper presents the moel structure of an open-source engine moel an valiates it. The engine is a 2.7 liters CI inline 6 cyliner Scania engine. The moel structure is a mean-value engine moel MVEM) Heywoo, 988), this type of structure oes not moel the piston movement explicitly. Instea the mean flow in an out of the cyliners is moele. This makes the moel computationally efficient, an suitable for control an optimization of the air an fuel path of the engine. It has a minimal number of states for efficient simulations, an is continuously ifferentiable for use with graientbase optimization solvers. The moel is a continuation of previous moeling work by the authors, escribe in Ekberg et al. 207). In contrast to the previous work, inicate mean effective pressure IMEP), pump mean effective pressure PMEP) an friction mean effective pressure FMEP), have been remoele, the compressor moel has been change for a more avance moel presente in Llamas an Eriksson 207), the turbine has been remoele to better escribe the efficiency, an the moel is valiate as a complete system. The purpose of this paper is to provie an open moel to the research community, an to invoke confience in the moel by valiating it. The paper is outline as follows. In Section 2 the ata sets are presente, in Section 3 the estimation criterion is presente, in Section 4 the moel equations are presente an the sub-moels are valiate, in Section 5 all submoels are connecte an the complete moele is tune an valiate against measurement ata, an in Section 6 the moel is simulate an its basic simulation properties are presente.. Contribution The main contribution of this paper is a valiate open-source MVEM of a Scania 2.7 liters 6 cyliner engine, ownloaable from Also, new component moels for the engine torque, an an aaptation of an existing turbine moel are introuce. 2 Data Six atasets have been use for moeling an valiation, see Table. Dataset A is ynamometer ata of the engine, an is the primary moeling set. Dataset B is simulation ata from a moel of the same engine obtaine using a etaile moel implemente in GT-Power Gamma Technologies, 2004). In B, the air-to-fuel ratio is varie for the operating points an is primarily use to evelop the torque moel. Dataset C is use to moel the compressor, an ataset D is use for moeling the turbine. Dataset E is use to valiate the complete moel, an ataset F is use for throttle moeling. Table. Datasets use to fin moel parameters. Dataset Signals Samples A. Stationary measurement ata B. GT Power Simulation C. Compressor map 4 73 D. Turbine map 4 38 E. Dynamic measurement ata F. Throttle effective area Proceeings of The 59th Conference on Simulation

2 3 Parameter Estimation To parameterize the sub-moels, the following criterion is use: θ = argmin θ K k= e 2 k θ) ) where θ are the criterion minimizing parameters, e k the moel error at sample k, an K the number of samples. Some of the submoels are not moele using ataset A, which is the esire moel behavior at steay-state. To compensate for this, the parameters nee to be refitte to represent ataset A. This is one using a regularization technique, which is selecte in orer to preserve the moel structure, accoring to: θ K = argmin θ k=e 2 I k θ) +C i= µi θ i θ i θ i ) 2 ) where θ are the parameters refitte to ataset A, θ the parameters obtaine using ) an a ataset ifferent than A, I the numbers of parameters to refit, µ i the weight assigne to parameter i, an C the cost of changing the parameters. To evaluate the moel fit, the following measures are use: ē = K 2) K e k 3) k= e σ = V [ e k ] 4) ē rel = K K e k s k 5) k= e rel,σ = V [ e k /s k ] 6) where ē is the mean absolute error, e σ the variance of the absolute error, ē rel the relative error, s k the k:th sample, an e rel,σ the variance of the relative error. The variance was calculate using the comman var in Matlab R207b. 4 Moel In the presentation of the valiate moel structure, the time epenence, t), is use to istinguish variables from constants, epenence on other variables is omitte for notational simplicity. The moel has four states xt): xt) = [p c t), p im t), p em t),ω tc t)] 7) where p c is the pressure after the compressor, p im the