Abstract:
A method for calibrating an electronic fuel injector may include: setting a supply voltage to a control module; applying a control voltage signal having a pulse width to an electronic fuel injector by the control module; determining whether a fuel pressure of a fuel supply to the electronic fuel injector decreases by a predetermined amount; and in response to determining that the fuel pressure of the fuel supply to the electronic fuel injector decreases by the predetermined amount, recording the pulse width and the supply voltage to the control module.

Description:
BACKGROUND 
     Over the last 30 years there have been increasing proportions of internal combustion engines that are equipped with electronic fuel injection (EFI). The reason for this is multifold: increased reliability, performance, and longevity are key factors, along with significantly tighter engine calibration over the full engine operating range. As of the end of the 1990&#39;s, practically all original equipment manufacturer (OEM) passenger car engines were converted from carburetion to EFI; smaller engines like motorcycles followed suit. 
     The automotive aftermarket also followed the trend, offering EFI conversion systems for existing engine applications. Many of these EFI conversion systems were offered to retrofit existing carburetor-equipped engines, with the carburetor eliminated and replaced with a throttle body for air flow regulation. Other systems provided by the aftermarket serve as a replacement to OEM engine controls, permitting adjustments to calibrations and operating parameters. 
     Engine controls for automotive aftermarket engines most often employ fuel injection methods involving port or centralized throttle fuel metering strategies. These systems use one or a plurality of electromechanical solenoids to control the flow of a combustible hydrocarbon such as gasoline and inject the fuel into the airstream in order to produce a desired air-fuel ratio for combustion within the cylinder. These fuel injector solenoids are most often located in the individual port runners upstream of the air intake valves, or right above or below the air throttle plates. 
     An automotive engine has a large dynamic operating range and the air-fuel operating range requirements can be extreme, especially for a high-output or air boosted engine. This dynamic operating range is often expanded compared to an OEM application, which places additional demands on the controls. In particular, the operating range of fuel injectors for aftermarket use can place the fuel injectors outside of their intended use. Fuel injectors are sized such that they provide the required fuel mass at the highest engine mass air flow rates. High crankshaft revolutions-per-minute (RPMs) and high mass air flow rates require larger injector flow rates. However, these same injectors are needed to accurately operate the engine during idle and low engine output regions. This low operating range translates into very small time duration pulse widths for operating the fuel injectors. 
     Solenoid fuel injectors utilize an electromechanically-operated pintle valve which is magnetically coupled to an electric solenoid. A current flow in the solenoid produces a magnetic field, and this magnetic field causes the pintle valve to move within the bore of the fuel injector. The pintle valve movement opens a metered orifice arrangement which permits the flow of fuel. The valve as designed is intended to operate in a flow/no-flow arrangement, and the duration of the applied solenoid current dictates the amount of mass fuel flow. 
     Due to the fact that the current within a solenoid coil ramps up after its initial application due to the inductance of the actuator solenoid coil, there is an inherent lag time between the application of solenoid current and the build-up of the magnetic field around the coil. This in turn causes a delay in time between the first application of current and the movement of the pintle valve. Determination of this time delay is important for the prediction of the mass of fuel flow through the injector for a given solenoid current application time. 
     The ramp-up time of the solenoid current is dependent on the inductance of the coil, the coil resistance, and the applied voltage. In a practical vehicle engine application, the voltage available to the fuel injector solenoid is not always constant. Situations such as cold starting, vehicle charging variability, electrical load variations such as headlights, heater blowers, etc., affect the instantaneous voltage available to the solenoid. This change in voltage will change the dynamic rate of solenoid energizing and hence, the time delay in pintle valve movement. The effect of this voltage variation is significant over the realistic range of available battery voltages within a vehicle. 
     It is therefore important to determine the dynamic characteristics of the fuel injector opening time as a function of battery voltage. However, information regarding these dynamic characteristics is not readily available. 
     SUMMARY 
     Apparatuses and methods for determining the dynamic operation of an automotive engine fuel injector are provided. 
     According to various embodiments there is provided a method for calibrating an electronic fuel injector. In some embodiments, the method may include: setting a supply voltage to a control module; applying a control voltage signal having a pulse width to an electronic fuel injector by the control module; determining whether a fuel pressure of a fuel supply to the electronic fuel injector decreases by a predetermined amount; and in response to determining that the fuel pressure of the fuel supply to the electronic fuel injector decreases by the predetermined amount, recording the pulse width and the supply voltage to the control module. 
     According to various embodiments there is provided an apparatus for calibrating an electronic fuel injector. In some embodiments, the apparatus may include: a control module installed in a vehicle; and a variable power supply configured to provide a supply voltage to the control module. 
     The control module may include: a processor; a storage unit; and driver circuitry configured to provide a control voltage signal to an electronic fuel injectors installed in the vehicle. The control module configured to: apply the control voltage signal having a pulse width to the electronic fuel injector; determine whether a fuel pressure of a fuel supply to the electronic fuel injector decreases by a predetermined amount based on a signal received from a fuel pressure sensor; and in response to determining that the fuel pressure of the fuel supply to the electronic fuel injector decreases by a predetermined amount, record the pulse width and the supply voltage to the control module. 
     According to various embodiments there is provided a non-transitory computer readable medium having stored thereon instructions for causing one or more processors to perform a calibration method for an electronic fuel injector. In some embodiments, the non-transitory computer readable medium may include instructions for setting a supply voltage to a control module; applying a control voltage signal having a pulse width to an electronic fuel injector by the control module; determining whether a fuel pressure of a fuel supply to the electronic fuel injector decreases by a predetermined amount; and in response to determining that the fuel pressure of the fuel supply to the electronic fuel injector decreases by the predetermined amount, recording the pulse width and the supply voltage to the control module. 
     Other features and advantages of the various embodiments should be apparent from the following description which illustrates by way of example aspects of the various embodiments. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Aspects and features of the various embodiments will be more apparent by describing example embodiments with reference to the accompanying drawings, in which: 
         FIG. 1  is a diagram illustrating a multiport fuel injection system commonly used for aftermarket fuel injection setups; 
         FIG. 2  is a diagram illustrating electronic controls for the multiport fuel injection system of  FIG. 1 ; 
         FIG. 3  is a diagram illustrating a cross-section of automotive electronic fuel injector; 
         FIG. 4  is a graph illustrating the effect of control signal voltage on electronic fuel injector pintle valve open time; 
         FIG. 5  is a diagram illustrating an electronic fuel injector calibration system according to various embodiments; 
         FIG. 6  is a flowchart illustrating a calibration method for an electronic fuel injector according to various embodiments; and 
         FIG. 7  is a diagram illustrating a test apparatus for electronic fuel injector calibration according to various embodiments. 
     
