Methods and systems for controlling fuel injection in a high-pressure common rail engine

Abstract

A non-transitory computer-readable storage medium with memory, comprising: Fuel injector activation data indexed in the memory by two input parameters; Instructions for determining a modified pressure difference value across a nozzle orifice of a fuel injector based on determined pressures upstream and downstream of the nozzle orifice, engine speed, injection timing, and a modified pressure difference function; and Instructions to generate a fuel injector activation output by interpolating among the indexed fuel injector activation data with the modified pressure differential value as the first of the two input parameters.

Description

BACKGROUND TECHNICAL AREA

[0001] Embodiments of the subject matter disclosed herein relate to methods and systems for controlling a so-called high-pressure common rail (common rail) fuel system. DISCUSSION OF THE TECHNOLOGY

[0002] Vehicles, such as rail cars, include power sources such as diesel engines or dual-fuel engines that use both diesel fuel and another type of fuel, such as natural gas. In some vehicles, diesel fuel is delivered to the diesel or dual-fuel engine via a common rail fuel system. In the common rail system, fuel injectors inject fuel (e.g., diesel fuel) from the common rail to cylinders of the engine for combustion. Some engine systems may utilize an injector map stored in memory of a control module to determine a fuel injector activation output. In one example, the fuel injector activation output may include a fuel injector activation time and / or a period of time that the injectors inject fuel into the engine cylinders.The injector map may include a table of injector activation data, where each injector activation time corresponds to a fuel rail pressure and a fuel value or fuel quantity injected with a single fuel injector stroke. Thus, using the injector map, an engine control unit can output an injector activation time for a specific fuel value and a measured fuel rail pressure. Fuel injection can then be adjusted based on the determined injector activation time to deliver the desired amount of fuel to the engine cylinders.

[0003] Documents US 2014 / 0 330 504 A1, US 7 520 265 B2 and DE 10 2006 023 468 B3 each show methods and systems for controlling a fuel distribution system with the aid of a non-volatile computer-readable storage medium. SHORT DESCRIPTION

[0004] The object of the present invention is to further improve high-pressure injection.

[0005] The object is achieved by the features of the independent patent claims. Advantageous developments of the invention are described in the subclaims.

[0006] In one embodiment, a non-transitory computer-readable storage medium having memory comprises: fuel injector activation data indexed in the memory according to two input parameters; instructions for determining a modified pressure differential value across a nozzle orifice of a fuel injector based on determined pressures upstream and downstream of the nozzle orifice, engine speed, injection timing, and a modified pressure differential function; and instructions for generating a fuel injector activation output by interpolating among the indexed fuel injector activation data with the modified pressure differential value as a first of the two input parameters. BRIEF DESCRIPTION OF THE DRAWINGS Fig. 1 shows a schematic representation of a common rail system according to an embodiment of the invention. Fig. 2 shows a schematic representation of an exemplary cylinder of a multi-fuel engine according to an embodiment of the invention. Fig. 3 shows fuel injector tables according to an embodiment of the invention. Fig. 4-9 show graphs of relationships between pressures upstream and downstream of an orifice of a nozzle of a fuel injector and time or crank angle in a cylinder cycle for various engine operating conditions according to an embodiment of the invention. Fig. 10 shows a method for adjusting fuel injection to the engine based on injector activation time according to an embodiment of the invention. DETAILED DESCRIPTION

[0007] The following description relates to various embodiments for indexing an injector map and subsequently controlling fuel injection to an engine. The amount of fuel injected by a fuel injector into an engine cylinder may be based on a fuel rail pressure and an injector activation time (e.g., a period of time during which the injector injects fuel). Furthermore, fuel injection data for controlling fuel injection may be stored in a memory of an engine control unit. For example, the fuel injection data may include fuel injection activation times for various fuel values ​​and the fuel rail pressure. In other words, the fuel injection activation data may be indexed by fuel rail pressure and a fuel value.The engine control unit can then determine a fuel injection activation time by interpolating from the injector table data based on a determined fuel rail pressure (e.g., measured pressure) and the desired fuel value. In this way, the fuel injectors can be activated based on the resulting fuel injector activation time to deliver a desired amount of fuel at a given fuel rail pressure.

[0008] However, such indexing of the injector table can lead to inaccuracies in linear interpolation due to a nonlinear relationship between the injector data, increasing the error in fuel injector activation time. This, in turn, can reduce fuel economy and increase emissions variability.

[0009] By making the relationship between injector activation data more linear, interpolation inaccuracies can be reduced, thereby increasing the accuracy of injector activation time. For example, the injector table can be indexed by a modified pressure instead of fuel rail pressure alone. The modified pressure can be based on a modified pressure function and a determined or measured fuel rail pressure. As such, the modified pressure function can transform the fuel injector activation data stored in the injector table to be more linear between cells of the injector table. Interpolation between such transformed data can reduce the interpolation error relative to untransformed data, resulting in more accurate fuel injector activation time and more precise control of fuel injection to the engine.

[0010] The present inventors have also recognized that the fuel flow model represented in the injector tables discussed above may be prone to error under different operating conditions encountered in the engine. Specifically, the inventors have recognized that the pressure conditions on the engine (e.g., during engine operation) around the injector nozzle orifice are more dynamic and generally not the same as the pressure conditions around the same nozzle orifice on a test bench, which is used to create typical injector maps. Therefore, the modified pressure function described above can be further modified to account for physical changes in engine operation that cause the fuel flow model error.The modified pressure function (referred to herein as modified pressure difference function) may, for example, take into account changes in the fuel rail supply pressure as well as the pressures in the engine cylinder as a function of injection timing, engine speed, injection length, dual-fuel gas quantities in the cylinder (e.g., when the engine is a dual-fuel engine that burns both diesel fuel and a secondary fuel such as natural gas), and the like.

[0011] Fig. Figure 1 shows an exemplary common rail fuel system of an engine, such as the engine of Fig. 2. The common rail fuel system may include multiple injectors for injecting fuel, e.g., diesel fuel. As described in Fig. As shown in Figure 2, the engine can be either a pure diesel engine (which, for example, only injects liquid diesel fuel) or a dual-fuel engine, which injects both liquid fuel via the common rail fuel system and a secondary, gaseous fuel such as natural gas. Activation data for the multiple injectors can be stored as a map in the memory of an engine control unit, such as the Fig. 3. To account for errors in the fuel flow model of an injector seen during on-board engine operation, the injector activation data can be indexed in the injector map according to a modified pressure difference function based on a pressure difference across an orifice of the injector nozzle, a function of injection timing and engine speed, and a correction factor that accounts for pressure differences seen across the injector on-board the engine compared to on the test bench (e.g., during injector testing outside the engine). Fig. The graphs shown in Figures 4-9 illustrate pressure changes upstream and downstream of the injector nozzle orifice seen for various injection parameters, including single versus multiple injections, different injection timings, different gaseous fuel substitution ratios, and the like. Fig. 10 shows a method for indexing the stored fuel injector activation data according to the modified pressure difference function and then adjusting fuel injection based on an injector activation time determined from an injector map containing the indexed fuel injector activation data.

[0012] The modified pressure difference across the injector orifice functions discussed herein may enable more accurate high substitution ratio operation in a dual-fuel engine (e.g., a high natural gas to total fuel ratio including natural gas and diesel fuel), as well as accurate and efficient use of post-injections in a diesel engine for reduced emissions and fuel consumption.

[0013] The approach described here can be applied to various engine types and various engine-driven systems. Some of these systems may be stationary, while others may be mounted on semi-mobile or mobile platforms. Semi-mobile platforms can be relocated between operating hours, e.g., mounted on flatbed trailers. Mobile platforms also include self-propelled vehicles. These vehicles can include road vehicles, mining equipment, marine vessels, rail vehicles, and other over-the-road vehicles (OHVs). For clarity, a locomotive is shown as an example of a mobile platform supporting a system incorporating an embodiment of the invention.

[0014] Before further discussing the procedure for indexing an injector map and subsequently controlling fuel injection to an engine, an example fuel system for an engine is disclosed. Fig. For example, Figure 1 shows a block diagram of a common rail fuel system (CRS) 100 for an engine of a vehicle, such as a rail car. Liquid fuel, such as diesel fuel, is drawn from or stored in a fuel tank 102. A low-pressure fuel pump 104 is in fluid communication with the fuel tank 102. In the Fig. In the embodiment illustrated in Figure 1, the low-pressure fuel pump 104 is located inside the fuel tank 102 and can be submerged below the liquid fuel level. In alternative embodiments, the low-pressure fuel pump can be coupled to the outside of the fuel tank and pump fuel through a suction device. The operation of the low-pressure fuel pump 104 is controlled by a controller 106.

[0015] Liquid fuel is pumped by the low-pressure fuel pump 104 from the fuel tank 102 through a line 110 to a high-pressure fuel pump 108. A valve 112 is arranged in the line 110 and regulates fuel flow through the line 110. The valve 112 is, for example, an inlet metering valve (IMV). The IMV 112 is arranged upstream of the high-pressure fuel pump 108 to adjust a flow rate of fuel delivered to the high-pressure fuel pump 108 and further to a common rail 114 for distribution to a plurality of fuel injectors 118 for fuel injection. The IMV 112 can, for example, be a solenoid valve whose opening and closing is controlled by the control unit 106.In other words, the controller 106 controls the IMV to a position that is fully closed, fully open, or between fully closed and fully open to control fuel flow to the high-pressure fuel pump 108 to a desired fuel amount. During operation of the vehicle, the IMV 112 is adjusted to meter fuel based on operating conditions and may be at least partially open under at least certain conditions. It should be understood that the valve is only one example of a fuel metering control device, and any suitable control element may be employed without departing from the scope of this disclosure. For example, a position or state of the IMV may be electrically controlled by controlling an electrical current of the IMV.As another example, a position or state of the IMV can be mechanically controlled by controlling a servo motor that moves the IMV.