intake manifol pressure, p em the exhaust manifol pressure, an ω tc the turbocharger angular velocity.the moel further has three control inputs ut): ut) = [u f t),u thr t),u wg t)] 8) ω tc W comp W t u wg p c W wg p em u thr p im W thr W cyl u f Wcyl +W f N ice M ice Figure. Moel overview. Shown are the four states: pressure after the compressor p c, intake manifol pressure p im, exhaust manifol pressure p em an turbocharger angular velocity ω tc, an the three control inputs: Fuel injection per cycle u f, throttle effective area u thr, an wastegate effective area u wg. where u f is the fuel mass injecte per cycle, u thr the throttle position, an u wg the wastegate position. The engine spee, N ice, is treate as an exogenous input into the system. Figure shows an overview of the moel, where the states an control inputs are visualize. 4. Control Volumes The volume after the compressor, intake manifol an exhaust manifol are seen as thermoynamic control volumes, an moele as ynamic states with filling an emptying ynamics. Using an isothermal moel an by assuming mass conservation, an constant c p an c v, the moels are escribe as: t p ct) = R a T c t) W c t) W thr t)) V c 9a) t p imt) = R a T im W thr t) W cyl t)) V im 9b) t p emt) = R e T em t) W cyl t) +W f t) W t t) W wg t)) V em 4.. Parameters 9c) There are four parameters to estimate: volume after the compressor V c, intake manifol volume V im, exhaust manifol volume V em, an intake manifol temperature T im Parametrization an Valiation In ataset A, the mean value of the measure temperature in the intake manifol is K with a stanar eviation of. K, inicating that a constant temperature in the intake manifol is an acceptable moeling assumption. The charge air cooler is assume to be ieal, therefore the temperature in the intake manifol equals the surrouning temperature, T im = T amb. The sizes of the volumes V c, V im an V em are tune until the ynamics of the moel comply with the measurements. Valiation of the volume sizes is seen in section Proceeings of The 59th Conference on Simulation

3 4.2 Throttle In accorance with the throttle moeling approach in Eriksson an Nielsen 204), the mass flow through the throttle is moele as an isentropic compressible restriction, accoring to: W thr t) = p ct) Ra T c t) C D,thr A thr,max u thr t)ψ thr t) 0) where the air mass flow through the throttle is enote by W thr, the maximum throttle area by A thr,max, the flow coefficient by C D,thr, the temperature by T c, an the specific gas constant of air by R a. The throttle effective area is controlle irectly via the control signal u thr t). The flow parameter Ψ thr is taken from Shen an Ohata, 20), an represente as in Holmbom an Eriksson, 208): Ψ thr t) = Π thr t) = { pim t) p c t) γ a + γ a + Π thr t)) Π thr t) + γ ) a 2γ a γ a + a) if p imt) p c t) γ a + otherwise b) where γ a is the ratio of specific heats. The conitional equation b) oes not have a continuous erivative at the switching point. The Logistic function is therefore use to emulate the switching b): Π thr t) =Π choke + c switch t)πt) Π choke ) c switch t) = + e c ΨΠt) Π choke ) Π choke = γ a + Πt) = p imt) p c t) 2a) 2b) 2c) 2) where c Ψ is the steepness parameter of the Logistic function. The implemente flow parameter Ψ thr t) is moelle as a), where Π thr t) is moelle accoring to 2) Parameters thr t) thr Reference thr Moel thr Estimation thr t) Figure 2. Ψ thr t)-functions where the blue soli reference is escribe by ), the re trace is when Π thr t) is escribe accoring to 2). 4.3 Cyliner The cyliner air mass flow is moele with the help of the volumetric efficiency, η vol, Heywoo 988). It is expresse using a single constant as in Eriksson an Nielsen, 204): V D p im t) N ice t) W cyl t) = η vol n r R a T im 60 3) The cyliner fuel mass flow is calculate from the fuel injection per cycle an engine spee: W f t) = n cyl N ice t)u f t) 0 6 n r 60 The fuel-to-air equivalence ratio φt) is calculate as: 4) φt) = W ft) W cyl t) AF s 5) where AF s is the air-to-fuel stoichiometric ratio. To moel the engine torque M ice t), it is broken own into the components: gross inicate torque M ig t), pumping torque M pump t), an friction