System and method for estimating nitrogen oxides produced by an internal combustion engine

Abstract

Method (100) for estimating (110) NOx produced by an internal combustion engine (12), the method comprising: - monitoring (104) a fuel flow rate supplied to the internal combustion engine (12), - monitoring (106) several engine operating parameters, each of the several engine operating parameters being represented by an engine operating parameter variable TN, where N is a positive integer greater than 1, - determining (108) a number of model constants, - estimating (110) the NOx produced by the internal combustion engine (12) based on a product of a function of the fuel flow rate and at least one of the model constants and a function of the several engine operating parameters and remaining model constants according to the equation NOxE=(K⋅FF)⋅[(C1⋅T1)+(C2⋅T2)+…+(CN⋅TN)], where FF is the fuel flow rate and K and C1, C2, ..., CN the number of model constants is, and- storing (112) the NOx estimate in a memory (45).

Description

The present invention relates generally to systems and methods for determining components of the exhaust gas produced by internal combustion engines, and more particularly to systems and methods for estimating nitrogen oxides produced by internal combustion engines.When combustion occurs in an excess oxygen environment, peak combustion temperatures increase, leading to the formation of undesirable engine emissions such as oxides of nitrogen, e.g., NOx. It is desirable to determine the amount and / or rate of NOxgenerated by the operation of an internal combustion engine for diagnostic and / or engine control purposes.From DE 101 42 198 A1 and DE 103 16 062 A1, a method for estimating NOx produced by an internal combustion engine is known, each having the steps:monitoring a fuel quantity flow supplied to the internal combustion engine,monitoring a plurality of engine operating parameters,determining a number of model constants,estimating the NOx produced by the internal combustion engine based on a product of a function of the fuel quantity flow and at least one of the model constants and a function of the plurality of engine operating parameters and remaining ones of the model constants; andstoring the NOx estimate in a memory.The two aforementioned documents also disclose a correspondingly configured system for estimating NOxgenerated by an internal combustion engine.The above object is achieved by a method for estimating NOx, comprising the steps indicated in claim 1.Monitoring fuel flow, monitoring multiple engine operating parameters, estimating NOx produced by the engine, and storing the NOx estimate in the memory may be performed once per engine cycle. Storing the NOx estimate in memory may include adding the NOx estimate to an accumulated NOx estimate in memory.The method includes determining a set of model constants. Estimating NOx includes estimating NOx produced by the internal combustion engine based on a product of a function of fuel mass flow and at least one of the model constants and a function of the plurality of engine operating parameters and remaining ones of the model constants.Storing the NOx estimate in memory may include adding the NOx estimate to an accumulated NOx estimate in memory.Monitoring a plurality of engine operating parameters may include determining a charge mass value corresponding to a mass of charge entering the engine. The determination of a charge mass value may include a determination of a charge mass flow value corresponding to a mass flow of the charge entering the internal combustion engine, a determination of a rotational speed of the engine, and a determination of the charge mass value as a function of the charge mass flow value and the rotational speed of the engine.Monitoring a plurality of engine operating parameters may include determining a charge composition value corresponding to at least a partial composition of charge entering the engine. Determining a charge composition value may include determining an exhaust gas recirculation portion value corresponding to a portion of recirculated exhaust gas in the charge entering the engine. The determination of an exhaust gas recirculation portion value may include a determination of a charge flow rate value corresponding to a flow rate of the charge entering the internal combustion engine, a determination of an exhaust gas recirculation portion flow rate value corresponding to a flow rate of recirculated exhaust gas entering the internal combustion engine, and a determination of the exhaust gas recirculation portion value as a function of the charge flow rate value and the exhaust gas recirculation portion flow rate value. Determining a filling composition value may further include determining a second order exhaust gas recirculation portion value as a function of the exhaust gas recirculation portion value.Monitoring a plurality of engine operating parameters may alternatively or additionally include determining a charge temperature value corresponding to a temperature of the charge entering the engine. Monitoring a plurality of engine operating parameters may alternatively or additionally include determining a fuel injection timing value corresponding to a timing of supplying fuel to the engine relative to a reference timing value. Monitoring a plurality of engine operating parameters may alternatively or additionally include determining a speed of the engine. Monitoring a plurality of engine operating parameters may alternatively or additionally include determining an engine operating temperature. Determining an engine operating temperature may include determining a coolant temperature corresponding to a temperature of coolant circulating through the engine. Alternatively or additionally, determining an engine operating temperature may include determining an oil temperature in the internal combustion engine.A fuel system may include a fuel rail fluidly connected to a plurality of fuel injectors. The number of fuel injectors may be configured to selectively supply fuel from the fuel rail to the engine. Monitoring a plurality of engine operating parameters may include determining fuel rail pressure corresponding to a fuel pressure in the fuel rail.Each of the plurality of engine operating parameters is represented by an engine operating parameter variable T N where N is a positive integer greater than 1. The function of the plurality of engine operating parameters may be of the form (T 1+ T 2+... + T N). The method may further include determining a number of model constants. The estimation of NOx is performed by estimating the NOx (NO XE) generated by the internal combustion engine according to the equation NO XE= ( K·FF)·T 1+ T 2+... + T N), where FF is the fuel quantity flow and K is one of the number of model constants. The function of the plurality of engine operating parameters may be of the form [(C 1 · T 1) + ( C 2 · T 2)... + ( C N · T N)] where C 1, C 2,..., C N are the remaining one of the number of model constants.The object mentioned at the beginning is further achieved by a method for estimating NOx, comprising the steps indicated in claim 11.Determining a fuel flow rate, determining a fuel injection timing, determining an engine speed, determining a charge mass, determining a charge composition, determining a charge composition, estimating NOx produced by the engine, and storing the NOx estimate in the memory may be performed once per engine cycle. The method may further include monitoring engine cycles by monitoring an engine position relative to an engine reference position. Storing the NOx estimate in memory may include adding the NOx estimate to an accumulated NOx estimate in memory.The method may further include determining a number of model constants, wherein estimating NOxincludes estimating NOxgenerated by the engine as a function of the number of model constants. The estimation of NOx is carried out by estimating (NO XE) generated by the internal combustion engine according to the function NO XE= ( K·FF)·[(C 1 ·C M) + ( C 2 ·C C) + ( C 3· C T) + ( C 4 ·FT)+(C 5 ·ES)+C6], wherein FF is the fuel quantity flow, CMthe filling mass, CCthe filling composition, C T the charge temperature, FT the fuel injection timing, ES the engine speed, and K and C 1 to C 6 the number of model constants. Determining a charge mass may include determining a charge flow corresponding to a flow of the charge entering the engine and determining the charge mass as a function of the charge flow and engine speed. Determining a charge composition may include determining an exhaust gas recirculation fraction corresponding to a fraction of recirculated exhaust gas in the charge delivered to the engine. Determining an exhaust gas recirculation fraction may include determining an exhaust gas recirculation flow corresponding to a mass flow of recirculated exhaust