Patent Publication Number: US-11035315-B2

Title: Modeling to compensate for HEGO sensor drift

Description:
FIELD 
     The present description relates generally to methods and systems to compensate for HEGO sensor drift caused by hydrogen diffusion within the exhaust system. 
     BACKGROUND/SUMMARY 
     Engines combust fuel at specific air to fuel ratios (AFRs) to maintain efficient combustion and reduced emissions. Vehicles may use an exhaust gas sensor, such as a heated exhaust gas oxygen (HEGO) sensor, downstream of a catalyst to control the AFR to near stoichiometry. This is achieved by regulating the AFR based on a difference between HEGO output (e.g., voltage) from a pre-determined HEGO output (e.g., corresponding to stoichiometry). Thus, HEGO sensors provide a feedback adjustment to maintain a setpoint AFR. 
     Although such emissions control systems have been found to be useful, the accuracy and effectiveness of such systems may be impaired with use over time and component degradation. The combustion of air/fuel mixtures produces an exhaust gas stream comprised of various gaseous components including hydrogen (H2). Hydrogen in the exhaust gas may lead to issues, such as the promotion of ammonia formation. U.S. Pat. No. 5,433,071A (Willey et al., herein after Willey) discloses that the removal of hydrogen from the exhaust gas stream eliminates lean shifts and allows the oxygen sensor and closed loop control means to more accurately control AFR. 
     However, the inventors herein have recognized issues with the above approach. The approach described in Willey uses a dedicated catalyst to preferentially oxidize hydrogen from the exhaust stream, which is expensive and may not remove all hydrogen under all conditions. If hydrogen remains in the exhaust gas, the hydrogen may cause a bias in the output of one or more oxygen sensors, which may compromise emissions control. 
     The inventors herein have identified methods and systems which overcome the deficiencies of the approaches described above. In one embodiment, a method includes adjusting a fuel amount supplied to an engine based on an estimated amount of hydrogen in a reference cell of an oxygen sensor positioned in an exhaust passage coupled to the engine. The amount of hydrogen in the reference cell may be determined, in a temporal manner, by modeling the diffusion of hydrogen into and out of the HEGO reference cell which may then be used to trigger intentional lean shifts and/or correct the sensed AFR, thereby accounting for potential HEGO sensor drift without requiring expensive, hardware-based solutions that can create additional failures within the fuel system. 
     It should be understood that the summary above is provided to introduce in simplified form a selection of concepts that are further described in the detailed description. It is not meant to identify key or essential features of the claimed subject matter, the scope of which is defined uniquely by the claims that follow the detailed description. Furthermore, the claimed subject matter is not limited to implementations that solve any disadvantages noted above or in any part of this disclosure. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  shows a schematic depiction of an engine system of a vehicle. 
         FIG. 2  shows a schematic diagram of an example oxygen sensor. 
         FIG. 3  depicts an example physical model of hydrogen infiltration into an oxygen sensor. 
         FIG. 4  shows a set of graphs illustrating the effect of hydrogen diffusion on AFR. 
         FIG. 5  provides a flow chart illustrating a method for utilizing hydrogen diffusion modeling to estimate a hydrogen amount in the reference cell of a HEGO sensor in a temporal manner and adjusting fuel injection amounts based on the estimated hydrogen amount. 
         FIG. 6A  shows a first part of a control diagram depicting air-fuel ratio control according to the method of  FIG. 5 . 
         FIG. 6B  shows a second part of the control diagram presented in  FIG. 6A . 
         FIG. 7  shows a series of plots illustrating instances of air-fuel ratio control due to modeled hydrogen over a series of drive cycles. 
     
    
    
     DETAILED DESCRIPTION 
     The following description relates to systems and methods for modeling hydrogen diffusion into and out of an oxygen sensor&#39;s reference cell, such as that of a heated exhaust gas oxygen (HEGO) sensor, to identify and compensate for HEGO sensor drift caused by hydrogen infiltration into the reference cell. Though utilized to sense oxygen, HEGO sensors have a cross-sensitivity to hydrogen. The low molecular weight of hydrogen may allow it to preferentially diffuse through cracks and/or seals in the HEGO sensor and enter into the reference cell of the HEGO sensor. The hydrogen in the reference cell causes the HEGO sensor to detect a leaner mixture than is actually present in the exhaust stream thereby leading to inaccurate AFR control. Further, because hydrogen is generated at rich air-fuel ratio conditions, the HEGO sensor detecting a leaner-than-actual air-fuel ratio may lead to even more hydrogen generation, as the amount of fuel provided to the engine may be increased in an attempt to bring the air-fuel ratio back to (detected) stoichiometry, thus causing more hydrogen to be generated. Additionally, this excess hydrogen generation may lead to ammonia formation, thus increasing emissions, and potentially altering the HEGO sensor&#39;s surface that is exposed to exhaust, further desensitizing the HEGO to the magnitude of reductant in the exhaust. 
     Gas that enters the HEGO sensor reference cell undergoes an electrochemical reaction that causes a change in the output of the sensor. The output of the HEGO sensor may then be used to adjust the vehicle&#39;s AFR for optimal vehicle operation and clean emissions. Thus, any hydrogen that enters the HEGO sensor reference cell may bias sensor output thereby impacting the AFR. Hydrogen may relatively rapidly diffuse in the reference cell, driven by the difference in pressure and temperature between the exhaust stream and the reference cell. Diffusion of hydrogen from the reference cell to ambient air may occur over a longer time period, however, as the hydrogen travels down the length of a breather tube attached to the reference cell to exit to ambient air. By modeling the timing of hydrogen movement into and out of the reference cell, a temporal model of the effect of hydrogen on the HEGO sensor response can be determined. This temporal model can then be used to correct the sensed air fuel ratio and thereby correct for any bias in HEGO sensor output due to hydrogen contamination of the reference cell. As used herein, the term “temporal model” may include an estimate of hydrogen concentration in the reference cell that reflects the amount of time that it takes for the hydrogen to diffuse out of the reference cell, which may be longer than the amount of time it takes for hydrogen to diffuse into the reference cell. In this way, even if operating conditions change and hydrogen is no longer present in the exhaust gas traveling through the exhaust passage and past the HEGO sensor, hydrogen may still be present in the reference cell of the HEGO sensor. By using the temporal model, this additional time where hydrogen is present in the reference cell but not the exhaust gas may be accounted for, which may increase the accuracy of the detection and compensation of the hydrogen in the reference cell of the HEGO sensor. 
