Abstract:
A device for controlling an internal combustion engine capable of estimating the amount of NOx emission within short periods of time maintaining high precision and realizing improved control performance without increasing the cost as a result of not using map data in the ROM. The device includes NOx operation means  34 A for estimating the amount of NOx in the exhaust gas from a theoretical formula and an empirical formula based upon the intake air amount Qa, intake air temperature To, pressure Pb, air-fuel ratio λ and EGR rate β, and control means for controlling at least either the NOx purifying catalyst  17  or the combustion state in the internal combustion engine in order to lower the amount of NOx emission.

Description:
BACKGROUND OF THE INVENTION  
         [0001]    1. Field of the Invention  
           [0002]    The present invention relates to a device for controlling an internal combustion engine by using a NOx purifying catalyst to reduce NOx (nitrogen oxides) in the exhaust gas. More particularly, the invention relates to a device for controlling an internal combustion engine capable of estimating the amount of NOx emission within short periods of time maintaining high precision and realizing improved control performance without increasing the cost that results when a memory having a large capacity is used.  
           [0003]    2. Prior Art  
           [0004]    Devices for controlling internal combustion engines of this kind have heretofore been provided with NOx amount estimating means for estimating the amount of NOx adsorbed by a NOx adsorbing agent as taught in, for example, Japanese Patent No. 2586739.  
           [0005]    [0005]FIG. 3 is a block diagram illustrating the constitution of a conventional device that is adapted to a gasoline engine.  
           [0006]    To avoid complexity, here, the description deals with one cylinder only. It should, however, be noted that the same constitution applies to plural cylinders.  
           [0007]    In FIG. 3, an internal combustion engine  1  includes a piston  2 , a combustion chamber  3 , a spark plug  4 , an intake valve, an intake port  6 , an exhaust valve  7  and an exhaust port  8 .  
           [0008]    The intake port  6  is coupled to a surge tank  10  through a corresponding intake pipe  9  which is provided with a fuel injection valve  11  for injecting fuel into the intake port  6 .  
           [0009]    The surge tank  10  is coupled to an air cleaner  13  through an intake duct  12  in which a throttle valve  14  is disposed. The intake duct  12  is further provided with an air flow sensor (not shown) for detecting the amount of the air taken in.  
           [0010]    On the other hand, the exhaust port  8  is connected, through an exhaust manifold  15  and an exhaust pipe  16 , to a casing  18  in which a NOx absorbing agent  17  is contained.  
           [0011]    The NOx absorbing agent  17  absorbs NOx in the exhaust gas and works as a NOx purifying catalyst.  
           [0012]    An electronic control unit (ECU)  30  comprises a digital computer which includes a ROM  32 , a RAM  33 , a CPU  34 , an input port  35  and an output port  36  which are connected to each other through a bidirectional bus  31 , as well as A/D converters  37 ,  38  inserted on the input side of the input port  35  and drive circuits  39  inserted on the output side of the output port  36 .  
           [0013]    A pressure sensor  19  is mounted in the surge tank  10  to generate an output voltage in proportion to an absolute pressure in the surge tank  10 . An output voltage of the pressure sensor  19  is fed to the input port  35  through the A/D converter  37 .  
           [0014]    An air-fuel ratio sensor  25  is mounted on the exhaust pipe  16 . An output voltage of the air-fuel ratio sensor  25  is fed to the input port  35  through the A/D converter  38 .  
           [0015]    Further, a known EGR pipe (not shown) is provided between the exhaust pipe  16  and the intake pipe  9  to recirculate part of the exhaust gas. The EGR pipe is provided with an EGR valve for adjusting the EGR amount.  
           [0016]    An idle switch  20  is attached to the throttle valve  14  to detect the idle opening degree of the throttle valve  14 . An output signal of the idle switch  20  is input to the input port  35 . Similarly, an output signal (engine rotational speed Ne) of a rotational speed sensor  26  is fed to the input port  35 .  
           [0017]    The operation of the conventional device shown in FIG. 3 will be briefly described below with reference to FIGS. 4 and 5. The control operation of the conventional device is as disclosed in detail in the above-mentioned patent publication, and is not described here.  
           [0018]    The CPU  34  in the ECU  30  constitutes NOx amount estimating means in cooperation with the ROM  32  and RAM  33 , and estimates the amount of NOx adsorbed by the NOx adsorbing agent  17 .  
           [0019]    It is difficult to directly detect the amount of NOx adsorbed by the NOx adsorbing agent  17 . Therefore, the amount of NOx in the exhaust gas emitted from the engine  1  is found to estimate the amount of NOx adsorbed by the NOx adsorbing agent  17  from the amount of NOx in the exhaust gas.  
           [0020]    In general, the amount of the exhaust gas emitted from the engine  1  per a unit time increases with an increase in the engine rotational speed Ne. Accordingly, the amount of NOx emitted from the engine  1  per a unit time increases with an increase in the engine rotational speed Ne.  
           [0021]    Further, as the engine load increases (i.e., as the absolute pressure PM in the surge tank  10  increases), the amount of the exhaust gas emitted from the combustion chamber  3  increases and the combustion temperature increases. As the engine load increases (absolute pressure PM in the surge tank  10  increases), therefore, the amount of NOx emitted from the engine  1  per a unit time increases.  
           [0022]    [0022]FIG. 4 is a diagram illustrating the amount of NOx emitted from the engine  1  per a unit time, and wherein the values found through experiment are related to the absolute pressure PM (ordinate) in the surge tank  10  and the engine rotational speed Ne (abscissa).  