[0016] The high-pressure fuel pump 108 raises the fuel pressure from a lower pressure to a higher pressure. The high-pressure fuel pump 108 is fluidly connected to the common rail 114. The high-pressure fuel pump 108 supplies the fuel to the common rail 114 through a line 116. A plurality of fuel injectors 118 are in fluid communication with the common rail 114. Each of the plurality of fuel injectors 118 supplies fuel to one of a plurality of engine cylinders 120 in an engine 122. The fuel is combusted in the plurality of engine cylinders 120 to power the vehicle, for example, via an alternator and traction motors. The operation of the plurality of fuel injectors 118 is controlled by the controller 106. In the embodiment of Fig. 1, the engine 122 includes four fuel injectors and four engine cylinders. In alternative embodiments, more or fewer fuel injectors and engine cylinders may be included in the engine.

[0017] Fuel pumped by the low-pressure fuel pump 104 from the fuel tank 102 to an inlet of the IMV 112 may operate at what is known as a lower fuel pressure, or engine fuel pressure. Accordingly, components of the CRS 100 upstream of the high-pressure fuel pump 108 operate in a lower fuel pressure, or engine fuel pressure, range. Conversely, the high-pressure fuel pump 108 may pump fuel from the lower fuel pressure to a higher fuel pressure, or distributor fuel pressure. Accordingly, components of the CRS 100 downstream of the high-pressure fuel pump 108 operate in a higher fuel pressure, or distributor fuel pressure, range of the CRS 100.

[0018] Fuel pressure in the lower fuel pressure range is measured by a pressure sensor 126 positioned in line 110. Pressure sensor 126 sends a pressure signal to controller 106. In an alternative application, pressure sensor 126 is in fluid communication with an outlet of low-pressure fuel pump 104. Fuel temperature in the lower fuel pressure range is measured by a temperature sensor 128 positioned in line 110. Temperature sensor 128 sends a temperature signal to controller 106.

[0019] Fuel pressure in the higher fuel pressure range is measured by a pressure sensor 130 positioned in line 116. Pressure sensor 130 sends a pressure signal to control unit 106. Control unit 106 uses this pressure signal to determine a fuel rail pressure (e.g., FRP) in the common rail. Thus, the fuel rail pressure (FRP) is provided to control unit 106 by pressure sensor 130. In an alternative application, pressure sensor 130 is in fluid communication with an outlet of high-pressure fuel pump 108. It should be noted that in some applications, various operating parameters may generally be determined or inferred indirectly in addition to, or instead of, direct measurement.

[0020] In addition to the sensors mentioned above, controller 106 receives various signals from a plurality of engine sensors 134 coupled to engine 122, which may be used to assess the functionality of the fuel control and associated engine operation. For example, controller 106 receives sensor signals indicating air-fuel ratio, engine speed, engine load, engine temperature, ambient temperature, fuel level, a number of cylinders actively combusting fuel, and the like. In the illustrated implementation, controller 106 is a computing device such as a microcomputer that includes a processor unit 136, a non-transitory computer-readable storage medium 138, input / output ports, memory, and a data bus.The computer-readable storage medium 138 contained in the controller 106 is programmable with computer-readable data representing processor-executable instructions for performing the control routines and methods described below, as well as other variations not specifically listed.

[0021] The controller 106 is capable of adjusting various actuators in the CRS 100 based on various operating parameters received or derived from the various signals received from the various sensors to dynamically evaluate the health of the CRS and control the operation of the engine based on the evaluation. For example, in one embodiment, the controller 106 is capable of adjusting fuel injection to the engine. Specifically, the controller may adjust the fuel injection timing of one or more fuel injectors based on a determined injector activation time. This may include adjusting a pulse width modulation signal to command the plurality of fuel injectors to inject fuel for a period of time.

[0022] The controller 106 may also be capable of generating an output for fuel injector activation based on operating conditions of the CRS and stored fuel injector activation data, such as the fuel injector activation time. The fuel injector activation data may be stored in the memory of the computer-readable storage medium of the controller. In one example, the fuel injector activation data may be stored in an injector table or injector map, such as the first injector table 300 or the second injector table 302, which may be Fig. 3 are shown.

[0023] Fig. 2 shows an embodiment of a combustion chamber or cylinder 200 of a multi-cylinder internal combustion engine 202, such as an engine having the configuration described above with reference to Fig. 1. The cylinder may be defined by a cylinder head 201, which houses the intake and exhaust valves and the liquid fuel injector described below, and a cylinder block 203.

[0024] The engine may be controlled at least in part by a control system including controller 106, which may be in further communication with a vehicle system. As described above, the controller may also receive signals from various engine sensors, including, but not limited to, engine speed, engine load, boost pressure, exhaust pressure, turbocharger speed, ambient pressure, CO2 levels, exhaust temperature, NOx emissions, engine coolant temperature (ECT) from temperature sensor 230 coupled to cooling sleeve 228, etc. Accordingly, the controller may control an engine system by sending commands to various components such as the alternator, cylinder valves, throttle body, fuel injectors, etc.

[0025] The cylinder (i.e., combustion chamber) may include a cylinder liner 204 with a piston 206 disposed therein. The piston may be coupled to a crankshaft 208 such that reciprocating motion of the piston is translated into rotary motion of the crankshaft. The crankshaft may include a crankshaft speed sensor for outputting a rotational speed (e.g., instantaneous speed) of the crankshaft. In some embodiments, the engine may be a four-stroke engine in which each of the cylinders fires in a firing sequence during two revolutions of the crankshaft. In other embodiments, the engine may be a two-stroke engine in which each of the cylinders fires in a firing sequence during one revolution of the crankshaft.

[0026] The cylinder receives intake air for combustion from an intake having an intake port 210. The intake port receives intake air via an intake manifold. For example, the intake port may communicate with other cylinders of the engine in addition to the cylinder, or the intake port may communicate exclusively with the cylinder.

[0027] The exhaust gas produced during combustion in the engine is fed to an outlet with an exhaust duct 212. Exhaust gases flow through the exhaust duct, in some versions (not in Fig. 2) to a turbocharger and then to the atmosphere via an exhaust manifold. In addition to the cylinder, the exhaust duct can also accommodate exhaust gases from other cylinders of the engine.

[0028] Each cylinder of the engine may include one or more intake valves and one or more exhaust valves. For example, the cylinder is illustrated with at least one intake poppet valve 214 and at least one exhaust poppet valve 216 located at an upper portion of the cylinder. In some embodiments, each cylinder of the engine, including the cylinder, may include at least two intake poppet valves and at least two exhaust poppet valves located at the cylinder head.

[0029] The intake valve can be controlled by the control unit using an actuator 218. The exhaust valve can be controlled similarly by the control unit using an actuator 220. Under certain conditions, the control unit can vary the signals provided to the actuators for controlling the opening and closing of the respective intake and exhaust valves. The position of the intake valve and the exhaust valve can be determined by respective valve position sensors 222 and 224, respectively, and / or by cam position sensors. The valve actuators can be, for example, of the electric valve actuation type or cam actuation type, or a combination thereof.

[0030] The intake and exhaust valve timing may be controlled simultaneously, or any of variable intake cam timing, variable exhaust cam timing, dual independent variable cam timing, or fixed cam timing may be used. In other embodiments, the intake and exhaust valves may be controlled by a common valve actuator or actuation system, or by a variable valve timing actuator or actuation system. Additionally, the intake and exhaust valves may be controlled by the controller to have variable lift based on operating conditions.

[0031] In still further embodiments, a mechanical cam lobe may be used to open and close the intake and exhaust valves. Furthermore, while a four-stroke engine is described above, in some embodiments, a two-stroke engine may be used, omitting intake valves and providing ports in the cylinder wall to allow intake air to enter the cylinder as the piston moves, opening the ports. This may also extend to the exhaust, although exhaust valves may be used in some examples.

[0032] In some embodiments, each cylinder of the engine may be configured with one or more fuel injectors for supplying fuel thereto. As a non-limiting example, Fig. 2, the cylinder with a fuel injector 226. The fuel injector is shown coupled directly to the cylinder for injecting fuel directly therein. In this way, the fuel injector provides injection into the combustion chamber known as direct fuel injection. The fuel may be supplied from a first liquid fuel system 232, which may include a fuel tank, fuel pumps, and a fuel distributor, as described above with reference to Fig. 1, to the fuel injector. In one example, the fuel is diesel fuel combusted in the engine by compression ignition. In other non-limiting embodiments, the fuel may be gasoline, kerosene, biodiesel, or other petroleum distillates of similar density by compression ignition (and / or spark ignition). In one example, the controller may control the amount, duration, timing, and spray pattern of fuel delivered to the cylinder via the fuel injector. As explained further below, the fuel delivery to the cylinder may be controlled by the controller actuating the fuel injector based on engine operating conditions and a stored injector table.

[0033] Furthermore, each cylinder of the engine can be configured to receive gaseous fuel (e.g., natural gas) as an alternative or in addition to diesel fuel. The gaseous fuel can be supplied to the cylinder via the intake manifold. As shown in Fig. 2, the intake passage may be supplied with gaseous fuel from a second gaseous fuel system 234 via one or more gaseous fuel lines, pumps, pressure regulators, etc. located upstream of the cylinder. In some embodiments, the gaseous fuel system may be located remotely from the engine, e.g., on another car (e.g., on a fuel tank car), and the gaseous fuel may be supplied to the engine via one or more fuel lines that run through each car. However, in other embodiments, the gaseous fuel system may be located on the same car as the engine.