     As shown in  FIG. 1 , an engine system may include a HEGO sensor downstream of an emission control device. A schematic cross section of an example oxygen sensor, which may be a HEGO sensor, indicating its key components, including the reference cell, is provided in  FIG. 2 . Though construction of the HEGO sensor is optimized to prevent any exhaust from contaminating the reference cell, minor leaks can occur. A higher pressure and temperature differential exists between the exhaust stream and the HEGO reference cell that can drive hydrogen diffusion through such leaks. A physical model of hydrogen diffusion into and out the HEGO reference cell is illustrated in  FIG. 3  and further demonstrated in  FIG. 4 .  FIG. 4  shows the effect of hydrogen diffusion into the HEGO reference cell on sensed AFR as compared to actual AFR. By modeling diffusion of hydrogen into and out of the reference cell in a control system, a temporal model of HEGO offset due to hydrogen can be determined and utilized to adjust engine fuel amounts as outlined in  FIGS. 5 and 6 . Example plots of instances of model-based fuel adjustments under different driving conditions is shown in  FIG. 7 . 
       FIG. 1  illustrates a schematic diagram showing one cylinder of multi-cylinder engine  10 , which may be included in a propulsion system of an automobile. Engine  10  may be controlled at least partially by a control system including controller  12  and by input from a vehicle operator  132  via an input device  130 . In this example, input device  130  includes an accelerator pedal and a pedal position sensor  134  for generating a proportional pedal position signal PP. Combustion chamber (i.e., cylinder)  30  of engine  10  may include combustion chamber walls  32  with piston  36  positioned therein. Piston  36  may be coupled to crankshaft  40  so that reciprocating motion of the piston is translated into rotational motion of the crankshaft. Crankshaft  40  may be coupled to at least one drive wheel of a vehicle via an intermediate transmission system. Further, a starter motor may be coupled to crankshaft  40  via a flywheel to enable a starting operation of engine  10 . 
     Combustion chamber  30  may receive intake air from intake manifold  44  via intake passage  42  and may exhaust combustion gases via exhaust passage  48 . The pressure and temperature within exhaust passage  48  may be determined by an exhaust pressure sensor  148  and exhaust temperature sensor  150 , respectively. Intake manifold  44  and exhaust passage  48  can selectively communicate with combustion chamber  30  via respective intake valve  52  and exhaust valve  54 . In some embodiments, combustion chamber  30  may include two or more intake valves and/or two more exhaust valves. In this example, intake valve  52  and exhaust valve  54  may be controlled by cam actuation via one or more cams and may utilize one or more of cam profile switching (CPS), variable cam timing (VCT), variable valve timing (VVT), and/or variable valve lift (VVL) systems that may be operated by controller  12  to vary valve operation. The position of intake valve  52  and exhaust valve  54  may be determined by position sensors  55  and  57 , respectively. In alternative embodiments, intake valve  52  and/or exhaust valve  54  may be controlled by electric valve actuation. For example, cylinder  30  may alternatively include an intake valve controlled via electric valve actuation and an exhaust valve controlled via cam actuation including CPS and/or VCT systems. 
     In some embodiments, each cylinder of engine  10  may be configured with one or more fuel injectors for providing fuel thereto. As a non-limiting example, cylinder  30  is shown including one fuel injector  66 , which is supplied fuel from fuel system  172 . Fuel injector  66  is shown coupled directly to cylinder  30  for injecting fuel directly therein in proportion to the pulse width of signal FPW received from controller  12  via electronic driver  68 . In this manner, fuel injector  66  provides what is known as direct injection (hereafter also referred to as “DI”) of fuel into combustion cylinder  30 . 
     It will be appreciated that in an alternate embodiment, injector  66  may be a port injector providing fuel into the intake port upstream of cylinder  30 . It will also be appreciated that cylinder  30  may receive fuel from a plurality of injectors, such as a plurality of port injectors, a plurality of direct injectors, or a combination thereof. 
     Continuing with  FIG. 1 , intake passage  42  may include a throttle  62  having a throttle plate  64 . In this particular example, the position of throttle plate  64  may be varied by controller  12  via a signal provided to an electric motor or actuator included with throttle  62 , a configuration that is commonly referred to as electronic throttle control (ETC). In this manner, throttle  62  may be operated to vary the intake air provided to combustion chamber  30  among other engine cylinders. The position of throttle plate  64  may be provided to controller  12  by throttle position signal TP. Intake passage  42  may include a mass air flow sensor  120  and a manifold air pressure sensor  122  for providing respective signals MAF and MAP to controller  12 . 
     Ignition system  88  can provide an ignition spark to combustion chamber  30  via spark plug  92  in response to spark advance signal SA from controller  12 , under select operating modes. Though spark ignition components are shown, in some embodiments, combustion chamber  30  or one or more other combustion chambers of engine  10  may be operated in a compression ignition mode, with or without an ignition spark. 
     An upstream exhaust gas sensor  126  is shown coupled to exhaust passage  48  upstream of emission control device  70 . Upstream sensor  126  may be any suitable sensor for providing an indication of exhaust gas air-fuel ratio such as a linear wideband oxygen sensor or UEGO (universal or wide-range exhaust gas oxygen), a two-state narrowband oxygen sensor or EGO, a HEGO (heated EGO), a NOx, HC, or CO sensor. In one embodiment, upstream exhaust gas sensor  126  is a UEGO configured to provide output, such as a voltage signal, that is proportional to the amount of oxygen present in the exhaust. Controller  12  uses the output to determine the exhaust gas air-fuel ratio (AFR). 
     Emission control device  70  is shown arranged along exhaust passage  48  downstream of exhaust gas sensor  126 . Device  70  may be a three way catalyst (TWC), configured to reduce NOx and oxidize CO and unburnt hydrocarbons. In some embodiments, device  70  may be a NOx trap, various other emission control devices, or combinations thereof. Downstream of emission control device  70  is a selective catalytic reduction (SCR) device  152 . SCR device  152  may be a passive SCR device that stores ammonia generated in a TWC (e.g., in the emission control device  70 ) during slightly rich conditions, and the stored ammonia may then be used to reduce NOx emissions when the engine switches to lean operation. In some examples, the SCR device  152  may be the only NOx-controlling device in the exhaust system, e.g., there may not be a NOx trap in the exhaust system. In some examples, emission control device  70  may be a TWC and the only emission control devices present in the exhaust system may be the TWC and the SCR device. In other examples, the exhaust system may include a TWC, an SCR device, and a particulate filter, and no other emission control devices. 
