Abstract:
A method and apparatus determine exhaust gas temperature and control the heater of a heated exhaust gas oxygen sensor. Heater failures are diagnosed based on the level of current flowing through the heater. Exhaust gas temperature is determined by using a Kalman filter. The exhaust gas temperature sensor is eliminated while maintaining a high degree of accuracy. Current flowing through the heater is used to calculate the temperature of the heater. The temperature of the heater is compared to a desired temperature range and the current to the heater is adjusted to maintain the desired temperature range.

Description:
FIELD OF THE INVENTION 
     This invention relates to control systems for an internal combustion engine, and more particularly to the measurement of exhaust gas temperature and the control of a heater of an exhaust gas oxygen sensor for an internal combustion engine. 
     BACKGROUND OF THE INVENTION 
     There are many strategies for controlling the air-to-fuel ratio (A/F ratio) of an internal combustion engine. One approach measures the concentration of oxygen in the exhaust gas. A controller uses the oxygen concentration to control the A/F ratio. An oxygen sensor is used to sense the concentration of oxygen in the exhaust gas. The oxygen sensor must be operated within a specific temperature range to accurately sense the concentration of oxygen in the exhaust. Typically, the oxygen sensor must be operated between 650 and 850° C. to provide accurate results. Until the sensor reaches the operating temperature range, the output of the oxygen sensor cannot be used to control the A/F ratio. A heater is used to raise and maintain the temperature of the oxygen sensor within the operating temperature range. If current continues to flow through the heater after the oxygen sensor reaches the operating temperature range and the exhaust temperature is high, the heater overheats and may be damaged. 
     Monitoring exhaust gas temperature is also important for emissions control. The level of emissions processed by the catalytic converter is dependent upon the temperature of the catalyst. The temperature of the catalyst, in turn, depends on the exhaust gas temperature. The exhaust gas temperature must be monitored to prevent the catalytic converter from overheating. Usually, the exhaust gas temperature is measured using a sensor or is calculated from the operating conditions of the engine. The use of a temperature sensor is more accurate but generally costs more than using estimation techniques. 
     SUMMARY OF THE INVENTION 
     In a vehicle including an engine, an exhaust, and an exhaust gas oxygen sensor with a sensor heater, a system according to the present invention estimates exhaust gas temperature. The system includes a first sensor that measures heater current though the heater. A second sensor measures a first engine operating parameter. A controller communicates with the first and second sensors and calculates an exhaust gas temperature value using a Kalman filter. 
     In other features of the invention, the Kalman filter receives the first engine operating parameter and the heater current as inputs. The second sensor is a mass flow rate sensor and the first engine operating parameter is a mass flow rate of the exhaust gas. 
     In yet other features, the controller maintains a temperature of the heater within an operating temperature range. A voltage sensor generates a sensor voltage signal based on voltage across the exhaust gas oxygen sensor. The controller calculates current through the heater based upon the sensor voltage signal and a sensor resistance. The controller calculates total resistance based upon the current through the heater and a voltage drop across the heater. The controller calculates a resistance of the heater based on a difference between the total resistance and the sensor resistance. The controller calculates a temperature of the heater based on the heater resistance. The controller calculates an error signal based on a difference between the heater temperature and the operating temperature range and varies a temperature of the heater based on the error signal. The controller generates an estimate of oxygen concentration in the emissions. 
     In other features of the invention, the exhaust gas temperature is used to control at least one of engine diagnostics and engine control. 
     Further areas of applicability of the present invention will become apparent from the detailed description provided hereinafter. It should be understood that the detailed description and specific examples, while indicating the preferred embodiment of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The various features, advantages, and other uses of the present invention will become more apparent by referring to the following detailed description and drawings in which: 
     FIGS. 1 and 2 illustrate heat transfer in a heated exhaust gas oxygen sensor; 
     FIG. 3 is a functional block diagram of the control system according to the present invention; 
     FIG. 4 is a flowchart of an algorithm performed by the present invention; 
     FIG. 5 is a flowchart that is used to control the oxygen sensor heater; and 