[0034] Multiple gas inlet valves, such as gas inlet valve 236, may be configured to deliver gaseous fuel from the gaseous fuel system to each respective cylinder via corresponding intake ports. For example, a degree and / or duration of gas inlet valve opening may be adjusted to regulate an amount of gaseous fuel delivered to the cylinder. Therefore, each respective cylinder may be supplied with gaseous fuel via an individual gas inlet valve, allowing individual cylinder control of the amount of gaseous fuel delivered to the cylinders. However, in some embodiments, a single-point gassing system may be used, mixing gaseous fuel with intake air at a single point upstream of the cylinders. In such a configuration, each cylinder may be supplied with substantially equal amounts of gaseous fuel.To control the amount of gaseous fuel provided by the single-point aeration system, in some examples, a gaseous fuel control valve may be positioned at a junction between a gaseous fuel supply line and the engine intake air supply line or the intake manifold. The degree and / or duration of opening of the gaseous fuel control valve may be adjusted to control the amount of gaseous fuel admitted to the cylinders. In other examples, the amount of gaseous fuel delivered to the cylinders in the single-point aeration system may be controlled by another mechanism, such as controlling a gaseous fuel regulator, controlling a gaseous fuel pump, etc.

[0035] As discussed above, the fuel injectors may be actuated according to a fuel injector activation output, e.g., a fuel injector activation time (e.g., an open duration), based on estimated and / or measured engine operating conditions and stored fuel injector activation data. In one example, the fuel injector activation data may be stored in an injector table or map in the memory of the computer-readable storage medium of the controller.

[0036] Fig. 3 shows two example injector tables. A first injector table 300 contains fuel injector activation data indexed in memory by a pressure value, such as a fuel rail pressure (FRP). A second injector table 302 contains injector activation data indexed in memory by a modified pressure value, which may be a modified pressure differential across an orifice of the injector's nozzle. As explained further below, the modified pressure differential may be a function of a square root of a difference between a fuel rail pressure and a peak cylinder pressure, the peak cylinder pressure multiplied by a function of engine speed and injection timing, and the pressure differential compensated for by a correction factor. The second injector table 302 represents an example of an alternative method for indexing an injector table, which is discussed further below.The first injector table 300 represents an example of a standard method for indexing an injector table.

[0037] As in Fig. 3, the first injector table 300 includes a series of fuel rail pressure (FRP) values ​​on the x-axis (e.g., horizontal axis) or the first row 304 of the table. In one example, the series of fuel rail pressures may range from 600 to 2200 bar. In another example, the series of fuel rail pressures may range from 400 to 2800 bar. As shown in Fig. 3, the injector table 300 further includes a series of fuel values ​​on the y-axis (e.g., vertical axis) or the first column 306 of the table. In one example, the series of fuel values ​​may range from 0 to 3000 mm 3 / stroke. In another example, the range of fuel values ​​can range from 0 to a fuel value of over 3000 mm 3 / stroke. The ranges listed above for the series of fuel rail pressures and fuel values ​​may change (e.g., be larger or smaller) depending on the engine application and / or injector type. The injector table 300 also includes a series of cells 308 that contain fuel injector activation data. In one example, the fuel injector activation data may be fuel injector activation times (e.g., an injector open time or the amount of time the injectors are activated and injecting fuel into engine cylinders). In this example, each cell contains a fuel injector activation time that corresponds to a fuel rail pressure and a fuel value. In another example, the fuel injector activation data may be another fuel injection parameter.

[0038] The first injector table 300 may have a first number of columns and a second number of rows, both greater than 1. The first number and the second number may be a maximum number of rows and a maximum number of columns. In one example, the maximum number of rows and the maximum number of columns may not be the same. In another example, the maximum number of rows and the maximum number of columns may be less than 50. Thus, the table may contain a finite number of data points. For example, if the maximum number of rows is 10 and the maximum number of columns is 8, there may be 10 rows and 8 columns of fuel injector activation data. Specifically, there may be 8 fuel rail pressure values ​​in the first row 304 and 10 fuel values ​​in the first column 306.In this example, there are 80 fuel injector activation data points or fuel injector activation times. In one example, the maximum number of columns and rows may be based on the available amount of memory or space in the control module's computer-readable medium. For example, as the number of data points or columns and rows increases, memory consumption increases. For example, the number of data points in the injector table may be limited by memory requirements.

[0039] The controller 106 is capable of generating a fuel injector activation output, e.g., a fuel injector activation time, using a fuel injector table stored in the controller's memory, a sensed pressure, and a fuel value. In one example, the sensed pressure may be a measured fuel rail pressure measured with a pressure sensor in the CRS (e.g., the pressure sensor in Fig. 1). In another example, the determined pressure may be a fuel rail pressure estimated by the pressure sensor and / or additional engine operating conditions. The fuel value may be an amount of fuel injected in a single fuel injector stroke (also referred to as a fuel fill). In one example, the fuel value may be a predetermined value for the engine. Thus, the fuel value may be stored in the controller. In another example, the fuel value may be based on engine operating conditions, such as torque demands. The controller may inject the desired amount of fuel at a particular (e.g., determined) fuel rail pressure by activating the fuel injectors for a particular period of time. This period of time, or the injector activation time, may be determined from the injector activation table data.

[0040] Specifically, the ECU can look up the determined or measured fuel rail pressure and the desired fuel value in the injector table. As explained above, the injector activation table can contain a finite number of data points. Since the injector table can have a maximum number of rows and columns, the precisely determined fuel rail pressure and the desired fuel value may not be contained in the injector table. As a result, the ECU can interpolate between data points around the desired points to determine the injector activation time.

[0041] If the determined fuel rail pressure and the desired fuel value are outside the ranges listed in the injector table, the controller may, in an alternative embodiment, extrapolate using the nearest data points in the injector table. Therefore, similar methods as outlined below for injector map interpolation may be used for extrapolation to determine an injector activation time at the desired operating points.

[0042] The injector map interpolation can include a multi-stage (e.g., two-dimensional) linear interpolation. For a specific fuel value and fuel rail pressure, four data points can be selected in the injector table. In one example, the specified (e.g., determined) fuel rail pressure and fuel value can be 1100 bar and 75 mm, respectively. 3 / stroke. Using the first injector table 300, these two values ​​lie between two fuel values ​​and two fuel rail pressures listed in the first injector table 300. This requires the control module to perform a multi-stage linear interpolation between the four nearest data points (cells 314, 316, 318, and 320 in the table), each corresponding to a fuel rail pressure and a fuel value that are either above or below the specified values.

[0043] In another example, the commanded or desired fuel value may be listed in the injector table, while the determined fuel rail pressure is not. In this example, the controller may perform a one-way linear interpolation between the two nearest data points corresponding to a fuel rail pressure above and a fuel rail pressure below the measured fuel rail pressure at the commanded fuel value. Specifically, this may include interpolating between a first fuel injection activation time corresponding to a first fuel rail pressure and the commanded fuel value and a second fuel injection activation time corresponding to a second fuel rail pressure and the commanded fuel value.The first fuel rail pressure may be greater than the sensed fuel rail pressure, while the second fuel rail pressure may be less than the sensed fuel rail pressure.

[0044] However, linear interpolation between available fuel rail pressure values ​​and fuel values ​​in the injector map can lead to an interpolation error. In particular, indexing the injector map by fuel rail pressure, as illustrated in the first injector table 300, can result in a nonlinear relationship between fuel injector activation data. Consequently, linear interpolation of nonlinear data can lead to interpolation inaccuracies, thereby increasing the error in fuel injector activation time. This, in turn, can reduce fuel economy and increase emissions variability.

[0045] Alternatively, the resulting mass flow curve becomes more linear when mass flow is plotted against the square root of the fuel rail pressure. Thus, in a lookup table that indexes injector activation data by a modified pressure differential across an injector orifice using a square root function, fewer data points can be used while maintaining a similar level of accuracy. Storing fewer data points within the lookup table can reduce the memory requirements in the ECU's computer-readable medium.

[0046] The accuracy of linear interpolation increases as the relationship between selected variables becomes more linear. For example, linear interpolation of mass flow rate versus the square root of the modified pressure difference across the injector orifice reduces the interpolation error compared to linear interpolation of mass flow rate versus fuel rail pressure. For these reasons, indexing an injector map by a square root of the modified pressure difference, rather than by fuel rail pressure alone, can increase the accuracy of determining an output for fuel injector activation (e.g., fuel injector activation time). This, in turn, can reduce the error in fuel injector activation time, thereby increasing fuel economy and reducing emissions variability.

[0047] Furthermore, as discussed above, indexing fuel injector activation data by manifold pressure alone (as shown in fuel injector table 200) or a pressure differential across an injector orifice alone (e.g., fuel rail pressure minus peak cylinder pressure) may result in errors under varying engine operating conditions while the engine is operating. Because pressure conditions on the engine (e.g., during engine operation) around the injector orifice are more dynamic and generally not the same as the pressure conditions around the same orifice on a test bench from which the typical injector maps are created (e.g., map 300), injector activation time looked up in a conventional table indexed only by manifold pressure may result in inaccurate injector activation times for the current engine operating conditions. This may result in degraded engine performance.Thus, the fuel injector data can instead be indexed according to a modified pressure differential across an injector orifice, where the modified pressure differential is a function of the square root of the difference between a manifold pressure and a peak cylinder pressure, where the peak cylinder pressure is scaled (e.g., multiplied) by a function of engine speed and injection timing, and the pressure differential is compensated for by a correction factor. This modified pressure differential function can account for changes in fuel rail supply pressure as well as in-engine cylinder pressures as a function of injection timing, engine speed, injection length, in-cylinder dual-fuel gas quantities (e.g., if the engine is dual-fuel, burning both diesel fuel and a secondary fuel such as natural gas), and the like.

