Method for estimating the inlet pressure of a component of an exhaust system

Abstract

A method for a vehicle, comprising: setting the outlet pressure of a first component of an exhaust system of the vehicle equal to the inlet pressure of a second component located immediately downstream of the first component in the exhaust system, or to ambient air pressure; determining a pressure drop between an inlet of the first component and an outlet of the first component; determining an inlet pressure of the first component based on the sum of the outlet pressure of the first component and the pressure drop between the inlet and the outlet of the first component; and selectively controlling at least one machine actuator based on at least one of the inlet and outlet pressures of the first component; characterized in that the pressure drop between an inlet of the first component and the outlet of the first component is determined based on the temperature of the exhaust gas inlet to the first component.

Description

REGIONThe present disclosure relates to internal combustion engine systems and, more particularly, to a method according to the preamble of claim 1 for estimating the inlet pressure of an exhaust system component, as is known in the art substantially from US 2011 / 0 137 538 A1.BACKGROUNDAn engine burns a mixture of air and fuel to generate drive torque and propel a vehicle. Air is drawn into the engine through a throttle. Fuel provided by one or more fuel injectors mixes with the air to form the air / fuel mixture. The air / fuel mixture is burned in one or more cylinders to produce drive torque. An engine control module (ECM) controls the torque output of the engine.Exhaust gas resulting from the combustion of an air / fuel mixture is expelled from the engine to an exhaust system. The ECM may adjust one or more engine parameters based on signals from various sensors disposed in the exhaust system. For example only, one or more temperature sensors and / or exhaust flow sensors may be disposed in the exhaust system. For example, the ECM may adjust the air flow into the engine, the amount of fuel injected, and / or the spark timing based on the signals.The sensors provide measurements to the ECM regarding conditions within the exhaust system and allow the ECM to adjust one or more engine parameters to provide the desired exhaust conditions. However, as the number of sensors implemented in an exhaust system increases, the cost of manufacturing the vehicle also increases. The increased production costs can be attributable, for example, to the sensors themselves, to associated wiring and equipment, and also research and development. Additionally, a vehicle manufacturer may produce a number of different vehicles, and each of the different vehicles may have a different exhaust system. Calibrating and adjusting sensors implemented for each different vehicle and exhaust system may also increase the manufacturing cost of a vehicle.SUMMARYAccording to the invention, a method is proposed with the features of claim 1 for estimating the inlet pressure of an exhaust system component.In further features, the method further includes: setting an output pressure of a third component of the exhaust system that is immediately upstream of the first component in the exhaust system equal to the input pressure of the first component; determining a pressure drop between an input of the third component and an output of the third component based on a temperature of the exhaust input to the third component; and determining an input pressure of the third component based on a sum of the output pressure of the third component and the pressure drop between the input and the output of the third component.In further features, the method further includes: determining a viscosity of the exhaust input to the first component based on the temperature of the exhaust input to the first component; determining a density of the exhaust input to the first component based on the temperature of the exhaust input to the first component; and determining the pressure drop between the input and the output of the first component based on the viscosity and the density of the exhaust input to the first component.In further features, the method further includes: determining an exhaust gas flow rate (EGF) through the first component; determining a normalized EGF through the first component based on the EGF and the viscosity of the exhaust gas input to the first component; and determining the pressure drop between the input and the output of the first component based on the normalized EGF.In further features, the method further includes: determining a first normalization value for the first component based on the viscosity of the exhaust input to the first component and the density of the exhaust input to the first component; determining a normalized pressure drop between the input and the output of the first component based on the normalized EGF by the first component; and determining a pressure drop between the input and the output of the first component based on the normalized pressure drop and the first normalization value.In further features, the method further includes: determining the pressure drop between the input and the output of the first component based on the normalized pressure drop divided by the first normalization value.In further features, the method further includes: determining the first normalization value for the first component based on the viscosity of the exhaust input to the first component, a normalized viscosity of the exhaust input to the first component, the density of the exhaust input to the first component, and a normalized density of the exhaust input to the first component.In further features, the method further includes: determining the density of exhaust input to the first component further based on a normalized input pressure for the first component; and determining the normalized input pressure for the first component based on a normalized ambient air pressure, a previous value of the input pressure of the first component, an ambient air pressure, and the first normalization value.In further features, the method further includes: determining a second normalization value for the first component based on the viscosity of the exhaust input to the first component; and determining the normalized EGF by the first component based on the EGF by the first component and the second normalization value.In further features, the method further includes: determining the second normalization value for the first component based on the viscosity of the exhaust input to the first component and a normalized viscosity of the exhaust input to the first component.Further areas of applicability of the present disclosure will become apparent from the detailed description, the claims, and the drawings. The detailed description and specific examples are intended for purposes of illustration only.BRIEF DESCRIPTION OF THE DRAWINGSThe present disclosure will become more fully understood from the detailed description and the accompanying drawings, in which: FIG. 1 is a functional block diagram of an exemplary engine system according to the present disclosure; FIG. 2 is a functional block diagram of an exemplary exhaust system according to the present disclosure; FIG. 3 is a functional block diagram of an exemplary exhaust system module according to the present disclosure; FIG. 4 is a functional block diagram of an example pressure determination module according to the present disclosure; and FIG. 5 is a flow chart illustrating an example method for determining a pressure at an input of a component of an exhaust system according to the present disclosure.In the drawings, reference numerals may be reused to identify similar and / or similar elements.DETAILED DESCRIPTIONAn exhaust system of a vehicle includes various components, such as pipes, one or more catalysts, and one or more mufflers. Some exhaust systems include one or more turbochargers and other types of components. Exhaust gas output by an engine flows through the components before the exhaust gas is discharged from the vehicle.An exhaust system modeling module according to the present disclosure estimates the input gas temperature, the output gas temperature, the mass temperature, the input pressure, and the output pressure for one or more of the components of the exhaust system through which the exhaust gas flows. The input and output