    
    
     DETAILED DESCRIPTION 
     While certain embodiments are described, these embodiments are presented by way of example only, and are not intended to limit the scope of protection. The apparatuses, methods, and systems described herein may be embodied in a variety of other forms. Furthermore, various omissions, substitutions, and changes in the form of the example methods and systems described herein may be made without departing from the scope of protection. 
       FIG. 1  is a diagram illustrating a multiport fuel injection system  100  commonly used for aftermarket fuel injection setups. A fuel tank  110  may hold a reservoir of hydrocarbon fuel in either in gaseous or liquid form. A fuel pump  120  may transfer the fuel from the tank to a fuel rail  130 . The fuel rail  130  may mechanically mount a plurality of electronic fuel injectors  140  and provide the fuel under pressure such that the fuel injectors  140  may provide regulated fuel mass to the engine. A pressure regulator  150  may bleed excess fuel back to the fuel tank in order to maintain a regulated fuel rail pressure. The pressure regulator may provide a constant fuel rail pressure, additionally multiport fuel injection system  100  may contain a blocking valve  155  to hold the pressure even if the fuel pump  120  is not operating. 
       FIG. 2  is a diagram illustrating electronic controls for the multiport fuel injection system  100  of  FIG. 1 . The Powertrain Control Module  210  (PCM) may be a microprocessor-based controller programmed with algorithms for internal combustion engine control. The PCM  210  may provide control signals for the fuel pump  120  and electronic fuel injectors  140  via driver circuitry  218 . Sensors (not shown), such as intake and coolant temperature sensors, engine position sensor, ignition control, etc., may provide engine operating condition information to the PCM  210 . The PCM  210  may provide real-time control for engine operation and fault diagnostics. Algorithms contained in the PCM  210  firmware may be executed on the PCM  210  to provide the control law for the engine. 
     Various actuators, for example, but not limited to, the electronic fuel injectors  140 , may be calibrated in order for the PCM  210  to provide accurate fuel control. An electronic fuel injector is an electromagnetically-controlled valve that provides on/off fuel mass flow control. Electronic fuel injectors (e.g., the electronic fuel injectors  140 ) may have parameters corresponding physical characteristics that may be calibrated and the calibrated parameters made available to the PCM  210  in order to provide predictable fuel delivery to the internal combustion engine. 
     For OEM electronic fuel injectors, these parameters may be calculated off-line using specialized fuel flow testing equipment. For calibration of the electronic fuel injectors  140  for automotive applications, the electronic fuel injector flow parameter may be provided as a single value for static fuel flow with the electronic fuel injector fully open. Electronic fuel injector static flow is an important parameter for engine control; however, dynamic fuel injector parameters are also important for controlling overall mass fuel flow. 
       FIG. 3  is a diagram illustrating a cross-section of automotive electronic fuel injector  300 . The electronic fuel injector  300  may operate with an electronic control signal applied to a fuel injector solenoid  320  through an electrical connector  310 . The control signal may generate a magnetic field in the fuel injector solenoid  320  opening a normally-closed pintle valve  330 , and the pintle valve  330  may open a fuel chamber  340  to allow passage of fuel into the engine. 
     There may be a finite amount of time from the application of the control signal and the ramp-up to a given current to operate the fuel injector solenoid  320 . The amount of time may depend on several factors including, for example, but not limited to, solenoid inductance, wiring resistance, and applied voltage. The applied voltage may vary even over a short period of time due to vehicle charging system voltage variations resulting from engine RPM changes and electrical loads (e.g., headlights, windshield wipers, blower motors, etc.). The voltage variations may directly affect electronic fuel injector open time (i.e., the time required for the pintle valve  330  to open), also referred to herein as the injector open time, by changing the rate of current ramp-up in the fuel injector solenoid  320 . 
       FIG. 4  is a graph  400  illustrating the effect of control signal voltage on injector open time.  FIG. 4  illustrates that as control signal voltage (i.e., applied injector voltage) decreases, for example, due to charging system voltage variations, the time needed for the pintle valve (e.g., the pintle valve  330 ) to open (i.e., the injector open time) may increase. 
     The force on an electronic fuel injector pintle valve (e.g., the pintle valve  330 ) due to current flow in a fuel injector solenoid (e.g., the solenoid  320 ) may be expressed by Equation (1): 
     
