Common Rail Injection System On-Line Parameter Calibration for Precise Injection Quantity Control

Transcription

1 2010 American Control Conference Marriott Waterfront Baltimore MD USA June 30-July WeC19.6 Common Rail Injection System On-Line Parameter Calibration for Precise Injection Quantity Control Fengjun Yan and Junmin Wang * Department of Mechanical Engineering The Ohio State University Abstract This paper presents an iterative learning control (ILC)-based method to on-line calibrate the high-pressure common-rail (HPCR) injection system parameters for achieving precise injection quantity control for Diesel engines. Given the strongly increasing demands on engine fuel economy and emissions precise injection quantity control is of importance for realizing desired combustion particularly advanced combustion modes on a cycle-by-cycle basis. Current Diesel engine injection quantity control methods heavily rely on pre-calibrated static tables or injector models which cannot handle the effects of the rail pressure sensor reading inaccuracy and injector aging on injection quantity. In this paper by using an exhaust manifold oxygen fraction model an ILC-based HPCR injection system parameter on-line adaptation algorithm was developed to actively adjust the injection duration command for injection quantity correction. Simulation results based on a high-fidelity GT-Power engine model show the effectiveness of the designed injection quantity correction algorithm. I. INTRODUCTION IESEL engine high-pressure common-rail (HPCR) Dinjection systems have promising advantages in emission reductions and fuel economy improvement primarily because their high injection pressures can provide flexible injection timing and offer multiple injections (pilot- main- and post-injection) for each engine cycle. The precise fuel injection quantity control is significant not only for engine torque response and drivability concerns but also particularly for control of advanced combustion modes such as low temperature combustion (LTC) and homogenous charge compression ignition (HCCI) which are sensitive to injection and in-cylinder conditions (ICCs) variations [8][7][10]. Several injector models have been proposed in [17][11] for injection quantity control. In typical engine control practice injection quantity is controlled by adjusting the injection signal pulse width based on the measured rail pressure and a pre-calibrated injector table or model [6]. However precisely controlling the fuel injection quantity is quite challenging for HPCR systems due to the rail pressure reading inaccuracy and injector model uncertainties including the variations of fuel flow discharge coefficient the area of total out flow section and the density of fuel [19]. The discharge coefficient of fuel flow depends on flow velocity fuel density and viscosity and can also be influenced by occurrence of cavitation. The Fengjun Yan is with the Department of Mechanical Engineering at The Ohio State University ( yan.373@osu.edu). * Corresponding author. Junmin Wang is with the Department of Mechanical Engineering at The Ohio State University ( wang.1381@osu.edu). injector area of total out flow section changes with factors such as injector aging soot accumulation and environmental temperature. The fuel density may be altered by temperature pressure and fuel type (e.g. fossil Diesel and biodiesel fuels) as well. For instance for a typical Diesel fuel the fuel density varies from 850kg/m 3 (800 bar 40 ) to 890 kg/m 3 (1500 bar 20 ) [19]. Such variations however are not directly measurable by engine on-board sensors. As the engine fueling control is mostly exercised in a feedforward fashion periodic on-line calibration of the injection system parameters is beneficial to ensure the accurate fuel injection quantity control. For accommodating the injector parameter uncertainties and inaccuracy of HPCR pressure reading iterative learning control (ILC) could be an effective way. By combining the information of previous control signal and the feedback error an