gas temperatures of an exhaust system component correspond to temperatures of the exhaust gas entering and exiting the component, respectively. The mass temperature of an exhaust system component corresponds to the temperature of the material that constitutes the component.The input and output pressures from an exhaust system component correspond to pressures at an input and an output of the exhaust system component, respectively. The exhaust system modeling module determines the input pressure of an exhaust system component based on an estimated pressure drop across the component and the output pressure of that component. The exhaust system modeling module estimates the pressure drop across the component based on a temperature of the exhaust input to the component. This can increase the accuracy of the estimated pressure drop and therefore increases the accuracy of the estimated input pressure.Referring now to FIG. 1, a functional block diagram of an example engine system 100 is presented. An air / fuel mixture is burned in an engine 102 to produce drive torque for a vehicle. Engine 102 may be, for example, a gasoline-type engine, a diesel-type engine, a hybrid-type engine, or another suitable type of engine. Engine 102 may be configured in any suitable cylinder configuration. For example only, the machine 102 may be configured in a V-type configuration, a flat-type configuration, or a series-type configuration.Air is drawn into engine 102 through intake manifold 104 and throttle 106. The throttle 106 is actuated to control the flow of air into the engine 102. An electronic throttle control (ETC) 108 controls the throttle valve 106 and, therefore, the flow of air into the engine 102.A fuel system 110 injects fuel that mixes with the air to form the air / fuel mixture. The fuel system 110 may inject the fuel at any suitable location. For example only, fuel system 110 may provide fuel into intake manifold 104, into intake valves (not shown) associated with cylinders 112 of engine 102, and / or directly into each of cylinders 112. In various implementations, the fuel system 110 includes a fuel injector (not shown) for each of the cylinders 112.The air / fuel mixture is burned in the cylinders 112 of the engine 102. Combustion of the air / fuel mixture may be initiated, for example, by spark provided by spark plugs 114. In some engine systems, such as engine system 100, a spark plug may be provided for each of cylinders 112. In other engine systems, such as diesel engine systems, combustion may be achieved without the spark plugs 114. Combustion of the air / fuel mixture generates driving torque and rotatably drives a crankshaft (not shown).Engine 102 may have eight cylinders as shown in FIG. 1, although engine 102 may include a greater or lesser number of cylinders. Cylinders 112 of engine 102 are shown arranged in two cylinder banks: a left cylinder bank 116 and a right cylinder bank 118. While engine 102 is shown with left and right cylinder banks 116 and 118, engine 102 may include one or more than two cylinder banks. For example only, inline engines having cylinders arranged in a single cylinder bank may be considered.An engine control module (ECM) 150 controls the torque output of the engine 102. The ECM 150 may control the torque output of the engine 102 based on driver inputs provided by a driver input module 152. For example only, the driver inputs may include an accelerator pedal position, a brake pedal position, inputs to cruise control systems, and other types of driver inputs.For example only, the ECM 150 may communicate with a hybrid control module 154 to coordinate operation of the engine 102 and one or more electric motors, such as an electric motor (EM) 156. The EM 156 may also serve as a generator and may be used to selectively generate electrical energy for use by vehicle electrical systems and / or for storage in a battery.The ECM 150 makes control decisions based on parameters measured by various sensors. For example, an intake air temperature may be measured using an intake air temperature (IAT) sensor 158. An ambient air temperature may be measured using an ambient temperature sensor 160. A mass flow rate of air into engine 102 may be measured with a mass air flow (MAF) sensor 162. A pressure in the intake manifold 104 may be measured using a manifold absolute pressure (MAP) sensor 164. In various implementations, an engine negative pressure may be measured, where the engine negative pressure is determined based on a difference between ambient air pressure and the pressure in the intake manifold 104.A coolant temperature may be measured using a coolant temperature sensor 166. The coolant temperature sensor 166 may be disposed in the engine 102 or at other locations where the coolant is circulated, such as a radiator (not shown). Engine speed may be measured using an engine speed sensor 168. For example only, engine speed may be measured based on the speed of the crankshaft.The ECM 150 may include an actuator control module 170 that controls the operating parameters of the engine. For example only, the actuator control module 170 may adjust a throttle opening, fuel injection magnitude and timing, spark timing, cylinder deactivation, and / or turbocharger boost. The actuator control module 170 may also control other engine parameters, such as exhaust gas recirculation (EGR) valve opening and / or intake and exhaust valves (not shown) opening / closing associated with the cylinders 112 of the engine 102.Referring now to FIG. 2, a functional block diagram of an example exhaust system 200 is presented. The exhaust system 200 of FIG. 2 is a general exhaust system that includes, but does not need to include, exhaust system components that may be included in various models and types of vehicles manufactured by a vehicle manufacturer. The exhaust system 200 includes exhaust system components through which exhaust gas flows. While the exhaust system 200 is described, the present disclosure is applicable to other exhaust system configurations that may have fewer or greater numbers of components than the exhaust system 200. Reference numerals for similar components of the exhaust system 200 are used for differentiation purposes only and are not representative of the relative importance of the components.Exhaust gas resulting from the combustion of the air / fuel mixture is exhausted from the engine 102 to the exhaust system 200. More specifically, exhaust gas is expelled from the cylinders 112 of the right cylinder bank 118 to a right exhaust manifold 202. Exhaust gas is expelled from the cylinders 112 of the left cylinder bank 116 to a left exhaust manifold 204. With respect to the left exhaust manifold 204, the exhaust gas from the left exhaust manifold 204 bypasses a first wastegate 206 and a second wastegate 208. The first and second wastegates 206 and 208 are in communication with the first and second turbochargers 210 and 212, respectively.Turbochargers 210 and 212 each provide pressurized air to intake manifold 104. The turbochargers 210 and 212 draw in air, pressurize the air, and deliver the pressurized air to the intake manifold 104. Turbochargers 210 and 212 may draw air from intake manifold 104, ambient air, and / or another suitable source. One or more of turbochargers 210 and 212 may be variable geometry turbochargers, by way of example only.One or more intercoolers (not shown) may also be implemented to dissipate heat from the pressurized air provided to the intake manifold 104. The temperature of the pressurized air may be increased, for example, by pressurizing the air and / or proximity to the exhaust system 200.Turbochargers 210 and 212 are driven by exhaust gas expelled from cylinders 112 of left cylinder bank 116. Wastegates 206 and 208 may allow exhaust to bypass turbochargers 210 and 212, respectively. In this way, wastegates 206 and 208 may be used to reduce the output (i.e., boost) of turbochargers 210 and 212, respectively.The ECM 150 controls the output of the turbochargers 210 and 212. For example only, the actuator control module 170 may modulate the output of the turbochargers 210 and 212 by controlling the positions of the wastegates 206 and 208, respectively. The actuator control module 170 may control the positions of the wastegates 206 and 208 by controlling the duty cycle (DC) of power applied to the wastegates 206 and 208.The exhaust from the left cylinder bank 116 may flow from wastegates 206 and 208 to