torque M fric t), an calculate as: M ice t) = M ig t) M pump t) M fric t) 6) where the three components M ig t), M pump t) an M fric t) are expresse in the normalize quantities IMEP, PMEP an FMEP Eriksson an Nielsen, 204). The inicate torque is moele accoring to: There is one parameter to estimate, C D,thr. The throttle area A thr,max is known from ataset F Parametrization an Valiation A ataset for valiating the throttle moel was not obtaine. C D,thr is seen as a tuning parameter in optimizing the steay-state levels of the moel. A valiation of Ψ thr is epicte in Figure 2. M ig t) = V D n r 2π IMEPt) IMEPt) = η ig t) q HV u f t)0 6 n cyl η ig t) = r γ cylt) c V D ) η cal t) γ cyl t) = c γ,0 + c γ, φt) + c γ,2 φ 2 t) 7a) 7b) 7c) 7) Proceeings of The 59th Conference on Simulation

4 Where the operating point epenent losses, are moele using the following polynomial structure: ) uf t) 2 η cal t) = c cal,2 t) 00 c cal,t) + c cal,0 8a) c cal, t) = c cal,0 + c cal, N ice t) 000 c cal,2 t) = c cal,20 + c cal,2 N ice t) c cal,22 The pumping losses are moele as: V D M pump t) = n r 2π PMEPt) PMEPt) = c PMEP,0 + c PMEP, p em t) p im t)) 8b) ) Nice t) c) 9a) 9b) The losses which are not inclue in the pumping losses are lumpe into the friction term, which is moele as a polynomial in fuel injection an engine spee: M fric t) = V D n r 2π FMEPt) FMEPt) = c f,0 + c f, N ice t) + c f,2 u f t) + c f,3 u f t)n ice t) 20) The temperature of the gas exiting the cyliners, T e, is moele base on calculations on an ieal cycle an aing the parameter η sc to inclue non-ieal properties: ) T e t) = η sc Π /γ a cyl t)r γ a qin t) c + T im r γ a c q in t) = Π cyl t) = p emt) p im t) W f t) W f t) +W cyl t) q HV c p,a 2a) 2b) 2c) To take the heat transfer from the exhaust manifol to the surrounings into account, the mean value exhaust gas temperature moel from Eriksson 2002) is implemente: T em t) = T amb + T e t) T amb )e 4.3. Parameters c em,h W cyl t)+w f t))cp,e 22) There are 8 parameters to estimate: η vol, c γ,0, c γ,, c γ,2, c cal,0, c cal,0, c cal,, c cal,20, c cal,2, c cal,22, c f,0, c f,, c f,2, c f,3, c PMEP,0, c PMEP,, η sc, an c em,h Parametrization an Valiation To preserve the properties observe in the ata, the parameterization is carrie out in steps. The cyliner massflow is estimate using ataset A. The error function is calculate as: e k,ηvol = η vol,ata,k η vol ) 2 23) The resulting fit is shown in Table 2. The inicate torque is estimate using ata set B Table ). The parameterization was one by minimizing the following error function: e k,imep = IMEP ata,k IMEP moel,k θ IMEP )) 2 24a) θ IMEP = [c γ,0, c γ,, c γ,2, c cal,0, c cal,, c cal,20, c cal,2, c cal,22 ] 24b) The resulting fit is shown in Table 3. The pumping torque is estimate using ata set B Table ). The parameterization was one by minimizing the following error function: e k,pmep = PMEP ata,k PMEP moel,k θ PMEP )) 2 θ PMEP = [c PMEP,0, c PMEP, ] 25a) 25b) The resulting fit is shown in Table 3. The friction torque is estimate using ata set B Table ). The parameterization was one by minimizing the following error function: e k,fmep = FMEP ata,k FMEP moel,k θ FMEP )) 2 θ FMEP = [c f,0, c f,, c f,2, c f,3 ] 26a) 26b) The resulting fit is shown in Table 3. For the moel escribing the exhaust manifol temperature, the loss function is calculate as: e k,t = T em, ata, k T em, moel, k θ Tem )) 2 θ Tem = [η sc, c em,h ] The resulting fit is shown in Table 2. 27a) 27b) Table 2. Cyliner moel fit to ataset A. ē is the mean absolute an e rel,σ the variance of the relative error. η vol 0.84 % 0.6 % 0.92 % 0.69 % T em 5.20 K 3.40 K 0.78 % 0.49 % Table 3. Cyliner moel fit to ataset B. ē is the mean absolute an e rel,σ the variance of the relative error. IMEP 24.0 kpa.7 kpa.57 % 0.42 % PMEP 99.2 kpa 05. kpa 23.0 % 3.6 % FMEP 0.75 kpa 0.52 kpa 0.70 % 0.43 % 4.4 Turbocharger The turbocharger ynamics is moele from Newton s secon law of motion accoring to: t ω tct) = P t η m t) P c t) 28) ω tc t)j tc Proceeings of The 59th Conference on Simulation