gas entering the engine and determining the exhaust gas recirculation fraction value as a function of the charge flow and the exhaust gas recirculation flow. Determining a filling composition value may further include determining a second order exhaust gas recirculation portion value as a function of the exhaust gas recirculation portion value and calculating the filling composition value as a sum of the exhaust gas recirculation portion value and the second order exhaust gas recirculation portion value, such that estimating NOx comprises estimating NOx produced by the internal combustion engine according to the function NOx E= ( K·FF·[(C 1 ·f(CF,ES))+(C 2 ·[EGR F+ f(EGR F)) + ( C 3· C T) + ( C 4 ·FT)+(C 5 ·ES)+C 6] wherein CF is the charge flow, f(CF,ES) is the charge mass, EGR F are the exhaust gas recirculation portion value and f(EGR F) are the second order exhaust gas recirculation portion value.The object mentioned at the beginning is further achieved by a system for estimating NOx, which system has the features specified in claim 18.The memory may include a register in which an accumulated NOx estimate is stored. The instructions may further include instructions executable by the control circuit to add the NOx estimate to the accumulated NOx estimate stored in the memory.The system may further include a motor position sensor configured to generate a motor position signal corresponding to a rotational position of the motor relative to a reference position. The instructions may further include instructions to process the engine position signal to generate an engine position value, monitor the engine position value, and determine the fuel amount current value, determine the plurality of operating parameters, and estimate NOxgenerated by the engine once per engine cycle.The system may further include means for determining a charge mass value corresponding to a mass of the charge entering the engine, means for determining a charge composition value corresponding to at least a partial composition of the charge entering the engine, means for determining a charge temperature corresponding to a temperature of the charge entering the engine, means for determining a fuel injection timing value corresponding to a timing of supplying fuel to the engine relative to a reference timing value, and means for determining an engine speed value corresponding to a rotational speed of the engine. The plurality of operating parameters associated with operation of the engine may include the charge mass value, the charge composition value, the charge temperature value, the fuel injection timing value, and the engine speed value. The system also includes a number of model constants stored in the memory. The instructions include estimating NOx (NO XE) produced by the engine according to the equation NO XE= ( K·FF)·[(C 1 ·C u) + ( C 2 ·C C) + ( C 3· C T) + ( C 4 ·FT)+(C 5 ·ES)+C6], where FF is fuel flow, CMis charge mass, CCis charge composition, C T the charge temperature, FT the fuel injection timing, ES the engine speed, and K and C 1 to C 6 the number of model constants. The device for determining a filling composition value may comprise a device for determining an exhaust gas recirculation percentage value corresponding to a percentage of recirculated exhaust gas in the filling entering the internal combustion engine. The device for determining a filling composition value may further comprise a device for determining a second-order exhaust gas recirculation portion value as a function of the exhaust gas recirculation portion value and for determining the filling composition value as a sum of the exhaust gas recirculation portion value and the second-order exhaust gas recirculation portion value.Brief Description of the FiguresFIG. 1 is a block diagram of an illustrative embodiment of a system for estimating NOx produced by an internal combustion engine. FIG. 2 is a block diagram of an illustrative embodiment of the fuel system depicted in FIG. 1. FIG. 3 is a flow diagram of an illustrative embodiment of a method for estimating NOx produced by an internal combustion engine. FIG. 4 is a flow diagram of an illustrative embodiment of a method for performing monitoring of one or more engine operating parameters in the method depicted in FIG. 3. FIG. 5 is a flow diagram of an illustrative embodiment of a method for performing the determination of fill mass in the method depicted in FIG. 4. FIG. 6 is a flow diagram of an illustrative embodiment of a method for performing the at least partial determination of fill composition in the method of FIG. 4. FIG. 7 is a block diagram of an illustrative embodiment of the control circuit of FIG. 1 configured to estimate NOxgenerated by the internal combustion engine according to a particular implementation of the method of FIGS. 3-6. FIG. 8 is a block diagram of an illustrative embodiment of the logic block of FIG. 7 for determining the exhaust gas recirculation and charge flow.In order to aid in an understanding of the principles of the invention, reference will now be made to a number of illustrative embodiments shown in the accompanying drawings, and specific terms will be used to describe the same.Referring now to FIG. 1, a schematic illustration of an illustrative embodiment of a system 10 for estimating NOxgenerated by an internal combustion engine is shown. In the depicted embodiment, system 10 includes an internal combustion engine 12 having an intake manifold 14 fluidly connected to an outlet of a compressor 16 of a turbocharger 18 via an intake conduit 20. The compressor 16 includes a compressor inlet connected to an intake line 22 for receiving fresh air. In some embodiments, as shown in phantom in FIG. 1, system 10 may include a charge air cooler 24 of known construction disposed in series with intake conduit 20 between turbocharger compressor 16 and intake manifold 14. The turbocharger compressor 16 is mechanically coupled to a turbocharger turbine 26 via a rotatable driveshaft 28, and the turbine 26 includes a turbine inlet fluidly connected to an exhaust manifold 30 of the engine 12 by an exhaust conduit 32. The turbine 26 has a turbine outlet which is connected to the ambient atmosphere in a fluid-conducting manner by an exhaust gas line 34. The turbocharger 18 is shown surrounded by a dashed box in FIG. 1 to show that some embodiments, such as the illustrated embodiment, may include the turbocharger 18, while others may not. Accordingly, the turbocharger 18 is not a necessary component for estimating NOxgenerated by the engine 12 in accordance with the present disclosure, although in embodiments including the turbocharger 18, one or more engine operating parameters related to operation of the turbocharger 18 that affect the amount and / or rate of NOxgenerated by the engine 12 may be considered in estimating NOxin accordance with the present disclosure.In the embodiment shown in FIG. 1, the system 10 further includes an exhaust gas recirculation (EGR) system 35 having an exhaust gas recirculation valve 38 disposed in series with an exhaust gas recirculation line 36 fluidly connected at one end to the intake line 20 and at an opposite end to the exhaust line 32. An exhaust gas recirculation cooler 40 of known construction may optionally be arranged in series with the exhaust gas recirculation line 36 between the exhaust gas recirculation valve 38 and the intake line 20, as shown in phantom in Figure 1. The exhaust gas recirculation system 35 is shown surrounded by a dashed box in FIG. 1 to indicate that some embodiments, such as the illustrated embodiment, may include the exhaust gas recirculation system 35, but others may not. Accordingly, the exhaust gas recirculation system 35 is not a necessary component for estimating NOxgenerated by the engine 12 in accordance with the present disclosure, although in embodiments including the exhaust gas recirculation system 35, one or more engine operating parameters related to the operation of the exhaust gas recirculation system 35 that affect the amount and / or rate of NOxgenerated by the engine 12 may be considered in estimating NOxin accordance with the present disclosure. This disclosure further contemplates so-called "in-cylinder" exhaust gas recirculation systems in which valve timings are affected so that a certain amount of combusted charge remains in the cylinders, and that one or more engine operating parameters related to the operation of such an exhaust gas recirculation system that affect the amount and / or rate of NOxgenerated by the internal combustion engine 12 may likewise be considered in estimating NOxin accordance with the present disclosure.The system 10 includes a control circuit 42 generally operable to control and oversee the overall operation of the motor 12. The control circuit 42 includes a memory unit 45 and a number of inputs and outputs for coupling to various