[0048] During engine operation, changes in various injection parameters, such as changes in injection timing, cylinder pressure, multiple injections (e.g., main and post injection), duration of injection and / or duration between multiple injections, substitution ratio (e.g., quantity of injected natural gas divided by the total quantity of injected gas including natural gas and diesel fuel), and diesel fuel quantity, lead to changes in the pressure upstream of the injector nozzle (e.g., in one example, estimated / indicated by the pressure in the injector accumulator or the distributor pressure) and the pressure downstream of the injector nozzle (e.g., estimated / indicated by the pressure in the cylinder). As a result, with these varying injection parameters, the pressure difference across the injector nozzle opening (e.g.,the difference between the pressure upstream and downstream of the injector nozzle), which drives the fuel flow through the nozzle.

[0049] Fig. 4-9 show changes in a pressure upstream of the injector nozzle (injector accumulator pressure, which in one example can be estimated by and / or represents the manifold pressure) and a pressure downstream of the injector nozzle (cylinder pressure) compared to the injector test bench data (used for conventional injector maps such as map 300) and for various injection parameters. In particular, each of Fig. 4-9 shows a first graph indicating injector accumulator pressure (e.g., manifold pressure) on the y-axis and crank angle degrees (CAD) on the x-axis, and a second graph indicating cylinder pressure (representing injector nozzle outlet pressure) on the y-axis and CAD on the x-axis. Each of the x-axes indicates the timing for top dead center (TDC) in the cylinder cycle and additional timings that may represent times at which fuel injection by the injector starts, stops, and the like.

[0050] Turning first to Fig. 4, graph 400 shows a first diagram 402 of the injector accumulator pressure during an injection event of an injector on a test bench (e.g., during testing prior to installation for use in an engine), a second diagram 404 of the injector accumulator pressure during an injection event on board an engine (e.g., during practical engine operation), a third diagram 406 of the nozzle outlet pressure during the injection event of the injector on the test bench, and a fourth diagram 408 of the nozzle outlet pressure (represented as engine cylinder pressure) during the injection event on board the engine. While the fourth diagram 408 shows the total cylinder pressure during the entire combustion cycle, a fifth diagram 410 shows a pure compression cylinder pressure during the injection event during the combustion cycle.The pure compression cylinder pressure shown in the fifth diagram 410 ignores the contribution of the combustion event to the cylinder pressure, since combustion may occur some time after fuel injection. As shown in diagrams 402 and 404, the actual injector accumulator pressure during the injector's injection event on board the engine decreases by a greater amount than the injector accumulator pressure during the injector's injection event on the test bench. Furthermore, as shown in diagrams 406, 408 and 410, the nozzle outlet pressure (e.g., cylinder pressure) remains relatively constant on the test bench (diagram 406), but increases by a greater amount up to a peak value (peak cylinder pressure) and then decreases again during the injector's injection event on board the engine (diagrams 408 and 410). The peak cylinder pressure (PCP) for chart 408 is shown at 412 and the PCP for chart 410 is shown at 414.These PCPs 412 and 414 are significantly higher than the steady-state nozzle outlet pressure on the test bench. The injection duration (e.g., the period during which the injector nozzle is open and injecting fuel) for the injection lies between time t1 and time t2, as indicated by injection duration 416. This shows . Fig. 4 the differences between injector accumulator pressure and nozzle outlet pressure experienced on-board the engine and on the test bench. As explained herein, the injector activation data stored in an injector table generated from test bench data may not accurately reflect the conditions experienced on-board the engine. Therefore, using this test bench-derived injector activation data to request fuel injector activation times for on-board injectors during engine operation may result in a different amount of fuel being injected than desired for the current engine operating conditions, thereby degrading engine efficiency and emissions.

[0051] Fig. 5 shows a graph 500 with a first diagram 502 of the injector accumulator pressure during a first injection event during engine operation in which the injection time is further advanced, a second diagram 504 of the injector accumulator pressure during a second injection event during engine operation in which the injection time is further retarded (e.g., retarded relative to the time of the first injection event and / or relative to a standard injection time), a third diagram 506 of the cylinder pressure during the first injection event at the further advanced time, a fourth diagram 508 of the second injection event at the further retarded time, and a fifth diagram 510 of the pure compression cylinder pressure during the first injection event.The injection duration of the first injection event at the further advanced timing is shown at 512 (between time t1 and time t3), and the injection duration of the second injection event at the further retarded timing is shown at 514 (between time t2 and time t4). The shapes (e.g., size) of the injector accumulator pressure plots 502 and 504 are similar, however, due to the advanced timing of the first injection event, the injector accumulator pressure begins to decrease at an earlier time in the first plot 502 than in the second plot 504. Additionally, the PCP of the cylinder pressure in the first injection event (plot 506), which occurs immediately after TDC (top dead center), is greater than and occurs before the PCP of the cylinder pressure in the second injection event, which occurs between TDC and time t3 (plot 508).In this way, changes in an injector's injection timing affect the pressures upstream and downstream of the injector nozzle, thereby influencing the pressure differential across the injector nozzle orifice (and thus the fuel flow through the nozzle). Therefore, as explained below, the modified pressure differential function used in the injector table may be based at least in part on injection timing.

[0052] Fig. 6 shows a graph 600 with a first plot 602 of the injector accumulator pressure during an injection event during engine operation, a second plot 604 of the cylinder pressure during the injection event for a higher cylinder pressure (e.g., higher peak cylinder pressure), a third plot 606 of a corresponding compression-only cylinder pressure for the higher cylinder pressure, a fourth plot 608 of the cylinder pressure during the injection event for a lower cylinder pressure (e.g., lower peak cylinder pressure), and a fifth plot 610 of a corresponding compression-only cylinder pressure for the lower cylinder pressure. The injection duration of the injection event is shown at 612, between times t1 and t2. The PCPs in both cylinder pressure states, for plots 604 and 608, occur immediately after TDC, but have different magnitudes.Different cylinder pressures can influence the total pressure difference across the injector nozzle opening and thus the fuel flow through the nozzle. This means that, with the same injector activation time (e.g., duration 612), different amounts of fuel can be injected into the cylinder due to different pressure differences across the nozzle (due to different internal cylinder pressures).

[0053] Fig. 7 shows a graph 700 illustrating differences between injector accumulator pressure and cylinder pressure during a single injection (e.g., only one main injection) versus multiple injections (one main injection followed by one post-injection). Specifically, graph 700 includes a first plot 702 of injector accumulator pressure during a first injection event with only a single injection, a second plot 704 of injector accumulator pressure during a second injection event with two injections (one main injection and one post-injection), a third plot 706 of cylinder pressure during the first injection event with the single injection, a fourth plot 708 of cylinder pressure during the second injection event with the two injections, and a fifth plot 710 of pure compression cylinder pressure for the first injection event.The injection duration of the individual injection for the first injection event is shown at 712. The injection duration of the main injection (e.g., main injection duration) for the second injection event is shown at 714, and the injection duration of the post-injection (e.g., post-injection duration) for the second injection event is shown at 716. The time between the end of the main injection duration 714 and the beginning of the post-injection duration 716 is referred to herein as the post-residence time (or duration), as indicated at 718. Additionally, the main injection timing is at time t1, and the post-injection timing is at time t3.As plots 702 and 704 show, the injector accumulator pressure is similar for the main injections of both injection events; however, the post-injection causes plot 704 to show an additional drop in pressure before returning to a baseline value (due to the post-injection). The in-cylinder pressure during engine operation with one injection (plot 706) compared to two injections (plot 708) is similar (e.g., with similar PCPs); however, the post-injection results in a slower drop in cylinder pressure after the PCP and a higher total pressure after the main injection. This also creates different pressure differentials across the injector orifice due to the number of injections during an injection event (e.g., during a cylinder combustion cycle). This can cause the fuel flow through the injector nozzle to change depending on the number of injections.

[0054] The fuel flow through the nozzle and the total amount of injected fuel can also be influenced by the duration of the main and post-injection in a main / post-injection process, as in Fig. 8. In particular, Fig. 8 shows a graph 800 with a first diagram 802 of the injector accumulator pressure and a third diagram 806 of the cylinder pressure for a first injection event with a shorter main injection 812 and a longer dwell time 816 (compared to the second injection event described below). Graph 800 also includes a second diagram 804 of the injector accumulator pressure and a fourth diagram 808 of the cylinder pressure for a second injection event with a longer main injection 818 and a shorter dwell time 822. The post-injection for the first injection event (shown at 814) and the post-injection for the second injection event (shown at 820) both occur between times t4 and t5, at the end of their respective dwell times. Graph 800 also includes a fifth diagram 812 of the pure compression pressure for the second injection event. As in Fig. 8, the injector accumulator pressure remains lower after the main injection for the second injection event with the longer main injection 818 (plot 804) and rises back to the baseline more slowly than during the first injection event (plot 802). In addition, the cylinder pressure during the second injection event (plot 808) is slightly higher than during the first injection event (plot 806) after the main injection 808 for the second injection event has been completed. In this way, the duration of the main injection and post-injection, as well as the timing of these injections, including the dwell time, influence the pressure differential across the injector nozzle opening. Therefore, these injection parameters can also influence the fuel flow through the nozzle during injection during engine operation.