     A second, downstream exhaust gas sensor  128  is shown coupled to exhaust passage  48  downstream of emissions control device  70 . Downstream sensor  128  may be any suitable sensor for providing an indication of exhaust gas air-fuel ratio such as a UEGO, EGO, HEGO, etc. Downstream sensor  128  may have a breather tube  146  attached to an internal reference cell. Breather tube  146  terminates in ambient air. Breather tube  146  may couple the internal reference cell in downstream sensor  128  to ambient air. In one embodiment, downstream sensor  128  is a HEGO configured to indicate the relative enrichment or enleanment of the exhaust gas after passing through the catalyst. As such, the HEGO sensor may provide output in the form of a switch point, or the voltage signal at the point at which the exhaust gas switches from lean to rich. 
     Further, in the disclosed embodiments, an exhaust gas recirculation (EGR) system may route a desired portion of exhaust gas from exhaust passage  48  to intake passage  42  via EGR passage  140 . The amount of EGR provided to intake passage  42  may be varied by controller  12  via EGR valve  142 . Further, an EGR sensor  144  may be arranged within the EGR passage and may provide an indication of one or more of pressure, temperature, and concentration of the exhaust gas. Under some conditions, the EGR system may be used to regulate the temperature of the air and fuel mixture within the combustion chamber. 
     Controller  12  is shown in  FIG. 1  as a microcomputer, including microprocessor unit  102 , input/output ports  104 , an electronic storage medium for executable programs and calibration values shown as read only memory chip  106  in this particular example, random access memory  108 , keep alive memory  110 , and a data bus. Controller  12  may receive various signals from sensors coupled to engine  10 , in addition to those signals previously discussed, including measurement of inducted mass air flow (MAF) from mass air flow sensor  120 ; engine coolant temperature (ECT) from temperature sensor  112  coupled to cooling sleeve  114 ; a profile ignition pickup signal (PIP) from Hall effect sensor  118  (or other type) coupled to crankshaft  40 ; throttle position (TP) from a throttle position sensor; and absolute manifold pressure (MAP) signal from sensor  122 . Engine speed signal, RPM, may be generated by controller  12  from signal PIP. 
     Storage medium read-only memory  106  can be programmed with computer readable data representing non-transitory instructions executable by processor  102  for performing the methods described below as well as other variants that are anticipated but not specifically listed. 
     As described above,  FIG. 1  shows only one cylinder of a multi-cylinder engine, and each cylinder may similarly include its own set of intake/exhaust valves, fuel injector, spark plug, etc. Oxygen sensors are frequently used in internal combustion engines ( FIG. 1 ) to provide indications of various constituents in gasses. 
       FIG. 2  shows a schematic view of an example embodiment of an air-referenced oxygen sensor  200  configured to measure a concentration of oxygen ( 02 ) in an intake airflow in an intake passage or an exhaust gas stream in an exhaust passage. In some examples, the sensor  200  may be a HEGO sensor as shown in  FIG. 1 , such as downstream sensor  128 , for example. Hereafter, oxygen sensor  200  may be referred to as HEGO sensor  200 . 
     As shown in  FIG. 2 , HEGO sensor  200  comprises a plurality of layers of one or more materials arranged in a stacked configuration. This plurality of layers is shown in further detail in view  202  which depicts an enlarged cross-section of the sensor tip of HEGO sensor  200  with a cap  216  removed. In the embodiment of  FIG. 2 , three layers are depicted, that include electrode layer  204  and electrode layer  208  separated by a solid electrolyte layer  206  capable of conducting ionic oxygen. The electrode layers  204  and  208  may be made of various suitable materials. In some embodiments, electrode layers  204  and  208  may be at least partially made of a material that catalyzes the dissociation of molecular oxygen. Examples of such materials include, but are not limited to, electrodes containing platinum and/or silver. Examples of suitable solid electrolytes that may comprise electrolyte layer  206  include, but are not limited to, zirconium oxide-based materials. 
     Further, in some embodiments, a heater  210  may be disposed in thermal communication with the layers to increase the ionic conductivity of the layers. While the depicted oxygen sensor is formed from three layers, it will be appreciated that the oxygen sensor may include other suitable numbers of layers for additional enhancements (e.g., specific catalyzing, additional diffusion, modify adsorption). Internal to the sensor tip shown in view  202  is a reference cell  212  that has a small inlet of ambient air that is sampled outside the exhaust system through a body  218  of HEGO sensor  200 . 
     The pair of sensing electrode layers  204  and  208  detect a concentration gradient that may develop in electrolyte layer  206  due to an oxygen concentration in the exhaust gas that is higher than or lower than the stoichiometric level. A high oxygen concentration may be caused by a lean exhaust gas mixture, while a low oxygen concentration may be caused by a rich mixture. Electrode layer  208  is also exposed to ambient air that is present in reference cell  212 . The ambient air is sufficiently heated by HEGO sensor  200 , with the difference in concentration of oxygen molecules between the exhaust and ambient air driving oxygen ions from a higher to lower concentration thereby producing a voltage difference on the electrode layers  204  and  208 . The farther apart in AFR the rich exhaust is as compared to ambient air with no reductants, the higher the voltage potential. If the ambient air contains some reductants, such as stray hydrogen, the voltage will be lower. 
     During engine operation, the exhaust stream  214  passes along HEGO sensor  200  and diffuses through electrolyte layer  206 . Because the pressure and temperature within a vehicle&#39;s exhaust pipe is higher relative to that in HEGO reference cell  212  during engine operation, some penetration of hydrogen into reference cell  212  may occur at seals, interfaces, etc. of HEGO sensor  200  between reference cell  212  and the exhaust passage. Hydrogen is the smallest molecule generated within the exhaust stream and thereby more apt to diffuse into reference cell  212  than other generated molecules. Further, the concentration of hydrogen within the exhaust stream may build during sustained rich running or stoichiometric operations. Hydrogen in reference cell  212  may diffuse to ambient air via a breather tube  220  which couples reference cell  212  to ambient air. However, this diffusion takes time as hydrogen has to travel from reference cell  212  into breather tube  220 , down the length of breather tube  220 , and out into ambient air. Thus, the cross-sensitivity of HEGO reference cell  212  to hydrogen may bias HEGO sensor  200  output to report leaner conditions than actual as hydrogen alters reference cell  212  to actually be richer than the presumed lean ambient air without reductants, thereby generating a smaller voltage across layers  208  and  206 . Further, any bias caused by hydrogen contamination in reference cell  212  may not be resolved until the concentration of hydrogen in reference cell  212  has diffused to ambient air. Accordingly, hydrogen diffusion into HEGO reference cell  212  may cause the fuel system to further richen the exhaust, thus compounding the problem of hydrogen generation. 
     Thus, according to embodiments disclosed herein, the diffusion of hydrogen into and out of reference cell  212  may be modeled, which can subsequently be used to offset potential HEGO sensor drift. A real-time model of HEGO sensor response to hydrogen in the exhaust gas may be used to compensate for hydrogen diffusion into reference cell  212  and correct fuel control in an open or closed loop manner during vehicle operation. 