     FIG. 6 is a flowchart that is used to determine exhaust gas temperature. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The following description of the preferred embodiment(s) is merely exemplary in nature and is in no way intended to limit the invention, its application, or uses. 
     The first law of thermodynamics for a closed system containing a fixed mass of a solid over a time interval Δt(s) states that the change in internal energy within the system is equal to the heat transferred into the system plus the heat generated within the system.               u          t       =     Q   +     Q   v                              
     where               u          t       =     Change                 in                 internal                 energy                 within                 the                 system                            
     {dot over (Q)}=Heat transferred into the system 
     {dot over (Q)} v =Heat generated within the system 
     Therefore, the oxygen sensor sub-system is defined using the following three relations for the system.              e   H          v   H          c     v   H                   T   H            t         =       Q   .     VH       ,     
              e   H          v   E          c   E                 T   E            t         =         Q   .     EH     +       Q   .       v   E       +       Q   .       E   g           ,     
              e   g          v   g          c   p                 T   g            t         =         Q   .       g   E       +       Q   .       v   g           ,                          
     The amount of heat transferred from the element to the exhaust gas is approximately 0. The heat transferred from the element to the exhaust gas  {dot over (Q)}   Eg =0. There is no heat generated within the element and the exhaust gas therefore both  {dot over (Q)}   V     E    and  {dot over (Q)}   Vg =0. Hence, we have the following equations to define the sub-system.              e   H          v   H          c     v   H                   T   H            t         =       Q   .     VH       ,     
              e   E          v   E          c     v   E                   T   E            t         ≡       Q   .     EH       ,     
            e   g          v   g          c     p   s         ,              T   g            t       ≡       Q   .       g   E         ,                          
     where,            Q   .     HE     =           K   H          A   H         L   H            (       T   H     -     T   E       )                              
     where            K   H          A   H         L   H                            
     is the thermal resistance of the heater and e H v H c V     H    is the thermal capacitance.              Q   .     EH     =           K   E          A   E         L   E            (       T   H     -     T   E       )         ,                          
     where            K   E          A   E         L   E                            
     is the thermal resistance of the element and e H v H c V     H    is the thermal capacitance.  {dot over (Q)}   VH =Ri 2 . where R H =K o +K 1 T H −273K 1   {dot over (Q)}   g     E   =h c (T g −T E ) where h c  is the convective heat transfer coefficient. 
     The convective heat transfer coefficient is given by          h   c     =         .023                   K   .6          eg   .4          c     P   g     .4           D   g   .2          vv   g   .4              S   g   .8                              
     and the velocity of exhaust is related to the mass flow rate of exhaust gas as follows: m=e g A P     g   S g . Therefore, we have          S   g     =       m       e   g          A     P   g           .                            
     Substituting into h c  gives          h   c     =         .023                   K   g   .6          e   g     -   .4            c     P   g     .4           D   g   .2          vv   g   .4          A     P   g     .8                m   .8     .                              
     Finally, the system equations that define the oxygen sensor heater sub-system are:                    e   H          v   H          c   vH                 T   H            t         =         K   o          i   2       +       K   1          T   H          i   2       -     273                   K   1          i   2           ,           (   1   )                     e   E          v   E          c     v   g                   T   E            t         =             K   E          A   E         L   E            T   H       -           K   E          A   E         L   E            T   E           ,           (   2   )                     e   g          v   g          c     p   g                   T   g            t         =         h   c          T   g       -       h   c          T   e           ,           (   3   )                                
     Let,          B   =       .023                   K   .6          e   g     -   .4            c     P   g     .4           D   g   .2          v   g   .4          A     p   g     .8           ,                          