[0055] As illustrated above, in some embodiments, the engine may be a dual-fuel engine that can inject both liquid fuel (e.g., diesel fuel) via the fuel system, including the injector, and gaseous fuel (e.g., natural gas). A substitution ratio of gaseous fuel to total fuel (e.g., the amount of injected natural gas divided by the total amount of injected gas, including natural gas and diesel fuel) may be adjusted during engine operation based on engine operating conditions. However, the substitution ratio may affect the fuel flow through the injector nozzle and the total amount of fuel (e.g., diesel fuel) injected into the cylinder, as described in Fig. 9. In detail, Fig. 9 shows a graph 900 with a first diagram 902 of the injector accumulator pressure, a second diagram 906 of the cylinder pressure, and a third diagram 908 of the pure compression cylinder pressure for an injection event (e.g., diesel fuel injection event) during engine operation with a first, lower substitution ratio (e.g., only diesel fuel and / or a larger amount of diesel fuel as gaseous fuel). Graph 900 further includes a fourth diagram 904 of the injector accumulator pressure, a fifth diagram 910 of the cylinder pressure, and a sixth diagram 912 of the pure compression cylinder pressure for an injection event (e.g., diesel fuel injection event) during engine operation with a second, higher substitution ratio (e.g., smaller amount of diesel fuel as gaseous fuel).The injection duration 914 for the injection event with the lower substitution ratio is longer than the injection duration 916 for the injection event with the higher substitution ratio because the amount of diesel is greater for the injection event with the lower substitution ratio (and thus the injection activation time is longer to inject the larger amount of fuel). Due to the longer injection duration 914 and the larger amount of diesel injected for the injection event with the first, lower substitution ratio, the injector accumulator pressure drops by a greater amount and over a longer period of time (after time t3, as shown in diagram 902), and the cylinder pressure has a higher PCP (diagram 906) than for the injection event with the second, higher substitution ratio.In this way, the substitution ratio can influence the pressure difference across the injector nozzle opening and thus the fuel flow into the engine cylinder.

[0056] The pressure difference across the injector nozzle opening can be calculated based on the pressure Fig. The relationships described in Figures 4 to 9 can be modified to account for the injection parameters under different engine operating conditions. This allows errors in the fuel flow model to be reduced and a more accurate injection activation time for the current operating conditions to be determined and used to actuate the fuel injectors. This allows a desired amount of fuel to be injected into the engine cylinders and improves engine efficiency.

[0057] Back to Fig. 3, an example of a second injector table 302 is shown that includes injector activation data indexed in the controller's memory by a modified pressure differential across an orifice of the injector. In one example, the modified pressure differential is a function including the square root of a pressure differential across an orifice of the injector nozzle, a port exit pressure scaled by a multiplier that includes a function of engine speed and injection timing, and a correction factor (e.g., offset) subtracted from the pressure differential. As explained further below, the pressure differential across the orifice may be estimated by a difference between a manifold pressure (e.g., port inlet pressure) and a peak cylinder pressure (PCP) (e.g., port exit pressure). In one example, the PCP may be a pressure at the time of fuel injection.In some examples, fuel injection occurs within 20 degrees of top dead center in the engine cycle. Therefore, the cylinder firing pressure may be a peak cylinder firing pressure when fuel is injected into the engine cylinder. In another example, the peak cylinder pressure may be the peak cylinder pressure that occurs only during compression. The modified pressure differential may be a determined value that is continuously updated based on engine operating conditions. For example, the modified pressure differential may be determined based on current measured or estimated engine operating parameters, as explained further below.

[0058] The second injector table 302 can be generated by converting the first injector table 300 using a modified pressure difference function and / or stored in the memory of the control unit. In one example, the modified pressure difference function includes a square root approximation of a difference between a manifold pressure and a peak cylinder pressure, a function of engine speed and injection timing, and a correction factor. Specifically, in one example, the modified pressure difference function can be defined by the following formula: MP=RP−PCP∗f1(engine speed, injection timing)−f2(x) where RP is the fuel rail pressure determined based on an output of a pressure sensor located in a fuel rail of the fuel system (e.g., sensor 130 shown in Fig. 1) is measured and / or estimated. This RP can be the same or similar to the one in Fig. 4-9, as explained above. The RP represents the fuel injector nozzle opening inlet pressure, with additional pressure drops between the injector nozzle opening and the injector supply (e.g., fuel rail) being accounted for in the injector table values. The second term of Equation 1, which contains the multiplier or f1 term, is scaled by the peak cylinder pressure (PCP), which can be modeled in an example because it is assumed that the fuel is generally injected close to (e.g., at a similar crankshaft angle) when the PCP occurs in the engine (as in Fig. 4-9). The PCP may be modeled based on additional engine operating parameters, including one or more of intake manifold pressure, engine speed, intake oxygen fraction, main injection timing, intake manifold temperature, cylinder mass gas amount (for a dual-fuel engine), and / or fuel rail pressure. In one example, the PCP may be modeled based on the measured intake manifold pressure, engine speed, intake oxygen fraction, main injection timing, and fuel rail pressure. In a second example, for a multi-fuel engine, the PCP may be modeled based on intake manifold pressure, engine speed, intake manifold temperature, cylinder mass gas amount (mg per stroke), main injection timing, and fuel rail pressure. PCP may represent the outlet pressure at the injector nozzle orifice.The PCP term in Equation 1 is further corrected by a multiplier term, f1, which is a function of engine speed and diesel injection timing, as these engine operating parameters can narrow further where on the cylinder pressure curve (based on crank angle) fuel injection occurs. The f1 term corrects for the pressure downstream of the nozzle orifice. The f2 term can be either a constant value or a function of one or more other parameters (as explained further below) and corrects for both the cylinder pressure effects (which corrects the pressure downstream of the orifice) and the effective differences between the manifold accumulators on the test bench (e.g., test data) and on the engine (which corrects the pressure upstream of the orifice).

[0059] In one embodiment, the engine may operate with at least one main injection per cylinder cycle (e.g., combustion cycle of the cylinder). The engine may also operate with multiple injections in the same cylinder, such as a main and a post injection (as in the examples in Fig. 7 and Fig. 8). In this embodiment, the modified pressure equation of Equation 1 may be adapted to have the form of Equation 2 (for the main injection) and Equation 3 (for the post-injection and any additional injections that occur after the first injection, the main injection). MPMain=RP−PCP∗f1(Engine speed,Main time p.)−f2(), MPNach={RP+MD∗C1+PD∗C2}−PCP∗f1(Engine speed,Nachzeitp.)−f2()

[0060] In Equation 2, the PCP for the main injection of liquid fuel (e.g., diesel) is the PCP for the entire cylinder cycle (not just during compression), and the multiplier in the second term (PCP term) is the function f1 of engine speed and the target main injection timing of the diesel fuel. The target timing of the diesel main injection can be the time or crank angle within the cylinder cycle at which the diesel main injection starts (e.g., the crank angle, VOT, at which the injector is activated to open and inject diesel fuel into the cylinder). In one embodiment, the multiplier term f1 (engine speed, main timing) can be determined based on a lookup table stored in the memory of an engine control unit. The lookup table can, for example, contain the current engine speed and the main injection timing of the diesel injection as inputs and the multiplier term f1 as output.The offset value, f2, is a constant value that can correct both the cylinder pressure effects and the effective accumulator pressure differences on the test bench compared to the engine. This allows the offset value f2 to be determined in advance and stored in the control unit's memory.

[0061] In Equation 3, for the post-injection of liquid fuel (e.g., diesel), the multiplier in the second term is the function f1 of the engine speed and the specified start of diesel post-injection. The specified time of diesel post-injection may be the time or crank angle within the cylinder cycle at which diesel post-injection begins (e.g., the crank angle, BTDC (before top dead center), at which the injector is activated to open and injects diesel fuel into the cylinder for post-injection). In one embodiment, the multiplier term f1 (engine speed, post-injection time) may be determined based on a lookup table stored in the memory of the engine control unit. The lookup table may, for example, contain the current engine speed and the post-injection time of diesel injection as inputs and the multiplier term f1 as output.The offset value, f2, can be identical to the offset value in Equation 2, as described above. Additionally, in Equation 3, the pressure difference equation modified for post-injection adjusts the actual rail pressure, RP, to account for the observed decrease in fuel rail pressure (e.g., supply pressure) based on how long ago the most recent main injection occurred (referred to herein as pressure drop) and how long after the main injection the post-injection was requested to initiate (referred to herein as pressure recovery or post-residence time). In this way, the first term estimates what the effective rail pressure is at the start of post-injection, since the initial conditions of post-injection are influenced by how much fuel the accumulator lost during the previous main injection.Thus, the first term in Equation 3 adds the main injection duration, MD, multiplied by a first constant C1, and adds the post-residence time (e.g., the time between the end of the main injection duration and the start of the post-injection), multiplied by a second constant C2, to the manifold pressure RP. The first constant C1 is used to estimate the inlet pressure drop during the main injection, and the second constant C2 is used to estimate the inlet pressure recovered during the residence time between the main and post-injections.

[0062] If the engine performs more than two injections in a single cylinder cycle, equation 3 can be used for all subsequent post-injections, using the timing of the post-injection for the current post-injection.