       FIG. 3  depicts a physical model  300  of hydrogen infiltration into a HEGO reference cell  302 . HEGO reference cell  302  is a non-limiting example of reference cell  212  of HEGO sensor  200  and is connected to a channel  304 . Channel  304  holds a breather tube that attaches to HEGO reference cell  302  and spans the length of channel  304 , terminating in ambient air  306 . The breather tube may vent hydrogen out of reference cell  302  as shown in physical model  300 . During engine operation, the exhaust stream (e.g., output from the engine and past one or more catalysts) may pass reference cell  302  as it exits the exhaust pipe. 
     The pressure and temperature of the exhaust gas in the exhaust pipe may be higher relative to the pressure and temperature in HEGO reference cell  302 . This pressure and temperature differential may drive hydrogen diffusion across cracks and seals into reference cell  302  at the interface between reference cell  302  and the exhaust stream. Further, a pressure and temperature differential may exist between reference cell  302  and the gas in channel  304  and ambient air, which may drive hydrogen diffusion out of reference cell  302  into channel  304 . This diffusion of hydrogen is depicted in the plot  308  of physical model  300 . 
     Plot  308  depicts the diffusion of hydrogen from the exhaust stream into reference cell  302  and out of channel  304  into ambient air  306 . The concentration of hydrogen (ppm), on the Y-axis, is shown as a function of distance, on the X-axis. The X-axis starts at distance point 0, or d0, which is a point within exhaust stream  214  just before reference cell  302 . A first distance, d1, of plot  308  indicates the interface between the exhaust stream and reference cell  302 . A second distance, d2, of plot  308  indicates the transition point from reference cell  302  to channel  304 . A third distance, d3, of plot  308  indicates where channel  304  terminates in ambient air  306 . 
     As shown in example plot  308 , the hydrogen concentration  310  may be relatively high in the exhaust stream (e.g., from d0 to d1). The hydrogen concentration  310  from d1 to d2, while lower than the concentration in exhaust stream, is detectable as hydrogen diffuses into reference cell  302 . The hydrogen concentration  310  may remain relatively stable, going from d1 to d2, showing a gradual decrease as hydrogen diffuses from reference cell  302  to channel  304  at d2. Hydrogen concentration  310  continues this decreasing trend as hydrogen diffuses through channel  304  and out into ambient air  306  at d3. From this understanding, by modeling the diffusion of hydrogen into HEGO reference cell  302  and the diffusion out of channel  304 , the temporal responses of HEGO sensor offset due to hydrogen can be modeled and used to adjust engine fuel amounts, such as triggering intentional lean shifts. The physical model  300  of HEGO reference cell infiltration by hydrogen is further demonstrated in  FIG. 4 . 
       FIG. 4  shows a set of plots  400  illustrating the effect of hydrogen diffusion into an oxygen sensor reference cell, such as reference cell  302  of  FIG. 3 , on AFR during vehicle operation. A first plot  402  depicts vehicle speed (mph)  410  over time. A second plot  404  depicts vehicle exhaust pressure (inches Hg)  412  over time. A third plot  406  depicts vehicle exhaust temperature (° C.)  414  over time. A fourth plot  408  depicts sensed AFR  416 , actual AFR  420 , and the hydrogen effect on lambda  418  over time. All plots are time aligned as appreciated by the X-axis which is measured in seconds. 
     Following a tip-in, plot  402  shows an increase in vehicle speed  410  just after time point 1, or t1. As a result, exhaust pressure  412  increases and exhaust temperature  414  increases as indicated by spikes at t1 in plots  404  and  406 , respectively. The sensed AFR  416 , as determined by controller  12  based on output from an oxygen sensor, such as HEGO sensor  200 , at t1 shows no fluctuation and remains steady around stoichiometry. However, the actual AFR  420 , as determined by chemistry, shows that the AFR spiked rich just after the tip-in at t1. The same pattern may be observed at t2. At t2, an increase in vehicle speed  410  occurs, exhaust pressure  412  increases, exhaust temperature  414  increases, the sensed AFR  416  remains stable, and the actual AFR  420  spikes rich. Thus, as a result of the increased exhaust pressure  412  and exhaust temperature  414 , and due to the rich spikes where hydrogen is generated by the engine and is present in the exhaust gas, hydrogen may diffuse into the HEGO reference cell causing bias within the oxygen sensor due to its cross-sensitivity to hydrogen. This bias is demonstrated by the differences between sensed AFR  416  and actual AFR  420  that is observed after t2. 
     Further, during the engine operation shown in plots  400  the commanded/setpoint air-fuel ratio is generally a long, sustained stoichiometric operation. Under these conditions, hydrogen is not purposely generated, but due to a small rich bias that allows the catalyst to consume engine NOx, enough hydrogen may be generated to accumulate in the exhaust gas and diffuse into the reference cell of the HEGO sensor. This hydrogen effect is most noticeable during steady state driving conditions with minimal rich spikes, as further described with respect to  FIG. 7 . As shown at t1 in plot  408 , hydrogen diffusion into the reference cell biases HEGO sensor output to indicate a leaner exhaust gas than actual and less rich than the target AFR of controller  12  ( FIG. 1 ), leading to a small correction that increases fuel supply to the engine and an increased difference between sensed AFR  416  and actual AFR  420 . As operation is sustained going toward t2 and t3, hydrogen continues to be generated within the exhaust stream and the hydrogen continues to diffuse into the reference cell of the HEGO sensor. The hydrogen in the reference cell of the HEGO sensor results in an inaccurate reference oxygen concentration, which results in the HEGO sensor outputting a leaner-than-actual AFR. To bring the AFR back to target, controller  12  may command additional fuel be supplied to the engine. Over time, as shown between t2 and t3, the output of the HEGO sensor may indicate a near stoichiometric AFR (as shown by sensed AFR  416 ), yet the actual AFR may be rich (as shown by actual AFR  420 ). At t3, in response to a tip-out, sensed AFR  416  spikes lean whereas actual AFR  420  surges rich, then lean as fresh air passes through the engine due to deceleration fuel shutoff (DFSO) then surges rich again as combustion is restarted and excess carbon monoxide is used to reactivate the catalyst. The HEGO sensor appears to restore to correct operation temporarily, but a steady exhaust mass flow causes hydrogen to build within the HEGO sensor again leading the HEGO sensor to once again become desensitized to actual rich AFR. 