       
         
           
             
               
                 
                   F 
                   = 
                   
                     
                       
                         
                           ( 
                           NI 
                           ) 
                         
                         2 
                       
                       ⁢ 
                       
                         μ 
                         0 
                       
                       ⁢ 
                       A 
                     
                     
                       2 
                       ⁢ 
                       
                         g 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     In Equation (1), F is the solenoid force, N is the number of turns on the solenoid, I is the fuel injector solenoid current, μ 0  is a permeability constant, A is the cross-sectional area of the fuel injector solenoid, and g is the gap between the fuel injector solenoid and the pintle valve. 
     For an automotive throttle body fuel injector or port fuel injector, the parameters N, A, and g may be set during design and manufacturing, leaving the fuel injector solenoid current I as an available parameter for controlling the pintle valve force (i.e., force (F) is a function of I 2 ). 
     The fuel injector solenoid and pintle valve complete a resistive-inductive circuit, and movement of the pintle may change the inductance of the circuit. The equation for voltage with changing circuit inductance may be expressed by Equation (2): 
     
       
         
           
             
               
                 
                   V 
                   = 
                   
                     RI 
                     + 
                     
                       
                         ⅆ 
                         λ 
                       
                       
                         ⅆ 
                         t 
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     In Equation (2), V is the applied voltage (i.e., the control signal), R is the resistance of the fuel injector solenoid coil, and λ is the flux linkage. The flux linkage, λ, is dependent on the current I in the fuel injector solenoid coil and the air gap distance x between the fuel injector solenoid coil and the pintle valve. Equation (2) may be rewritten as Equation (3): 
     
       
         
           
             
               
                 
                   V 
                   = 
                   
                     RI 
                     + 
                     
                       
                         ( 
                         
                           L 
                           + 
                           
                             
                               ∂ 
                               
                                 λ 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     x 
                                     , 
                                     I 
                                   
                                   ) 
                                 
                               
                             
                             
                               ∂ 
                               I 
                             
                           
                         
                         ) 
                       
                       · 
                       
                         
                           ⅆ 
                           I 
                         
                         
                           ⅆ 
                           t 
                         
                       
                     
                     + 
                     
                       
                         
                           ∂ 
                           
                             λ 
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 I 
                               
                               ) 
                             
                           
                         
                         
                           ∂ 
                           x 
                         
                       
                       · 
                       
                         
                           ⅆ 
                           x 
                         
                         
                           ⅆ 
                           t 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     In Equation (3), L represents the fuel injector solenoid inductance. The first term in the expansion of Equation (3) is resistive and represents an associated voltage drop. The second term is an inductive voltage drop due to changing current. The third term represents the back electromotive force (EMF) generated by the pintle valve moving in the solenoid. Practical use of Equation (3) requires knowledge of the magnetic characteristics of the pintle valve and fuel injector solenoid, which are not readily available. 
     The rise of fuel injector solenoid current, I, over time may be represented to first-order as a function of time, applied, voltage, and loop resistance by Equation (4): 
     
       
         
           
             
               
                 