a first catalyst 218 through a first exhaust pipe 216. The exhaust pipe area between the left intake manifold 204 and wastegates 206 and 208, and / or between wastegates 206 and 208, may also be considered part of the first exhaust pipe 216. The first catalyst 218 may include, for example, a diesel oxidation catalyst (DOC), a selective catalytic reduction (SCR) catalyst, a catalytic converter, and / or any other suitable type of exhaust catalyst.The exhaust from the left cylinder bank 116 may flow from the first catalyst 218 through a second exhaust pipe 220 to a second catalyst 222. The second catalyst 222 may include, for example, a DOC, an SCR catalyst, a catalytic converter, and / or any other suitable type of exhaust catalyst.The exhaust from the left cylinder bank 116 may flow from the second catalyst 222 through a third exhaust pipe 224 into a third catalyst 226. The third catalyst 226 may also include, for example, a DOC, an SCR catalyst, a catalytic converter, and / or any other suitable type of exhaust catalyst. One or more of the catalysts may be implemented with other components, such as a diesel particulate filter (DPF). In various implementations, more than one of the first, second, and third catalysts 218, 222, and 226 may be combined and implemented as a multi-stage catalyst. For example only, the first and second catalysts 218 and 222 may be implemented as a two stage catalyst. In other implementations, the second and third catalysts 222 and 226 may be implemented as a two stage catalyst, or the first, second and third catalysts 218, 222 and 226 may all be implemented as a three stage catalyst.The exhaust from the left cylinder bank 116 may flow out of the third catalyst 226 to a first muffler / exhaust system 228. For example only, the first muffler / exhaust system 228 may include a fourth exhaust pipe 230, a first muffler 232, a fifth exhaust pipe 234, and a first flapper valve 236. The exhaust gas may flow from the third catalyst 226 through the fourth exhaust pipe 230 to the first muffler 232.The first silencer 232 attenuates acoustic noise generated by the cylinders 112 of the left cylinder bank 116. The exhaust gas may flow from the first muffler 232 through the fifth exhaust pipe 234 to the first flapper valve 236. The first flapper valve 236 may increase a pressure in the exhaust system 200, prevent entry of external objects into the exhaust system 200, and / or perform other functions. The exhaust gas exits the exhaust system 200 after the first flapper valve 236.The exhaust from the cylinders 112 of the right cylinder bank 118 may assume a path similar to that of the exhaust from the cylinders 112 of the left cylinder bank 116, as described above. By way of example, the exhaust gas expelled from the cylinders 112 of the right cylinder bank 118 may flow from the right exhaust manifolds 202 through a third wastegate 250 and a fourth wastegate 252.Wastegates 250 and 252 may be associated with third and fourth turbochargers 254 and 256, respectively. Wastegates 250 and 252 and turbochargers 254 and 256 may be similar or identical to wastegates 206 and 208 and turbochargers 210 and 212, respectively. The ECM 150 (e.g., the actuator control module 170) may control the wastegates 250 and 252 and may therefore control the supercharging of the turbochargers 254 and 256.The exhaust gas from the right cylinder bank 118 may flow from the wastegates 250 and 252 through a sixth exhaust pipe 258 to a fourth catalyst 260. The exhaust pipe surface between the right exhaust manifold 202 and wastegates 250 and 252 and / or between wastegates 250 and 252 may also be considered part of the sixth exhaust pipe 258. The fourth catalyst 260 may include, for example, a DOC, an SCR catalyst, a catalytic converter, and / or any other suitable type of exhaust catalyst.The exhaust gas from the right cylinder bank 118 may flow from the fourth catalyst 260 through a seventh exhaust pipe 262 to a fifth catalyst 264. The fifth catalyst 264 may include, for example, a DOC, an SCR catalyst, a catalytic converter, and / or any other suitable type of exhaust catalyst.The exhaust from the right cylinder bank 118 may flow from the fifth catalyst 264 through an eighth exhaust pipe 266 to a sixth catalyst 268. The sixth catalyst 268 may include, for example, a DOC, an SCR catalyst, a catalytic converter, and / or any other suitable type of exhaust catalyst. One or more of the catalysts may be implemented with other components, such as a diesel particulate filter (DPF).In various implementations, more than one of the fourth, fifth, and sixth catalysts 260, 264, and 268 may be combined and implemented as a multi-stage catalyst. For example only, the fourth and fifth catalysts 260 and 264 may be implemented as a two stage catalyst. In other implementations, the fifth and sixth catalysts 264 and 268 may be implemented as a two stage catalyst, or the fourth, fifth and sixth catalysts 260, 264 and 268 may all be implemented as a three stage catalyst.The exhaust from the right cylinder bank 118 may flow out of the sixth catalyst 268 to a second muffler / exhaust system 270. For example only, the second muffler / exhaust system 270 may include a ninth exhaust pipe 272, a second muffler 274, a tenth exhaust pipe 276, and a second flapper valve 278. The exhaust gas may flow from the sixth catalyst 268 through the ninth exhaust pipe 272 to the second muffler 274.The second silencer 274 attenuates acoustic noise generated by the cylinders 112 of the right cylinder bank 118. The exhaust gas may flow from the second muffler 274 through the tenth exhaust pipe 276 to the second flapper valve 278. The second flapper valve 278 may raise the pressure in the exhaust system 200, prevent entry of external objects into the exhaust system 200, and / or perform other functions. The exhaust may exit the exhaust system 200 after the second flapper valve 278.One or more exhaust gas recirculation (EGR) systems, such as EGR system 280, may also be implemented. For example only, the EGR system 280 may be associated with the right exhaust manifold 202, as shown in FIG. 2. While the EGR system 280 is shown connected to the right exhaust manifold 202, the EGR system 280 may be connected to the exhaust system 200 elsewhere, such as between the sixth catalyst 268 and the second muffler 274. The EGR system 280 or other EGR system may be implemented with components that receive exhaust gas from the left cylinder bank 116.The EGR system 280 includes an EGR valve 282, a first EGR pipe 284, a second EGR pipe 286, an EGR cooler 287, and a third EGR pipe 288. The EGR valve 282 is coupled to the right exhaust manifold 202 via the first EGR pipe 284. The EGR valve 282 selectively redirects exhaust gas from the right exhaust manifold 202 back to the intake system via the second EGR tube 286 and the third EGR tube 288. The EGR cooler 287 may be implemented to cool exhaust gas recirculated back to the intake system. The ECM 150 controls actuation of the EGR valve 282 and, therefore, exhaust flow rate (EGF) through the EGR system 280. For example, the actuator control module 170 may control opening of the EGR valve 282.The ECM 150 includes an exhaust system module 290 initially configured based on the exhaust system 200 of FIG. 2. While the exhaust system module 290 and the actuator control module 170 are shown and discussed as being disposed within the ECM 150, the exhaust system module 290 and / or the actuator control module 170 may be disposed at any suitable location, such as external to the ECM 150. The exhaust system module 290 receives data indicating the configuration of an actual exhaust system implemented in the vehicle, and performs reconfiguration according to the actual exhaust system. The actual exhaust system may include the same components as the exhaust system 200 or a fewer number of components than the exhaust system 200.The exhaust system module 290 estimates (i.e., models) an input gas temperature, an output gas temperature, a mass temperature, and a pressure for each component of the actual exhaust system. The actuator control module 170 selectively adjusts one or more engine operating parameters based on the input gas temperature, the output gas temperature, the mass temperature, and / or the pressure of one or more exhaust system components. In this way, the actuator control module 170 may use the temperatures and / or pressure provided by the exhaust system module 290 to generate desired