     Then, after rearranging and substituting for the convective heat constant, the system is defined as,                         T   H            t       =           K   o         e   H          v   H          c     v   H                i   2       +         K   1         e   H          v   H          c     v   H                T   H          i   2       -         273                   K   1           e   H          v   H          c     v   H                i   2           ,           (   1   )                          T   E            t       =             K   E          A   E           L   E          e   E          v   E          c   vE              T   H       -           K   E          A   E           L   E          e   E          v   E          c     vE   H                T   E           ,           (   2   )                          T   g            t       =         B       e   g          v   g          c     p   g                m   0.8          T   g       -       B       e   g          v   g          c     p   g                m   0.8          T   E           ,           (   3   )                                
     PH=Density of heater material [kg/m 3 ]. P E =Density of element material [kg/m 3 ]. P G =Density of exhaust gases [kg/m 3 ]. V E =Volume of element [m 3 ]. V H =Volume of heater [m 3 ]. C E =Constant volume specific heat of element [J/kg ° K]. C H =Constant volume specific heat of heater [J/kg ° K]. C PG =Constant pressure specific heat of heater[J/kg ° K]. T H =Heater temperature [° K]. T E =Element temperature [° K]. T G =Exhaust gas temperature [° K]. K 0 =Heater resistance [Ω]. K l =Heater coefficient [Ω/° C.]. h c =Convective heat transfer coefficient in [w/m 2  K]. S g =Velocity of exhaust gases [m/s]. K g =Thermal conductivity of exhaust gas [w/m K]. K H =Thermal conductivity of heater [w/m K]. K E =Thermal conductivity of sensor element [w/m K]. D g =Exhaust gas pipe diameter [m]. V g =Volume of exhaust gas [m 3 ]. vv g =Kinematic viscosity of exhaust gas [m/s]. m=Mass flow rate of exhaust gas [g/s]. A pg =Cross sectional area of exhaust pipe [m 2 ]. A E =Surface area of sensor element [m 2 ]. A H =Surface area of heater [m 2 ]. L E =Thickness of sensor element [m]. L H =Thickness of heater [m]. 
     Given a nonlinear plant model:                         T   H            t       =           K   o         e   H          v   H          c     v   H                i   2       +         K   1         e   H          v   H          c     v   H                T   H          i   2       -         273                   K   1           e   H          v   H          c     v   H                i   2           ,           (   1   )                          T   E            t       =             K   E          A   E           L   E          e   E          v   E          c   vE              T   H       -           K   E          A   E           L   E          e   E          v   E          c     vE   H                T   E           ,           (   2   )                          T   g            t       =         B       e   g          v   g          c     p   g                m   0.8          T   g       -       B       e   g          v   g          c     p   g                m   0.8          T   E           ,           (   3   )                                
     Let,            C   0     =       K   o         e   H          v   H          c   VH           ;                  C   1     =       K   1         e   H          v   H          c   VH           ;               C   3     =       273                   K   1           e   H          v   H          c   VH           ;                  C   4     =         K   E          A   E           L   E          e   E          v   E          c   vE           ;                         C 5 =−C 4 ; 
                 C   6     =     B       e   g          v   g          c     p   g             ;                         C 7 =−C 6   
     and linearizing at operating points, T H0 , T E0 , T G0 , i 0 , m 0 , a linear state space model for the oxygen sensor heater sub-system is given by,                                  Δ                     T   H            t       =         (       C   6          i   0   2       )        Δ                   T   H       +       (       2        C   0          i   0       +     2        C   1          T   H0          i   0       -     2        C   3          i   0         )        Δ                 i               (   1   )                          Δ                     T   H            t       =         C   4        Δ                   T   H       +       C   5        Δ                   T   E           ,           (   2   )                                Δ                     T   g            t       =                    (       C   6          m   0.8       )        Δ                   T   g       +       (       0.8        C   6          m     -   0.2            T   g0       +     0.8        C   7          T     E   0            m   0     -   0.2           )        Δ                 m     +                                               (       C   7          m   0   0.8       )        Δ                   T   E       ,                   (   3   )                                
     Let, 
     