sensors and systems connected to the internal combustion engine 12. The control circuit 42 is illustratively microprocessor based, although this disclosure contemplates other embodiments in which the control circuit 42 may alternatively be or may comprise a general purpose control circuit or application specific control circuit capable of operation described below. In any case, the control circuit 42 may be a known control circuit sometimes referred to as an electronic or engine control module (ECM), an electronic or engine control unit (ECU), or the like. Illustratively, the memory 45 of the control circuit 42 stores one or more sets of instructions executable by the control circuit 42 to estimate NOxgenerated by the internal combustion engine 12, as will be described in more detail below.The control circuit 42 includes a number of inputs for receiving signals from various sensors or sensing systems associated with the system 10. For example, the system 10 includes an engine speed and position sensor 44 electrically connected to an engine speed and position input ES / P of the control circuit 42 via a signal path 46. The engine speed and position sensor 44 is conventional and is operable to generate a signal from which the rotational speed of the engine, ES, and the engine position, EP, relative to a reference position may be determined in a conventional manner. The engine position EP may be, for example, or may include an angle of the engine crankshaft (not shown), i.e., a crankshaft angle relative to a reference crankshaft angle, e.g., top dead center (TDC) of a particular one of the pistons (not shown). In one embodiment, sensor 44 is a Hall effect sensor that is operable to determine the motor speed and position by detecting the passage of a number of spaced-apart teeth formed on a tooth or resolver wheel. Alternatively, the motor speed and position sensor 44 may be any other known sensor operable as just described, including, but not limited to, a variable reluctance sensor or the like. According to another alternative, the engine speed and position sensor 44 may be provided in the form of two separate sensors, one of which only senses the engine speed and the other of which only senses the engine position.The system 10 further includes an intake manifold temperature sensor 48 disposed in fluid communication with the intake manifold 14 of the engine 12 and electrically connected via a signal path 50 to an intake manifold temperature input IMT of the control circuit 42. The intake manifold temperature sensor 48 may be of known construction and is operable to generate a temperature signal on the signal path 50 indicative of the temperature of a "charge" flowing into the intake manifold 14. The term "charge" for purposes of this disclosure is generally defined as the gas that is mixed with fuel for combustion in the cylinders of the engine. In embodiments having an "in-cylinder" exhaust gas recirculation system as briefly described above, the term "charge" is defined as a combination of the fresh air flowing into the intake manifold 14 through the conduit 20 and the remaining, i.e., remaining, burned gas in the cylinders from the previous combustion cycle of the engine 12. For example, in embodiments including the exhaust gas recirculation system 35, the charge flowing into the intake manifold 14 is generally composed of fresh air supplied to the intake conduit 20 that may or may not be supplied by the turbocharger compressor 16, depending on whether the system 10 includes the turbocharger 18, combined with recirculated exhaust gas supplied through the exhaust gas recirculation valve 38. For example, in embodiments that do not include the exhaust gas recirculation system 35 or an "in-cylinder" exhaust gas recirculation system, the charge flowing into the intake manifold 14 is generally the fresh air supplied to the intake conduit 20 that may or may not be supplied by the turbocharger compressor 16, depending on whether the system 10 includes the turbocharger 18. Although the intake manifold temperature sensor 48 is shown in FIG. 1 as being disposed in fluid communication with the intake manifold 14, the sensor 48 may alternatively be disposed in fluid communication with the intake conduit 20. In such embodiments including the exhaust gas recirculation system 35, the sensor 48 will generally be in fluid communication with the intake conduit 20 but downstream of the junction of the intake conduit 20 and the exhaust gas recirculation conduit 36.The system 10 further includes an intake manifold pressure sensor 52 disposed in fluid communication with the intake manifold 14 and electrically connected to an intake manifold pressure input IMP of the control circuit 42 via a signal path 54. The intake manifold pressure sensor 52 may be of known construction and is operable to generate a pressure signal on the signal path 54 indicative of the pressure of the charge flowing into the intake manifold 14. Although the intake manifold pressure sensor 52 is shown in FIG. 1 as being disposed in fluid communication with the intake manifold 14, the sensor 52 may alternatively be disposed in fluid communication with the intake conduit 20.Illustratively, as will be described in more detail below, the control circuit 42 may be operable to estimate the mass flow of the charge entering the intake manifold, i.e., the charge mass flow, e.g., as a function of one or more engine operating parameters. As shown in phantom in FIG. 1, the system may alternatively or additionally include a mass flow sensor 76 disposed in fluid communication with the intake conduit 20 (or alternatively, in fluid communication with the intake manifold 14) and electrically connected to a charge mass flow input CMF of the control circuit 42 via a signal path 78. In this embodiment, mass flow sensor 76 may be of known construction and is operable to generate a mass flow signal on signal path 78 indicative of the mass flow of charge entering intake manifold 14. In embodiments where sensor 76 is included in system 10, the mass flow signal generated by sensor 76 may be used to determine the mass flow of the charge entering intake manifold 14, i.e., the charge flow, instead of a charge flow estimation algorithm, or to supplement an estimated charge mass flow value generated by a charge flow estimation algorithm, to compare and / or verify therewith. In the former case, a charge mass flow estimation algorithm may additionally be used to provide an estimated charge mass flow value which may be used to supplement, compare and / or verify the mass flow signal generated by the sensor 76.In embodiments of the system 10 having the exhaust gas recirculation system 35, the system further includes a differential pressure or ΔP sensor 56 fluidly connected by a conduit 60 at one end to the exhaust gas recirculation conduit 36 adjacent an exhaust inlet of the exhaust gas recirculation valve 38 and fluidly connected at its opposite end to the exhaust gas recirculation conduit 36 adjacent an exhaust outlet of the exhaust gas recirculation valve 38 by a conduit 58. Alternatively, the ΔP sensor 56 may be fluidly connected via another flow restrictor or flow restrictor disposed in series with the exhaust gas recirculation line 36. In any event, the ΔP sensor 56 may be of known construction and is electrically connected to a ΔP input of the control circuit 42 via a signal path 62. The ΔP sensor 62 is operable to generate a differential pressure signal on the signal path 62 indicative of the pressure differential across the exhaust gas recirculation valve 38 or other flow restriction or flow restriction device disposed in series with the exhaust gas recirculation line 36.In embodiments of the system 10 including the exhaust gas recirculation system 35, the system 10 further includes an exhaust gas recirculation valve actuator 64 and an exhaust gas recirculation valve position sensor 68 operatively connected to the exhaust gas recirculation valve actuator 64. The exhaust gas recirculation valve actuator 64 may be of a conventional type and is electrically connected via a signal path 66 to an exhaust gas recirculation valve control output EGRC of the control circuit 42. The exhaust gas recirculation valve actuator 64 is responsive to control signals generated by the control circuit 42 at the EGRC output for controlling the position of the exhaust gas recirculation valve 38 with respect to a reference position. In this regard, the EGR valve position sensor 68 is a conventional sensor electrically connected via a signal path 70 to an EGR valve position input EGRP of the control circuit 42 and operable to generate a position signal on the signal path 70 indicative of a position of the EGR valve 38 relative to a reference position. The control circuit 42 is operable to control the exhaust gas recirculation valve 38 to a desired exhaust gas