updated control law can be generated to reduce the effect of system variations/uncertainties without exactly knowing the system dynamics [14]. In this paper an ILC-based HPCR injection system on-line parameter calibration algorithm is presented. The algorithm can address the injection system parameter variations and help to achieve precise injection quantity control without additional hardware. In addition such an algorithm can also be used for injection system on-board diagnostic purposes. To generate the error based on which the effect of the pressure reading inaccuracy and parameter uncertainties can be reduced an oxygen mass fraction model is introduced. The arrangement of the rest of this paper is as follows. In section II the oxygen mass fraction models are presented. Section III describes a fuel injection on-line parameter calibration algorithm based on the enhanced ILC (EILC) method. In section IV the validation of the on-line calibration method is shown by applying it to a high-fidelity GT-Power engine model through simulations. Conclusive remarks are presented in the end. TABLE I αα KKiiiiii αα KKeeee h φφ ηη vv ρρ ffffffff PP θθ(tt) Symbol NOMENCLATURE Quantity Piston surface area effective parameter Piston surface area effective parameter Engine crank angle Engine volumetric efficiency Stoichiometric oxygen fuel mass ratio for complete combustion Fuel density Pressure difference between common rail and in-cylinder pressures Uncertainty parameter to be calculated /10/$ AACC 2248

2 AA cccccc cc ddcccccc dd EEEE FF ii FF ee FF cc FF eeee k mm iiii ee cc mm ff ΔΔmm rrrrrrrrrr ΔΔmm rrrrrrrrrr NN pp ii pp ee RR TT ii TT ee VV ii VV ee WW cc Area of the total outflow section Fuel flow discharge coefficient In-cylinder charge density during valve overlapping Injection duration Oxygen fractions of the gases in intake manifold at IVC Oxygen fractions of the gases in exhaust manifold at IVC Oxygen fractions of the gases in cylinder at IVC Oxygen fractions of the gases out of cylinder Index of engine cycle Mass of gas in the cylinder at IVC Mass of gas in exhaust manifold at IVC Mass of gas from intake manifold to cylinder per cycle Mass of gas from exhaust manifold to cylinder per cycle Mass of gas from cylinder to exhaust manifold per cycle Fuel mass quantity per cylinder per cycle Mass from exhaust manifold to cylinder caused by the volume change Mass from exhaust manifold to cylinder caused by the pressure difference Engine speed (rpm) Pressure in intake manifold Pressure in exhaust manifold Ideal gas constant Temperature in intake manifold Temperature in exhaust manifold Volume of intake manifold Volume of exhaust manifold Mass flow rate through cylinder II. OXYGEN MASS FRACTION MODELS In the EILC algorithm a base error which reflects the difference between actual value and desired value is needed to render the effects of model uncertainty to be zero. The signal reflects the actual fuel injection quantity can be chosen as the actual exhaust manifold oxygen fraction. To generate a value relating to the desired fuel injection quantity we use an exhaust manifold oxygen mass fraction model [4] which is based on the signals from the engine sensor measurements and the desired fuel injection quantity. A. Discrete Model In this section we develop a dynamic model that can describe the evolutions of both the in-cylinder gas oxygen fraction at the crankshaft angle of intake valve closing (IVC) and the predicted exhaust manifold oxygen fraction on a cycle-by-cycle basis [4]. The dynamic models were developed based on the mass conservation and are described by the following difference equations as: (kk + 1)FF ee (kk + 1) = cc (kk) FF eeee (kk) FF ee (kk) + (kk)ff ee (kk) (2) where k is the index of engine cycle (kk) and (kk) are the mass of charge in the cylinder and in the exhaust manifold at the kth IVC respectively. mm iiii (k) ee (kk) and cc (kk) are mass of charge from intake manifold to cylinder from exhaust manifold to cylinder from cylinder to exhaust during the period right before the kth IVC. FF ii (k) FF ee (kk) FF cc (kk) and FF eeee (kk) are the oxygen fractions of the gases in intake manifold in exhaust manifold in cylinder and out of cylinder after combustion at or right before the kth IVC respectively. mm ff (kk) is the mass of injected fuel before the kth IVC. Figure 1 illustrates the in-cylinder mass evolving process. kth IVC FF cc (kk) FF ii (kk) FF ee (kk) (kk) (kk) mm ff (kk) Fuel Injection cc (kk) ee (kk) mm iiii (kk) EVO IVO EVC FF ee (kk) (k+1)th IVC FF cc (kk + 1) FF ii (kk + 1) FF ee (kk + 1) (kk + 1) (kk + 1) Figure. 