     At a fourth time point, t4, another DFSO event occurs, thus the exhaust mass flow will be lower when the engine returns to combustion (to operate the vehicle at a lower speed). At t4, a small initial rich surge occurs as shown by actual AFR  420 , and, on reactivation of the catalyst, the HEGO sensor returns to expected operation. The buildup of hydrogen in the reference cell appears to be matched by the amount of breather tube diffusion at this sustained but lower exhaust mass flow. Thus, once hydrogen diffusion into the reference cell biases HEGO sensor output, continued hydrogen generation during steady state operation leads to further bias due to feedback control and/or an increased diffusion of hydrogen into the HEGO reference cell. Further, there may be a lag between when hydrogen in the exhaust gas decreases and/or is no longer generated and when the hydrogen in the reference cell and breather tube diffuses out to the ambient environment, and thus even after hydrogen is no longer generated, the HEGO sensor may continue to exhibit bias until the hydrogen in the reference cell dissipates. Additionally, once the hydrogen effect is initiated and more rich conditions develop, other reductants (such as ammonia) may coat HEGO sensor surfaces, further desensitizing the sensor. Thus, the desensitizing effects of other reductants have to dissipate before the HEGO sensor can be restored to functioning without bias. 
     Thus, hydrogen may be generated during rich AFR conditions and when the fueling system never goes lean, the lack of oxygen washing over the layers of chemistry on the catalyst brick allows the hydrogen concentration to build up in the exhaust system. For example, the engine may periodically be run rich to generate ammonia for a downstream, passive SCR device (e.g., SCR device  152 ). If the engine operates for a sustained period following the rich operation without swinging lean, the hydrogen in the exhaust gas may begin to infiltrate the HEGO sensor. The temperature and pressure in the exhaust drive a diffusion of hydrogen into the reference cell, which causes a further rich bias and yet higher hydrogen levels. These are the same conditions where un-wanted reactions can take place like the reduction of hydrogen with nitrogen forming ammonia. (It is to be noted that while ammonia may be generated by the TWC via reaction with hydrogen and then stored in the SCR device under certain conditions to facilitate reduction of NOx, and thus it may be desirable to generate hydrogen during some conditions, hydrogen and hence ammonia generation beyond what can be used by the SCR device may not be desired, and if the SCR device is not equipped to store/utilize the ammonia, hydrogen generation may be avoided). 
     When the exhaust has a high, always positive hydrogen concentration, any diffusion of hydrogen into the HEGO reference cell causes the fuel system to further richen the exhaust compounding the problem. Normally the hydrogen is flushed from the system by periodic lean swings due to hydrogen&#39;s affinity to oxygen, particularly in the catalyst. However, in highly steady load conditions, the hydrogen and fuel system reaction can gradually drift. To further compound the problem, under these rich conditions when ammonia is being generated much larger quantities of hydrogen are generated, making the problem even worse. 
     As will be explained in more detail below, during certain conditions where hydrogen is predicted to be in the exhaust gas, the diffusion of hydrogen into the reference cell of the HEGO sensor may be modeled in order to estimate an amount of hydrogen in the reference cell and an effect of that hydrogen on the output of the HEGO sensor. However, as explained above with respect to  FIG. 3 , the reference cell may comprise a relatively large volume (e.g., relative to the breather tube) and thus the hydrogen may enter the reference cell faster than the hydrogen may exit the reference cell, allowing hydrogen to build in the reference cell. Thus, model described herein may also model the rate of diffusion of hydrogen out of the reference cell, which may allow for an instantaneous estimation of hydrogen concentration in the reference cell to be determined, that takes into account the amount of hydrogen that may have already diffused into the reference cell but has not yet diffused out of the reference cell. 
       FIG. 5  is a flow chart showing a method  500  for using hydrogen diffusion modeling to create a temporal model of HEGO sensor responses to generate closed or open loop bias corrections on AFR in accordance with the current disclosure. Instructions for carrying out method  500  and the rest of the methods included herein may be executed by a controller (e.g., controller  12  of  FIG. 1 ) based on instructions stored on a memory of the controller and in conjunction with signals received from sensors of the engine system, such as the sensors described above with reference to  FIG. 1  (e.g., sensor  128  of  FIG. 1  and/or HEGO sensor  200  of  FIG. 2 ). The controller may employ engine actuators of the engine system to adjust engine operation (e.g., adjust engine fuel amounts by adjusting fuel injector  66  of  FIG. 1 ), according to the methods described below. 
     Method  500  may begin at  502 . At  502 , method  500  may include evaluating current operating conditions. As non-limiting examples, operating conditions may include engine operating status, engine speed, engine load, engine temperature, combustion AFR, mass air flow (e.g., as determined from MAF sensor  120 ), HEGO sensor data (e.g., output from HEGO sensor  200 ), engine coolant temperature, catalyst temperature, fuel control, etc. 
     At  504 , method  500  determines, based on the evaluated operating conditions, if the engine is operating in a first mode where correction the output from the HEGO sensor due to hydrogen is to be enabled. The first mode may include steady state operating conditions in which hydrogen is generated. Hydrogen may be generated during sustained rich running conditions which may occur when the engine is cold, accelerating, or under a load, and/or when ammonia formation over a TWC is desired. Alternatively, rich running may also result from dirty air filters, stuck open injectors, or faulty sensors. In some examples, hydrogen may be generated during sustained stoichiometric conditions, or conditions where the engine has not operated lean for a threshold amount of time. In some examples, operation in the first mode may include AFR changing by less than a threshold amount over a predetermined time period, the engine fuel amounts being controlled in closed loop feedback control, and a commanded or setpoint AFR being less than a minimum AFR, such as a lambda of less than 0.999 LAM. If operation in the first mode is detected, method  500  may then continue to  508 , which is described in more detail below. If operation in the first mode is not detected, method  500  may continue to  506 . 
     At  506 , the engine may be operating in a second mode where correction of the output from the HEGO sensor due to hydrogen is not enabled, and thus current vehicle operating conditions are maintained and method  500  may return to  502 . Maintaining the current vehicle operating conditions may include receiving voltage signals from the HEGO sensor and adjusting AFR accordingly, without the AFR sensed by the HEGO sensor being corrected by a modeled hydrogen effect. In some examples, such as when the engine fuel is not controlled in a closed loop manner, the output from the HEGO sensor may be ignored and thus any correction to the output may be moot. 