recirculation valve position by generating the exhaust gas recirculation valve control signal EGRC on the signal path 66 based on the exhaust gas recirculation position signal EGRP generated on the signal path 70 by the exhaust gas recirculation valve position sensor 68, using known control techniques. Thus, by controlling the position of the exhaust gas recirculation valve 38, the control circuit 42 is operable to control the flow of exhaust gas recirculated from the exhaust manifold 30 to the intake manifold 14.Illustratively, as will be described in more detail below, in embodiments including the exhaust gas recirculation system 35, the control circuit 42 may be operable to estimate the mass flow of recirculated exhaust gas, i.e., the exhaust mass flow from the exhaust manifold 30 into the intake manifold 14 through the intake valve 38 and the conduit 36, as a function of one or more engine operating parameters. Alternatively or additionally, as shown in phantom in FIG. 1, system 10 may include a mass flow sensor 84 disposed in fluid communication with exhaust gas recirculation line 36 and electrically connected to an exhaust gas recirculation mass flow input EGRMF of control circuit 42 via signal path 86. In this embodiment, mass flow sensor 84 may be of known construction and operable to generate a mass flow signal on signal path 86 indicative of the mass flow of exhaust gas flowing through exhaust gas recirculation line 36 into intake manifold 14 of engine 12. In embodiments where sensor 84 is included in system 10, the mass flow signal generated by sensor 84 may be used to determine the mass flow of recirculated exhaust gas flowing through exhaust recirculation line 36 and entering intake manifold 14, i.e., the exhaust recirculation flow rate, instead of an exhaust recirculation flow rate estimation algorithm, or to supplement, compare, and / or verify an estimated exhaust recirculation flow rate generated by an exhaust recirculation flow rate estimation algorithm. In the former case, an EGR flow rate estimation algorithm may additionally be used to provide an estimated EGR flow rate value which may be used to supplement, compare and / or verify the mass flow signal generated by sensor 84.Illustratively, as will be described in more detail below, in some embodiments, the control circuit 42 may be operable to estimate the temperature of the exhaust gas generated by the internal combustion engine 12, e.g., as a function of one or more engine operating parameters. Alternatively or additionally, as shown in phantom in FIG. 1, system 10 may include an exhaust temperature sensor 80 in fluid communication with exhaust conduit 32 (or in fluid communication with exhaust manifold 30) and electrically connected to an exhaust temperature input ET of control circuit 42 via signal path 82. In this embodiment, the engine exhaust temperature sensor 80 may be of known construction and operable to generate a temperature signal on signal path 82 indicative of the temperature of the exhaust gas generated by the internal combustion engine 12. In embodiments where sensor 80 is included in system 10, the exhaust temperature signal generated by sensor 80 may be used to determine the temperature of the exhaust gas generated by engine 12 instead of an exhaust temperature estimation algorithm, or to supplement, compare and / or verify an estimated exhaust temperature value generated by an exhaust temperature estimation algorithm. In the former case, an exhaust temperature estimation algorithm may additionally be used to provide an estimated exhaust temperature value which may be used to supplement, compare and / or verify the exhaust temperature signal generated by the sensor 80.The system 10 may further include a motor temperature sensor 88 electrically connected to a motor temperature input ENT of the control circuit 42 via a signal path 90, as shown in phantom in FIG. 1, in one or more embodiments. In embodiments including the engine temperature sensor 88, the sensor 88 may illustratively be provided in the form of a conventional coolant temperature sensor configured to generate an engine temperature signal indicative of the engine coolant temperature. Alternatively or additionally, the sensor 88 may be or include a conventional oil temperature sensor configured to generate an engine temperature signal indicative of the engine oil temperature. In either case, the engine temperature signal generated by the engine temperature sensor 88 is representative of the operating temperature of the engine 12.The system 10 further includes a fuel system 72 electrically connected to a fuel command output terminal of the control circuit 42 via a series of signal paths 74. In the embodiments shown in FIGS. 1 and 2, the engine 12 is a conventional six cylinder engine (e.g., cylinders C 1-C 6), and the fuel system 42 includes six associated fuel injectors I 1-I 6, each disposed in fluid communication with a corresponding one of the six cylinders C 1-C 6. In the illustrated embodiment, the six fuel injectors I1-I6 are each fluidly connected to a fuel rail 96 via a common fuel line 98, the fuel rail including pressurized fuel supplied by a conventional fuel pump (not shown). The six fuel injectors I1-I6 are further electrically connected to the control circuit 42 via the signal paths 74. Each of the six fuel injectors I1-I6 is individually controlled by the control circuit 42 and the fuel command output terminal of the control circuit is therefore labeled FC1-FC6 in FIG. 1 to indicate that the control circuit 42 generates six separate fuel signals on six respective signal paths 74. The fuel system 72 is generally responsive to the fuel instructions FC1-FC6 generated by the control circuit 42 on the signal paths 74 to supply fuel to the engine 12 through the fuel injectors I1-I6, and the control circuit is configured to generate such fuel metering instructions FC1-FC6 in a manner well known in the art. More specifically, the fuel metering instructions FC1-FC6 each include a fuel injection timing component FT and a fuel amount component FF.The fuel injection timing component FT corresponds to the fuel injection timing by each of the fuel injectors I 1-I 6 relative to a reference timing. Illustratively, fuel injection timing is based on the position of engine 12, e.g., crank angle, relative to a reference engine position, e.g., top dead center TDC of the piston (not shown) in each cylinder C 1-C 6. The control circuit 42 then controls, via the fuel injection timing constituent FT of the fuel metering instructions FC1-FC6, a start-of-injection (SOI) for each fuel injector I1-I6 corresponding to the engine position relative to the reference engine position at which the fuel injector I1-I6 begins to inject fuel into a corresponding one of the cylinders C1-C6. The fuel amount component FF corresponds to the fuel amount flow supplied from each of the fuel injectors I 1-I 6 to a corresponding one of the cylinders C 1-C 6. The fuel quantity flow FF can typically be measured in units of mm 3 / stroke. It should be understood that although a six cylinder engine 12 is shown in FIG. 2, the engine 12 may alternatively have any number of cylinders, and that the fuel flow rate FF corresponds to the fuel flow rate supplied by any such number of fuel injectors to the engine 12.In one or more embodiments, as shown in phantom in FIG. 1, fuel system 72 may include a pressure sensor 92 electrically connected to a rail pressure input RP of control circuit 42 via a signal path 94. As shown in FIG. 2, pressure sensor 92 is fluidly connected to fuel rail 96 (or to common rail 98) and the pressure signal generated by sensor 92 therefore indicates the pressure of the fuel in fuel rail 96, i.e., rail pressure.This disclosure describes embodiments in which some of the information from which NOxgenerated by the internal combustion engine is calculated and / or derived may be estimated by one or more conventional estimation algorithms, i.e., so-called "virtual sensors.". It should be appreciated that for purposes of this disclosure, any one or more of the engine operating conditions from which the NOxgenerated by the internal combustion engine is calculated and / or derived may be determined using one or more conventional estimation algorithms executed by the control circuit 42 to estimate one or more such engine operating conditions based on one or more engine operating parameters.Referring now to FIG. 4, shown is a flow diagram of an illustrative embodiment of a method 100 for estimating NOxgenerated by the internal combustion engine 12. Illustratively, the method 100 is stored in the memory 45 of the control circuit 42 in accordance with instructions executable by the control circuit 42 to estimate NOxgenerated by the internal combustion engine 12. The method 100 begins with a step 102 and thereafter, in step 104, the control circuit 