1 Gas exchanging process from the kth IVC to the (k+1)th IVC. We assume the mass of engine inlet gas equals to that of outlet gas for both the cylinder and the exhaust manifold in each cycle [9][12] i.e. cc (kk) = mm iiii (kk) + ee (kk) + mm ff (kk) (3) So (kk + 1) = (kk) + mm ff (kk) + mm iiii (kk) + ee (kk) cc (kk) = (kk) (4) and (kk + 1) = (kk). (5) The oxygen fraction of the gas after combustion can be derived by: (kk) + mm ff (kk) FF eeee (kk) = (kk)ff cc (kk) mm ff (kk) (6) i.e. FF eeee (kk) = (kk)ff cc (kk) mm ff (kk) (7) (kk)+mm ff (kk) where is the stoichiometric oxygen fuel mass ratio for complete combustion. Thus we get the resultant dynamic models as follows: FF cc (kk + 1) = CC 1 FF cc (kk) + CC 2 FF ee (kk) + CC 3 FF ii (kk) + CC 4 mm ff (kk) (8) FF ee (kk + 1) = CC 5 FF cc (kk) + CC 6 FF ii (kk) + CC 7 mm ff (kk) (9) where CC 1 = 1 cc (10) +mm ff CC 2 = ee (11) 2249

3 CC 3 = mm iiii (12) CC 4 = cc ( +mm ff ) +mm ff (13) CC 5 = cc +mm ff (14) CC 6 = 1 cc (15) CC 7 = cc. +mm ff (16) Here we denote cc ee mm iiii mm ff as cc (kk) ee (kk) mm iiii (kk) (kk) (or (kk + 1)) (kk) (or (kk + 1)) mm ff (kk) respectively for simplicity. B. Mean-Value Model According to the aforementioned models we can derive the continuous mean-value models (MVM) as follows: FF cc = ρρ 1 FF cc + ρρ 2 FF ee + ρρ 3 FF ii + ρρ 4 mm ff (17) FF ee = ρρ 5 FF cc + ρρ 6 FF ee + ρρ 7 mm ff (18) with the parameters being defined as: WW cccc ρρ 1 = + 120WW cccc +mm ff NNNN ee WW eeee +mm ff (19) ρρ 2 = WW eeee 1 120WW cccc NNNN ee (20) ρρ 3 = WW iiii (21) ρρ 4 = ρρ 5 = WW cccc WW cccc NN 120WW eeee WW cccc ( +mm ff ) 120( +mm ff ) NN mm cc +mm ff (22) +mm ff (23) ρρ 6 = WW cccc (24) ρρ 7 = WW cccc +mm ff (25) where WW iiii WW cccc and WW eeee are the mass flow rates from intake manifold to cylinder from cylinder to exhaust manifold from exhaust manifold to cylinder (during valve overlapping period). NN is the engine speed. From the aforementioned model the oxygen fraction can be described as a linear parameter-varying system with ρρ = (ρρ 1 ρρ 2 ρρ 3 ρρ 4 ρρ 5 ρρ 6 ρρ 7 ) TT. (26) The system states are: xx = [FF cc FF ee ] TT. (27) System inputs are: uu = FF ii mm ff TT. (28) System output is: yy = FF ee. (29) We consider the density of in-cylinder charge at IVC the same as the one in intake manifold [15][18]. By the ideal gas law can be approximated as below: = pp iivv IIIIII RRRR ii (30) = pp eevv ee. RRRR ee (31) By using the speed-density equation WW iiii can be calculated as WW iiii = NNηη vvpp ii VV IIIIII. (32) 120RRTT ii Here pp ii pp ee and TT ii TT ee are pressures and temperatures of intake manifold and exhaust manifold respectively. ηη vv is the engine volumetric efficiency. RR is the gas constant. The mass flowed from exhaust manifold to cylinder during intake and exhaust valve overlapping period can be derived by using the model developed in [18]: ee = (ΔΔmm rrrrrrrrrr + ΔΔmm rrrrrrrrrr ) (33) where ΔΔmm rrrrrrrrrr and ΔΔmm rrrrrrrrrr are flowed mass caused by the volume change and pressure difference respectively. The two terms can be written as: ΔΔmm rrrrrrrrrr = dd KK 1 (34) ΔΔmm rrrrrrrrrr = SSSSSS(pp ee pp ii )AA KK 2dddddddd(pp ee pp ii ) dddd KK dddd 2 (35) where KK 1 = KK 2 = dddd αα 2 EEEEEE KKeeee h IIIIII dddd EEEEEE αα KK_eeee h αα KK_iiiiii IIIIII αα 2 KK_eeee h +αα 2 KK_iiiiii dddd αα 2 KKeeee h +αα 2 (36) KKiiiiii dddd (37) WW eeee = NNee 120 (38) WW cccc = WW iiii + WW eeee. (39) Here dd is the in-cylinder charge density during valve overlapping and can be approximated by the intake manifold charge density calculated through ideal gas law. The term ABS(pp ee pp ii ) denotes the absolute value of pressure difference between intake manifold and exhaust manifold. AA KK is the piston surface area. αα KKiiiiii and αα KKeeee h are piston surface area effective parameters. φφ is the crank angle F_int N(rpm) F_exh GT_Power 0.1 MVM Cycle Figure. 