Patent Publication Number: US-8527186-B2

Title: Method and apparatus for adaptive feedback control of an excess air ratio in a compression ignition natural gas engine

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention relates generally to compression ignition engines, and, more particularly, relates to a method and apparatus for controlling a gas excess air ratio in a compression ignition natural gas engine. 
     2. Discussion of the Related Art 
     Recent years have seen an increased demand for the use of gaseous fuels as fuel source in internal combustion engines. Gaseous fuels such as propane or natural gas are considered by many to be superior to diesel fuel and the like as a dual source for compression ignition engines because gaseous fuels are generally less expensive, provide equal or greater power with equal or better mileage, and produce significantly lower emissions. This last benefit renders gaseous fuels particularly attractive because recently enacted and pending worldwide regulations may tend to prohibit the use of diesel fuel in many engines. In addition, adapting an engine to be fueled at least in part by gaseous fuels can significantly reduce an engine&#39;s carbon footprint, particularly if the gaseous fuel is obtained from biomass or another carbon-neutral source. The attractiveness of gaseous fuels is further enhanced by the fact that existing compression ignition engine designs can be readily adapted to burn gaseous fuels. 
     When used to fuel compression ignition engines, the relatively compressible gaseous fuel typically is ignited through the autoignation of a “pilot charge” of a relatively incompressible fuel, such as diesel fuel, that is better capable of compression ignition. 
     Lean burn engines, including standard diesel engines and dual fuel engines, have a wide range of desired lambdas as compared to a gasoline engine which generally operates in a small band around the stoichiometric (lambda=1). To improve performance, some lean burn engines have relied on open loop lambda control using empirical data obtained during system development. Such systems control fuel and/or air supply (such as through exhaust gas recirculation (EGR) or turbo wastegate control) to achieve or maintain an experimentally determined ideal lambda for prevailing speed and load conditions. 
     However, gaseous fuels have a relatively narrow range of useful excess air ratios or lambdas (defined as the ratio of total air available for combustion to that required to burn all of the fuel). In any fuel, if lambda drops below a minimum threshold, NO x  and other emissions increase to unacceptable levels. On the other hand, if lambda rises above a maximum acceptable threshold, misfiring can occur, resulting in excessive unwanted emissions and sharply decreased thermal efficiency. 
     It is therefore essential for optimum control of combustion in gas fueled engines to maintain lambda values within a permissible range, and preferably to cause lambda values to approach optimum levels. This control is hindered by the fact that engine performance and exhaust emissions may change over time and/or may not correlate precisely with pre-calibrated characteristics when the engine is operated in the field under varying operating conditions. As a result, given air and fuel supplies and a given EGR ratio may not achieve a predetermined lambda at prevailing engine operation conditions. 
     This problem could be alleviated through closed loop lambda control using EGO (EGO) concentration as a feedback, it being recognized that EGO concentration correlates directly to lambda. However, closed loop lambda control based on desired EGO concentration is complicated by a variety of factors. The desired EGO concentration can change significantly depending on prevailing operating conditions, fuel quality, and other factors affecting fuel and air supply. Lambda variations and variations in combustion efficiency also hinder the determination of a desired EGO concentration. In addition, even if the desired EGO content can be precisely calculated, the lag between the generation of the fuel demand signal and the resultant EGO concentration determination hinders real-time feedback of lambda control using EGO concentration measurements. 
     The need therefore has arisen to provide lambda control in gaseous fueled compression ignition engines using a closed loop feedback in view of the variations in operating conditions and fuel quality, and in view of limitations imposed by feedback loop timing. 
     SUMMARY OF THE INVENTION 
     In accordance with a preferred aspect of the invention, a computer-implemented method is implemented for correcting deviations between a predicted gas excess air ratio and the actual gas excess air ratio in a compression ignited natural gas engine. The method includes calculating or predicting a gas excess air ratio for the engine based on at least one detected current operating parameter and calculating a predicted exhaust gas oxygen (EGO) concentration based on the determined gas excess air ratio. A time-based filtered value dependent on this value is compared to a time-based filtered measured EGO concentration value. The resultant EGO concentration deviation value may be used to generate a corrected gas excess air ratio for open loop control. Both predicted and measured gas excess air ratios may be corrected 
     In accordance with another aspect of the invention, the time based filtering may compensate for the lag between the time that fuel is demanded for a given combustion cycle and the time that the resultant EGO concentration for that cycle is measured. 