     At  508 , a model of the temporal responses of the HEGO sensor to hydrogen may be determined by modeling hydrogen diffusion into and out of the HEGO reference cell. Determining the model may include, at  510 , modeling the mass and concentration of hydrogen into the volume of the HEGO reference cell. In an example, modeling the mass and concentration of hydrogen into the volume of the HEGO reference cell may include empirically determining the composition of the gas mixture within the reference cell and determining the proportional percent of the mixture that is occupied by hydrogen during different operational conditions as compared to that to of a reference standard, and storing the hydrogen mass and/or concentration in a look-up table that is indexed by air fuel ratio, exhaust pressure, and/or exhaust temperature. Then, during execution of method  500 , current exhaust pressure and exhaust temperature may be determined (e.g., based on output from sensor  148  and sensor  150 , respectively, of  FIG. 1 ) and a pressure difference (dP) between the exhaust pressure and ambient pressure and a temperature difference (dP) between the exhaust temperature and ambient temperature may be calculated. Ambient pressure and temperature may be based on onboard sensors (e.g., based on the output of sensors  148  and  150  of  FIG. 1 ), GPS, weather service information, or another suitable source. The dP and dT may be entered into the look-up table to determine the mass flow of hydrogen into the reference cell. The concentration of hydrogen in the reference cell may be determined by subtracting the mass flow of hydrogen out of the reference cell (explained in more detail below) from the mass flow of hydrogen into the reference cell and dividing by the volume of the reference cell. 
     Further, determining the model may include, at  512 , modeling and identifying conditions for hydrogen diffusion out of the HEGO reference cell and the concentration at the reference cell. The rate of hydrogen diffusion may be modeled by determining the rate of hydrogen diffusion from the reference cell in relation to the volume and dimensions of the reference cell and the breather tube as a function of varying temperatures and pressures along the diffusion pathway. For example, the mass flow of hydrogen out of the reference cell may be determined by entering the hydrogen concentration in the reference cell (determined as explained above) into a look-up table that stores hydrogen mass flow out of the reference cell as a function of hydrogen concentration and a length of the reference cell and/or breather tube. 
     Determining the model may also include, at  514 , modeling the effect of the hydrogen concentration in the reference cell on actual AFR. The effect of the hydrogen concentration in the reference cell may be determined by entering the percent of hydrogen present within the reference cell into a look-up table, which may store an expected effect on oxygen sensor output and/or AFR as a function of the hydrogen concentration. The look-up table may be populated during vehicle manufacture or otherwise offline based on observed effects of reference cell hydrogen concentration and the actual AFR over a length of time during a designated drive cycle. The effect of the hydrogen on the sensed AFR may be quantified as a hydrogen effect correction factor, also referred to as a hydrogen effect, that may be applied to the AFR sensed by the HEGO sensor. 
     At  516 , method  500  may include adjusting the operating parameters based on the model of temporal responses of the HEGO sensor (e.g., based on the hydrogen effect) determined at  508 . Adjusting the operating parameters may include, at  518 , implementing the hydrogen effect on the actual AFR to correct the fuel control, which may include triggering an open loop response that adjusts fuel control based on the determined hydrogen effect. In an open loop response, there is no feedback control and oxygen sensor data is ignored so the engine may be managed to run at AFRs other than stoichiometry. For example, the controller may control the fuel injectors to adjust engine fuel amounts without relying on feedback from the HEGO sensor. However, the open loop control may rely on an offset that is learned during closed loop control, and thus in some examples this offset may be adjusted based on the hydrogen effect. In still further examples, the hydrogen effect may be used to directly adjust the AFR sensed by the HEGO sensor during closed loop control. While these approaches may proactively respond to the hydrogen and result in accurate AFR control, these approaches also assume that the hydrogen effects acts on the system with little variability. Thus, in some examples, adjusting the operating parameters based on the model may include, at  520 , triggering a lean swing to purge hydrogen from the HEGO reference cell and catalyst. This approach may be more conservative and may include triggering a brief shift in a scheduled rich AFR to a value that is closer to stoichiometry to counteract the hydrogen effect, if such a shift (including a DFSO event) has not occurred from active drive-induced AFR scheduling changes. This may benefit both open loop fuel operation (which uses an offset that is adaptively learned during steady state closed loop operation) and closed loop control (which uses post-catalyst HEGO sensor feedback). This conservative approach only briefly alters AFR scheduling to a more stoichiometric set point, which may be sufficient for steady state operation, though the brief swing to a more stoichiometric AFR may be calibrated with respect to limiting NOx production/emissions. 
     The lean swing to purge hydrogen from the HEGO reference cell and catalyst may cause reduction of the oxygen in the exhaust gas by the hydrogen via a catalyst (e.g., device  70  of  FIG. 1 ), forming water which may pass safely through the exhaust pipe into the atmosphere. The lean (relatively less rich) fuel shifts triggered at  520  may be calibratable and torque compensated thereby allowing for the hydrogen to diffuse out of the HEGO sensor without affecting vehicle operation. For example, the lean swing may be set for the minimum amount of time required to allow hydrogen to diffuse out the reference cell while keeping NOx emissions under a set target and still delivering requested torque. In some examples, the duration of the lean swing and/or AFR during the lean swing (e.g., the amount of leanness of the exhaust gas) may be selected based on the current hydrogen concentration in the reference cell and/or based on the current mass flow of hydrogen out of the reference cell. In some examples, the lean swing may be triggered in response to the hydrogen effect determined by the model having an absolute value that is greater than a threshold, which may indicate that a large amount of hydrogen is present in the exhaust gas, catalyst, and/or reference cell and may need additional oxygen to purge the hydrogen from the system. Method  500  may then return to  502 . 
       FIGS. 6A and 6B  show a control diagram  600  graphically depicting a detailed example of method  500  presented in  FIG. 5 . Control diagram  600  will be described herein with reference to the components and systems depicted in  FIGS. 1 and 2 , though it should be understood that the control diagram may be applied to other systems without departing from the scope of this disclosure. Control diagram  600  may be carried out by controller  12 , and may be stored as executable instructions in non-transitory memory. 
     Control diagram  600  includes a first portion  602  where control diagram  600  determines if HEGO sensor output should be corrected for the effect of hydrogen diffusion into reference cell  212  based on the change in the feedgas AFR over time and a setpoint (e.g., schedule) AFR. In the example shown, control diagram  600  determines the derivative of the feedgas AFR (which may be determined based on output from an upstream oxygen sensor positioned upstream of the catalyst and upstream of the HEGO sensor, such as sensor  126  of  FIG. 1 ) and determines if the derivative is between an upper boundary (UB) and a lower boundary (LB) at block  601 . If the derivative is between the UB and the LB (e.g., “true” in  FIG. 6A ), an inbounds timer is set to inb_tmr+dt (where inb_tmr is an inbounds timer and dt is the time between the updates of method  600 ) and if the derivative is not between the UB and the LB (e.g., “false” in  FIG. 6A ), the inbounds timer is set to zero. At block  603 , the inbounds timer is compared to a stable time threshold. If the inbounds timer is greater than the stable time threshold, the HEGO sensor correction is enabled and a determination is made at  605  whether closed outer loop fuel control is enabled and the setpoint lambda is greater than a minimum lambda. The minimum lambda may be an experimentally determined value where at prolonged steady state operation, the HEGO sensor becomes desensitized to rich operation, which could begin at rich values such as 0.999 LAM. If not, the lambda effect is set to zero at  614  and sensed AFR from the HEGO sensor is not corrected. 