exhaust system conditions.Referring now to FIG. 3, a functional block diagram of an example implementation of the exhaust system module 290 is presented. The exhaust system module 290 includes a configuration module 302, an exhaust system modelling module 304, and a storage module 305. The exhaust system modelling module 304 includes an exhaust flow rate (EGF) determination module 306, an input temperature module 308, a steady state temperature (SS) module 310, a mass temperature module 312, an output temperature module 314, and a pressure determination module 316.The exhaust system modelling module 304 is initially configured based on the exhaust system 200 of FIG. 2. In other words, the exhaust system modelling module 304 is initially configured based on a general exhaust system applicable to a variety of models and types of engine systems and vehicles.The configuration module 302 receives actual configuration data 320 that indicates an actual exhaust system configuration of the vehicle in which the exhaust system module 290 is implemented. If the actual exhaust system configuration is different than the configuration of the exhaust system 200, the configuration module 302 reconfigures the exhaust system modeling module 304 based on the actual configuration data 320. The reconfiguration may include, for example, activating and deactivating components of the general configuration based on the actual configuration and / or reconfiguring parameters of a turned-on component based on the actual configuration. The configuration module 302 may receive the actual configuration data 320 from any source, such as a memory or device used to calibrate the vehicle.The exhaust system modeling module 304 models (i.e., determines) one or more pressures and temperatures for each component of the actual exhaust system. More specifically, the exhaust system modelling module 304 models an input temperature, an output temperature, a mass temperature, an input pressure, and an output pressure for each exhaust system component through which exhaust gas flows. The input and output temperatures of a component correspond to the temperature of the exhaust gas input to and output from the components, respectively. The mass temperature corresponds to the temperature of the material(s) forming the component itself. The input and output pressures of a component correspond to pressures at an input and an output of the component, respectively.The exhaust system modelling module 304 stores the temperatures and pressures for each component of the exhaust system in the storage module 305. The memory module 305 may be implemented in a memory, for example. An example portion of a table of temperatures and pressures for a portion of the components in the exhaust system 200 stored in the storage module 305 is provided below.Input Temp.TLM-INTT1-INTT2-INTP1-INTC1-INTP2-INTC2-INMass temp.TLM-MTT1-MTT2-MTP1-MTC1-MTP2-MTC2-MInitial Temp.TLM-OUTTT1-OUTTT2-OUTTP1-OUTTC1-OUTTP2-OUTTC2-OUTInput PressurePLM-INPT1-INPT2-INPIN-P1PIN-C1PIN-P2PIN-C2Output PressurePLM-OUTPT1-OUTPT2-OUTPOUT-P1POUT-C1POUT-P2POUT-C2The EGF determination module 306 determines an EGF for each component of the exhaust system. The EGF of a component corresponds to a mass flow of exhaust gas through the component. The EGF determination module 306 may determine the EGF for each of the exhaust system components based on one or more operating parameters. For example only, the EGF for a component may be determined based on coolant temperature, injected fuel ethanol concentration, spark timing, equivalence ratio, vehicle speed, ambient air temperature, intake air temperature, and accelerator pedal position. The EGF for the component may also be determined based on EGR flow rate, MAF, air per cylinder (APC), ambient air pressure, engine speed, flap valve position(s), and / or wastegate duty cycles. The EGF determination module 306 may determine the EGFs using, for example, functions and maps that map the operating parameter / parameters to the EGFs, respectively.The EGF determination module 306 may also determine the EGF(s) based on the operating mode of the engine 102. For example only, the EGF(s) may be determined based on whether one or more of the cylinders 112 are deactivated, whether the engine is idling, whether the engine 102 is running or deactivated (e.g., hybrid applications), and / or whether the fuel is injected for each ignition event in one or more pulses (e.g., two pulses).When one or more cylinders are deactivated, the EGF(s) may be determined based on the number of deactivated and / or activated cylinders. The EGF(s) may be determined based on the amount of time the engine has been shut down (i.e., OFF) when the engine is shut down. The EGF determination module 306 may also determine the EGF(s) based on various exhaust system modes, such as whether air is injected into the exhaust system (e.g., by an auxiliary air pump), whether catalyst warming is occurring, and / or whether light-off is occurring in one or more catalysts of the exhaust system.The EGF determination module 306 may also determine the EGF(s) based on the actual configuration of the exhaust system and / or characteristics of the various components. For example only, the exhaust system may be configured to combine the exhaust gas from the right and left exhaust manifolds 202 and 204 at a confluence point (not shown). The EGF determination module 306 may sum the two EGFs of upstream components for the components downstream of the confluence point. Characteristics that may affect EGF may include, for example, curvature and / or cross-sectional area.The input temperature module 308 estimates an input temperature for each of the components of the actual exhaust system. The inlet temperature of a component corresponds to the temperature of exhaust gas at an inlet of that component. The input temperature module 308 stores the input temperatures for the components in the memory module 305, respectively. The input temperature module 308 may set the input temperature for a component equal to or based on the output temperature of the previous (i.e., upstream) component of the exhaust system. For example only, the input temperature module 308 may set the input temperature for an Nth component of the exhaust system based on the output temperature of an (N-1)th component.For an exhaust manifold (e.g., right and left exhaust manifolds 202 and 204), the input temperature module 308 may set the input temperature equal to or based on an engine output temperature The input temperature module 308 may determine the engine output temperature based on one or more operating parameters, such as engine load, APC, engine speed, spark timing, equivalence ratio, ethanol concentration of fuel, vehicle speed, and / or warm-up state of the engine 102. The input temperature module 308 may determine the engine output temperature using a function or mapping that associates the operating parameters with the engine output temperature.If the exhaust system includes an EGR system (e.g., EGR system 280), the input temperature module 308 determines an input temperature for the EGR system based on a temperature of the exhaust gas at the point where the EGR system is connected to the exhaust system. The inlet temperature module 308 may also determine an inlet temperature for each component of the EGR system, such as the EGR tubes, the EGR valve, and / or the EGR cooler.The SS temperature module 310 estimates an SS temperature for each component of the actual exhaust system. The SS temperature for a component corresponds to a temperature that the component itself reaches when the engine load conditions remain constant (i.e., steady state). The SS temperature module 310 may determine the SS temperature for the component based on the input temperature of the component, the ambient temperature, and an SS coefficient determined for the component.The SS temperature module 310 determines the SS coefficient for the component based on the EGF for the component. For example only, the SS temperature module 310 may determine the SS temperature for the component using the equation: where T SS is the SS temperature of the component, T IN is the input temperature of the component, T A is the ambient air temperature, and C SS is the SS coefficient for the component.The SS temperature module 310 determines the SS coefficient for a turbocharger (e.g., turbochargers 210, 212, 254, and / or 256) based on the