     In accordance with yet another aspect of the invention, the method further include calculating at least a lean corrected gas excess air ratio limit, a desired corrected gas excess air ratio, and a rich corrected gas excess air ratio limit. 
     In accordance with another aspect the invention, a gaseous fueled compression ignition engine is provided having a control system providing adaptive feedback control of excess air ratio using a technique generally as described above. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       A preferred exemplary embodiment of the invention is illustrated in the accompanying drawings in which like reference numerals represent like parts throughout, and in which: 
         FIG. 1  is a schematic view of a gaseous fueled compression ignition engine constructed in accordance with a preferred embodiment of the invention and of fuel supply systems for the engine; 
         FIG. 2  is a schematic view of the engine of  FIG. 1  and of the air supply system for the engine; 
         FIG. 3  is a partially schematic, sectional side elevation view of a cylinder of the engine of  FIGS. 1 and 2  and of associated engine components; 
         FIG. 4  is a schematic control diagram of the engine of  FIGS. 1 and 2 ; 
         FIG. 5  is a flowchart illustrating a preferred computer-implemented technique for implementing the feedback linearization for lambda control for the engine of  FIGS. 1 and 2 ; 
         FIG. 6  is a graph illustrating a linearized predicted oxygen mole fraction; 
         FIG. 7  is a graph illustrating allowable exhaust oxygen mole fraction errors; and 
         FIG. 8  is a graph illustrating defined regions of interest for the exhaust oxygen mole fraction. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Referring now to  FIGS. 1-3 , an engine  10  is illustrated that incorporates a control system constructed in accordance with a preferred embodiment of the invention. Before discussing the engine and the associated control system in detail, it must be emphasized that they are exemplary only and that the invention as claimed herein is usable with a wide variety of dual fuel engines incorporating a wide variety of gaseous fuel supply systems, liquid fuel supply systems, and air supply systems. 
     The exemplary engine  10  illustrated in  FIGS. 1-3  is a compression ignition-type internal combustion engine having a plurality of cylinders  12 , each capped with a cylinder head  14  ( FIG. 3 ). As is also shown in  FIG. 3 , a piston  16  is slidably disposed in the bore of each cylinder  12  to define a combustion chamber  18  between the cylinder head  14  and the piston  16 . Piston  16  is also connected to a crankshaft  20  in a conventional manner. Conventional inlet and exhaust valves  22  and  24  are provided at the end of respective passages  26  and  28  in the cylinder head  14  and are actuated by a standard camshaft  30  so as to control the supply of an air/fuel mixture to and the exhaust of combustion products from the combustion chamber  18 . Gases are supplied to and exhausted from engine  10  via an intake air manifold  34  and an exhaust manifold  35 , respectively. However, unlike in conventional engines, a throttle valve which would normally be present in the intake manifold  34  is absent or at least disabled, thereby producing an “unthrottled” engine. An intake air control system may also be provided. 
     The engine  10  typically will be fueled alternatively by pilot ignited gas (“gas mode”) or by diesel fuel only (diesel mode). It will most typically be fueled by pilot ignited gas over part of the speed/load range of the engine  10  and by diesel only during the remainder of the speed/load range. Depending on factors such as the desired application and the capabilities of the various components, it could be fueled by pilot ignited gas over the full speed/load range of the engine. The present invention is applicable to all compression ignited natural gas engines. 
     Gaseous fuel could be supplied via a single metering valve discharging into a single throttle body at the entrance of the manifold  34 , via a similarly-situated mechanically controlled valve, or even via a plurality of high pressure direct injector, each of which injects fuel directly into one of the combustion chambers  18 . In the illustrated embodiment, however, a separate external injector  40  is provided for each cylinder  12 . Each injector  40  receives natural gas, propane, or another gaseous fuel from a common tank  39  and a manifold  36  and injects fuel directly into the inlet port  26  of the associated cylinder  12  via a line  41 . Gas flow to the injectors  40  can be disabled by closing a shutoff valve  43  located in the line leading to the manifold  36 . 
     The illustrated engine  10  employs multiple electronically controlled liquid fuel injectors  32  as pilot fuel injectors. Each pilot fuel injector  32  could comprise any electronically controlled fuel injector. Referring to  FIGS. 1 and 3 , each injector  32  of this embodiment is a so-called “common rail” injectors fed with diesel fuel or the like from a conventional tank  42  via a supply line or common rail  44 . Disposed in line  44  are a filter  46 , a pump  48 , a high pressure relief valve  50 , and a pressure regulator  52 . A return line  54  also leads from the injector  32  to the tank  42 . 