42 is operable to monitor the fuel flow rate FFcorresponding to the flow rate of fuel supplied by the plurality of fuel injectors to the internal combustion engine 12. Illustratively, the control circuit 42 is operable to execute step 104 by monitoring the fuel metering instructions generated by the control circuit 42 and determining the fuel quantity flow FF therefrom. Following step 104, control circuit 42 is operable, at step 106, to monitor a plurality of engine operating parameters EOP. The plurality of engine operating parameters EOP überwacht by the control circuit 42 in step 106 generally include engine operating parameters that affect the amount and / or rate of NOxgenerated by the internal combustion engine 12, and the accuracy of the estimated NOxvalue will generally depend at least in part on the quality and quantity of the engine operating parameters EOP In step 106. Examples of motor operating parameters EOPthat may be monitored by the control circuit 42 in step 106 are then given.From step 106, the method 100 proceeds to step 108 in which the control circuit 42 is operable to retrieve a number of model constants MC from the memory 45. Generally, the number of model constants MC will be dictated by the choice of the NOx estimation model and the values of the model constants MC will be determined using test data. A procedure for determining the model constant MC for an example of a NOx model will be described with reference to an example given below. From step 108, the method 100 proceeds to step 110 in which the control circuit 42 is operable to calculate an estimated NOxvalue NO XE corresponding to an estimate of the NOxgenerated by the internal combustion engine 12. In the illustrated method, the control circuit 42 is operable to calculate NO XE generally based on a product of the fuel flow FF and a function of the plurality of engine operating parameters EOP. In equation form and including the model constants MC, the control circuit 42 is operable, at step 110, to calculate NO XE according to the relationship NO XE= f(MC, FF)·f(MC, EOP), where f(MC, FF) is a function of the fuel flow rate FF and at least one of the model constants MC, and f(MC, EOP) is a function of the plurality of engine operating parameters EOP and remaining ones of the model constants MC.Generally, this NOx estimation model is based primarily on the fuel flow FF and a function of several other engine operating parameters that affect NOx generation. In an illustrative embodiment, the function of the plurality of engine operating conditions EOC has the general form (T 1+ T 2+... + T N), where each T X- value corresponds to a different one of the plurality of engine operating conditions, and where N may be any positive integer greater than 1. The NOx estimation model then takes the general form, where K represents one of the model constants MC. Including the remaining model constants in the equation (1), the NOx estimation model takes the general form, where C 1, C 2,..., C N represent remaining ones of the model constants MC. It should be understood that although equations (1) and (2) represent an illustrative embodiment of the NOx estimation model, other functions of the plurality of engine operating parameters EOP are contemplated by this disclosure.After step 110, the method 100 proceeds to step 112 in which the control circuit 42 is operable to store the NOx estimate NO XE in the memory 45. Illustratively, the memory 45 includes an accumulator that has stored therein an accumulated NOx estimate corresponding to an amount of NOx generated by the engine 12 since the accumulator was reset last time. In this embodiment, the control circuit 42 is operable, at step 112, to store the NOx estimate NO XE in the memory 45 by adding the current NO XE- value to the accumulated NOx estimate stored in the accumulator of the memory 45. Those skilled in the art will know other conventional approaches for storing the NOx estimate NO XE in the memory 45, and any such conventional techniques are contemplated by the present disclosure.From step 112, the method 100 proceeds to step 114 in which the control circuit 42 is operable to monitor the engine position EP and then to step 116 in which the control circuit 42 is operable to determine whether the current engine cycle has been completed based on EP. Illustratively, control circuit 42 is operable to perform steps 114 and 116 by monitoring the signal generated by engine speed and position sensor 44 and determining that the current engine cycle has been completed when EP reaches a particular engine position. If, in step 114, the control circuit 42 determines that the current engine cycle is not yet complete, the method 100 returns to step 114. If, in step 114, the control circuit 42 determines that the current engine cycle is complete, the method 100 returns to step 104. Thus, the NOx estimate NO XE is calculated once per engine cycle in the illustrated embodiment, although it should be understood that the NOx estimate NO XE may alternatively be calculated more or less frequently.Referring now to FIG. 4, a flowchart of an illustrative embodiment of step 106 of method 100, i.e., monitoring multiple engine operating parameters, is shown. Generally, it has been found that engine operating parameters that sufficiently affect NOx generation to warrant inclusion in the NOx estimation model include, but are not limited to, the mass, composition (at least a partial composition), and temperature of the charge entering the engine 12, the timing of fuel entering the engine, i.e., the fuel metering component FT of the fuel instructions generated by the control circuit 42, and optionally one or more additional parameters AP that affect NOx generation. For example, in the embodiment shown in FIG. 4, step 104 begins at step 150 where the control circuit 42 is operable to determine the charge mass CM entering the internal combustion engine. Thereafter, in step 152, the control circuit 42 is operable to determine at least the partial composition CC of the charge entering the internal combustion engine 12. Following step 152, the control circuit 42 is operable, at step 154, to determine the temperature CTof the charge entering the engine 12. Thereafter, in step 156, the control circuit 42 is operable to determine the injection timing FT of the fuel entering the engine 12. Following step 156, the control circuit 42 is operable to determine one or more additional parameters AP that sufficiently affect NOx generation to warrant inclusion in the monitored engine operating parameters EOP.In embodiments of method 100 where step 106 is implemented according to the method illustrated in FIG. 4, the NOx estimation model illustratively takes the form where C M is mass of charge, C C is charge composition, C T is charge temperature, FT is fuel injection timing, AP includes one or more additional parameters, i.e., additional engine operating conditions, and K and C 1- C 6 are model constants MC. Examples of the one or more additional parameters AP may include, but are not intended to be limited to, the speed of the engine, which may be provided by the engine speed signal ES generated by the engine speed and position sensor 44, and / or the operating temperature of the engine, which may be provided by the engine temperature signal ET generated by the engine temperature sensor 88 in the form of an engine coolant temperature signal and / or an engine oil temperature signal, and / or the fuel rail pressure, which may be provided by the fuel rail pressure signal RP generated by the pressure sensor 92.Referring now to FIG. 5, a flow diagram of an illustrative embodiment of step 150 of the engine operating parameter monitoring method of FIG. 4 is shown. In the embodiment shown in Figure 5, step 150 begins at step 170 in which the control circuit 42 is operable to determine the charge flow rate CF entering the engine corresponding to the flow rate of charge entering the engine 12. In one embodiment, control circuit 42 is operable to perform step 170 by determining CFin accordance with a conventional charge flow estimation algorithm, an example of which will be described in more detail below for an illustrative configuration of motor 12. Alternatively, in embodiments of the system including mass flow sensor 76, control circuit 42 may be operable to perform step 170 by monitoring the signal generated by mass flow sensor 76 and processing this signal in a known manner to determine charge flow rate CF. Thereafter, in step 172, the control circuit 42 is operable to monitor the engine speed ES corresponding to the speed of the engine 12. Illustratively, the control circuit is operable to execute step 172 by monitoring the engine speed signal generated by the engine speed and position sensor 44 and processing this signal in a known manner to determine the engine speed value ES. Thereafter, in