[0063] In another embodiment, the engine may be a multi-fuel engine configured to combust at least two fuels, including a liquid fuel (e.g., diesel fuel) and a gaseous fuel (e.g., natural gas). The diesel fuel may be injected via the injector using the equations and injector maps discussed herein, and the gaseous fuel may be injected via another injector or a gas inlet valve. As discussed above, during engine operation, the substitution ratio (SR) of gaseous fuel to total fuel (liquid + gaseous fuel) may be adjusted based on engine operating conditions. In some embodiments, as much gaseous fuel as possible may be used while maintaining efficient engine operation.Under other engine operating conditions, only diesel fuel could be injected (and no gaseous fuel). For this multi-fuel engine embodiment (e.g., dual-fuel), the modified pressure equation of Equation 1 can be adapted to the form shown in Equation 4 (for the main injection, which may be the only liquid fuel injection for the cylinder cycle). MPMain,DF=RP−PCPCO∗f1(engine speed,diesel timing)−f2(CGQ,CDQ)

[0064] In the above equation, the PCP COthe pure compression contribution of the modeled PCP discussed above. In one embodiment, the PCP model may include a "pure compression" term in addition to an adder term for when combustion increases the PCP beyond the "pure compression" term (e.g., the "pure compression" cylinder pressure may be modeled separately from the "additional combustion" cylinder pressure). Thus, the PCP COthe "pure compression" term of the modeled PCP. As discussed above with reference to Equation 2, the PCP term is corrected by a function f1 of the engine speed and the (main) diesel injection timing. As explained above, the f1 term can be looked up in a lookup table stored in the ECU's memory with engine speed and the requested diesel injection timing (e.g., crank angle degrees before TDC) as inputs. The offset, f2, is not a constant value in Equation 4 and is instead a function of the requested gaseous fuel quantity, CGQ, (e.g., mg / stroke) and the requested diesel fuel quantity, CDQ, (e.g., mm 3 / stroke). In one embodiment, the offset term f2 can be looked up by the ECU during engine operation in a lookup table stored in ECU memory with CGQ and CDQ as inputs. The f2 term corrects for differences between the test bench and engine upstream of the nozzle orifice and downstream of the nozzle orifice. Upstream, the effect is that a high substitution ratio results in lower diesel quantities and thus lower accumulator-related pressure drops compared to the injector test bench data. Downstream, the effect is that different gas substitution ratios (e.g., different quantities of gas and / or diesel in combination) affect the combustion profile and heat release rate based on crank angle. For example, the cylinder pressure profile for dual-fuel combustion may be different from the cylinder pressure profile for diesel-only combustion.Therefore, the pressure downstream of the orifice should be compensated accordingly, as shown above in Equation 4. In some embodiments, the f2 term in Equations 2 and 3 may be a function of the amount of diesel rather than a constant value.

[0065] Back to Fig. 3, the fuel rail pressures listed in the first row 304 of the first injector table 300 may be input into the modified pressure difference function (e.g., one of Equations 1-4 presented above) to determine a set of modified pressure difference values. These modified pressure difference values, which may be outputs of any of Equations 1-4, are presented in the first row 310 of the second injector table 302. The first row 310 therefore includes a range of modified pressure difference values ​​corresponding to a range of fuel rail pressures. In the first row, 310, F, represents the remaining terms in the modified pressure difference equation (e.g., in addition to RP). As discussed above, in one example, the range of fuel rail pressures may vary from 600 to 2200 bar.The second injector table 302 now contains the same injector activation data at the same fuel values ​​as the first injector table 300. For example, the same range of fuel values ​​as discussed above is listed in a first column 312 of the second injector table 312. However, the second injector table 302 now indexes the injector activation data by the modified pressure differential, rather than just by the fuel rail pressure.

[0066] As explained above, adjusting the data in the fuel injector table with the terms in the modified pressure difference function(s) described herein corrects for differences between the predetermined injector activation data and actual engine operating conditions. For example, an injector table (such as the first injector table 300) may be created during bench testing using a test bench instead of the actual engine in which the injector table will be used. Therefore, the test bench must not have the same pressure drop characteristics across the fuel injector nozzle orifice as in the running engine. Furthermore, the test bench must not have the same backpressure or cylinder pressure (e.g., peak cylinder pressure) as the running engine.Thus, the modified pressure difference equation terms (discussed above with reference to Equations 1-4) can compensate for any pressure-related differences between the running engine and the equipment used to create the injector map. This engine-specific correction allows the same injector map to be used in multiple different engines. Furthermore, the correction factor can change based on a current engine operating condition, improving the accuracy of the injector map in a given engine as engine system variables change.

[0067] The conversion in the injector table index by the square root function causes the fuel injector activation data stored in the second injector table 302 to be more linear than the fuel injector activation data stored in the first injector table 300. Consequently, linear interpolation between data in the second injector table 302 may result in a smaller error in the resulting fuel injector activation output (e.g., fuel injector activation time). Because the accuracy of linear interpolation can be improved by indexing the fuel injector activation data by the modified pressure differential, fewer data points may result in the same accuracy. This may reduce the size of the injector table stored in the controller's memory, thereby reducing memory consumption.

[0068] When indexing the injector table by the modified pressure difference, the input to the injector table must also be converted by the modified pressure difference function. Thus, in equations 1-4 above, the RP can be a determined fuel rail pressure. In one example, the determined fuel rail pressure can be measured using a pressure sensor, such as the one shown in Fig. 1, upstream of the fuel injectors. Thus, a modified pressure differential is determined by inputting the determined fuel rail pressure and the additional required engine operating parameters into the modified pressure function. The determined modified pressure, as well as the additional engine operating parameters (e.g., engine speed, injection timing, and the like), can then be used as inputs to the indexed injector table to interpolate among the nearest indexed fuel injector activation data to determine a fuel injector activation output, such as a fuel injector activation time.

[0069] As discussed above, the fuel injector activation output can be used to control the fuel injection of the engine system. Thus, the technical effect of the above-described (and below using Fig. The purpose of the indexing and interpolation method (further explained in section 5) is to increase the accuracy of fuel injector control. In particular, by indexing an injector activation table according to a modified pressure differential, the control unit can determine a more precise fuel injection activation time for the determined fuel rail pressure and the desired fuel value. The fuel injection timing can thus be adjusted based on the determined fuel injector activation time to deliver the desired amount of fuel. Delivering the precise amount of fuel can increase engine fuel economy while reducing engine emissions variability.Additionally, in multi-fuel engines, using the modified multi-fuel pressure difference equation (Equation 4) for injector control allows for higher natural gas substitution ratios while maintaining efficient and reliable engine operation. Thus, the approach described above and below provides reduced engineering time and increased cost savings.

[0070] In some implementations, computer-readable storage medium 138 includes a memory with one or more sets of instructions and / or data stored thereon that, when accessed and executed by an electronic device (e.g., processor unit 136), cause the electronic device to take various actions. Specifically, the computer-readable storage medium with memory may include fuel injector activation data indexed in the memory by two input parameters, instructions for determining a modified pressure differential value based on a determined pressure, current engine operating conditions, and a modified pressure differential function, and instructions for generating a fuel injector activation output by interpolating among the indexed fuel injector activation data with the modified pressure differential value as an input parameter.In one example, the determined pressure is a measured fuel rail pressure, where the measured fuel rail pressure is measured upstream of a fuel injector, and the modified pressure difference function includes a square root approximation.

[0071] In one embodiment, the fuel injector activation data may be stored in an injector table, the injector table having a first number of columns and a second number of rows, both greater than one. A first row of the second number of rows includes a range of modified pressure differential values ​​corresponding to a range of fuel rail pressures, and a first column of the first number of columns includes a range of fuel values, the range of fuel values ​​including a range of fuel amounts injected by a single fuel injector. Additionally, each cell in the injector table includes a fuel injector activation time corresponding to one of the modified pressure values ​​in the range of modified pressure values ​​and one of the fuel values ​​in the range of fuel values.

[0072] The modified pressure differential values ​​may be determined using one or more equations or one or more tables stored in the controller's memory. For example, the modified pressure differential values ​​may be calculated by the controller according to a stored modified pressure differential function (e.g., one of Equations 1-4) and measured and / or estimated engine operating conditions. In another example, the modified pressure differential values ​​may be looked up in the controller's memory using one or more stored lookup tables that use the operating parameters of the modified pressure differential equation as inputs.

[0073] The modified pressure function converts the fuel injector activation data stored in the injector table to be more linear between cells of the injector table. The computer-readable storage medium further includes instructions to perform multi-stage linear interpolation between indexed fuel injector activation data in the injector table to determine a fuel injector activation time at the determined pressure differential and the determined fuel value. Additionally, the computer-readable storage medium includes instructions to output the determined fuel injector activation time and to adjust fuel injection based on the determined fuel injector activation time. In one example, adjusting fuel injection includes adjusting an injector opening time.

[0074] In addition, the system of Fig. 1 proposes a fuel distribution system comprising a common rail, a plurality of fuel injectors operable to inject fuel from the common rail to cylinders of an engine, an injector table stored in a computer memory, and a controller operable to adapt fuel injection to the cylinders based on a fuel injector activation time, wherein the fuel injector activation time is determined by indexing injector data stored in the injector table according to a modified pressure difference function, wherein the modified pressure difference function includes a square root of a distributor pressure balanced by a peak pressure in the cylinders, multiplied by a function of engine speed and injection timing, and further by a correction term,The pressure differences between engine and test bench injector data are corrected and compensated for both upstream and downstream of the injector's nozzle orifice, and by interpolating the indicated injector data based on a determined fuel rail pressure, a quantity of fuel injected with a single fuel injector stroke, and additional engine operating conditions. In one example, the determined fuel rail pressure is measured from one or more pressure signals sent to the control unit by at least one pressure sensor located upstream of the common rail.