     Referring to  FIG. 2 , the air intake control system may include (1) an exhaust gas recirculation (EGR) subsystem permitting recirculated exhaust gases to flow from an exhaust manifold  35  to the intake manifold  34  and/or (2) a turbocharging subsystem which charges non-EGR air admitted to the intake manifold  34 . The EGR subsystem is useful for increasing combustion reactivity and extending the upper limit for optimum air fuel ratio (lambda). The EGR subsystem has an EGR metering valve  60  located in a return line  58  from the exhaust manifold  35  to the intake manifold  34 . Valve  60  has an outlet connected to an intake line  64  leading to an intake port  66  of the intake manifold  34 . A second line  62  leads from a turbo bypass valve  76  to the line  64  downstream from valve  60 . 
     As is further shown in  FIG. 2 , the turbocharging subsystem of the intake air control system includes a turbocharger  70  and an aftercooler  72  provided in line  62  upstream of the valve  60  and intake port  66 . Operation of the turbocharger  70  is controlled in a conventional manner by a turbo wastegate control valve  74  and/or a turbo air bypass valve  76 . 
     Referring now to  FIG. 4 , all of the controlled components of the engine are controlled via a control system that includes multiple dedicated controllers  100  and  102  connected to one another via a communications link  104  as disclosed, for example, in U.S. Pat. No. 6,694,242. (The term “dedicated controller,” as used herein, means that the controller controls only the engine  10 , not other engines slaved to or otherwise operably connected to the engine.) In the illustrated embodiment, the controller  100  is a dual fuel controller and the controller  102  is a diesel controller. The dual fuel controller  100  is configured, based on information received directly from sensors and from information received from the diesel controller  102  via the link  104 , to control operation of the gaseous fuel supply system. The diesel controller  102  is configured, based on information received directly from sensors and from information received from the dual fuel controller  100  via the link  104 , to control operation of the liquid fuel supply system. The controllers  102  and  104  are also preferably programmed so that the engine  10  can be operated in both a dual fuel mode and a diesel only mode. In this case, dual fuel controller  100  is configured to control the diesel controller  102  in a master-slave relationship when the engine is operating in the dual fuel mode, and the diesel controller  102  is configured to control all aspects of engine operation when the engine  10  is operating in the diesel only mode. Both controllers  100  and  102  may comprise any of a variety of commercially available programmable systems, preferably a programmable electronic control unit (ECU). A programmable ECU that is well-suited for use as the dual fuel controller  100  is available from Clean Air Power, Inc. of San Diego, Calif. under the designation Hawk. A number of programmable ECUs are well-suited for use as the diesel controller  102  and are available from original equipment manufacturers of diesel engines, including Robert Bosch GmbH, Volvo, and Caterpillar, Inc. 
     The communication link  104  preferably comprise a broadband controller link such as a CAN link permitting broadband two-way communication between the controllers  100  and  102 . The controllers  100  and  102  may also additionally connected to one another by a traditional hardwire link  106 . Link  106  provides limited back-up communications capability in the event of communication network overload. Specifically, when the engine  10  is operating in dual fuel mode, the commanded liquid fuel quantity is transmitted to the diesel controller  102  from the dual fuel controller  100  by both the link  104  and by the hardwire link  106 . This redundant transmission assures timely receipt of the fuel command signal by the controller if the CAN link is temporarily busy transmitting other information. 
     Still referring to  FIG. 4 , the gaseous fuel supply system components are coupled to the dual fuel controller  100 , and the liquid fuel supply system components are coupled to the diesel controller  102 . Information required by both controllers  100  and  102  may be obtained in each case by a single sensor and transmitted to only one of the controllers. The information may then be relayed to the other controller via the link  104 , thereby negating the need to incorporate redundant sensors into the control system. Examples of information obtained via a single source and shown in this manner is information indicative of intake manifold air temperature, intake manifold air pressure, pedal position, and engine speed. 
     In the illustrated embodiment, the dual fuel controller  100  receives signals from a gas pressure sensor  110 , a gas temperature sensor  112 , a universal exhaust gas oxygen sensor or “UEGO” sensor  113  and possibly other sensors collectively denoted  114 . The diesel controller  102  receives engine timing/speed signals from a camshaft speed/timing sensor  84 , which is also preferably connected directly to the dual fuel controller  100 , and from a crankshaft speed/timing sensor  85 . The diesel controller  102  also receives signals from a boost pressure sensor  86 , an intake manifold air temperature sensor  88 , an atmospheric air pressure sensor  90 , an oil pressure sensor  92 , a coolant temperature sensor  94 , a diesel fuel temperature sensor  96 , an ambient air temperature sensor  98 , and possibly other sensors, collectively denoted  99 . One or both of the controllers  100 ,  102  also may ascertain exhaust gas absolute pressure (EGAP), either directly from an EGAP sensor or indirectly from an exhaust back pressure (EBP) sensor (neither of which is shown). Other values, such as indicated mean effective pressure (IMEP) and the volume and quantity of gas (Q gas  and V gas , respectively) injected may be calculated by the controller(s)  100  and/or  102  using data from one or more of the sensors  80 - 99  and known mathematical relationships. Still other values, such as maximum intake manifold absolute pressure (MAP max ), maximum indicated mean effective pressure (IMEP max ), maximum engine speed (RPM max ), volumetric efficiency (T vol ), and various system constants are preferably stored in a ROM or other storage device of one or both of the controllers  100  and  102 . 