EGF for the turbochargers and the DC power applied to the associated wastegate. For example only, the SS temperature module 310 may determine the SS coefficient for the turbocharger 212 based on the EGF for the turbocharger 212 and the DC power applied to the wastegate 206. When the turbocharger draws ambient air, the SS temperature module 310 also adjusts the SS temperature for the turbocharger based on the intake air temperature. For example only, the SS temperature module 310 may determine the SS temperature for the turbocharger using the equation: where T SS-T is the SS temperature of the turbocharger, IAT is the intake air temperature, C SS-T is the SS coefficient for the turbocharger, and T IN-T is the input temperature for the turbocharger.The mass temperature module 312 determines a mass temperature for each of the exhaust system components. The mass temperature module 312 stores the mass temperatures in the storage module 305. The mass temperature module 312 determines the mass temperature for a component based on the SS temperature of the component and a mass coefficient determined for the component. The mass temperature corresponds to the temperature of the material constituting the component.The mass temperature module 312 determines the mass coefficient for the component based on the EGF determined for the component. The mass coefficient corresponds to the rate at which the mass temperature changes to the SS temperature of the component. For example only, the mass coefficient may increase as EGF decreases. The mass temperature module 312 determines the mass temperature for the component based on a product of the SS temperature and the mass coefficient, for example.The mass temperature module 312 determines the mass coefficient for a turbocharger (e.g., turbochargers 210, 212, 254, and / or 256) based on the EGF for the turbochargers and the DC power applied to the associated wastegate. For example only, the mass temperature module 312 may determine the mass coefficient for the turbocharger 212 based on the EGF for the turbocharger 212 and the DC power applied to the wastegate 206.The output temperature module 314 determines an output temperature for each of the exhaust system components. The output temperature of a component corresponds to the temperature of exhaust gas at an output of that component. The output temperature module 314 stores the output temperatures in the storage module 305.The output temperature module 314 may determine the output temperature for a component based on the input temperature for the component, the mass temperature of the component, and an output coefficient for the component. The output temperature module 314 determines the output temperature for the component based on the input temperature of the component plus or minus the change in temperature attributable to heat transfer between the component and air passing through the component. More specifically, the output temperature module 314 determines the output temperature by adjusting the input temperature to the mass temperature based on the output coefficient.The output temperature module 314 determines the output coefficient for the component based on the EGF on the component. For example only, the output temperature module 314 may determine the output temperature for the component using the equation: where T OUT is the output temperature of the component, T IN is the input temperature of the component, T MASS is the mass temperature of the component, and C OUT is the output coefficient of the component.Exhaust system catalysts, such as catalysts 218, 222, 226, 260, 264, and 268, may also generate heat. Accordingly, the output temperature module 314 increases the output temperature of a catalyst of the exhaust system based on the heat generated by the catalyst. The SS temperature module 310 and the mass temperature module 312 may also increase the SS temperature and mass temperature of the catalyst, respectively, based on the heat generated by the catalyst.The amount of heat generated by the catalyst is referred to as a heat generation term. The heat generation term for the catalyst may be determined based on the EGF of the catalyst, the equivalence ratio, and / or the ethanol concentration of the fuel. For example only, if the equivalence ratio is 1.0 (i.e., if a stoichiometric air / fuel mixture is burned), the heat generation term may be negligible. The heat generation term for the catalyst may also be determined based on whether air is delivered in, whether air is injected into the exhaust system (e.g., by an auxiliary air pump), and / or whether the fuel is injected for each ignition event in one or more pulses (e.g., two pulses).The output temperature module 314 determines the output coefficient for a turbocharger (e.g., turbochargers 210, 212, 254, and / or 256) based on the EGF for the turbochargers and the DC power applied to the associated wastegate. The output temperature module 314 determines the output coefficient for the turbocharger 212 based on the EGF for the turbocharger 212 and the DC power applied to the wastegate 206. For example only, the output temperature module 314 may determine the output temperature for the turbocharger using the equation: where T OUT-T is the output temperature of the turbocharger, T IN-T is the input temperature for the turbocharger, C OUT-T is the output coefficient for the turbocharger, and T M-T is the mass temperature for the turbocharger.The pressure determination module 316 determines an input pressure, an output pressure, and a pressure drop for each of the exhaust system components. The input pressure of a component corresponds to the pressure at the input of this component. The output pressure of a component corresponds to the pressure at the output of this component. The pressure drop of a component corresponds to the pressure drop present between the input pressure of the component and the output pressure of the component. The pressure determination module 316 stores the input pressures and the output pressures in the storage module 305. The pressure determination module 316 may also store the pressure drops in the storage module 305.FIG. 4 includes a functional block diagram of an example implementation of the pressure determination module 316. The pressure determination module 316 begins with the last component in the actual exhaust system. The final component is the final component through which the exhaust gas passes before it exits the exhaust system to the atmosphere. Dual-output exhaust systems have two final components.The pressure determination module 316 sets the output pressure for the last component equal to or based on an ambient (barometric) air pressure. The pressure determination module 316 determines the pressure drop for the last component, as discussed further below. The pressure determination module 316 determines the input pressure for the last component based on the output pressure of the last component and the pressure drop of the last component.For the next component upstream of the last component (as it proceeds toward the exhaust manifold), the pressure determination module 316 sets the output pressure for that component based on or equal to the input pressure of the last component. The pressure determination module 316 determines the pressure drop for the next component and determines the input pressure for the next component based on the output pressure of the next component and the pressure drop of the next component. This process continues for each component operating upstream until the exhaust manifold is reached. An example of how to determine the pressure drop for a component and the input pressure for a component is now discussed.Referring now to FIG. 4, a specific gas constant module 404 determines a specific gas constant 408 for the exhaust gas in the actual exhaust system. The specific gas constant 408 may be used for each component of the actual exhaust system, as the amount of variation from component to component may be negligible.The specific gas constant module 404 determines the specific gas constant 408 based on an equivalence ratio (EQR) 412 of the air / fuel mixture burned in the engine 102, a stoichiometric fuel / air ratio (FAR), and a humidity 416 of ambient air. The humidity 416 may be measured, for example, using a humidity sensor, or determined based on one or more other parameters, such as the IAT. The specific gas constant module 404 may determine