5 3 0 5 PMEP For the turbine efficiency, the stanar approach of moeling it from the blae-spee-ratio BSR) is taken. However, since the BSR lines o not overlap in the BSR η plane in ataset D, a spee epenence is inclue. The moel is escribe by: Measurment Moel 0 5 Figure 3. PMEP fit to ataset B. Re line shows the one-to-one ratio Parameters η t t) = η t,max t) k η t)bsrt) BSR opt t)) 2 ω tc t)d t /2 BSRt) = 2c p,e T em t) Π t t) γe ) BSR opt t) = c BSR,0 + c BSR, N tc,corr,ii t)+ c BSR,2 N 2 tc,corr,iit) η t,max t) = c ηt,0 + c ηt, N tc,corr,ii t) k η t) = c max,0 + c max, N tc,corr,ii t) N tc,corr,ii t) = ω tct) Tem t) 30 π a) 32b) 32c) 32) 32e) 32f) 32g) There is one parameter to estimate: J tc. The valiation is seen in Section Turbine The turbine power, incluing the mechanical efficiency of the turbocharger shaft is calculate accoring to: ) P t η m t) = W t t)c p,e T em t)η t t) Π t t) /γ e Π t t) = p ats p em t) 29a) 29b) where p ats is the pressure in the exhaust aftertreatment system. For the flow, the square root turbine flow moel in Eriksson an Nielsen, 204) is aapte to to escribe ataset D: W t,corr t) = k 0 t) ) Π t t) k k 2 t) t) k 0 t) = c 00 + c 02 N 2 tc,corr,it) k t) = c 0 + c N tc,corr,i t) 30a) 30b) 30c) k 2 t) = c 20 + c 2 N tc,corr,i t) + c 22 N 2 tc,corr,it) 30) N tc,corr,i t) = ω tct) Tem t) 30 π 000 The turbine mass flow is calculate as: 30e) W t t) = W t,corr t) p em0 3 Tem 3) 4.5. Parameters There are 4 parameters to estimate: c 00, c 02, c 0, c, c 20, c 2, c 22, c BSR,0, c BSR,, c BSR,2, c ηt,0, c ηt,, c max,0, an c max, Parametrization an Valiation The parameterization is carrie out by parameterizing the mass flow moel an efficiency moel separately using ataset D. For the mass flow, the loss function is calculate as: e k,wt = W t, ata, k W t, moel, k θ Wt )) 2 θ Wt = [c 00 c 02 c 0 c c 20 c 2 c 22 ] 33a) 33b) The moel fit is shown in Table 4. For the efficiency, the following loss function is use: e k,ηt = η t, ata, k η t, moel, k θ ηt )) 2 34) θ ηt = [c BSR,0 c BSR, c BSR,2 c ηt,0 c ηt, c max,0 c max, ] 35) The moel fit is shown in Table Wastegate The wastegate is evelope in the same way as the throttle see section 4.2), apart from γ a which is replace by γ e. The wastegate mass flow is escribe by: W wg t) = p emt) Re T em C D,wg A wg,max u wg t)ψ wg t) 36) where Ψ wg t) is similar to a), but Π thr t) is replace by Π wg t). Π wg t) is efine as in Equation 2), where Πt) is replace by Π t t) in 29b). Table 4. Turbine moel fit to ataset D. ē is the mean absolute an e rel,σ the variance of the relative error. W t,corr % 0.95 % kg/s K/kPa kg/s K/kPa η t 0.92 % 0.99 %.34 %.47 % Proceeings of The 59th Conference on Simulation

6 4.6. Parameters There is only one parameter to estimate, C D,wg. The wastegate area A wg,max is etermine from measuring the iameter. C D,wg is seen as a tuning constant. Since ata was not available to parameterize the wastegate as a separate component, the same approach as for the throttle is taken. The moeling of the wastegate an throttle is similar ue to both being controllable valves for restricting the gas flow. 4.7 Compressor The parameterization of the compressor was one using ataset C an by using LiU CPgui Llamas an Eriksson, 208), which parameterizes a high-orer control-oriente compressor moel base on the total least squares algorithm. The fit to ataset A is shown in Table 5. Table 5. Compressor moel fit to ataset A. ē is the mean absolute error, e σ the variance of the absolute error, ē rel the relative error, an e rel,σ the variance of the relative error. W c %.5 % kg/s kg/s η c 0.92 % 0.99 %.34 %.47 % 5 Full System Parametrization An approach taken in Wahlström an Eriksson 20) an Sivertsson an Eriksson 20) is to refit the parameters to the measurements when all moel components are assemble in orer to achieve goo fit. A similar approach is taken here, but with a slightly ifferent cost function see equation 2) where a regularization technique is use in orer to limit the changes in parameter values in orer to preserve the moel structure. This proceure is ivie into two steps. The first step is to refit the torque moel to ataset A. The secon step is to tune all parameters influencing the steay state levels of the states when the complete moel is fully assemble. 