     If HEGO sensor correction is not enabled (e.g., because the inbounds timer is not greater than the stable time threshold), the HEGO output does not need to be corrected (e.g. the AFR is continually shifting therefore hydrogen is not expected to be generated in the exhaust, the scheduled AFR is too high, etc.), the hydrogen effect on sensed lambda (where sensed lambda may be referred to as LAMBSE) is set to zero at  614 . After  614 , LAMBSE is corrected at corrector block  612  based on the determined hydrogen effect. When the determined hydrogen effect is set to zero as described above, LAMBSE is not corrected. 
     If closed outer loop fuel control is enabled and the setpoint lambda is greater than a minimum lambda, control diagram  600  continues at  604 . At  604 , the mass flow (m) of hydrogen into the reference cell is determined using a look-up table programmed with reference values for hydrogen mass flow indexed as a function of the temperature and pressure within the exhaust pipe relative to ambient temperature and pressure (e.g., a temperature difference (dT) and a pressure difference (dP)). Subsequently, at block  606  (shown in  FIG. 6B ), the mass of hydrogen in the reference cell (H2_ref_cell_m) and the percent of total volume occupied by hydrogen within the reference cell (also referred to as the hydrogen concentration) is determined at block  607 . The mass of hydrogen in the reference cell may be determined by subtracting the mass flow of hydrogen out of the reference cell (determined at block  608  and described in more detail below) from the mass flow of hydrogen into the reference cell. 
     In some examples, the mass of hydrogen that is output from block  606  may be fed back to block  606  (after being clipped to the minimum of a hydrogen concentration) and added to the mass of hydrogen determined in a subsequent iteration of the control diagram (e.g., from an immediately subsequent point in time). For example, the control diagram may be executed at a predetermined frequency (e.g., 10 Hz), and the output from block  606  at a first point in time may be added to the output from block  606  at a second point in time (e.g., one-tenth of a second later). Doing so may provide for the mass of hydrogen currently determined to be in the reference cell to be combined with the mass of hydrogen previously determined to be in the reference cell, which may at least in part account for the accumulation of hydrogen that may occur due to the diffusion rate out of the reference cell being lower than the diffusion rate into the reference cell. 
     In such examples, the feedback of the prior mass of hydrogen may be multiplied by a DFSO reset value that is set to either one or zero, dependent on the length of time since the last DFSO event. During DFSO, no fuel is injected while the engine pumps air through the catalyst. Following a DFSO event, the HEGO sensor may return to normal operation and there is a predictable space of time before the hydrogen effect re-asserts itself if the qualifying conditions are still present (e.g., steady state operation with setpoint AFR at or below the threshold AFR). As mentioned previously, a post-DFSO fuel system operation, referred to as catalyst reactivation, may inadvertently hasten the return of the hydrogen effect; however, this is considered in the DFSO reset time, which may elapse in order for method  600  to return to  606 . To that end, an incrementing timer may be triggered when a DFSO event ends and reset upon beginning the next DFSO event. If the timer has not passed a threshold time, the DFSO reset value may be set to zero, while if the timer has passed the threshold time, the DFSO reset value may be set to one, indicating that enough time has elapsed since the last DFSO event to allow the hydrogen effect to re-start. Output of block  606  at the DFSO reset feeds back from the previous loop iteration. The next iteration flows through and the total mass of hydrogen within the reference cell is then determined based on the m of hydrogen into the reference cell for the current iteration and the mass of hydrogen within the reference cell from the previous iteration. 
     The mass of hydrogen in the reference cell that is output from block  606  may be converted to a hydrogen concentration (or a percent volume of the reference cell that is occupied by hydrogen, vol_ref_cell_pct) at  607 . The mass of hydrogen in the reference cell is divided by the volume of the reference cell to determine the hydrogen concentration (or mass per volume of the hydrogen) in the reference cell. The example shown in the current disclosure uses a percent volume of the reference cell; however, in other examples, the mass of hydrogen in the reference cell may be entered into the look-up table rather than first converting the mass to a concentration. 
     At block  608 , the m of hydrogen out of the reference cell is determined using a look-up table programmed with reference values for hydrogen m indexed as a function of the percent of total volume within the reference cell occupied by hydrogen and calibrated for the total length of the reference cell and the breather tube. The output of block  608  is fed back to block  606 , as described above. 
     At block  610 , control diagram  600  includes determining a predicted effect of hydrogen diffusion into and out of the reference cell on LAMBSE (e.g., the sensed AFR relative to stoichiometric AFR), referred to in the control diagram as H2_lambse_effect. This effect may be determined using a look-up table programmed with H2_lambse_effect values as a function of the percentage of the volume of the reference cell occupied by hydrogen. Once the effect of hydrogen diffusion into the reference cell on LAMBSE has been determined, control diagram  600  may continue at  612 . At  612 , LAMBSE may be corrected so that the commanded AFR is based on an accurate determination of exhaust AFR. The sensed lambda (e.g., as sensed from the output of the HEGO sensor) may be corrected with the hydrogen lambse effect determined at block  610  by subtracting the hydrogen lambse effect from the LAMBSE. 
     An example hydrogen lambse effect  418  is shown in plot  408  of  FIG. 4 . In  FIG. 4 , the calculated hydrogen lambse effect  418  is added to one, so that the effect can be plotted on the scale of plot  408 . If hydrogen lambse effect  418  was correcting LAMBSE (shown by sensed AFR  416  in  FIG. 4 ), a drift would not be observable between sensed AFR  416  and actual AFR  420  going from time point t1 to t2 in  FIG. 4 . Additionally, since the sensed lambda from the HEGO sensor is stoichiometric, the effect shown in  FIG. 4  also shows how the sensed lambda would be corrected. For example, if the lambda were corrected as shown, the rich AFR would be mitigated or reduced because the controller would know not to add additional fuel to the engine. As previously described with respect to  FIG. 4 , fresh air passing through the engine during DFSO (e.g., at time t3) restores HEGO functioning. However, the hydrogen effect is still capable of forming after DFSO, which occurs after t3. At t4, the hydrogen effect has ended, as the exhaust mass flow/pressure is low enough to restore normal operation. 