the specific gas constant 408 using, for example, a function or mapping (e.g., a look-up table) that maps EQRs, stoichiometric FARs, and ambient humidity to specific gas constants. An example function for determining the specific gas constant 408 for a gasoline and / or ethanol powered engine is: where R S is the specific gas constant 408, Stoich is the stoichiometric FAR, EQR is the EQR 412 of the air / fuel mixture burned in the engine 102, and H is the ambient humidity 416. Other functions may be used for other types of fuel delivery.A viscosity module 420 determines a viscosity 424 of the exhaust gas within the component and a normalized viscosity 428 of the exhaust gas within the component. The viscosity 424 and the normalized viscosity 428 may be determined specifically for each different component of the actual exhaust system.The viscosity module 420 determines the viscosity 424 for the component based on the input temperature 432 determined for the component (by the input temperature module 308). The viscosity module 420 may receive the input temperature 432 from the storage module 305. In the case of a catalyst, due to the heat generating catalyst, a temperature of the catalyst (for example, the mass temperature of the catalyst) may be used instead of the input temperature of the catalyst.The viscosity module 420 may determine the viscosity 424 for the component using, for example, a function or mapping that maps input temperatures of the components to the viscosities. An example function for determining viscosity 424 is: where μ is viscosity 424 (e.g., in kg / m*s) and T IN is input temperature 432 of the component (e.g., in degrees Celsius). In the case of an assignment, the assignment is calibrated with entries for values of viscosity 424 at different input temperatures.Because the function or mapping may be calibrated under various operating conditions, the viscosity module 420 determines the normalized viscosity 428 based on a normalization temperature at which the function or mapping was calibrated. The viscosity module 420 may determine whether to use a first relationship or mapping or to use a second relationship or mapping based on whether the normalization temperature is greater than a predetermined temperature. For example, if the normalization temperature is greater than the predetermined temperature, the viscosity module 420 may determine the normalized viscosity 428 using the first relationship or mapping that is the same as that used to determine the viscosity 424.If the normalized temperature is less than the predetermined temperature, the viscosity module 420 may determine the normalized viscosity 428 using the second relationship. The predetermined temperature may be calibrated and may be, for example, about 40 degrees Celsius or any other suitable temperature. An example of the second normalized viscosity determination function 428 is: where μ N is the normalized viscosity 428 (e.g., in kg / m*s), and T IN is the input temperature 432 of the component. In the case of a second mapping, the second mapping is calibrated with entries for values of normalized viscosity 428 at different input temperatures while at a normalized temperature. The normalization temperature may be a predetermined value stored in a memory. Along with the normalization temperature, predetermined values of an associated specific normalization gas constant (R N) and an associated normalization exhaust density (ρ U,N) for normalizing other parameters are also stored.A density module 436 determines a density 440 of the exhaust gas in the component and a normalized density 444 of the exhaust gas in the component. The density 440 and the normalized density 444 may be determined specifically for each different component of the actual exhaust system.The density module 436 determines the viscosity 424 for the component based on the input temperature 432 determined for the component (by the input temperature module 308) and a last input temperature 448 determined for the component. The temperatures and pressures for each component may be determined at a predetermined rate, such as every 12.5 milliseconds or any other suitable rate. The final input pressure 448 determined for the component therefore corresponds to the input pressure determined for the component the last time the pressures and temperatures were determined. The density module 436 may receive the input temperature 432 and the last input pressure 448 from the storage module 305. As noted above, in the case of a catalyst due to the heat-generating catalyst, the temperature of the catalyst (for example, the mass temperature of the catalyst) may be used instead of the input temperature of the catalyst.The density module 436 may determine the density 440 for the component using, for example, a function or mapping that maps input temperatures and input pressures of the component to the densities. An example function for determining the density 440 is: where ρ is the density 440 (e.g., in kg / m 3) T IN is the input temperature 432 of the component (e.g., in degrees Celsius), and P IN-L is the last input pressure 448 of the component (e.g., in kPa). In the case of an assignment, the assignment is calibrated with entries for values of density 440 at different input temperatures and last input pressures.Because the function or mapping may be calibrated using various operating conditions, the density module 436 determines the normalized density 444 based on the normalization temperature, a normalized upstream pressure for the component, and a specific normalization gas constant (R N). An example function for determining normalized density 444 is: where ρ N is normalized density 444 (e.g., in kg / m 3) T N is the predetermined normalization temperature, and P IN-N is the normalized input pressure for the component (e.g., in kPa).The density module 436 determines the normalized input pressure for the component (p IN-N) based on a normalized ambient air pressure for the component, the ambient air pressure 452, the last input pressure 448 of the component, and a pressure normalization value 456 for the component. The density module 436 may determine the normalized input pressure for the component using, for example, a function or map. An example function for determining the normalized input pressure is: where p IN-N is the normalized input pressure for the component, p amb,n is the normalized ambient air pressure for the component, P IN-L is the last input pressure for the component, p AMB is the ambient air pressure 452, and f P is the pressure normalization value 456 for the component. The normalized ambient air pressure may be a predetermined value for the component stored in the memory. A normalized ambient air pressure may be stored for each different component of the actual exhaust system. The ambient air pressure 452 may be measured using a sensor or determined based on one or more other parameters.A first normalization value module 460 determines the pressure normalization value 456. When the engine 102 is started, the first normalization value module 460 may initialize the pressure normalization value 456 to a predetermined initialization value, such as 1.0. After initialization, the first normalization value module 460 determines the pressure normalization value 456 based on the last value of viscosity 424, the last value of normalized viscosity 428, the last value of density 440, and the last value of normalized density 444. The first normalization value module 460 may determine the pressure normalization value 456 using, for example, a function or a mapping. An example of a function for determining the pressure normalization value 456 is: where f P is the pressure normalization value 456, μ is the last value of the viscosity 424, μ N is the last value of the normalized viscosity 428, ρ is the last value of the density 440, and ρ N is the last value of the normalized density 444.EGF normalization module 464 determines normalized EGF 468 for the component based on EGF 472 determined for the component (by EGF determination module 306) and flow normalization value 476. The EGF normalization module 464 may receive the EGF 472 from the storage module 305. The EGF normalization module 464 may determine the normalized EGF 468 using, for example, a function or a mapping. An example of a function for determining normalized EGF 468 is: where EGF N is normalized EGF 468, EGF is EGF 472 determined for the