2. Evaluation of the exhaust manifold oxygen fraction model with a high-fidelity GT-Power engine model. Figure. 2 illustrates the comparison of the foregoing MVM model with a high-fidelity one-dimensional computational 2250

4 GT-Power engine model. As can be observed the MVM can predict both the steady-state and the transit processes well even the oxygen fractions in intake and exhaust manifolds and the engine speed vary. The intake and exhaust manifold signals (including pressures temperatures and oxygen fractions) can be obtained by sensors and/or air-path observers [8][9] for calculating the predicted exhaust manifold oxygen fraction based on the desired (commanded) fuel injection quantity. As the effectiveness of the method proposed in this paper relies on the accuracy of the model the parameters in which need to be carefully calibrated. III. EILC-BASED HPCR ON-LINE PARAMETER A. EILC Algorithm Review CALIBRATION Here ILC and Enhanced ILC algorithms are briefly reviewed. In [2][3] the ILC algorithm can be written as: uu ii (nn) = uu ii bb (nn) + uu ii ff (nn) (40) where uu ii ff (nn) is the feedforward control in the form of: uu ff ii mm ii mm ii (nn) = jj =ii 1 GG jj uu jj (nn) + jj =ii 1 LL jj (nn)ee jj (nn + 1) (41) and uu ii bb (nn) is the feedback controller in the form of: zz ii (nn + 1) = pp zz ii (nn) + qq zz ii (nn) ee ii (nn) (42) uu ii bb (nn) = rr zz ii (nn) + ss zz ii (nn) ee ii (nn). (43) Here ee jj (nn + 1) denotes the tracking error between the desired and system outputs at time nn + 1 in iteration j. GG jj and LL jj denote the forgetting factor and learning gain operator. In the basic ILC GG jj is chosen as 1. ee ii (nn) is the current tracking error and p q r and s are the functions for bounded conditions. In ILC the control law includes the control signal and the error signal in the last iteration. However the convergence of ILC above requires the identical initial condition which may not be satisfied in the highly nonlinear engine systems [2]. Thus in this paper we use the enhanced ILC [3] to release the identical initial condition requirement. The control law is given as: uu ii (nn) = uu ii 1 (nn) + LLee ii 1 (nn + 1) + KK[ee ii (nn) ee ii 1 (nn)]. (44) Here K is the compensation gain and KK[ee ii (nn) ee ii 1 (nn)] term compensates the state difference between two iterations at time n. Thus there is no requirement for the same initial conditions for all iterations as in normal ILC [2]. B. HPCR Fuel Injection Parameter On-Line Calibration via EILC The predicted exhaust manifold oxygen fraction can be generated by the oxygen fraction model presented in section II based on the desired fuel injection amount and the signals measured on the engine. Thus the difference between the predicted exhaust manifold oxygen fraction and the one measured from the engine can be chosen as the base error in injector model parameter on-line calibration algorithm design. The HPCR injection mass quantity can be modeled by [17]: mm ff = ρρ ffffffff ssssss( PP) cc ddcccccc AA cccccc EEEE 2 PP (45) ρρ ffffffff where AA cccccc is the area of the total outflow section cc ddcccccc is the fuel flow discharge coefficient ET is the injection duration and PP is the pressure difference between common rail and in-cylinder pressures. ρρ ffffffff is the fuel density. The model (45) can be used to generate the injection duration with the information of the desired fuel quantity and the pressure difference between HPCR and cylinder pressures. However the pressure difference reading may not be accurate due to sensor bias and the injector parameters may change with injector aging and environmental conditions. These