       
           R   0   =C   1   i   0   2   , R   1 =2 C   0   i   0 +2 C   1   T   H0   i   0 −2 C   3   i   0 , 
       
     
     
       
           R   2   =C   4 , 
       
     
     
       
           R   4   =C   6   m   0.8   , R   3   =C   5 , 
       
     
     
       
           R   6   =C   7   m   0   0.8   , R   5 =0.8 C   6   m   −0.2   T   g0 +0.8 C   7   T   E0   m   0   0.2 , 
       
     
     A linearized system equation for control and estimator design is defined by the following equations:                         Δ                     T   H            t       =         R   0        Δ                   T   H       +       R   1        Δ                 i         ,           (   1   )                          Δ                     T   E            t       =         R   2        Δ                   T   H       +       R   3        Δ                   T   E           ,           (   2   )                          Δ                     T   g            t       =         R   4        Δ                   T   g       +       R   5        Δ                 m     +       R   6        Δ                   T   E           ,           (   3   )                                
     Referring now to FIG. 3, an exhaust gas oxygen sensor heater that heats the oxygen sensor is represented by a resistor R H    12 , which is a temperature dependent resistance. A current sensor resistor is represented by a resistor R S    10 . An operational amplifier  14  supplies an output voltage V amp  that is proportional to the voltage across the resistor  10  to a control module  16 . 
     One end of the resistor  10  is connected to ground  18  and the other end of the resistor  10  is connected to a drain of a MOSFET  20 . A source of the MOSFET  20 , represented by V source , is connected through the heater resistor  12  to an ignition voltage V ign . Preferably, V ign  is the operating voltage of the control module  16 . 
     The control module  16  is connected to an engine controller  22  that can be implemented as software that is executed by a processor and memory, as an application specific integrated circuit or in any other suitable manner. The controller module  16  includes a processor  24  and analog to digital (A/D) converters  26  and  28 . An exhaust gas mass flow rate sensor  29  is connected to the engine controller  22 . The controller  16  also includes read only memory (ROM), random access memory (RAM), and an input/output interface (not shown). Preferably, the converters  26  and  28  are 8-bit converters although other converters can be used. The control module  16  is activated by V ign  when the engine is started. When activated, the control module  16  executes engine control, diagnostic and maintenance operations as will be described below. In a preferred embodiment, the control module  16  is a Motorola Model No. MC68332. 
     Referring now to FIG. 4, steps performed by the processor  24  of the control module  16  are shown. Control begins at step  40 . In step  42 , the converted output voltage V amp  of the operational amplifier  14  is received by control module. In step  44 , the output voltage V amp  is used to determine the actual current flowing through the heater resistor  12 . The actual current I H =V amp /R S , where V amp  is the converted output voltage of the operational amplifier  14 ; R S  is the resistance of the sensor resistor  10 ; and I H  is the actual current through the heater  12 . 
     The processor  24  determines whether the heater is operating outside of the manufacturer&#39;s specification. In step  46 , I H  is compared to a predetermined current value. For example, a typical value that would indicate a problem with the heater is 10 −8  amps. In step  48 , if I H  is less than or equal to a predetermined current value, a diagnostic code FLAG is set equal to one. If however, I H  is greater than the predetermined value then FLAG is set equal to zero in step  50 . 
     Returning now to FIG. 3, the current I H  through the heater  12  and the diagnostic code FLAG are output by the processor  24  to the engine controller  22  that performs additional steps described below in conjunction with FIGS. 3 and 4. The controller  22  employs the inputs I H  and FLAG to generate the exhaust gas temperature  30  and a control signal  32 . The control signal  32  is converted by the D/A converter  28  and output to a voltage controlled, pulse width modulated (PWM) driver  34 . The gate of the MOSFET  20  receives a pulsed signal  36  from the PWM driver  34 . The duration of the pulses determines the amount of current that is supplied to the heater  12  and the temperature of the heater  12 . 
     Referring now to FIG. 5, steps for controlling the oxygen sensor heater are shown. Control begins at step  54 . In step  56 , the current I H  through the heater  12  is received from the control module  16 . In step  58 , the total resistance of the sensor resistor  10  and the heater resistor  12  are determined according to the following formula: 
     