component, and f M is flow normalization value 476.A second normalization value module 480 determines the flow normalization value 476. When the engine 102 is started, the second normalization value module 480 may initialize the flow normalization value 476 to a predetermined initialization value, such as 1.0. After initialization, the second normalization value module 480 determines the flow normalization value 476 based on the last value of viscosity 424 and the last value of normalized viscosity 428. The second normalization value module 480 may determine the flow normalization value 476 using, for example, a function or a mapping. An example of a function for determining the flow normalization value 476 is: where f M is the flow normalization value 476, μ is the last value of the viscosity 424, and μ N is the last value of the normalized viscosity 428.A pressure drop module 484 determines a pressure drop 488 for the component based on a normalized pressure drop of the component and the pressure normalization value 456. The pressure drop module 484 may determine the pressure drop 488 using, for example, a function or mapping that maps normal pressure drops and pressure normalization values to the pressure drops. An example function for determining the pressure drop 488 is: where PDropis the pressure drop 488, PDropis N the normalized pressure drop of the component, and f is P the pressure normalization value 456. The pressure drop module 484 determines the normalized pressure drop of the component based on the normalized EGF 468 of the component. For example, the pressure drop module 484 may determine the normalized pressure drop of the component using a function or map that maps normalized EGFs to normalized pressure drops.An input pressure module 492 determines the input pressure 496 for the component based on the pressure drop 488 of the component and the output pressure 498 determined for the component. An output pressure module 497 sets the output pressure 498 of a component equal to or based on the input pressure of a next component immediately downstream of that component. For the final component of the actual exhaust system, the output pressure module 497 sets the output pressure 498 equal to or based on the ambient air pressure 452. The output pressure module 497 receives the input pressures from the storage module 305 and stores the output pressures of the components in the storage module 305.The input pressure module 492 determines the input pressure 496 by adding the pressure drop 488 to the output pressure 498. The input pressure module 492 stores the input pressure 496 in the storage module 305 in association with the component. This process continues for each component in the actual exhaust system operating upstream of the exhaust manifold(s).The actuator control module 170 selectively adjusts one or more engine operating parameters based on parameters stored in the memory module 305. More specifically, the actuator control module 170 selectively adjusts one or more engine parameters based on the temperatures and / or pressures of one or more of the components of the actual exhaust system. For example only, the actuator control module 170 may adjust the amount of fuel injected, the air flow into the engine 102, and / or the spark timing based on one or more of the pressures and temperatures stored in the storage module 305.Referring now to FIG. 5, a flowchart depicting an example method of determining the input pressure for the components of the actual exhaust system is shown. Control begins at 550 where control is initialized. For example only, at 550, the configuration module 302 may reset previously stored values and / or configure the exhaust system modeling module 304. The configuration module 302 configures the exhaust system modeling module 304 based on the actual exhaust system configuration of the vehicle.The configuration module 302 may also reset a counter value (an N value) to a predetermined reset value (an M value) at 550. The predetermined reset value may be set to the total number of components of the exhaust system, for example only. In this way, control begins at the final component of the exhaust system, such as a muffler / exhaust system.The pressure determination module 316 determines at 554 whether the counter value is less than 1. If 554 is true, control of the pressure determination module 316 sets the counter value to the predetermined reset value at 558. In this way, the pressure determination module 316 sets the counter value to the total number of components of the actual exhaust system. If 554 is false, control continues to 562. The pressure determination module 316 decreases the counter value at 562 and control continues to 566. While reset of the counter value (N value) to the predetermined reset value (M value) and decreasing the counter value are provided as an example, reset of the counter value to zero, increment of the counter value, and compare the counter value with the total number of components in the actual exhaust system may be used.At 566, the pressure determination module 316 sets the output pressure for the Nth component of the actual exhaust system to the input pressure for the N+1th component of the actual exhaust system. In the case of the last component of the actual exhaust system (i.e., when N=M), the pressure determination module 316 sets the output pressure equal to or based on the ambient air pressure 452.At 570, the viscosity module 420 determines the viscosity 424 of the exhaust input to the Nth component and determines the normalized viscosity 428 of the exhaust input to the Nth component. The specific gas constant module 404 determines the specific gas constant 408 at 574. As noted above, the specific gas constant 408 may be used for each component of the actual exhaust system. The specific gas constant 408 may therefore be determined at a different time, such as at 558.The first normalization value module 460 determines the pressure normalization value 456 at 578. The second normalization value module 480 also determines the flow normalization value 476 at 578. At 582, the density module 436 determines the density 440 of the exhaust input to the Nth component and determines the normalized density 444 of the exhaust input to the Nth component. As discussed above, the density module 436 determines the density 440 and the normalized density 444 based on the temperature of the exhaust input to the Nth component.At 586, the EGF normalization module 464 receives the EGF 472 for the Nth component from the storage module 305. The EGF normalization module 464 determines the normalized EGF 468 for the Nth component at 586. The pressure drop module 484 determines the normalized pressure drop for the Nth component of the actual exhaust system at 588. At 590, the pressure drop module 484 determines the pressure drop 488 for the Nth component of the actual exhaust system.The input pressure module 492 determines the input pressure 496 for the Nth component of the actual exhaust system at 594 based on the output pressure of the Nth component and the pressure drop 488 across the Nth component. The input pressure module 492 stores the input pressure 496 in the storage module 305 in association with the Nth component. Control then returns to 554 to continue with the next component upstream of the Nth component (i.e., the N-1th component). Thus, this process is iterative in nature. The actuator control module 270 may control one or more operating parameters based on one or more of the parameters stored in the memory module 305.In this application, including in the following definitions, the term "module" or the term "controller" may be replaced by the term "circuit". The term "module" may be part of or include: an application specific integrated circuit (ASIC); a digital, analog, or mixed analog / digital discrete circuit; a digital, analog, or mixed analog / digital integrated circuit; a combinational logic circuit; a field programmable logic array (FPGA); a processor circuit (shared, dedicated, or group) that executes code; a memory circuit (shared, dedicated, or group) that stores code executed by the processor circuit; other suitable hardware components that provide the described functionality; or a combination of some or all of the above as embodied in a system-on-chip.The module may include one or more interface circuits. In some examples, the interface circuits may include wired or wireless