                   I 
                   = 
                   
                     
                       V 
                       R 
                     
                     ⁢ 
                     
                       ( 
                       
                         1 
                         - 
                         
                           ⅇ 
                           
                             Rt 
                             L 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     In Equation (4), V is the applied voltage (i.e., the control signal) across the fuel injector solenoid, R is the circuit resistance which includes the fuel injector solenoid coil, driver electronics, wiring, etc.), t is the elapsed time that the voltage is applied, and L is the fuel injector solenoid inductance. Rearranging Equation (4) to solve for t results in Equation (5): 
     
       
         
           
             
               
                 
                   t 
                   = 
                   
                     
                       
                         - 
                         L 
                       
                       R 
                     
                     ⁢ 
                     
                       ln 
                       ⁡ 
                       
                         ( 
                         
                           1 
                           - 
                           
                             RI 
                             V 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     Equation (5) determines the time, t, required for the fuel injector solenoid current, I, to ramp up to a given after application of the voltage, V (i.e., the control signal). Equation (5) shows that the fuel injector solenoid current ramp-up time, t, depends on both the circuit resistance, R, and the applied voltage, V. For multiport fuel injection systems (e.g., the multiport fuel injection system  100 ), the value of the circuit resistance, R, may not vary appreciably, other than from temperature effects on solenoid resistance. Thus, the applied voltage, V (i.e., the control signal), may be a primary factor affecting the fuel injector solenoid current ramp-up time, t. Therefore, the change in electronic fuel injector opening time as a function of applied voltage, V, may be determined. Analytical calculation methods may be possible, but may provide only a rough indicator for a correction factor. 
     Aspects of the various embodiments may measure injector open time based on control signal pulse width with respect to control signal voltage. Further, aspects of the various embodiments may perform the injector open time measurements using the PCM (e.g., the PCM  210 ) driver circuitry for one or more electronic fuel injectors to replicate conditions experienced by the one or more electronic fuel injectors that may be installed in an internal combustion engine. 
       FIG. 5  is a diagram illustrating an electronic fuel injector calibration system  500  according to various embodiments. Referring to  FIG. 5 , the multiport fuel injection calibration system  500  may include a fuel tank  590 , a fuel pump  520 , a fuel rail  530 , a pressure regulator  550 , a blocking valve  555 , and one or more electronic fuel injectors  540 . These components may be similar to the corresponding components in the multiport fuel injection system  100  previously described and illustrated in  FIGS. 1 and 2  and so will not be further described. In various embodiments, the above components of the multiport fuel injection calibration system  500  may be installed in a vehicle. 
     The multiport fuel injection calibration system  500  may also include a control module  510 , for example, but not limited to a PCM (e.g., the PCM  210 ) or another controller, a fuel pressure sensor  560 , and a variable power supply (VPS)  570 . The control module  510  may include a control unit  515 , for example, but not limited to, a microprocessor, a microcontroller, or other programmable device, and may further include a storage unit  517 , for example, but not limited to, RAM, ROM, EEPROM, or other memory, or combinations thereof, and driver circuitry  518  configured to provide control signals to the electronic fuel injectors  540  and the fuel pump  520 . 
     The control unit  515  may cause the control module  510  to provide control signals to the one or more electronic fuel injectors  540  and to the fuel pump  520 . The fuel pressure sensor  560  may sense fuel pressure in the fuel rail  530  (or at another location in the multiport fuel injection calibration system  500 ). In various embodiments, the control module  510  and the fuel pressure sensor  560  may be installed in a vehicle. The VPS  570  may provide supply voltage to the control module  510  in place of voltage supplied from a vehicle electrical system. 
     The control unit  515  may cause the control module  510  to provide pulsed voltage control signals to one of the one or more electronic fuel injectors  540  installed in an engine and may receive a signal indicating fuel pressure from the fuel pressure sensor  560 . The control module  510  (e.g., the control unit  515 ) may be configured to control the pulse widths of the pulsed voltage control signals. The VPS  570  may be configured to provide adjustable supply voltages to the control module  510 . Various embodiments of the present inventive concept may determine an injector open time based on the pulse width of the pulsed voltage control signals at various supply voltages of the control module  510 . 
     The VPS  570  may provide a preset supply voltage to the control module  510 . The preset supply voltage may be a minimum supply voltage necessary for operation of the control module  510 . For example, the VPS  570  may provide a minimum supply voltage of about twelve volts to the control module  510 . The control unit  515  may cause the control module  510  to provide a pulsed voltage control signal having a preset pulse width to one of the one or more electronic fuel injectors  540  and may monitor the fuel pressure in the fuel rail  530  (or at another location in the multiport fuel injection system  500 ) via the fuel pressure sensor  560 . The preset pulsed voltage control signal pulse width may be a minimum pulse width. 