step 174, the control circuit is operable to calculate the fill mass CM as a function of the fill mass flow CF and the engine speed ES, i.e., CM=f(CF, ES). A specific example of the function of calculating the charge mass CM for an illustrative engine configuration will be given below with reference to an overall system example.Generally, the determination of one or more of the engine operating parameters EOP by the control circuit 42 according to the method of step 106 shown in FIG. 4 will depend at least in part on the configuration of the engine 12. For example, in embodiments where the charge composition C C is determined using a conventional estimation model, the shape of this model may be different for engines that include the exhaust gas recirculation system 35 than those that do not include it. Referring, for example, to FIG. 6, a flowchart of an illustrative embodiment of step 152 of the engine operating parameter monitoring step 106 of FIG. 4 is shown for an example engine configuration that includes the exhaust gas recirculation system 35. In the illustrated embodiment, step 152 begins at step 180, where the control circuit 42 is operable to determine a proportion of EGR F recirculated exhaust gas in the charge entering the engine. Illustratively, as will be described in more detail in the following system example, control circuit 42 may be operable to determine EGR F by first determining the mass flow EGRFof recirculated exhaust gas and the mass flow CFof the charge entering engine 12 and calculating EGR F as a ratio of EGRFand CF. However, it should be appreciated that the present disclosure contemplates other conventional approaches for determining the proportion of recirculated exhaust gas in the charge entering the internal combustion engine 12.It should be appreciated that any of the plurality of engine operating conditions may be or may include higher order EOC terms. For example, in the method depicted in FIG. 6, filling composition C C further includes a second order exhaust gas recirculation portion component that affects NOx generation. More specifically, step 180 proceeds to step 182, in which control circuit 42 is operable to calculate a second order exhaust gas recirculation portion term EGR F2 as a function of the exhaust gas recirculation portion EGR F. A specific example of the function of calculating EGR F2 as a function of EGR F for an illustrative engine configuration is provided in the following overall system example.Example:Referring now to FIG. 7, an illustrative embodiment of some of the functional features of the control circuit 42 is shown for a particular implementation of the motor 12. It should be appreciated that the logic blocks shown in FIG. 7 are provided by way of example only and that the NOx estimation model may alternatively be configured for other implementations of the engine 12 as described above. For the embodiment shown in FIG. 7, the engine 12 is a six cylinder engine including the turbocharger 18 and the exhaust gas recirculation system 35. Illustratively, the control circuit 42 includes conventional exhaust gas recirculation and charge flow determination logic 200 configured to estimate the charge flow rate CF and the recirculated exhaust gas flow rate EGRF as a function of the plurality of engine operating parameters. The control circuit 42 further includes an arithmetic block 204 having a multiplication input receiving the exhaust gas recirculation amount current value EGRF and having a division input receiving the charge amount current value CF and producing at an output the exhaust gas recirculation portion value EGR F as a ratio of EGRF and CF. As an alternative to the EGR and charge flow rate determination logic block 200, the EGR flow rate value and charge flow rate value may be determined from EGR mass flow and charge mass flow signals obtained from respective mass flow sensors 76 and 84, in embodiments including such mass flow sensors. In any case, the control circuit 42 further comprises conventional fuel metering determination logic 202 configured to receive the engine speed signal ES and other inputs and to calculate the fuel metering instructions FC1-FC6 in a conventional manner as a function thereof. The corresponding fuel flow rate FF and fuel injection timing FT are provided as inputs to the EGR and charge flow rate determination logic block 200.Referring now to FIG. 8, a flow diagram of an illustrative embodiment of the exhaust gas recirculation and charge mass flow determination logic 200 of FIG. 7 is shown. Logic block 200 of FIG. 8 includes a charge flow rate determination logic block 210 receiving as inputs the pressure differential signal ΔP on signal path 62, the intake manifold temperature signal IMT on signal path 50, the intake manifold pressure signal IMP on signal path 54, and the engine speed signal ES on signal path 46. Charge flow rate determination logic block 210 is configured to process these input signals and, as a function thereof, generate the charge flow rate value CF. Logic block 200 further includes an exhaust temperature determination logic block 212 receiving as inputs the charge flow rate value CF, the intake manifold temperature signal IMP on signal path 50, the intake manifold pressure signal IMP on signal path 54, the engine speed signal ES on signal path 46, and the fuel amount flow and fuel injection timing values FF and FT, respectively, generated by the fuel metering determination logic block 202. The exhaust temperature determination logic block 212 is configured to process these input signals and, as a function thereof, generate an estimated exhaust temperature value T EX. In embodiments of system 10 including exhaust temperature sensor 80, exhaust temperature signal ET produced by temperature sensor 80 may be directly provided to exhaust gas recirculation mass flow determination logic block 214, and exhaust temperature determination block 212 may be omitted. Logic block 200 further includes an exhaust gas recirculation flow rate determination logic block 214 receiving as inputs the pressure difference signal ΔP on signal path 62, the intake manifold pressure signal IMP on signal path 54, the exhaust temperature value T EX, generated by exhaust temperature determination logic block 212, and an effective flow area value EFA generated by an effective flow area determination logic block 216. The EGR flow rate determination logic block 214 is configured to process these input signals and generate the EGR flow rate value EGRF as a function thereof. The effective flow area determination logic block 216 receives the EGR valve position signal EGRP on signal path 70 and is configured to process this signal to determine and generate an effective flow area value EFA corresponding to an effective flow area through the EGR valve 36.The charge flow rate determination logic block 210 is operable to calculate an estimate of the charge flow rate CF by first estimating the volumetric efficiency (η V) of the charge intake system and then calculating CF as a function of (η V) using a conventional velocity / density equation. Any known approach for estimating η V may be used, and in an illustrative embodiment of logic block 210, η V is calculated according to a known Taylor Mach number-based volumetric efficiency equation, which is: where A 1, A 2, A 3 and B are all calibrateable parameters fitted into the volumetric efficiency equation based on map-based engine data, bore is the intake valve bore length, D is the intake valve diameter, stroke is the piston stroke length, wherein bore, D and stroke depend on the engine geometry, γ and R are known constants (e.g., γR=387.414 J / kg / degree K), IT is engine speed, IMP is intake manifold pressure, EP is exhaust pressure, where EP=IMP+ΔP, and IMT is intake manifold temperature.With the volumetric efficiency value η V determined according to equation (4), the charge flow rate value CFis calculated by block 210 according to the equation where η V is the estimated volumetric efficiency, V DIS is the engine displacement and generally depends on the engine geometry, ES is engine speed, IMP is intake manifold pressure, R is a known gas constant (e.g., R=53.3 ft-Ibf / Ibmgrade R or R=287 J / Kggrade K), and IMT is intake manifold temperature.The exhaust temperature determination logic block 212 is operable to calculate an estimate of the engine exhaust temperature T EX according to the model, where A, B, C, and D are model constants, and LHV is a lower heating value of the fuel, which is a known constant depending on the type of fuel used by the internal combustion engine 12.The EGR flow rate determination logic block 214 is operable to calculate an estimate of the EGR flow rate value EGRFaccording to the model: where R is a known gas constant as indicated above. The effective flow area determination block 216 illustratively includes one