interfaces connected to a local area network (LAN), the Internet, a wide area network (WAN), or combinations thereof. The functionality of a particular module of the present disclosure may be distributed among multiple modules connected via interface circuits. For example, multiple modules may allow load balancing. In another example, a server (also known as a remote or cloud) module may achieve some functionality on behalf of a client module.The term code as used above may include software, firmware, and / or microcode, and may refer to programs, routines, functions, classes, data structures, and / or objects. The term shared processor circuit includes a single processor circuit that executes some or all of the code from multiple modules. The term group processor circuit includes a processor circuit that, in combination with additional processor circuits, executes some or all of the code from one or more modules. References to multiprocessor circuits include discrete-chip multiprocessor circuits, single-chip multiprocessor circuits, multiple cores of a single processor circuit, multiple threads of a single processor circuit, or a combination of the foregoing. The term shared memory circuit includes a single memory circuit that stores some or all of the code from multiple modules. The term group memory circuit includes a memory circuit that, in combination with additional memories, stores some or all of the code from one or more modules.The term memory circuitry is a subset of the term computer readable medium. The term computer-readable medium as used herein does not include transitory electrical or electromagnetic signals propagating through a medium (such as on a carrier wave); the term computer-readable medium may therefore be considered an object and non-transitory. Non-limiting examples of a non-transitory, tangible computer-readable medium include nonvolatile memory circuits (such as a flash memory circuit, an erasable programmable read-only memory circuit, or a masked read-only memory circuit), volatile memory circuits (such as a static random-access memory circuit and a dynamic random-access memory circuit), magnetic storage media (such as analog or digital magnetic tape or hard disk drive), and optical storage media (such as a CD, a DVD, or a Blue-ray disk).The apparatuses and methods described in this application may be partially or fully implemented by a special purpose computer created by configuring a general purpose computer to perform one or more particular functions provided as computer programs. The above-described function blocks and flowchart elements serve as software specifications that can be translated into the computer programs by routine work by a person skilled in the art or programmer.The computer programs include processor-executable instructions stored on at least one non-transitory tangible computer-readable medium. The computer programs may also contain and / or rely on stored data. The computer programs may include a basic input / output system (BIOS) that interacts with the hardware of the special purpose computer, device drivers that interact with particular devices of the special purpose computer, one or more operating systems, user applications, background services, background applications, etc.The computer programs may include: (i) Description text for parsing, such as HTML (hypertext markup language) or XML (extensible markup language), (ii) assembler code, (iii) object code generated from source code by a compiler; (iv) source code for execution by an interpreter, (v) source code for compilation and execution by a just-in-time compiler, etc. For example only, the source code may be written using syntax from languages including: C, C++, C#, Objective C, Haskell, Go, SQL, R, Lisp, Java® Fortran, Perl, Pascal, Curl, OCaml, Javascript® HTML5, Ada, ASP (active server pages), PHP, Scala, Eiffel, Smalltalk, Erlang, Ruby, Flash® Visual Basic® Lua, and Python®.

Claims

A method for a vehicle, comprising: setting an output pressure of a first component of an exhaust system of the vehicle equal to an input pressure of a second component located immediately downstream of the first component in the exhaust system or an ambient air pressure; determining a pressure drop between an input of the first component and an output of the first component; determining an input pressure of the first component based on a sum of the output pressure of the first component and the pressure drop between the input and the output of the first component; and selectively controlling at least one engine actuator based on at least one of the input and output pressures of the first component; characterized in that the pressure drop between an input of the first component and the output of the first component is determined based on a temperature of the exhaust input to the first component.The method of claim 1, further comprising: setting an output pressure of a third component of the exhaust system that is immediately upstream of the first component in the exhaust system equal to the input pressure of the first component; determining a pressure drop between an input of the third component and an output of the third component based on a temperature of the exhaust input to the third component; and determining an input pressure of the third component based on a sum of the output pressure of the third component and the pressure drop between the input and the output of the third component.The method of claim 1, further comprising: determining a viscosity of the exhaust input to the first component based on the temperature of the exhaust input to the first component; determining a density of the exhaust input to the first component based on the temperature of the exhaust input to the first component; and determining the pressure drop between the input and the output of the first component based on the viscosity and the density of the exhaust input to the first component.The method of claim 3, further comprising: determining an exhaust gas flow rate (EGF) through the first component; determining a normalized EGF through the first component based on the EGF and the viscosity of the exhaust gas input to the first component; and determining the pressure drop between the input and the output of the first component based on the normalized EGF.The method of claim 4, further comprising: determining a first normalization value for the first component based on the viscosity of the exhaust input to the first component and the density of the exhaust input to the first component; determining a normalized pressure drop between the input and the output of the first component based on the normalized EGF by the first component; and determining the pressure drop between the input and the output of the first component based on the normalized pressure drop and the first normalization value.The method of claim 5, further comprising determining the pressure drop between the input and the output of the first component based on the normalized pressure differential drop divided by the first normalization value.The method of claim 5, further comprising determining the first normalization value for the first component based on the viscosity of the exhaust input to the first component, a normalized viscosity of the exhaust input to the first component, the density of the exhaust input to the first component, and a normalized density of the exhaust input to the first component.The method of claim 5, further comprising: determining the density of exhaust input to the first component further based on a normalized input pressure for the first component; and determining the normalized input pressure for the first component based on a normalized ambient air pressure, a previous value of the input pressure of the first component, an ambient air pressure, and the first normalization value.The method of claim 4, further comprising: determining a second normalization value for the first component based on the viscosity of the exhaust input to the first component; and determining the normalized EGF by the first component based on the EGF by the first component and the second normalization value.The method of claim 9, further comprising determining the second normalization value for the first component based on the viscosity of the exhaust input to the first component and a normalized viscosity of the exhaust input to the first component.

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