     The minimum pulse width may be based on, for example, but not limited to, the type of electronic fuel injector  540  and/or control module  510  (e.g., manufacturer, model, etc.). For example, the minimum pulse width may be about 50 microseconds (μs) (or another value). The control module  510  (e.g., the control unit  515 ) may increase the pulse width in increments, for example, in increments of 50 μs (or another value) until the control module  510  receives a signal from the fuel pressure sensor  560  indicating a decrease in fuel pressure, or until the pulse width reaches a maximum pulse width (for example, about five milliseconds (ms) or another value). The decrease in fuel pressure may indicate that the pulsed voltage control signal caused the pintle valve (e.g., the pintle valve  330 ) of the electronic fuel injector (e.g., electronic fuel injector  540 ) to open. 
     The control unit  515  of the control module  510  may record (e.g., in the storage unit  517  of the control module  510 ) the preset supply voltage provided by the VPS  570  and the injector open time (i.e., the pulse width) at the preset supply voltage. One of ordinary skill in the art will appreciate that the minimum pulse width, the maximum pulse width, and the pulse width increment described above are merely exemplary and that other values for the minimum pulse width, the maximum pulse width, and the pulse width increment may be used without departing from the scope of the present inventive concept. 
     The supply voltage to the control module  510  may affect the amplitude of the pulsed voltage control signals and therefore, the injector open time. After the control module  510  (e.g., the control unit  515 ) records the injector open time at the preset supply voltage, the control unit  515  of the control module  510  may cause the VPS  570  to increment the supply voltage provided to the control module  510 . For example, the control module  510  (e.g., the control unit  515 ) may cause the VPS  570  to increment the supply voltage by 0.5 volts. The control unit  515  of the control module  510  may provide a signal to operate the fuel pump  520  for a short period (e.g., several seconds) to recharge the fuel pressure in the fuel rail  530 . In various embodiments, the control unit  515  may cause the control module  510  to provide a control signal to the VPS  570  to increment the supply voltage. In various embodiments, the control unit  515  may cause the control module  510  to provide an indication, for example, but not limited to, an indicator light, audible beep, etc., for manual adjustment of the control module  510  supply voltage provided by the VPS  570 . 
     After causing the VPS  570  to increment the supply voltage and causing the fuel pump  520  to recharge the fuel pressure in the fuel rail  530 , the control unit  515  may cause the control module  510  to reset the pulse width to the minimum pulse width (e.g., 50 or another value) and provide the pulsed voltage control signals to the one of the one or more electronic fuel injectors to determine the injector open time at the incremented supply voltage to the control module  510 . For example, the supply voltage provided to the control module  510  by the VPS  570  may be set to twelve volts and the pulse width of the pulsed voltage control signal may be set to 50 μs. The control unit  515  may cause the control module  510  to apply the pulsed voltage control signal to the one of the one or more electronic fuel injector (e.g., the electronic fuel injector  540 ) and may monitor the fuel pressure signal from the fuel pressure sensor  560 . 
     The control module  510  (e.g., the control unit  515 ) may cause the supply voltage provided to the control module  510  by the VPS  570  to be incrementally increased, for example by 0.5 volts, in a range of about twelve volts to fifteen volts. At each supply voltage increment, the control unit  515  may cause the control module  510  to reset the pulse width of the pulsed voltage control signal to the minimum pulse width and may determine the injector open time at each supply voltage increment based on the pulse width of the pulsed voltage control signal causing a sensed decrease in the fuel pressure. 
     Fuel pressure in the multiport fuel injection system  500  may be recharged (e.g., by operating the fuel pump  520  or by other pressurizing methods) before each successive test after the supply voltage provided by the VPS  570  is incremented. For example, after the injector opening time is determined based on the pulse width of the pulsed voltage control signal, control unit  515  may cause the control module  510  (e.g., the control unit  515 ) may cause the fuel pump  520  to operate to recharge the fuel pressure in the fuel rail  530 . The procedure may be repeated for each incremental increase in supply voltage to the control module  510  to characterize the injector open time with respect to control module  510  supply voltage. The control unit  515  of the control module  510  may control the electronic fuel injectors (e.g., the electronic fuel injectors  540 ) during engine operation based on the injector open times and corresponding control module  510  supply voltages stored in the storage unit  517  to compensate for variations in the control module  510  supply voltage provided by the vehicle electrical system. 
     Various embodiments may configure the multiport fuel injection system  500  separately from a vehicle, for example, as a test apparatus mounted to a suitable structure as known to those of ordinary skill in the art. In a test apparatus configuration, the one or more of the electronic fuel injectors  540  may be installed in the test apparatus rather than being installed in an engine. 