       
         ( V   ign   −V   drain )/ I   H   =R   total , 
       
     
     where V ign  is the ignition voltage (in volts); V drain  is the voltage (in volts) at the drain pin of the MOSFET  20 ; I H  is the actual current through the heater  12 , as determined in step  44  of FIG. 2; and R total  is the total resistance of the current sensor resistance  10  and the heater  12 . 
     In step  60 , the resistance of the heater  12  is determined according to the following formula: 
     
       
           R   total   −R   S   =R   H , 
       
     
     R total  is the total resistance of the sense resistor  10  and the heater resistor  12 , as calculated in step  58 , R S  is the resistance of the sense resistance  10  R s  is a predetermined value based on the specification of the heater &amp; MOSFET driver. R H  is the resistance of the heater  12  in ohms. 
     Since the resistance of the heater  12  as defined by the manufacturer is R H =K 0 +(K 1 *Temperature), the measured temperature of the heater  12  is calculated in step  62  according to the following formula: 
     
       
         ( R   H   −K   0 )/ K   1   =T   1 ( t ), 
       
     
     R H  is the resistance of the heater  12  in ohms. K 0  is the heater resistance parameter in ohms. K 1  is the heater resistance coefficient in ohms per ° C. T 1 (t) is the actual temperature in degrees Celsius (° C.) of the heater  12  at time t. K 0  and K 1  are constants that depend on the wattage of the heater selected and are provided by the manufacturer of the heated exhaust gas sensor. 
     In step  64 , the actual temperature is converted to temperature in degrees Kelvin (° K) according to the following formula: 
     
       
           T ( t )= T   1 ( t )+273.15 
       
     
     In step  66 , an ERROR between the derived temperature and a desired temperature is calculated. The desired temperature is an experimentally derived constant temperature. For example, the desired temperature can be 750° C. (1023.15° K). The resultant ERROR is input into a state feedback controller in step  70 . The gains of the state feedback controller are derived as a function of the target current which also control the heater temperature of the oxygen sensor heater. 
     The control signal  32  from the state feedback controller is output by the engine controller  22  to the control module  16  in step  72 . The D/A converter  28  outputs a signal to the PWM driver  34  in step  74  to regulate the duty cycle of the PWM driver  26 . The pulsed signal  36  supplied to the gate of the MOSFET  20  in step  76  drives the MOSFET  20 . Generally, the MOSFET  20  operates as a switch that allows current to flow through the heater  12  when the MOSFET  20  is enabled. The amount of time that the MOSFET  20  is enabled varies the amount of current flowing through the heater  12 . Specifically, the current supplied to the heater  12  is represented by the formula: 
     