       FIG. 7  shows a series of plots  700  illustrating example incidences in which the model described above with respect to  FIGS. 5, 6A, and 6B  would have corrected for HEGO sensor bias resulting from hydrogen diffusion into a HEGO sensor reference cell. Plots  700  depict vehicle speed as a function of time under three different types of drive cycles as well as incidences in which the hydrogen diffusion model would have output a non-zero hydrogen effect correction factor (also referred to as a hydrogen lambse effect). A first plot  702  depicts vehicle speed in curve  708  and model correction for HEGO sensor bias in curve  710  as a function of time under a Federal Test Procedure (FTP) drive cycle. A second plot  704  depicts vehicle speed in curve  712  and model correction for HEGO sensor bias in curve  714  as a function of time under Highway Fuel Economy emissions testing conditions. A third plot  706  depicts vehicle speed in curve  716  and model correction for HEGO sensor bias in curve  718  as a function of time during steady state vehicle emissions testing. 
     The FTP depicted in plot  702  is a drive cycle that mimics city driving or stop and go traffic as demonstrated by consistent increases and drops in vehicle speed. Under the driving conditions in plot  702 , the model correction for HEGO sensor bias occurred fourteen times (mostly due to engine idling) over the course of 1400 seconds. The model correction shown in the plots  700  only indicates whether or not the model correction would have been implemented to correct the output of the HEGO sensor, and does not indicate a relative value of the correction, which for lower mass flows/pressures may be zero. 
     The Highway Fuel Economy emissions testing in plot  704  is a drive cycle that mimics highway driving conditions under sixty mph as demonstrated by the vehicle speed shown by curve  712 . Under the driving conditions in plot  704 , the model correction for HEGO sensor bias occurred five times over the course of 3200 seconds, as shown by curve  714 . 
     The steady state vehicle emissions testing in plot  706  is a drive cycle that mimics a high engine load on a 0% grade of incline as demonstrated by the vehicle speed shown by curve  716 . Under the driving conditions in plot  706 , the model correction for HEGO sensor bias occurred six times over the course of 2000 seconds, as shown by curve  718 . During steady state vehicle emissions testing, the engine is operating in a steady state condition which allows for hydrogen generation over relatively long periods of time, and thus the model correction for HEGO sensor bias shown by curve  718  occurs for longer durations as compared to drive cycles that include lean swings such as shown in plot  702 . 
       FIGS. 1-2  show example configurations with relative positioning of the various components. If shown directly contacting each other, or directly coupled, then such elements may be referred to as directly contacting or directly coupled, respectively, at least in one example. Similarly, elements shown contiguous or adjacent to one another may be contiguous or adjacent to each other, respectively, at least in one example. As an example, components laying in face-sharing contact with each other may be referred to as in face-sharing contact. As another example, elements positioned apart from each other with only a space there-between and no other components may be referred to as such, in at least one example. As yet another example, elements shown above/below one another, at opposite sides to one another, or to the left/right of one another may be referred to as such, relative to one another. Further, as shown in the figures, a topmost element or point of element may be referred to as a “top” of the component and a bottommost element or point of the element may be referred to as a “bottom” of the component, in at least one example. As used herein, top/bottom, upper/lower, above/below, may be relative to a vertical axis of the figures and used to describe positioning of elements of the figures relative to one another. As such, elements shown above other elements are positioned vertically above the other elements, in one example. As yet another example, shapes of the elements depicted within the figures may be referred to as having those shapes (e.g., such as being circular, straight, planar, curved, rounded, chamfered, angled, or the like). Further, elements shown intersecting one another may be referred to as intersecting elements or intersecting one another, in at least one example. Further still, an element shown within another element or shown outside of another element may be referred as such, in one example. 
     In this way, HEGO sensor output bias caused by hydrogen diffusion into the reference cell of the HEGO sensor may be overcome according to the systems and methods described herein. The embodiments disclosed herein allow the effect of the hydrogen on the sensed AFR to be quantified as a hydrogen effect correction factor that may be applied to the AFR sensed by the HEGO sensor and the AFR subsequently adjusted toward near stoichiometry. By applying the hydrogen correction factor, potential HEGO sensor bias on sensed AFR caused by hydrogen diffusion into the HEGO sensor reference cell may be corrected without introducing an expensive, dedicated catalyst to remove hydrogen from the exhaust stream. Further, the method presented herein allows the sensed AFR to be corrected in real-time thereby improving overall fuel economy. The technical effect of identifying and compensating for HEGO sensor drift by modelling hydrogen diffusion into and out of the sensor&#39;s reference cell is that sensed AFR may be corrected in real-time thereby maintaining efficient combustion and reduced emissions. 
     Note that the example control and estimation routines included herein can be used with various engine and/or vehicle system configurations. The control methods and routines disclosed herein may be stored as executable instructions in non-transitory memory and may be carried out by the control system including the controller in combination with the various sensors, actuators, and other engine hardware. The specific routines described herein may represent one or more of any number of processing strategies such as event-driven, interrupt-driven, multi-tasking, multi-threading, and the like. As such, various actions, operations, and/or functions illustrated may be performed in the sequence illustrated, in parallel, or in some cases omitted. Likewise, the order of processing is not necessarily required to achieve the features and advantages of the example embodiments described herein, but is provided for ease of illustration and description. One or more of the illustrated actions, operations, and/or functions may be repeatedly performed depending on the particular strategy being used. Further, the described actions, operations, and/or functions may graphically represent code to be programmed into non-transitory memory of the computer readable storage medium in the engine control system, where the described actions are carried out by executing the instructions in a system including the various engine hardware components in combination with the electronic controller. 
     It will be appreciated that the configurations and routines disclosed herein are exemplary in nature, and that these specific embodiments are not to be considered in a limiting sense, because numerous variations are possible. For example, the above technology can be applied to V-6, I-4, I-6, V-12, opposed 4, and other engine types. The subject matter of the present disclosure includes all novel and non-obvious combinations and sub-combinations of the various systems and configurations, and other features, functions, and/or properties disclosed herein. 
     As used herein, the term “approximately” is construed to mean plus or minus five percent of the range unless otherwise specified. 
     The following claims particularly point out certain combinations and sub-combinations regarded as novel and non-obvious. These claims may refer to “an” element or “a first” element or the equivalent thereof. Such claims should be understood to include incorporation of one or more such elements, neither requiring nor excluding two or more such elements. Other combinations and sub-combinations of the disclosed features, functions, elements, and/or properties may be claimed through amendment of the present claims or through presentation of new claims in this or a related application. Such claims, whether broader, narrower, equal, or different in scope to the original claims, also are regarded as included within the subject matter of the present disclosure.