       FIG. 6  is a flowchart illustrating a calibration method  600  for an electronic fuel injector according to various embodiments. Referring to  FIGS. 5 and 6 , at block  605 , the control unit  515  may cause the control module  510  to initialize the fuel pressure and the fuel pressure upper and lower limits. For example, the control module  510  (e.g., the control unit  515 ) may cause the fuel pump  520  to operate to charge the fuel pressure in the fuel rail  530  to a pressure in a range of about 30-70 pounds-per-square-inch (PSI) or another value. Alternatively, the fuel pressure in the fuel rail  530  may be charged by manual operation of the fuel pump  520  or by another pump. At block  610 , the control module  510  (e.g., the control unit  515 ) may cause the VPS  570  to initialize the control module  510  supply voltage to a voltage in the range of about 11.5-12.5 volts. Alternatively, the control unit  515  may cause the control module  510  to provide an indication, for example, but not limited to, an indicator light or audible alert, to prompt manual initialization of the control module  510  supply voltage provided by the VPS  570 . 
     After initializing the fuel pump pressure, fuel pressure limits, and control module  510  supply voltage, at block  615 , the control unit  515  may cause the control module  510  to initialize the pulse width of the pulsed voltage control signal and the upper and lower pulse width limits. At block  620 , the control unit  515  may cause the control module  510  to supply the pulsed voltage control signal having the set pulse width to an electronic fuel injector (e.g., one of the electronic fuel injectors  540 ) at the set control module  510  supply voltage. 
     At block  625 , the control unit  515  may cause the control module  510  to monitor the fuel pressure in the fuel rail  530  (e.g., via a signal from the fuel pressure sensor  560 ) when the pulsed voltage control signal having the set pulse width is applied to the electronic fuel injector. At block  630 , the control unit  515  may determine based on the signal received from the fuel pressure sensor  560  whether a change in fuel pressure occurs when the pulsed voltage control signal is applied to the electronic fuel injector (e.g., one of the electronic fuel injectors  540 ). For example, the control unit  515  may determine based on the signal received from the fuel pressure sensor  560  whether the fuel pressure decreases by about 0.2 psi (or another value) when the pulsed voltage control signal is applied to the electronic fuel injector. 
     In response to determining that the fuel pressure did not decrease (i.e., fuel pressure decreased less than about 0.2 psi or another value) ( 630 —N), at block  635  the control unit  515  of the control module  510  may determine if the upper pulse width limit for the pulsed voltage control signal has been reached. In response to determining that the upper pulse width limit for the pulsed voltage control signal has not been reached ( 635 —N), at block  640  the control unit  515  may increment (e.g., increase) the pulse width of the pulsed voltage control sign (e.g., by 50 μs or another value), and the method may continue at block  620 . 
     In response to determining that the upper pulse width limit for the pulsed voltage control signal has been reached ( 635 —Y), at block  650  the control unit  515  may determine if the upper limit for the control module  510  supply voltage has been reached. In response to determining that the upper limit for the control module  510  supply voltage has been reached ( 650 —Y), the calibration method  600  may be complete. 
     In response to determining that the upper limit for the control module  510  supply voltage has not been reached ( 650 —N), at block  655  the control unit  515  may increment (e.g., increase) the control module  510  supply voltage provided by the VPS  570  by about 0.5 volts or another value. For example, the control unit  515  may cause the VPS  570  to increment the control module  510  supply voltage by about 0.5 volts or another value. Alternatively, the control unit  515  may cause the control module  510  to provide an indication, for example, but not limited to, an indicator light or audible alert, to prompt manual incrementing of the control module  510  supply voltage provided by the VPS  570 . 
     At block  660 , the control module  510  (e.g., the control unit  515 ) may cause the fuel pump  520  to operate to recharge the fuel pressure in the fuel rail  530  to a pressure in a range of about 30-70 pounds-per-square-inch (PSI) or another value. Alternatively, the fuel pressure in the fuel rail  530  may be charged by manual operation of the fuel pump  520  or by another pump. The control module  510  (e.g., the control unit  515 ) may cause the method to continue at block  615 . At block  615 , the control unit  515  may again cause the control module  510  to initialize the pulse width of the pulsed voltage control signal and the upper and lower pulse width limits, and operation may continue with the incremented control module  510  supply voltage provided by the VPS  570 . 
     In response to determining that the fuel pressure did decrease (i.e., fuel pressure decreased by about 0.2 PSI or another value) ( 630 —Y), at block  645 , the control unit  515  of the control module  510  may record the pulse width of the pulsed voltage control signal and the corresponding control module  510  supply voltage. For example, the control unit  515  of the control module  510  may record the pulse width of the pulsed voltage control signal and the corresponding control module  510  supply voltage in the storage unit  517 . 
     At block  650 , the control unit  515  may determine if the upper limit for the control module  510  supply voltage has been reached. In response to determining that the upper limit for the control module  510  supply voltage has been reached ( 650 —Y), the calibration method  600  may be complete. 
     In response to determining that the upper limit for the control module  510  supply voltage has not been reached ( 650 —N), at block  655  the control unit  515  may increment the control module  510  supply voltage provided by the VPS  570  by about 0.5 volts or another value. For example, the control unit  515 ) may cause the VPS  570  to increment the control module  510  supply voltage by about 0.5 volts or another value. Alternatively, the control unit  515  may cause the control module  510  to provide an indication, for example, but not limited to, an indicator light or audible alert, to prompt manual incrementing of the control module  510  supply voltage provided by the VPS  570 . 