     Based on these received and calculated values, the dual fuel controller  100  transmits signals to the gas injectors  40 , the gas shut-off valve  43 , the turbo wastegate control valve  74 , the TAB valve  76 , and an indicator  78 . (The indicator  78  provides a visual indication of the current operational state of the engine  10 , i.e., dual fuel mode or diesel only mode). Similarly, the diesel controller  102  is operable, based on information obtained directly from the sensors  84 - 86 , etc. and information received from the dual fuel controller  100  via the CAN  104 , to control operation of the diesel injectors  32  and possibly other equipment such as retarder solenoids  118 . 
     Link  104  can also accommodate one or more sub-system controllers, such as the illustrated controller  124  in  FIG. 4 . The controller  124  controls one or more subsystems such as the subsystem  126  in  FIG. 4  using information obtained from the sensors and/or the controllers  100  and  102  and transmitted over link  104 . The controlled subsystem  126  may, for example, be an EGR subsystem, a water injection subsystem and/or another aftertreatment and/or pretreatment subsystem. 
     In use, during operation of the system in gas mode, the dual fuel controller  100  controls operation of the gas injectors  40 , gas shut off valve  43 , turbo wastegate control valve  74 , TAB valve  76 , gas injectors  40 , and possibly other system components. The components preferably are manipulated to control lambda to optimize one or more desired engine operational characteristics as described in further detail below with reference to  FIG. 5 . The components preferably are also manipulated to control the timing and/or quantity of gaseous fuel injection and/or other characteristics of the gaseous fuel charge. The optimized characteristic(s) may, for example, be performance and/or one or more emissions. The dual fuel controller  100  also transmits a command signal to the diesel controller  102  via the CAN  104  to inject liquid fuel at a timing and quantity determined by the dual fuel controller  100 . Hence, the diesel controller  102  may be controlled in a master-slave relationship, but acts as a conduit for some information required by the dual fuel controller  100  to control engine operation. Conversely, when the engine  10  is operating in a diesel-only mode, the gas shut-off valve  43  is closed, and the engine is controlled exclusively by the diesel controller  102 . Selection between these two modes may occur manually via a suitable switch, but preferably occurs automatically based on a determined ability of the engine  10  to effectively operate in gas mode under prevailing engine operational characteristics. This determination preferably is made by the dual fuel controller  100  based on signals received directly from the sensors and/or indirectly from the diesel controller  102  via the link  104 . Preferably, in the absence of a system fault, the engine  10  runs in diesel only mode only during engine start and warm-up, and otherwise runs in dual fuel mode. 
     Turning now to  FIG. 5 , a flowchart of a routine  120  that can be implemented by the controller  100  to correct gas lambda determination is illustrated. Specifically, routine  120  may be implemented to provide modified open loop lambda control based on desired EGO concentrations. 
     The routine  120  initially calculates or predicts gas lambda as pre-calibrated for current engine operating conditions in a block  122 . The operating conditions may include, for example, current speed, current load, demanded fuel quality, MAP, etc. The predicted lambda may be determined by applying sensed prevailing engine operating conditions to a look up table of calculated lambdas that are associated with those operating conditions and that were obtained using empirical data obtained during system development. 
     In block  124 , the routine  120  then determines a predicted EGO concentration as a function of the calculated or predicted gas lambda. The predicted EGO calculation is greatly affected by tolerances stacked up from factors such as fuel delivery calibrations, speed density maps, and natural gas composition. These tolerances may be improved by the use of UEGO sensor feedback as will now be described. Assuming 100% combustion efficiency of a gas fueled engine, i.e., assuming complete combustion of the fuel mixture, the predicted EGO concentration in terms of predicted oxygen mole fraction in exhaust gas can be derived from the equation: 
                     O   2     =         (     λ   -   1     )     ⁢     (     1   +     x   4       )                 λ   ⁡     (     4.76   +     1.19   ⁢   x       )       +     x   4     -   1   +                 1   n     ⁡     [     1   +       (       4.76   ⁢   a     +     1.44   ⁢   b       )     ⁢     (       1   y     -   1     )         ]                       (     Equation   ⁢           ⁢   1     )               
Where:
 