       
         Beta*Duty_Cycle= I   supplied , 
       
     
     Where Beta is the proportionality constant and Duty_Cycle is the duty cycle of the pulsed signal  36  generated by the PWM driver  34 . The control sequence ends at step  78 . The control sequence is preferably performed synchronously with the sampling operation. 
     Referring now to FIG. 6, steps for determining the exhaust gas temperature are shown. Control begins at step  80 . In step  82  the diagnostic code FLAG that was set in either step  48  or step  50  in FIG.  2  and the heater temperature from step  64  in FIG. 3 are polled. In step  84 , the value of FLAG is checked. If FLAG is equal to one, a disabled code is set in step  86  to signify that the exhaust gas temperature cannot be used. Control ends at step  88 . Returning to step  84 , if FLAG is not equal to one, then control calculates the exhaust gas temperature. 
     The exhaust gas temperature is preferably estimated using a Kalman estimator. The measured heater current and the mass air flow measurement are input to the Kalman estimator that calculates the oxygen sensor heater temperature, the oxygen sensor element temperature, and the exhaust gas temperature. The Kalman estimator relates each of the input variables including the measured current and the mass air flow sensor to the outputs including the exhaust gas temperature, the oxygen sensor element temperature, and the oxygen sensor heater temperature. The Kalman estimator is preferably implemented in software using the following equations. The Kalman estimator calculates the exhaust gas temperature, oxygen sensor element temperature, and oxygen sensor heater temperature at time k:          [           x   1               x   2               x   3               x   4           ]     =           [           R   4           R   6         0         R   s             0         R   3           R   2         0           0       0         R   0         0           0       0       0       1         ]            A   e              [           x   1               x   2               x   3               x   4           ]       +           [         0           0             R   1             0         ]            B   e            U   1                 y   =         [         1       1       1       1         ]            C   e              [           x   1               x   2               x   3               x   4           ]                     States   _           Input   _                 x   1     =     Δ                   T   g                                 x   2     =     Δ                   T   E                              U   1     =     Δ                 i                     x   3     =     Δ                   T   H                                   x   4     =     Δ                 m                                                           
     Using a Zero order hold and discretizing the estimator matrix results in the discrete state space representation of the estimator matrices. That is, 
      Φ e =ε A     e       T     
     
       
         Γ e =∫ T   0 ε A     c     η   dηB   e   
       
     
     
       
         
           H 
           e 
           =C 
           e 
         
       
     
     The A e , B e  and C e  are the state estimator augmented matrices and the discrete estimator system model is defined: 
     
       
           {overscore (x)} ( k +1)=Φ c   {circumflex over (x)} ( k )+Γ e   U ( k ) 
       
     
     
       
           {overscore (y)} ( k )= H   e   {overscore (x)} ( k ) 
       
     
     The estimator gains and state estimates are determined using the Kalman estimator as follows: 
     
       
           P ( k )= M ( k )− M ( k ) H   e   T   [H   e   M ( k ) H   e   T   +R   v ] −1   H   e   M ( k ); and 
       
     
     
       
           x ( k )= x ( k )− P ( k ) H   e   TR   v   −1   [y ( k )− H   e   x ( k )]. 
       
     
     The time-updated equations are: 
     
       
           M ( k +1)=Φ e   P ( k )Φ e   T   +Γ   1 R w Γ 1   T ; and 
       
     
     
       
           x ( k +1)=Φ e   x ( k )+Γ e   u ( k ). 
       
     
     P(k) is the estimate accuracy immediately after a measurement at time k. M(k) is the propagated value of P(k) and is valid just before measurement. M(k+1) is the time updated value of P(k) and is valid after measurement. Φ e , Γ e , and H e  calculated using equation 5. R v  is the noise level from the sensing activity and electronics (predetermined). x(k) are the state estimates at time k, including: x 1 (k), which is the state estimate of exhaust gas temperature at time k; and x 1  (x+1) at time k+1. x 2 (k), which is the state estimate of the sensor element temperature at time k; x 3 (k), which is the state estimate of the heater temperature at time k; and, x 4 (k), which is the state estimate of the mass air flow rate at time k. Γ 1  is the noise disturbance distribution matrix. R w  is the predetermined process noise level. 
     The output of the Kalman estimator obtained in step  96  is the exhaust gas temperature  30 , which can be used for engine control and diagnostics. Control ends at step  88  and then repeats while the engine is operating. 
     Thus, the present invention provides a unique apparatus and method capable of calculating both exhaust gas temperature and controlling the heater of an oxygen sensor. It eliminates the need for a separate temperature sensor yet maintains the accuracy of such a sensor. By controlling the amount of current through the heater, electrical consumption is reduced and the possibility of damage to the heated exhaust gas oxygen sensor due to excessive temperatures is reduced. 
     Those skilled in the art can now appreciate from the foregoing description that the broad teachings of the present invention can be implemented in a variety of forms. Therefore, while this invention has been described in connection with particular examples thereof, the true scope of the invention should not be so limited since other modifications will become apparent to the skilled practitioner upon a study of the drawings, specification, and the following claims.