or more equations, graphs, and / or tables that map the exhaust gas recirculation valve position EGRPto effective flow area values EFA. It should be understood that equation (7), as well as the calculation of the EGR portion value EGR F, described above, represent simplified approximations of these two parameters based on assumptions of a constant exhaust gas temperature through the EGR valve 38 and a steady state exhaust gas flow through the EGR valve 38 disregarding effects resulting from a variable time delay between the flow of recirculated exhaust gas through the EGR valve 38 and the arrival of the corresponding EGR portion in the engine cylinders.In the embodiment depicted in FIG. 7, the control circuit 42 further includes NOx determination logic 206 configured to calculate an estimated NOx value NO XE and store NO XE at a storage location 208, e.g., an estimated NOx accumulator as described above. The NOx determination logic 206 includes the method 100 shown in FIG. 3 and the methods shown in FIGS. 4-6 in the form of instructions executable by the control circuit 42 to determine NOx generated by the engine. In this example, the NOx determination logic 206 includes a specific implementation of the NOx estimation model of equation (3) above, in which the additional parameters AP comprise only the engine speed ES, the charge mass term C M is calculated in step 174 according to equation C M=[(333,3 · CF) / ES], the charge composition term C C is calculated in steps 180 and 182 as the sum of EGR F and EGR F2 where EGR F2 is calculated in step 182 according to equation EGR F2=(1 - EGR F)2, and the charge temperature term C T is determined from the temperature signal IMT generated by the intake manifold temperature sensor 48. Substituting these relationships into equation (3) yields the following NOx estimation model: where CF is the charge mass flow (kg / min), ES is the speed of engine 12 (U / min), EGR F is the proportion of recirculated exhaust gas in the charge entering engine 12, IMT is the intake manifold temperature, FT is the fuel injection timing value, and K and C are 1 to C 6 model constants, and where constant C is 2 modified to form two separate constants C 21 and C 22.An illustrative approach to determining the model constants is a Monte Carlo-like sampling of random points. An initial calibration tool is run until a match better than a first threshold, e.g., R 2 >0.8, is found. A conventional global optimization routine is then applied to the nominal solution. This procedure typically yields R 2 >0.9 on the calibration datasets and close to or over R 2 >0.9 on auxiliary datasets. A calibration data set is generally the data set from which the model constants are generated, and an auxiliary data set is one generated by the same or similar internal combustion engine 12 after the model constants have been generated. An illustrative procedure for calibrating the model constants using this approach is as follows: 1st Set equation (8) to using experimental data for NO XE, with nominal values, e.g., 0.1 for the constants K, C 1, C 3 to C 6, C 21 and C 22. 2. compare the NO XE- test data to the model data to determine fault values, e.g., R 2, etc. A percent NOx fault is illustratively used, although an absolute NOx fault may alternatively be used. 3. Let the initial optimizer run to determine a "nominal solution.". This should be done until R 2 >0.85, or the like, to ensure better final solution. 4. Let a conventional optimizer run to minimize the sum of the error terms, to minimize the sum of the quadratic error terms, or to minimize another error function.Step 3 (initial optimizer) may illustratively operate as follows: 1st read at a wormhole rate (e.g., 20-200 per 1,000). The optimizer randomly sets the calibration terms in a small range, but allows a wormhole to change a term drastically when and when. 2. read the current RSQ value. 3. start a counter for the number of iterations: a) change each parameter to obtain a high value, a low value and an original value: i) If no wormhole: + / - randomness 0-1%, i.e. new value between 0.99 and 1.01 of the old value. Parameter is allowed to go through zero if the sign of the relationship is ambiguous. ii) If wormhole: + / - randomness 0-100%, i.e., new value is between 0.01 and 2.00 of the old value. Parameters may go through zero if the sign of the relationship is ambiguous, otherwise a zero crossing may be disabled (a small absolute change instead of a percentage change must take place to go through zero). b) Repeat a) until all parameters are verified. The parameters should be changed in a random manner on each cycle. 4. increment the iterator. 5. if the iterator is < as a threshold, go back to 3, otherwise end the iterator.Generally, between 400 and up to several thousand iterations may be required to converge to an R 2 >0.85 solution. Wormhole rates can be 0-1,000. Wormhole rates above 200 can produce strange solution sets that must be scaled later, and wormhole rates above 400 can greatly extend convergence time due to a large number of useless checks.The final optimization from the nominal solution to minimize the error terms can be performed with any conventional optimizer. Such optimizers typically find local minima quickly, although if a conventional optimizer is used before a nominal solution, the R 2 may converge to 0.6 to 0.7 or less and may not likely yield a good final solution. If the nominal solution is first determined as described above, a conventional optimizer will typically take the R 2- value above 0.9.While the invention has been described and illustrated in detail in the specification and drawings, the same is to be considered as exemplary and not restrictive in nature, it being understood that only illustrative embodiments of the invention have been shown and described and that all changes and modifications that come within the scope of the appended claims are intended to be protected.

Claims

A method (100) for estimating (110) NOx produced by an internal combustion engine (12), the method comprising: - monitoring (104) a flow of fuel delivered to the internal combustion engine (12), - monitoring (106) a plurality of engine operating parameters, each of the plurality of engine operating parameters being represented by an engine operating parameter variable T N where N is a positive integer greater than 1, - determining (108) a number of model constants, estimating (110) the NOx produced by the internal combustion engine (12) based on a product of a function of the fuel quantity flow and at least one of the model constants and a function of the plurality of engine operating parameters and remaining ones of the model constants according to the equation NOx E = ( K ⋅ FF ) ⋅ [ ( C 1 ⋅ T 1 ) + ( C 2 ⋅ T 2 ) + ... + ( C N ⋅ T N ) ], wherein FF is the fuel quantity flow and K and C 1, C 2,..., C N is the number of model constants, and storing (112) the NOx estimate in a memory (45).The method (100) of claim 1, wherein monitoring (104) a fuel flow, monitoring (106) a plurality of engine operating parameters, determining (108) a number of model constants, estimating (110) NOx produced by the internal combustion engine (12), and storing (112) the NOx estimate in the memory (45) is performed all once per engine cycle.The method (100) of claim 1, wherein storing (112) the NOx estimate in the memory (45) comprises adding the NOx estimate to an accumulated NOx estimate (208) in the memory.The method (100) of claim 1, wherein monitoring (106) a plurality of engine operating parameters comprises determining (150) a charge mass value corresponding to a mass of charge entering the internal combustion engine (12).The method (100) of claim 1, wherein monitoring (106) a plurality of engine operating parameters comprises determining (152) a charge composition value corresponding to an at least partial composition of a charge entering the internal combustion engine (12).The method (100) of claim 1, wherein monitoring (106) a plurality of engine operating parameters comprises determining (154) a charge temperature value corresponding to a temperature of a charge entering the internal combustion engine (12).The method (100) of claim 1, wherein monitoring (106) a plurality of engine operating parameters comprises determining (156) a fuel injection timing value corresponding to an injection timing of fuel supplied by the internal combustion engine (12) relative to a reference timing value.The method (100) of claim 1, wherein monitoring (106) a plurality of engine operating parameters comprises determining a speed of the internal combustion engine (12).The method (100) of claim 1, wherein monitoring (106) a plurality of engine operating parameters comprises determining an operating temperature of the internal combustion engine (12), wherein determining an engine operating temperature comprises determining at least