     λ is the predicted gas lambda, 
     CH x  is the natural gas chemical formula, with x normally ranges from 3.8 to 4.0, 
     C a H b  is the liquid fuel chemical formula. For diesel fuel, a=10.8 and b=18.7, 
     y is the mole fraction of natural gas in the diesel and natural gas mixture, and 
     n is the mole fraction of hydrocarbons (CH x ) in the natural gas composition that may include inert gases such as nitrogen and normally ranges from 0.96 and 1.0. 
     The mole fraction of natural gas in the diesel and natural gas mixture will depend on the fuel quantity delivered to the combustion chamber  18 . 
     Referring now to  FIG. 6  a graph  600  illustrates the predicted oxygen mole fractions  605  in exhaust for a plurality of predicted gas lambda values  610  between the lean and rich limits, and individual predicted oxygen mole fraction in exhaust  615  for each specific predicted gas lambda, using these normal and predicted values, where x=3.9, a=10.8, b=18.7, n=0.98 and y=0.974. 
     The predicted oxygen concentration in exhaust can therefore be reasonably linearized by the straight line  620 , and a linear equation. 
     Equation 2 is the linear equation calculating the predicted oxygen mole fraction in exhaust when gas lambda is operated between the lean and rich limits, 1.3 and 1.9, respectively.
 