           [0023]    In FIG. 4, the continuous curves represent the same amounts of NOx.  
           [0024]    As shown in FIG. 4, the amount of NOx emitted from the engine  1  per a unit time increases with an increase in the absolute pressure PM in the surge tank  10  and with an increase in the engine rotational speed Ne.  
           [0025]    The amounts of NOx shown in FIG. 4 have been stored in advance in the ROM  32  in the form of map data N 11  to Nij shown in FIG. 5.  
           [0026]    The map data shown in FIG. 5 vary depending upon other various operating conditions. When it is attempted to correctly find the amount of NOx by operating the map, a large amount of memory capacity is necessary driving up the cost.  
           [0027]    According to the conventional device of controlling the internal combustion engine as described above, the data used by the NOx amount estimating means in the ECU  30  are stored as map data N 11  to Nij as shown in FIG. 5. Therefore, the map data must be formed for every operating condition of the engine  1  and must be stored in the ROM  32 , requiring laborious work and extended periods of time and driving up the cost.  
         SUMMARY OF THE INVENTION  
         [0028]    The present invention was accomplished in order to solve the above-mentioned problem, and has an object of providing a device for controlling an internal combustion engine by estimating the amount of NOx emission within short periods of time maintaining high precision and improving control performance without the need of storing great amounts of map data in the ROM and, hence, without driving up the cost.  
           [0029]    A device for controlling an internal combustion engine according to the present invention comprises:  
           [0030]    an air flow sensor provided in an intake pipe of the internal combustion engine to detect the amount of the intake air;  
           [0031]    temperature detector means and pressure detector means for detecting the temperature and the pressure of the air taken in by the internal combustion engine;  
           [0032]    air-fuel ratio detector means provided in the exhaust pipe of the internal combustion engine and for detecting the air-fuel ratio in the exhaust gas;  
           [0033]    EGR rate detector means for detecting the EGR rate of the exhaust gas recirculated into the intake air;  
           [0034]    a NOx purifying catalyst provided in the exhaust pipe of the internal combustion engine;  
           [0035]    NOx operation means for estimating the amount of NOx in the exhaust gas from a theoretical formula and an empirical formula based upon the amount of the intake air, temperature and pressure of the intake air, air-fuel ratio and EGR rate; and  
           [0036]    control means for controlling at least either the NOx purifying catalyst or the combustion state in the internal combustion engine in order to lower the amount of NOx emission.  
           [0037]    In the device for controlling an internal combustion engine according to the present invention, the theoretical formula and the empirical formula contains a correction coefficient that varies depending upon at least either the model of the internal combustion or the combustion mode.  
           [0038]    In the device for controlling an internal combustion engine according to the present invention, the combustion mode includes a stratified combustion mode and a homogeneous combustion mode.  
           [0039]    In the device for controlling an internal combustion engine according to the present invention, the NOx operation means estimates the oxygen concentration, nitrogen concentration and temperature of the combustion gas in the internal combustion engine from the theoretical formula and the empirical formula, and estimates the amount of NOx emission in the exhaust gas based upon the oxygen concentration, nitrogen concentration and temperature of the combustion gas.  
           [0040]    In the device for controlling an internal combustion engine according to the present invention, the control means controls the air-fuel ratio to control the NOx purifying catalyst.  
           [0041]    In the device for controlling an internal combustion engine according to the present invention, the control means controls at least one of the fuel injection amount, fuel injection timing, ignition timing and EGR rate of the internal combustion engine as the combustion state of the internal combustion engine.  
           [0042]    In the device for controlling an internal combustion engine according to the present invention, the air-fuel ratio detector means includes:  
           [0043]    an air-fuel ratio sensor provided in the exhaust pipe upstream of the NOx purifying catalyst and for producing an oxygen concentration detection signal depending upon the oxygen concentration in the exhaust gas; and  
           [0044]    air-fuel ratio operation means for estimating the air-fuel ratio based upon the oxygen concentration detection signal.  
           [0045]    In the device for controlling an internal combustion engine according to the present invention, the air-fuel ratio detector means includes air-fuel ratio operation means for estimating the air-fuel ratio from the fuel injection amount and from the intake air amount of the internal combustion engine. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0046]    [0046]FIG. 1 is a block diagram illustrating the constitution of an embodiment 1 of the present invention;  
         [0047]    [0047]FIG. 2 is a flowchart illustrating the estimation processing operation and the control operation according to the embodiment 1 of the present invention;  
         [0048]    [0048]FIG. 3 is a block diagram illustrating the constitution of a conventional device for controlling an internal combustion engine;  
         [0049]    [0049]FIG. 4 is a diagram illustrating the amount of NOx emitted by a general internal combustion engine per a unit time; and  
         [0050]    [0050]FIG. 5 is a diagram illustrating map data representing the amounts of NOx emission by using a conventional device for controlling the internal combustion engine. 
     