     At block  660 , the control module  510  (e.g., the control unit  515 ) may cause the fuel pump  520  to operate to recharge the fuel pressure in the fuel rail  530  to a pressure in a range of about 30-70 pounds-per-square-inch (PSI) or another value. Alternatively, the fuel pressure in the fuel rail  530  may be charged by manual operation of the fuel pump  520  or by another pump. The control module  510  (e.g., the control unit  515 ) may cause the method to continue at block  615 . At block  615 , the control unit  515  may again cause the control module  510  to initialize the pulse width of the pulsed voltage control signal and the upper and lower pulse width limits, and operation may continue with the incremented control module  510  supply voltage provided by the VPS  570 . 
     Subsequent to performing the calibration method  600 , the control unit  515  of the control module  510  may control the electronic fuel injectors (e.g., the electronic fuel injectors  540 ) during engine operation based on the injector open times and corresponding control module  510  supply voltages stored in the storage unit  517  to compensate for variations in the control module  510  supply voltage provided by the vehicle electrical system. For example, the control unit  515  of the control module  510  may select a stored pulse width corresponding to a stored supply voltage that most closely corresponds to the control module  510  supply voltage provided by the vehicle electrical system, and cause the control module  510  to supply a control voltage signal having the selected pulse width to one or more of the electronic fuel injectors. 
     The control module  510  may be externally programmed with instructions for performing the method  600 . Alternatively, the control module  510  may not be externally programmable and the instructions for performing the method  600  may be pre-programmed in firmware of the control module  510 . For instance, a programmable logic device, for example, but not limited to, an electronically programmable read-only memory (EPROM), electronically erasable programmable read-only memory (EEPROM), etc., may be preprogrammed and installed in the control module  510 . 
     The method  600  described with respect to  FIG. 6  may be embodied on a non-transitory computer readable medium, for example, but not limited to, the storage unit  517  or other non-transitory computer readable medium known to those of skill in the art, having stored therein a program including computer executable instructions for making a processor, computer, or other programmable device execute the operations of the method. 
     In some embodiments, the calibration method  600  for a multiport fuel injection system may be performed on a test apparatus.  FIG. 7  is a diagram illustrating a test apparatus  700  for electronic fuel injector calibration according to various embodiments. Referring to  FIG. 7 , the test apparatus  700  may include a fuel tank  790 , a fuel pump  720 , a fuel rail  730 , a pressure regulator  750 , a blocking valve  755 , a fuel pressure sensor  760 , and a variable power supply (VPS)  770 . One or more electronic fuel injectors  740  to be calibrated may be mounted to the fuel rail  730 . These components may be similar to the corresponding components in the multiport fuel injection calibration system  500  previously described and illustrated in  FIG. 5  and so will not be further described. 
     The test apparatus  700  for multiport fuel injection calibration may also include a test control module  710 . The test control module  710  may include a control unit  715 , for example, but not limited to, a microprocessor, a microcontroller, or other programmable device, and may further include a storage unit  717 , for example, but not limited to, RAM, ROM, EEPROM, or other memory, or combinations thereof, and driver circuitry  718  configured to provide control signals to the electronic fuel injectors  740  and the fuel pump  720 . The test control module  710  may be, for example, a commercially available PCM (e.g., the PCM  210 ), a control module (e.g., the control module  510 ), or other circuitry configured to provide pulsed voltage control signals having adjustable pulse widths to one or more electronic fuel injectors undergoing calibration. The components of the test apparatus  700  may be configured on a test stand  705 , for example a bench or table, separate from a vehicle. 
     In various embodiments, the control unit  715  may cause the test control module  710  to provide a control signal to the VPS  770  to increment the supply voltage. In various embodiments, the control unit  715  may cause the test control module  710  to provide an indication, for example, but not limited to, an indicator light, audible beep, etc., for manual adjustment of the control module  710  supply voltage provided by the VPS  770 . The control unit  715  of the test control module  710  may cause the test apparatus  700  to perform the method  600  and store injector open times and corresponding test control module  710  supply voltages in the storage unit  717  of the test control module  710 . 
     The injector open times and corresponding test control module  710  supply voltages stored in the storage unit  717  of the test control module  710  may be read out of the storage unit  717  and programmed into a programmable logic device, for example, but not limited to, an electronically programmable read-only memory (EPROM), electronically erasable programmable read-only memory (EEPROM), etc., using techniques and equipment known to those of skill in the art. The programmable device thus programmed may be installed in a PCM or other control module (e.g., the PCM  210  or control module  510 ) that is part of a vehicle engine control system. Alternatively, the programmable device may be programmed while installed in the PCM or other control module (e.g., the PCM  210  or control module  510 ) of the vehicle via an electronic interface and equipment known to those of skill in the art. The PCM or other control module (e.g., the PCM  210  or control module  510 ) may control the electronic fuel injectors (e.g., the electronic fuel injectors  540 ) during engine operation based on the injector open times and corresponding PCM or control module supply voltages stored in the programmable logic device to compensate for variations in the PCM or control module supply voltage provided by the vehicle electrical system. 