uncertainties/variations will affect the actual fuel injection quantity. To ensure the injection quantity control accuracy we introduce in the injector model an uncertainty parameter θθ(tt) to be calibrated on-line. Thus the injection model (45) can be modified as: mm ff = θθ(tt) ρρ ffffffff ssssss( PP) cc ddcccccc AA cccccc EEEE 2 PP ρρ ffffffff where the nominal value of θθ(tt) is 1. (46) In the EILC algorithm (44) the ee was chosen by the difference of the oxygen fraction FF ee and the θθ = θθ(tt) 1 as the u in (44). Each of the iterations contains 10 engine cycles. Thus the EILC algorithm in (44) can be written as θθ ii (nn) = θθ ii 1 (nn) + LL FF eeii 1 (nn + 1) + KK FF eeii (nn) FF eeii 1 (nn) (47) As can be seen from the simulation scheme in Figure. 3 the input signal is the desired fuel injection quantity. The nominal values of the injector model parameters can be obtained by injector calibration and measurement from the rail pressure sensor. By applying the EILC a compensating value θθ can be generated and it can be used in the injector model to generate the adjusted injection duration signals for delivering accurate injection quantity to the cylinders. 2251

5 Figure. 3 Simulation scheme of the fuel injection on-line parameter calibration system. A. Simulation Setup IV. SIMULATION STUDIES In this section a high-fidelity GT-Power engine model is utilized to evaluate the injection quantity correction algorithm. In the GT-Power combustion model the fuel injection quantity was assumed to be precise. To evaluate the algorithm a real engine including injection system were constructed with the typical parameters as follows: HPCR pressure is 1350bar; the fuel flow discharge coefficient cc ddcccccc = 0.75; the fuel density ρρ ffffffff = 850kg/m 2 ; the area of injection section AA cccccc = m 2. Whereas the parameters of injector model with the uncertainty and variations were assumed as: HPCR pressure sensor reading pp = 1500bar; the fuel flow charge coefficient cc ddcccccc = 0.71; the fuel density ρρ ffffffff = 870kg/m 2 ; the area of injection section AA cccccc = m 2. Thus without the active fuel injection system parameter on-line calibration the actual fuel injection quantity delivered into GT-Power combustion model will be different from the desired one due to the unknown uncertainties. To evaluate the developed injection system parameter on-line calibration algorithm co-simulations within Matlab/SIMULINK and GT-Power were conducted. The parameters in the controller are chosen as: LL = 1.2 KK = 1.2. B. Simulation Results In the simulation the uncertainty parameter θθ(tt) on-line calibration was initiated at the 6 th second. As can be seen from Figure. 4 the error between the predicted and measured exhaust manifold oxygen fractions was rendered to zero after the algorithm was applied. The predicted exhaust manifold oxygen fraction Fe_model in Figure. 4 was modeled based on the desired injection quantity and measured intake and exhaust manifold signals according to the MVM in section II. The difference between this predicted exhaust manifold oxygen fraction and the measured one is related to the injection quantity error. Therefore such an oxygen fraction difference can provide an error signal in EILC algorithm. Fe_real Fe_model Delta_Fe Time(s) Figure. 4 Exhaust manifold oxygen fractions. Uncertainty Time(s) Figure. 5. Model uncertainty parameter adjustment. As can be seen from Figure. 5 the uncertainty parameter of the injection model θθ(tt) was calibrated to after the EILC conducted for a period of about 4s (that is 40 cycles or 4 iterations with the engine speed being 1200 rpm). In Figure. 6 it is shown that the desire fuel injection amount is 20 mg whereas the actual injection amount before 2252