O 2 =0.0764λ−0.0586  (Equation 2)
 
     Turning again to the routine  120  of  FIG. 5 , the measured O 2  is then determined in block  126  using the UEGO sensor  113  of  FIG. 4 . The controller  100  then obtains a filtered measured EGO concentration value in block  128 , using a variable or fixed time based filtering factor. The filtering factor preferably is determined by accumulating the measured exhaust gas concentration over time to compensate for the time lag between the prediction of lambda at the generation of the fueling command signal and the subsequent receipt of the EGO concentration signal after the fuel is delivered, combusted, and exhausted. Predicted EGO concentration values also preferably are filtered, using the same or a different factor used to filter the measured values. 
     In an especially preferred embodiment, time based filtering of both the measured and predicted EGO concentration values categorizes the correlation between predicted and measured EGO concentrations into regions or groups of interest that, in turn, can be divided into several zones as shown in  FIG. 8 .  FIG. 8  depicts a graph  800  illustrating defined regions of interest for the exhaust oxygen mole fraction for the predicted O 2  value  805  compared to the measured O 2  value  810  as described in block  130  of routine  120 , shown in  FIG. 5 . Three regions of interest may be defined to include a Lambda_Desired_Region  820 , Lambda_Rich_Region  815  and Lambda_Lean_Region  825 . Each region may further be divided into a plurality of zones. 
     For instance, in the case of the Lambda-Lean_Region  825 , the region  825  is divided into an upper zone  830  including fractions above the defined tolerance range, a middle zone  835  including fractions within the defined tolerance range, and a lower zone  840  including fractions below the defined tolerance range. Each measured EGO concentration value is correlated with the corresponding predicted EGO concentration value and associated with the appropriate zone/region. The time based filtering factor is applied to all measured and predicted EGO concentration data associated with a given zone. According to a preferred embodiment, the time filtered measured and predicted EGO concentration values for each zone may be determined and stored as a moving average of the measured EGO concentration (Avg_Measured_O2) and a moving average of the predicted EGO concentration (Avg_Predicted_O2) in that zone. 
     The system continues to filter data until a statistically significant data sample is accumulated. For example, the filtering process may occur for a predetermined period of time such as a total operating time of an engine between switch on and switch off or a threshold number of engine revolutions, whichever is higher. Alternatively, it may occur until the data count in any one of the zones reaches a predefined threshold of, e.g., 500. The system then evaluates the collected and filtered data to determine whether lambda values need to be updated or corrected. In the presently disclosed embodiment, the Avg_Measured_O2 and Avg_Predicted_O2 values in the zone from each group that has the highest data count of the zones within that group are selected for potential evaluation, and the data for the remaining two zones in each group are discarded because they are considered to be statistically less significant. However, in an especially preferred embodiment, even the zone with the highest data count will not be evaluated unless the data count within that zone is significantly higher than the data count in the other two zones. For example, if the data count of the upper zone  830  of the Lambda_Lean region is less than 60% of the total data count of all three zones  830 ,  835  and  840 , no values will be updated the Lambda_Lean region. However, the values will be evaluated in Lambda_Rich_Limit and the Lambda_Desired if the highest data count within one of the zones of each region is above 60% of the total data count. 
     Under ideal circumstances, the filtered measured EGO concentration value will match the filtered predicted EGO concentration value within an allowable error range, and no correction would be necessary.  FIG. 7  depicts a graph  700  illustrating allowable exhaust oxygen mole fraction error ranges. Graph  700  illustrates that, for any given predicted O 2  value  705 , a tolerance range  710  of, e.g., 0.010, may be defined within an upper measured O 2  limit  715  and a lower measured O 2  limit  720 . 
     If, on the other hand, the deviation between the filtered measured and predicted EGO concentration values for the selected zone is above a designated threshold, at least one engine parameter has deviated from the calibrated value and has adversely impacted the calculation of lambda and the resultant predicted EGO concentration. In this eventuality, the routine  120  proceeds to block  132  and corrects predicted and determined gas lambda values for prevailing engine operation in the region containing that zone. 
     A preferred example of the evaluation process will now be provided to facilitate understanding of this embodiment of the invention. 
     Assume that, upon termination of the filtering phase of operation, the routine  120  has accumulated the following data. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 FILTERED DATA 
               