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0051]    Embodiment 1  
         [0052]    An embodiment 1 of the present invention will now be described in detail with reference to the drawings.  
         [0053]    [0053]FIG. 1 is a block diagram illustrating the constitution of the embodiment 1 of the present invention, wherein the same portions as those described above (see FIG. 3) are denoted by the same reference numerals or by putting “A” to the ends of the numerals but are not desired here again in detail.  
         [0054]    For simplifying the diagram, the A/D converters  37 ,  38  and the drive circuits  39  (see FIG. 3) in the ECU  30 A are not shown here.  
         [0055]    In FIG. 1, an intake air temperature sensor  21  is provided on the upstream of the air cleaner  13  in the intake pipe  9  to detect the temperature To of the intake air.  
         [0056]    Further, an air flow sensor  22  is provided on the downstream of the air cleaner  13  in the intake pipe  9  to detect the flow rate Qa of the intake air.  
         [0057]    The pressure sensor  19  detects the pressure Pb in the intake pipe  9  as the pressure of the intake air, and substantially works as an intake-air-pressure sensor.  
         [0058]    The intake air pressure Pb, intake air temperature To and intake air flow rate Qa are fed, together with the air-fuel ratio λ from the air-fuel ratio sensor  25 , to the input port  35  in the ECU  30 A as various sensor data representing the operating conditions of the engine  1 .  
         [0059]    As various sensor means, further, there is provided an EGR sensor for detecting the EGR rate from the opening degree β of the EGR valve that adjusts the EGR amount in the EGR pipe (not shown). The EGR rate representing the amount of the exhaust gas recirculated into the intake air is fed to the input port  35 .  
         [0060]    As operating conditions, further, not only the engine rotational speed Ne and the accelerator opening degree a but also the intake air amount Qa from the air flow sensor, are fed to the input port  35 .  
         [0061]    The CPU  34 A in the ECU  30 A includes NOx operation means for estimating the amount of NOx emission in the exhaust gas from a theoretical formula and an empirical formula (described later) based upon the intake air amount Qa, intake air temperature To, intake air pressure Pb and upon the air-fuel ratio λ and the EGR rate (EGR opening degree β).  
         [0062]    The CPU  34 A includes control means for controlling at least either the NOx purifying catalyst  17  or the combustion state in the engine  1  so as to decrease the amount of NOx emission.  
         [0063]    Here, the theoretical formula and the empirical formula contain a correction coefficient that has been stored in advance in the ROM  32 A and that varies depending upon at least either the model of the engine  1  or the combustion mode.  
         [0064]    The combustion modes may include a stratified combustion mode of the case of an direct cylinder injection engine and a homogeneous combustion mode during the normal stoichiometric operation control.  
         [0065]    The NOx operation means in the CPU  34 A estimates the oxygen concentration, nitrogen concentration and temperature of the combustion gas in the engine  1  from the theoretical formula and the empirical formula, and estimates the amount of NOx emission in the exhaust gas based upon the oxygen concentration, nitrogen concentration and temperature of the combustion gas.  
         [0066]    The control means in the CPU  34 A controls the air-fuel ratio λ to control the NOx purifying catalyst  17 .  
         [0067]    The control means in the CPU  34 A further controls at least one of the fuel injection amount, fuel injection timing, ignition timing and EGR rate of the engine  1  as the combustion state of the engine  1 .  
         [0068]    As shown, the air-fuel ratio detector means is constituted by an air-fuel ratio sensor  25  provided in the exhaust pipe  16  upstream of the NOx purifying catalyst  17  and for producing an oxygen concentration detection signal depending upon the oxygen concentration in the exhaust gas, and air-fuel ratio operation means in the CPU  34 A for estimating the air-fuel ratio A/F based upon the oxygen concentration detection signal.  
         [0069]    Further, the air-fuel ratio detector means may be constituted by air-fuel ratio operation means in the CPU  34 A for estimating the air-fuel ratio A/F from the fuel injection amount and the intake air amount Qa of the engine  1 .  
         [0070]    Next, described below is the operation for estimating the amount of NOx emission according to the embodiment 1 of the present invention shown in FIG. 1.  
         [0071]    First, NOx (nitrogen oxide) formed by the engine  1  comprises chiefly Zeldvich NO (nitrogen monoxide), the reaction mechanism being expressed by the following formulas (1) and (2), 
         N2+O→NO+N  (1) 
         N+O2→NO+O  (2) 
         [0072]    The rate of NO formation based on the above formulas (1) and (2) is expressed by the following formulas (3) and (4),  
                      [   NO   ]            t       =           k        [     N                 2     ]            [     O                 2     ]         1   /   2                       (         k      mol     /     m   3          s     )               (   3   )               k   =     4.52   ×     10   15          T       -   1     /   2            exp        (     -     69460   T       )                 (   4   )                               
 