one coolant temperature corresponding to a temperature of coolant circulating through the internal combustion engine (12) and / or determining an oil temperature in the internal combustion engine (12).The method (100) of claim 1, wherein a fuel system (72) includes a fuel rail (96) fluidly connected to a plurality of fuel injectors (11-16), the plurality of fuel injectors (11-16) configured to selectively supply fuel from the fuel rail (96) to the internal combustion engine (12), and wherein monitoring (106) a plurality of engine operating parameters comprises determining a fuel rail pressure corresponding to a fuel pressure in the fuel rail (96).Method (100) for estimating (110) NOx produced by an internal combustion engine (12), the method comprising: - determining (104) a fuel quantity flow (FF) corresponding to a quantity flow of fuel supplied by the internal combustion engine (12), - determining (156) a fuel injection time (FT) corresponding to an injection time of fuel supplied by the internal combustion engine (12) relative to a reference time value, - determining (172) an engine speed (ES) corresponding to a rotational speed of the internal combustion engine (12), - determining (150) a filling mass (CM) corresponding to a mass of a filling entering the internal combustion engine (12), - determining (152) a filling composition (CC) corresponding to an at least partial composition of a filling entering the internal combustion engine (12), determining (154) a charge temperature (CT) according to a temperature of a charge entering the internal combustion engine (12), estimating (110) NOx produced by the internal combustion engine (12) as a function of the fuel quantity flow (FF), the fuel injection time (FT), the engine speed (ES), the charge mass (CM), the charge composition (CC) and the charge temperature (CT), wherein estimating NOx comprises estimating NOx (NO XE) produced by the internal combustion engine (12) according to the function NOx E = ( K ⋅ FF ) [( C 1 ⋅ C M ) + ( C 2 ⋅ C c ) + ( C 3 ⋅ C T ) + ( C 4 ⋅ FT ) + ( C 5 ⋅ ES ) + C 6 ] wherein FF is the fuel quantity flow, C M is the charge mass, C C is the charge composition, C T is the charge temperature, FT is the fuel injection timing, ES is engine speed and K and C are 1 to C 6 model constants, and storing (112) the NOx estimate in a memory (45).Method (100) according to Claim 11, in which the determination (104) of a fuel quantity flow (FF), the determination (156) of a fuel injection time (FT), the determination (172) of an engine speed (ES), the determination (150) of a filling mass (CM), the determination (152) of a filling composition (CC), the determination (154) of a filling temperature (CT), the estimation (110) of the NOx produced by the internal combustion engine (12) and the storage (112) of the NOx estimate in the storage (45) are carried out once per engine cycle.The method (100) of claim 11, wherein storing (112) the NOx estimate in the memory (45) comprises adding the NOx estimate to an accumulated NOx estimate (208) in the memory (45).Method (100) according to claim 11, wherein said determining (150) a charge mass (CM) comprises: - determining (170) a charge flow rate (CF) corresponding to a flow rate of a charge entering the internal combustion engine (12), and - determining (174) the charge mass (CM) as a function of the charge flow rate (CF) and the engine speed (ES).Method (100) according to claim 14, wherein said determining (152) a charge composition (CC) comprises determining (180) an exhaust gas recirculation fraction (EGR F) corresponding to a fraction of recirculated exhaust gas in the charge supplied to the internal combustion engine (12).Method (100) according to claim 15, wherein said determining (180) an exhaust gas recirculation fraction (EGR F) comprises: - determining an exhaust gas recirculation flow rate (EGRF) corresponding to a flow rate of recirculated exhaust gas entering the internal combustion engine (12), and - determining (180) the exhaust gas recirculation fraction value as a function of the charge flow rate (CF) and the exhaust gas recirculation flow rate (EGRF).The method (100) of claim 16, wherein determining (152) a charge composition value further comprises: - determining (182) a second order exhaust gas recirculation portion value as a function of the exhaust gas recirculation portion value; and - calculating the charge composition value as a sum of the exhaust gas recirculation portion value and the second order exhaust gas recirculation portion value such that estimating NOx comprises estimating NOx produced by the internal combustion engine (12) according to the function NO XE = ( K ⋅ FF ) [ ( C 1 ⋅ f ( CF,ES ) ) + ( C 2 ⋅ [ EGR F + f ( EGR F ) ) + ( C 3 ⋅ C T ) + ( C 4 ⋅ FT ) + ( C 5 ⋅ ES ) + C 6 ], where CF is the charge mass flow, f(CF, ES) is the charge mass, EGR F is the exhaust gas recirculation portion value and f(EGR F) is the second order exhaust gas recirculation portion value.A system (10) for estimating NOx produced by an internal combustion engine (12), the system (10) comprising: - a fuel system (72) connected to a fuel source and the internal combustion engine (12) and configured to supply fuel from the fuel source to the internal combustion engine (12), - means for determining (150) a charge mass value (C M) corresponding to a charge mass (CM) entering the internal combustion engine (12), - means for determining (152) a charge composition value (C C) corresponding to an at least partial composition of the charge entering the internal combustion engine (12), means for determining (154) a charge temperature (C T) corresponding to a temperature of the charge entering the internal combustion engine (12), means for determining (156) a fuel injection time value corresponding to an injection time of fuel supplied by the internal combustion engine (12) relative to a reference time value, means for determining (172) an engine speed value corresponding to a rotational speed of the internal combustion engine (12), and control circuitry (42) including memory (45) storing a number of model constants and instructions executable by the control circuitry (42) for determining a fuel amount current value corresponding to a flow of fuel supplied by the fuel system from the internal combustion engine (12) to determine a plurality of operating parameters related to the operation of the internal combustion engine (12), estimating (110) NOx produced by the internal combustion engine (12) as a product of the fuel amount current value and a function of the plurality of operating parameters according to the equation NO XE= ( K·FF) [(C 1 C M) + ( C 2 · C C) + ( C 3· C T) + ( C 4 ·FT) + (C 5 ·ES) + C 6], where a. FF is the fuel amount current, b. C M is the charge mass value corresponding to a mass of a charge entering the internal combustion engine (12), c. C c is the charge composition value corresponding to an at least partial composition of the charge entering the internal combustion engine (12), d. C T is the charge temperature corresponding to a temperature of the charge entering the internal combustion engine (12), e. FT is the fuel injection timing corresponding to an injection timing of fuel supplied from the internal combustion engine (12) relative to a reference timing value, f. ES is the engine speed corresponding to a rotational speed of the internal combustion engine (12), and K and C 1 to C 6 comprise the number of model constants, and storing (112) the estimated NOxin the memory (45), wherein the plurality of operating parameters associated with operation of the internal combustion engine (12) include the charge mass value, the charge composition value, the charge temperature value, the fuel injection timing value, and the engine speed value.The system (10) of claim 18, wherein the memory (45) includes an accumulator (208) having an accumulated NOx estimate stored therein, and wherein the instructions further include instructions executable by the control circuit (42) to store the estimated NOx in the memory (45) by adding the estimated NOx to the accumulated NOx estimate stored in the memory (45).The system (10) of claim 18 wherein said means for determining (152) a charge composition value comprises means for determining (180) an exhaust gas recirculation portion value (EGR F) corresponding to a portion of recirculated exhaust gas in the charge entering said internal combustion engine (12).The system (10) of claim 20, wherein the means for determining (152) a charge composition value further comprises means for determining a second order exhaust gas recirculation portion value f(EGR F) as a function of the exhaust gas recirculation portion value (EGR F) and for determining the charge composition value as a sum of the exhaust gas recirculation portion value (EGR F) and the second order exhaust gas recirculation portion value f(EGR F).

Images