[0075] In another embodiment of the invention, the system of Fig. 1 proposes: a fuel distribution system comprising a common rail, a plurality of fuel injectors operable to inject fuel from the common rail to cylinders of an engine, a non-transitory computer-readable storage medium having memory, wherein an injector table is stored in the memory, and wherein the injector table comprises injector data indexed according to a modified pressure difference function, and a controller operable to control the fuel injectors based on a fuel injector activation time, wherein the controller is configured to determine the fuel injector activation time by interpolating the indexed injector data based on a determined fuel rail pressure and an amount of fuel injected by a single fuel injector stroke.The modified pressure function comprises a square root of a fuel rail pressure compensated by a peak pressure in the cylinders, and an additional correction term comprising a constant value or a function of the amounts of liquid and gaseous fuel injected into the engine. Furthermore, the determined fuel rail pressure can be measured from one or more pressure signals sent to the control unit by at least one pressure sensor located upstream of the common rail.

[0076] In one embodiment, an engine production line may include multiple different engines and / or engine types. All engines in the engine production line may have the same injectors. Additionally, the same fuel injector activation data may be stored in a fuel injector table in a memory of a computer-readable storage medium in each engine. Therefore, each engine may have a common fuel injector table. However, the multiple engines in the engine production line may have different peak cylinder pressures, injection timing, and / or gaseous fuel substitution ratios.As described above, the data stored in the common fuel injector table may be indexed according to a modified pressure difference function that includes a square root of a manifold pressure compensated by the peak cylinder pressure, scaled by a function of engine speed and injection timing, and further compensated by a correction factor for pressures upstream and downstream of the injector nozzle orifice. The peak cylinder pressure for each engine may be stored individually in the corresponding engine's memory and / or determined using an engine-specific peak cylinder pressure model.Thus, when indexing the data in the common fuel injector table, an engine control module can input the stored or modeled peak cylinder pressure, as well as additional engine operating conditions, into the modified pressure function and then index the stored fuel injector activation data. In this way, the same fuel injector activation table can be stored in multiple engines and / or engine types and used to determine fuel injector activation times with increased accuracy. In some embodiments, differential modified pressure functions can be used in different functions while still using the same fuel injector activation table.For example, the modified pressure difference equation shown in equation 4 above can be used in a multi-fuel engine, while the modified pressure difference equations shown in equations 2 and 3 can be used in a liquid fuel only engine operating with multiple injections in each cylinder cycle.

[0077] In one example, the engine production line may include a first and a second engine, both engines having the same fuel injectors. The first engine may include a first injector table stored in a first computer memory, and the second engine may include a second injector table stored in a second computer memory, wherein the first injector table and the second injector table are identical. Furthermore, the first engine may have a first peak cylinder pressure and the second engine may have a second peak cylinder pressure, wherein the first peak cylinder pressure is different from the second peak cylinder pressure.A first controller included in the first engine may then index injector data stored in the first injector table according to a modified pressure difference function, wherein the modified pressure difference function includes a square root of a fuel rail pressure compensated by the first peak cylinder pressure, scaled by a multiplier that is a function of engine speed and injection timing, and a correction factor term. A second controller included in the second engine may analogously index injector data stored in the second injector table according to the same modified pressure difference function, but compensated by the second peak cylinder pressure, scaled by a multiplier that is a function of engine speed and injection timing, and the correction factor term.

[0078] Turning to Fig. 10, an embodiment of a method 1000 for determining a fuel injector activation output, such as a fuel injector activation time, and for adjusting fuel injection to the engine based on the determined fuel injector activation output is shown. In one example, the method 1000 is implemented by the method shown in Fig. 1, according to instructions stored in the controller's memory. Specifically, during engine operation, the controller 106 repeatedly executes method 1000 to determine an injector activation time.

[0079] The method 1000 begins at 1002 by estimating and / or measuring engine operating conditions. The engine operating conditions may include engine speed and load, pressures in the fuel rail system, engine cylinder pressures, torque demand, boost pressure, injection timing of the injector(s), a substitution ratio of gaseous fuel to total fuel, a requested liquid fuel amount, a requested gaseous fuel amount, or the like. In particular, the estimation and / or measurement of engine operating conditions at 1002 may include determining a fuel rail pressure. As discussed above, in one example, the fuel rail pressure may be determined based on the output of a pressure sensor (such as pressure sensor 130 in Fig. 1) positioned in the fuel rail system upstream of a fuel injector and / or the common rail system. Estimating and / or measuring engine operating conditions at 1002 may further include determining a requested injection timing, engine speed, and a requested diesel and / or gaseous fuel quantity. For example, at 1002, the method may include determining engine operating conditions (e.g., parameters) using the modified pressure difference function, such as one or more of Equations 1-4 presented above.

[0080] At 1004, the method includes obtaining a fuel value. In one example, a fuel value for all engine operating points may be stored in the controller's memory. In another example, the fuel value may be estimated based on engine operating conditions, such as torque demand. Moving to 1006, the method includes determining the desired modified pressure difference function for indexing the fuel injector activation data. In one example, the desired modified pressure difference function may be predetermined and stored in the controller based on engine type (e.g., multi-fuel or single-fuel) and / or whether or not multiple injections (e.g., main and post injection) are used during a single cylinder cycle.For example, one or more of equations 1-4 presented above may be stored in the memory of the control unit, and the control unit may select the desired equation or combination of equations for use as the modified pressure difference function based on the engine type and / or the types of injectors or fuels used in the engine.

[0081] The method then proceeds to 1008 to incorporate the determined fuel rail pressure and additional engine operating conditions into the selected (or predetermined) modified pressure difference function to determine the modified pressure difference value. Specifically, at 1008, the controller inputs the determined fuel rail pressure and additional engine operating conditions (e.g., engine speed, injection timing, time between multiple injections, and / or requested amounts of liquid and / or gaseous fuel) to the modified pressure difference function. In one example, the modified pressure difference function is one or more of the functions represented by Equations 1-4 above. As explained above, the modified pressure difference function may be a square root approximation. In other examples, the modified pressure function may be another function close to the square root function.For example, the fuel rail pressure minus PCP term minus f2 term of the modified pressure difference function can be increased to the power of 0.45 instead of 0.5.

[0082] Once the controller has determined the modified pressure difference value at 1008, the method proceeds to 1010 to index the fuel injector activation data as a function of the modified pressure difference function. As described above, the fuel injector activation data may be stored in an injector table, such as the one shown in Fig. 3. The injector table may further be stored in a non-transitory, computer-readable storage medium having memory. Thus, when determining fuel injection setpoints, the controller may actively index the data in the stored injector table by the modified pressure differential function during engine operation. In one example, the modified pressure differential function used to index the fuel injector activation data is equal to the modified pressure differential function used to determine the modified pressure differential at 1006. Thus, the resulting output from indexing the stored fuel injector activation data during engine operation may be a modified injector table indexed by the modified pressure differential (rather than fuel rail pressure alone or based on a pressure differential across the injector nozzle orifice alone).An example of the modified injector table is the second injector table 302 shown in . Fig. 3. In one example, the modified injector table may then be stored in memory. The method then proceeds to 1012 to look up the fuel value (obtained at 1004) and the modified pressure differential in the modified injector table.

[0083] At 1014, the controller interpolates the indexed injector activation data in the modified injector table to determine an injector activation time for the determined modified pressure differential and fuel value. The method at 1014 may include determining the injector activation data points in the injector table that are around the predetermined modified pressure differential and fuel value. For example, the controller may locate a first modified pressure differential value above the determined modified pressure differential and a second modified pressure differential value below the determined modified pressure differential. The first and second modified pressure differential values ​​are two modified pressure differential values ​​from the plurality of modified pressure differential values ​​listed in the first row of the injector table (e.g., the first row 310 in the second injector table 302).The controller may then locate a first fuel value above the selected fuel value and a second fuel value below the selected fuel value. The first and second modified fuel values ​​are two fuel values ​​from the plurality of fuel values ​​listed in the first column of the injector table (such as the first column 312 in the second injector table 302). Next, the cells in the injector table (containing dates or times of injector activation) corresponding to the first and second modified pressure differential values ​​and the first and second fuel values ​​are selected. The controller then interpolates between the selected data points to determine the fuel injector activation time for the determined modified pressure differential and fuel value.

[0084] At 1016, the controller outputs the determined injector activation time. At 1018, the controller then adjusts fuel injection based on the determined injector activation time. As discussed above, adjusting fuel injection may include adjusting the fuel injection timing of one or more fuel injectors. Specifically, in one example, the controller may adjust a pulse-width modulation signal to command the fuel injectors to inject fuel for a period of time. The duration may be based on the fuel injector activation time. Therefore, the fuel injector activation time may be a period of time during which the fuel injectors are open and injecting fuel to the engine cylinders.