         [0073]    In the formula (3), [NO], [N2] and [O2] are concentrations of NO, N2 (nitrogen) and O2 (oxygen) and in the formula (4), T is a temperature.  
         [0074]    The combustion reaction mechanism in the engine  1  is expressed by the following formula (5),  
                 C                 8      H                 18     +       λ   15          (       12.5      O                 2     +     47      N                 2       )       +     β        {       8      CO                 2     +     9      H                 2      O     +     12.5        (       λ   15     -   1     )       +     47        λ   15        N                 2       }         →       (     1   +   β     )          {       8      CO                 2     +     9      H                 2      O     +     12.5        (       λ   15     -   1     )        O                 2     +     47        λ   15        N                 2       }               (   5   )                               
 
         [0075]    In the formula (5), β is an EGR rate and λ is an air-fuel ratio.  
         [0076]    The concentrations [N2] and [O2](kmol/m3] of N2 and O2 are expressed by the following formulas (6) and (7),  
                 [     N                 2     ]     =         47        (     λ   /   15     )          (     1   +   β     )                   ɛ                 P   ×     273   /     T   0           22.4        (     1   +   β     )          (     4.5   +     59.5        (     λ   /   15     )         )         =       47        (     λ   /   15     )                   ɛ                 P   ×     273   /     T   0           22.4        (     4.5   +     59.5        (     λ   /   15     )         )                                (   6   )                 [     O                 2     ]     =         12.5        (       (     λ   /   15     )     -   1     )          (     1   +   β     )                   ɛ                 P   ×     273   /     T   0           22.4        (     1   +   β     )          (     4.5   +     59.5        (     λ   /   15     )         )         =       0.558   ×     (       (     λ   /   15     )     -   1     )                   ɛ                 P   ×     273   /     T   0           (     4.5   +     59.5        (     λ   /   15     )         )                 (   7   )                               
 