6 EILC algorithm correction was 21.3 mg and 20 mg after parameter on-line calibration took place. The actual fuel injection quantity was adjusted to the desired value by updating the uncertainty parameter in the inverse injector model (46) and thus the injection duration for the injector. Fuel_d(mg) Fuel_real(mg) Time(s) Figure. 6. Desired and actual fuel injection quantities during the injection model parameter on-line calibration. V. CONCLUSIONS AND FUTURE WORK In this paper a HPCR injection system on-line parameter calibration method based on the EILC algorithm was developed for precise fuel injection quality control of Diesel engines. Such an algorithm can significantly reduce the effects of the HPCR pressure sensor uncertainty and variations associated with injector aging and fuel properties on the fuel injection quantity control accuracy. Simulations using a high-fidelity GT-Power engine model with added pressure reading inaccuracy and model parameter uncertainty were utilized to demonstrate the effectiveness of the developed algorithm. It was observed that by the on-line calibration the actual HPCR fuel injection quantity can be precisely controlled around the desired value. The future work will primarily include the experimental investigation of the algorithm as well as combination of the precise fuel injection algorithm with air-path system control for advanced combustion mode engine control. REFERENCES [1] B. Alzahabi and K. Schulz Analysis of pressure wave dynamics in fuel rail system Int. Jnl. of Multiphysics Vol. 2 No [2] C. J. Chien A discrete iterative learning control for a class of nonlinear time-varying systems IEEE Transactions on Automatic Control 43 (5) (1998) [3] C. J. Chien F. Lee and J. Wang Enhanced iterative learning control for a piezoelectric actuator system using wavelet transform filtering Journal of Sound and Vibration 299 (2007) pp [4] F. Yan and J. Wang In-cylinder oxygen mass fraction cycle-by-cycle estimation via a Lyapunov-based observer design Proceedings of the American Control Conference 2010 (accepted). [5] G. Stumpp and M. Ricco Common rail an attractive fuel injection system for passenger car DI Diesel engines SAE paper [6] J. Baumann and U. Kiencke Practical feasibility of measuring pressure waves in common rail injection systems by magneto-elastic sensors SAE paper [7] J. Wang and C. Chadwell On the advanced air-path control for multiple and alternative combustion mode engines SAE Paper [8] J. Wang Hybrid Robust Air-Path Control for Diesel Engines Operating Conventional and Low Temperature Combustion Modes IEEE Transactions on Control Systems Technology Vol. 16 No. 6 pp [9] J. Wang Air fraction estimation for multiple combustion mode Diesel engines with dual-loop EGR systems Control Engineering Practice Vol. 16 Issue 12 pp [10] J. Wang Smooth In-Cylinder Lean-Rich Combustion Switching Control for Diesel Engine Exhaust-Treatment System Regenerations SAE International Journal of Passenger Cars Electronic and Electrical Systems Vol. 1 No. 1 pp [11] K. Huhtala and M. Vilenius Study of a common rail fuel injection system SAE paper [12] M. Ammann N. P. Fekete L. Guzella and A. H.G. lattfelder Model-based control of the VGT and EGR in a turbocharged common-rail Diesel engine: theory and passenger car implementation SAE Paper [13] M. Norrlof and S. Gunnarsson Disturbance aspects of iterative learning control Engineering Applications of Artificial Intelligence 14 (2001) [14] M. Norrlof Disturbance rejection using an ILC algorithm with iteration varying filters Asian Journal of Control Vol. 6 No [15] N. J. Killingsworth S. M. Aceves D. L. Flowers and M. Krstic A Simple HCCI Engine Model for Control Proceedings of the 2006 IEEE International Conference on Control Applications pp [16] P. Lino B. Maione and A. Rizzo Nonlinear modeling and control of a common rail injection system for Diesel engines Applied Mathematical Modeling 31: [17] P. Lino B. Majone and A. Rizzo A control-oriented model of a common rail injection system for Diesel engines Emerging Technologies and Factory Automation 2005 ETFA th IEEE conference. [18] U. Koehler and M. Bargende A Model for a Fast Prediction of the In-Cylinder Residual Gas Mass. SAE Paper [19] X. L. J. Seykens L. M. T. Somers and R. S. G. Baert Detailed modeling of common rail fuel injection process MECCA III (2005) 2253