5. Torque moel For the torque moel, the following parameters are refitte: θ M = [c cal,0, c cal,0, c cal,, c cal,20, c cal,2, c cal,22, c f,0, c f,, c f,2, c f,3, c PMEP,0, c PMEP, ] using criterion 2). The resulting fit is shown in Table 6 37) Table 6. Torque moel refit to ataset A. ē is the mean absolute an e rel,σ the variance of the relative error. M ice 8.42 Nm 6.59 Nm.8 % 3.05 % 5.2 Tuning of steay-state levels In the same manner as for the torque moel, using criterion 2), the parameters influencing the steay-state levels of the states are re-parameterize. To o this, the full moel is simulate an the wastegate is controlle, using a PID-controller to minimize the error: e wg = W c W c,ref 38) where the compressor massflow reference W c,ref is taken from the massflow measurment in ataset A. The resulting fit is shown in Table 7. Table 7. Steay-state levels of states fit to ataset A for the fully parameterize moel. ē is the mean absolute error, e σ the variance of the absolute error, ē rel the relative error, an e rel,σ the variance of the relative error. p c 2.78 kpa 4.00 kpa.89 % 2.80 % p im 2.76 kpa 3.96 kpa.89 % 2.79 % p em 4.73 kpa 3.96 kpa 7.33 % 3.69 % ω tc.98 krpm 2.42 krpm 4.88 % 7.93 % 6 Full System Valiation The complete system moel is simulate with the control signals recore from a ynamic engine test part of ata set E). The result from the simulate system, in comparison with the measurement ata is isplaye in Figure 4. p c p im p em tc Part of ataset E Simulate moel Time Figure 4. State valiation, simulate engine moel compare to ynamic measurement ata. The control signals are taken from measurements. 7 Conclusions A mean value engine moel of a Scania 2.7 liters heavy-uty iesel engine has been evelope an valiate using both stationary an ynamic measurements. The results show goo agreement with measurements, showing that both ynamics an steay-state levels are well represente inicating that the moel is well suite for stuying the engine ynamics an fuel optimal control. The moel is open-source an ownloaable from Proceeings of The 59th Conference on Simulation

7 Acknowlegment The work was finance by Sweish Governmental Agency for Innovation Systems uner the program Strategic Vehicle Research an Innovation, grant FROST ) an LINK-SIC. The authors woul like to thank Scania, an especially Henrik Höglun an Björn Johansson at Scania, for proviing the ata an for moeling iscussions. References Kristoffer Ekberg, Viktor Leek, an Lars Eriksson. Optimal control of wastegate throttle an fuel injection for a heavy-uty turbocharge iesel engine uring tip-in. In 58th Conference on Simulation an Moelling SIMS 58), Reykjavik, Icelan, 207. Lars Eriksson. Mean value moels for exhaust system temperatures. SAE 2002 Worl Congress & Exhibition, ISSN URL Lars Eriksson an Lars Nielsen. Moeling an Control of Engines an Drivelines. John Wiley an Sons Lt, 204. Gamma Technologies. GT-Power User s Manual. GT-Suite Version 6., John B. Heywoo. Internal Combustion Engine Funamentals. McGraw-Hill, 988. Robin Holmbom an Lars Eriksson. Analysis an evelopment of compact moels for mass flows through butterfly throttle valves. In WCX Worl Congress Experience. SAE International, Apr 208. URL Xavier Llamas an Lars Eriksson. Control-oriente compressor moel with aiabatic efficiency extrapolation. SAE International Journal of Engines, 04), 207. Xavier Llamas an Lars Eriksson. LiU CPgui: A toolbox for parameterizing compressor moels. Technical Report LiTH-ISY-R-302, Department of Electrical Engineering, Linköpings Universitet, SE Linköping, Sween, 208. Tielong Shen an Akira Ohata. Moeling an Control Design for Automotive Engines - with MATLAB Engine Simulator CD-ROM. ISBN 978e , 20. Martin Sivertsson an Lars Eriksson. Moeling for Optimal Control: A Valiate Diesel-Electric Powertrain Moel. SIMS th International Conference on Simulation an Moelling, Ålborg, Denmark, 20. Johan Wahlström an Lars Eriksson. Moelling iesel engines with a variable-geometry turbocharger an exhaust gas recirculation by optimization of moel parameters for capturing non-linear system ynamics. Proceeings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 2257): , Proceeings of The 59th Conference on Simulation