     While the example embodiments are described in terms of multiport fuel injection systems, on of ordinary skill in the art will appreciate that the present inventive concept is extended to all types of electronic fuel injectors, for example, but not limited to throttle body fuel injectors, port fuel injectors, direct fuel injectors, etc., without departing from the scope of protection of the present inventive concept. 
     One of ordinary skill in the art will also appreciate that the term powertrain control module (PCM) will encompass any control module, controller, or circuitry capable of performing the above-described operations at least with respect to the electronic fuel injectors and fuel supply system without departing from the scope of protection of the present inventive concept. 
     The accompanying claims and their equivalents are intended to cover such forms or modifications as would fall within the scope and spirit of the protection. For example, the example apparatuses, methods, and systems disclosed herein can be applied to electronic fuel injection systems. The various components illustrated in the figures may be implemented as, for example, but not limited to, software and/or firmware on a processor, ASIC/FPGA/DSP, or dedicated hardware. Also, the features and attributes of the specific example embodiments disclosed above may be combined in different ways to form additional embodiments, all of which fall within the scope of the present disclosure. 
     The foregoing method descriptions and the process flow diagrams are provided merely as illustrative examples and are not intended to require or imply that the operations of the various embodiments must be performed in the order presented. As will be appreciated by one of skill in the art the order of operations in the foregoing embodiments may be performed in any order. Words such as “thereafter,” “then,” “next,” etc., are not intended to limit the order of the operations; these words are simply used to guide the reader through the description of the methods. Further, any reference to claim elements in the singular, for example, using the articles “a,” “an,” or “the” is not to be construed as limiting the element to the singular. 
     The various illustrative logical blocks, modules, circuits, and algorithm operations described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both. To clearly illustrate this interchangeability of hardware and software, various illustrative components, blocks, modules, circuits, and operations have been described above generally in terms of their functionality. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the overall system. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the various embodiments. 
     The hardware used to implement the various illustrative logics, logical blocks, modules, and circuits described in connection with the aspects disclosed herein may be implemented or performed with a general purpose processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A general-purpose processor may be a microprocessor, but, in the alternative, the processor may be any conventional processor, controller, microcontroller, or state machine. A processor may also be implemented as a combination of receiver devices, e.g., a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration. Alternatively, some operations or methods may be performed by circuitry that is specific to a given function. 
     In one or more exemplary aspects, the functions described may be implemented in hardware, software, firmware, or any combination thereof. If implemented in software, the functions may be stored as one or more instructions or code on a non-transitory computer-readable storage medium or non-transitory processor-readable storage medium. The operations of a method or algorithm disclosed herein may be embodied in processor-executable instructions that may reside on a non-transitory computer-readable or processor-readable storage medium. Non-transitory computer-readable or processor-readable storage media may be any storage media that may be accessed by a computer or a processor. By way of example but not limitation, such non-transitory computer-readable or processor-readable storage media may include RAM, ROM, EEPROM, FLASH memory, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that may be used to store desired program code in the form of instructions or data structures and that may be accessed by a computer. Disk and disc, as used herein, includes compact disc (CD), laser disc, optical disc, digital versatile disc (DVD), floppy disk, and Blu-ray disc where disks usually reproduce data magnetically, while discs reproduce data optically with lasers. Combinations of the above are also included within the scope of non-transitory computer-readable and processor-readable media. Additionally, the operations of a method or algorithm may reside as one or any combination or set of codes and/or instructions on a non-transitory processor-readable storage medium and/or computer-readable storage medium, which may be incorporated into a computer program product. 
     Although the present disclosure provides certain example embodiments and applications, other embodiments that are apparent to those of ordinary skill in the art, including embodiments which do not provide all of the features and advantages set forth herein, are also within the scope of this disclosure. Accordingly, the scope of the present disclosure is intended to be defined only by reference to the appended claims.