            
           
           
               
               
               
               
            
               
                   
                   
                 Filtered O 2   
                 Filtered O 2   
               
               
                 Region/Zone 
                 Data Count 
                 Predicted 
                 Measured 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                 Lambda Rich Region 
                 350 
                 0.050 
                 0.07 
               
               
                 Upper Zone 
               
               
                 Lambda Rich Region 
                 75 
                 0.055 
                 0.055 
               
               
                 Middle Zone 
               
               
                 Lambda Rich Region 
                 20 
                 0.045 
                 0.035 
               
               
                 Lower Zone 
               
               
                 Lambda Desired Region 
                 450 
                 0.07 
                 0.086 
               
               
                 Upper Zone 
               
               
                 Lambda Desired Region 
                 80 
                 0.068 
                 0.065 
               
               
                 Middle Zone 
               
               
                 Lambda Desired Region 
                 25 
                 0.072 
                 0.055 
               
               
                 Lower Zone 
               
               
                 Lambda Lean Region 
                 500 
                 0.090 
                 0.106 
               
               
                 Upper Zone 
               
               
                 Lambda Lean Region 
                 250 
                 0.096 
                 0.095 
               
               
                 Middle Zone 
               
               
                 Lambda Lean Region 
                 90 
                 0.088 
                 0.075 
               
               
                 Lower Zone 
               
               
                   
               
            
           
         
       
     
     In this example, evaluation is triggered by the data count in the upper zone of the Lambda Lean region reaching 500. At this time, the upper zone of Lambda Rich region, the upper zone of Lambda Desired region, and the upper zone of Lambda Lean region are all selected for evaluation because each of these three zones has more than a 60% occupancy of the data points in the corresponding region. Since the deviation between measured and predicted EGO concentrations in the evaluated zone of each of these three regions exceeds the 0.005 O 2  mole fraction limit, Lambda values for all three regions need to be corrected. 
     The measured and predicted lambdas in each region are then updated or corrected using the data shown in Table 1 as indicated below: 
     Lambda Rich Region:
 
λ Rich     —     Measured =13.09×0.07+0.767=1.68
 
λ Rich     —     Predicted =13.09×0.05+0.767=1.42
 
Lambda Desired Region:
 
λ Desired     —     Measured =13.09×0.086+0.767=1.89
 
λ Desired     —     Predicted =13.09×0.07+0.767=1.68
 
Lambda Lean Region:
 
λ Lean     —     Measured =13.09×0.106+0.767=2.15
 
λ Lean     —     Predicted =13.09×0.09+0.767=1.95
 
     The Lambda_Desired, Lambda_Rich_Limit and Lambda_Lean_Limit will then be updated or corrected as follows using the measured and predicted lambdas: 
     
       
         
           
             
               
                 λ 
                 
                   
                     Rich 
                     ⁢ 
                     _ 
                     ⁢ 
                     Limi 
                     ⁢ 
                     t 
                   
                   ⁢ 
                   
                     _ 
                     ⁢ 
                     New 
                   
                 
               
               = 
               
                 
                   1.3 
                   × 
                   
                     ( 
                     
                       1 
                       + 
                       
                         
                           1.68 
                           - 
                           1.42 
                         
                         1.42 
                       
                     
                     ) 
                   
                 
                 = 
                 1.54 
               
             
             , 
           
         
       
     
     where 1.3 is the Lambda_Rich_Limit used during the sampling period. 
     
       
         
           
             
               
                 λ 
                 
                   Desired 
                   ⁢ 
                   _ 
                   ⁢ 
                   New 
                 
               
               = 
               
                 
                   1.75 
                   × 
                   
                     ( 
                     
                       1 
                       + 
                       
                         
                           1.89 
                           - 
                           1.68 
                         
                         1.68 
                       
                     
                     ) 
                   
                 
                 = 
                 1.97 
               
             
             , 
           
         
       
     
     where 1.75 is the Lambda_Desired used during the sampling period. 
     
       
         
           
             
               
                 λ 
                 
                   
                     Lean 
                     ⁢ 
                     _ 
                     ⁢ 
                     Limi 
                     ⁢ 
                     t 
                   
                   ⁢ 
                   
                     _ 
                     ⁢ 
                     New 
                   
                 
               
               = 
               
                 
                   1.9 
                   × 
                   
                     ( 
                     
                       1 
                       + 
                       
                         
                           2.15 
                           - 
                           1.95 
                         
                         1.95 
                       
                     
                     ) 
                   
                 
                 = 
                 2.09 
               
             
             , 
           
         
       
     
     where 1.9 is the Lambda_Lean_Limit used during the sampling period. 
     Following block  132 , all average values and data counts for each zone may then be reset, and routine  120  can be reinitiated in a step  134 . 
     To the extent that they might not be apparent from the above, the scope of variations falling within the scope of the present invention will become apparent from the appended claims.