[0085] In this way, a controller in an engine may index fuel injector activation data in computer memory as a function of a modified pressure difference function, linearly interpolate between the indexed injector activation data to determine an injector activation time at a determined fuel rail pressure based on the modified pressure difference function, and adjust the engine's fuel injection based on the injector activation time. In one example, adjusting fuel injection includes adjusting a pulse width of one or more fuel injectors, where the pulse width increases with increasing injector activation time. Additionally, the controller may inject fuel at a cylinder pressure within 20 degrees of top dead center.In one example, indexing the fuel injector activation data comprises indexing stored fuel injector activation data by a square root of a modified pressure differential across an orifice of the fuel injector nozzle, wherein the stored fuel injector activation data is stored in computer memory of multiple engines that use the same fuel injectors. The modified pressure differential function may scale an outlet pressure at the nozzle exit by a function of engine speed and injection timing, and compensate for the pressure differential by an additional correction factor that corrects for pressure differences between actual pressure values ​​at the engine and pressure values ​​when testing an injector (off-engine) on the test bench. In alternative embodiments, the additional correction factor may be a function of the amounts of liquid fuel (e.g.,diesel fuel) and gaseous fuel injected into the engine of a multi-fuel engine. Furthermore, the controller may linearly interpolate between a first indicated fuel injector activation time and a second indicated fuel injector activation time based on a fuel value and a modified pressure differential, wherein the modified pressure differential is a square root of the pressure differential across the injector nozzle orifice less the additional correction factor and the outlet pressure of the orifice multiplied by a function of engine speed and injection timing. As explained above, the indexing of the injector table according to a modified pressure differential (e.g.Based on the modified pressure difference function, the fuel injector activation data stored in the injector table is converted to be more linear between cells of the injector table and to account for pressure differences that occur on-board the engine under different engine operating conditions. This can reduce the interpolation error, thereby increasing the accuracy of the fuel injector activation time output by the ECU. Furthermore, more accurate injector activation times can be determined for the current engine operating conditions. Consequently, the accuracy of fuel injector control can be increased, thereby increasing engine fuel economy while reducing engine emissions variability.

[0086] In one embodiment, a system includes an engine, a fuel injector, and a controller having one or more processors. The controller is configured to determine a modified pressure differential value across a nozzle orifice of the fuel injector based on the determined pressures upstream and downstream of the nozzle orifice, an engine speed of the engine, the injection timing, and a modified pressure differential function. The controller is further configured to generate a fuel injector activation output by interpolating between indexed fuel injector activation data with the modified pressure differential value as a first input parameter; the fuel injector activation data is indexed according to the first input parameter and a second input parameter.For example, in one aspect, the second input parameter may be a fuel value; the fuel value includes an amount of fuel injected by a single fuel injector stroke of the injector.

[0087] In one embodiment, a system includes an engine, a fuel injector, and a controller having one or more processors. The controller is configured to control fuel injection by activating the injector for a specific activation time. The controller is configured to determine the activation time based on a requested fuel and a function of a modified pressure differential across a nozzle of the injector. The modified pressure differential is based on a difference between a manifold pressure and a peak cylinder pressure, where the peak cylinder pressure is scaled by a function of engine speed and injection timing, and the pressure differential is compensated for by a correction factor.

[0088] As used herein, an element or step recited in the singular and preceded by the word "a" or "an" is to be understood as not excluding multiple such elements or steps, unless such exclusion is expressly stated. Furthermore, references to "one embodiment" of the invention do not preclude the existence of additional embodiments that also include the recited features. Moreover, embodiments that "comprise," "include," or "have" one or more elements with a particular property may include additional such elements that do not have that property, unless expressly stated otherwise. The terms "with" and "wherein" are used as plain language equivalents of the respective terms "comprising" and "wherein." In addition, the terms "first," "second," and "third," etc.are used merely as designations and are not intended to specify any numerical requirements or a specific order of position for their objects.

[0089] The control methods and routines disclosed herein may be stored as executable instructions in non-volatile memory and executed by the control system, including the controller combined with the various sensors, actuators, and other engine hardware. The particular routines described herein may represent one or more of a number of processing strategies, such as event-driven, interrupt-driven, multitasking, multithreading, and the like. Thus, various steps, operations, and / or functions shown may be performed in the sequence shown, in parallel, or skipped in some cases. Similarly, the order of processing is not necessarily required to achieve the features and advantages of the exemplary embodiments described herein, but is provided for ease of illustration and description.Depending on the particular strategy used, one or more of the illustrated steps, operations, and / or functions may be performed repeatedly. Furthermore, the described steps, operations, and / or functions may graphically represent code to be programmed into a non-volatile memory of the computer-readable storage medium in the engine control system, wherein the described steps are performed by executing the instructions in a system including the various engine hardware components combined with the electronic control unit.

[0090] This written description uses examples to disclose the invention, including the best mode contemplated, and also to enable one of ordinary skill in the art to practice the invention, including making and using devices or systems and performing any included methods. The patentable scope of the invention is defined by the claims and may include other examples that would be obvious to one of ordinary skill in the art. Such other examples are intended to be within the scope of the claims if they include structural elements that do not differ from the language of the claims, or if they include equivalent structural elements with insubstantial departures from the language of the claims.

Claims

[1] Non-transitory computer-readable storage medium with memory, comprising: Fuel injector activation data indexed in the memory by two input parameters; Instructions for determining a modified pressure difference value across a nozzle orifice of a fuel injector based on determined pressures upstream and downstream of the nozzle orifice, engine speed, injection timing, and a modified pressure difference function; and Instructions to generate a fuel injector activation output by interpolating among the indexed fuel injector activation data with the modified pressure differential value as the first of the two input parameters. [2] The medium of claim 1, wherein the determined pressures upstream and downstream of the nozzle orifice comprise a measured fuel rail pressure, wherein the measured fuel rail pressure is measured upstream of the fuel injector, and a modeled peak cylinder pressure. [3] The medium of claim 2, wherein the measured fuel rail pressure is a liquid fuel rail pressure of liquid fuel injected into an engine by the fuel injector. [4] The medium of claim 1, wherein the modified pressure difference function is a square root approximation of a pressure difference between a pressure upstream and a pressure downstream of the nozzle opening, compensated by a correction factor, the pressure downstream of the nozzle opening being scaled by a function of engine speed and injection timing, the square root approximation linearizing the fuel injector activation data stored in an injector map in the memory. [5] The medium of claim 1, wherein a second of the two input parameters is a fuel value, wherein the interpolating among the indexed fuel injector activation data is further based on the fuel value, wherein the fuel value comprises an amount of fuel injected by a single fuel injector stroke of the injector, and wherein the fuel injector activation data is stored in the memory in an injector table, the one injector table having a first number of columns and a second number of rows, both greater than one. [6] The medium of claim 5, wherein a first row of the second number of rows comprises a range of modified pressure differential values ​​corresponding to a range of fuel rail pressures, and a first column of the first number of columns comprises a range of fuel values, the range of fuel values ​​comprising a range of fuel amounts injected by a single fuel injector, and each cell in the one injector table comprises a fuel injector activation time corresponding to one of the modified pressure values ​​in the range of modified pressure values ​​and one of the fuel values ​​in the range of fuel values. [7] The medium of claim 5, wherein the modified pressure difference function transforms the fuel injector activation data stored in the one injector table to be more linear between cells of the one injector table. [8] The medium of claim 5, wherein the instructions for generating the fuel injector activation output by interpolating among the indexed fuel injector activation data comprise instructions for performing a multi-stage linear interpolation between the indexed fuel injector activation data in the one injector table to determine a fuel injector activation time at the determined pressure differential and fuel value. [9] The medium of claim 8, further comprising instructions for outputting the determined fuel injector activation time and for adjusting fuel injection based on the determined fuel injector activation time. [10] The medium of claim 9, wherein adjusting fuel injection comprises adjusting an injector opening time. [11] A method for an engine, comprising: Injecting fuel by activating an injector over a determined activation time, wherein the activation time is determined based on a required fuel value and a function of a modified pressure difference across an orifice of a nozzle of the injector, wherein the modified pressure difference is based on a difference between a distributor pressure and peak cylinder pressure, wherein the peak cylinder pressure is scaled by a function of engine speed and injection time and the pressure difference is compensated by a correction factor. [12] A method according to claim 11, wherein the correction factor is a value or a function that corrects for differences in the pressures upstream and downstream of the orifice between when the injector is operating on board the engine and when the injector is operating during testing on the test bench away from the engine. [13] A method according to claim 12, wherein the fuel injected by means of the injector is a liquid fuel, wherein the correction factor is the function which is a function of a required amount of gaseous fuel to be injected by a gas inlet valve or gas injector and a required amount of liquid fuel to be injected by the injector, and wherein the engine is a multi-fuel engine. [14] The method of claim 13, wherein the injection timing is a time of injection of the liquid fuel and wherein the function of the modified pressure difference across the orifice is a square root approximation. [15] The method of claim 11, wherein the injection timing is a main timing of a main injection from a plurality of injections during a same cylinder cycle. [16] Method according to claim 11, wherein the injection time is a post-injection time of a plurality of injections during a same cylinder cycle, the post-injection taking place after a main injection. [17] The method of claim 16, wherein the difference between the manifold pressure and peak cylinder pressure comprises a difference between a sum of the manifold pressure, a first duration of the main injection scaled by a first constant, and a second duration of the post-injection scaled by a second constant. [18] The method of claim 11, wherein the peak cylinder pressure is the peak cylinder pressure occurring only during compression. [19] Fuel distribution system comprising: a common rail; multiple fuel injectors capable of injecting liquid fuel from the common rail to cylinders of an engine; a non-transitory computer-readable storage medium having memory, wherein an injector table is stored in the memory, and wherein the one injector table comprises injector data indexed by a modified pressure difference function that creates a more linear relationship between the injector data in the one injector table, the modified pressure difference function being a function of each of a pressure difference across an orifice of a nozzle of the plurality of fuel injectors, engine speed, and injection timing; and a controller capable of controlling the fuel injectors based on a fuel injector activation time, the controller configured to determine the fuel injector activation time by interpolating the indexed injector data in the one injector table based on a determined fuel rail pressure and an amount of fuel injected by a single fuel injector stroke. [20] The system of claim 19, wherein the modified pressure function comprises a square root of a difference between a determined fuel rail pressure and a modeled peak cylinder pressure, the difference being compensated for by a correction factor and the modeled peak cylinder pressure being multiplied by a function of engine speed and injection timing, and the determined fuel rail pressure being measured from one or more pressure signals sent to the controller from at least one pressure sensor positioned upstream of the common rail.

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