         [0077]    In the formulas (6) and (7), ε is a compression ratio, P (atom) is an intake air pressure, and To (K) is an intake air temperature.  
         [0078]    Further, the nitrogen concentration [N2] is approximately expressed by the following formula (8),  
               [     N                 2     ]     =         47                 ɛ                 P   ×     273   /     T   0           22.4   ×   64       =       8.95                 ɛ                 P       T   0                 (   8   )                               
 
         [0079]    From the above formulas (3), (4), (7) and (8), the concentration [NO] of NO emitted per a stroke (per a combustion) is expressed by the following formulas (9) and (10),  
               [     N                 O     ]     =       60     n   E       ×   4.52   ×     10   15     ×     T       -   1     /   2            exp        (     -     69460   T       )       ×       8.95                 ɛ                 P       T   0       ×       [       0.558   ×     (       (     λ   /   15     )     -   1     )                   ɛ                 P   ×     273   /     T   0           4.5   +     59.5        (     λ   /   15     )           ]       1   /   2                       (       k      mol     /     m   3       )               (   9   )                            =         3.0   ×     10   19         n   E            T       -   1     /   2            exp        (     -     69460   T       )       ×       [         (     λ   /   15     )     -   1       4.5   +     59.5        (     λ   /   15     )           ]       1   /   2                       ɛ     3   /   2            p     3   /   2              T   0         -   3     /   2                   (   10   )                               
 
         [0080]    In the above formulas (9) and (10), nE (rpm) is an engine rotational speed Ne.  
         [0081]    Here, if the amount of fuel injection per a stroke is denoted by Gf (kg), the amount of NO Gno(kg) emitted by a four-cycle engine per a stroke is expressed by the following formulas (11) and (12),  
               G   no     =                    [   NO   ]     2          (       k      mol     /     m   3       )     ×       M   NO          (     kg   /     k      mol       )       ×   amount                 of                 exhaust                 gas                   (     m   3     )                                            =         3.0   ×     10   19         2        n   E              T       -   1     /   2            exp        (     -     69460   T       )       ×       [         (     λ   /   15     )     -   1       4.5   +     59.5        (     λ   /   15     )           ]       1   /   2       ×     ɛ     3   /   2       ×     P     3   /   2       ×       T   0         -   3     /   2       ×   30   ×     {         G   f     114     ×     (     4.5   +     59.5        λ   15         )     ×   22.4     }                     (   kg   )                 (   11   )                            =         8.84   ×     10   19         n   E            T       -   1     /   2            exp        (     -     64900   T       )       ×       {       (       (     λ   /   15     )     -   1     )          (     4.5   +     59.5        (     λ   /   15     )         )       }       1   /   2       ×     G   f     ×     ɛ     3   /   2       ×     P     3   /   2       ×       T   0         -   3     /   2                       (   kg   )                 (   12   )                               
 
         [0082]    Further, a total amount of NO GnoT (kg) emitted per a unit time is expressed by the following formulas (13) and (14),  
                 G   noT     =       CG   no            n   E     60                            (   13   )                            =     14.7   ×     10   17     ×     T       -   1     /   2            exp        (     -     64900   T       )       ×                  {       (       λ   /   15     -   1     )          (     4.5   +     59.5        (     λ   /   15     )         )       }       1   /   2       ×                G   f     ×     ɛ     3   /   2       ×     P     3   /   2       ×       T   0         -   3     /   2       ×   C                   (     kg   /   s     )                 (   14   )                               
 
         [0083]    In formulas (13) and (14), C is a correction coefficient.  
         [0084]    As the temperature T, there is typically employed a maximum adiabatic frame temperature of the case where there is no heat loss. The flame temperature T is expressed by the following formulas (15) to (17) by using an average specific heat at constant pressure Cp, an intake air temperature To and a polytropic index κ,  
               T   =       (         Δ                 H         c   p        G       +     T   0       )     ×     ɛ     κ   -   1                              (   15   )                 =       (         10670   ×   0.114                 c   p          (     1   +   β     )            {       8   ×   0.044     +     9   ×   0.018     +                     12.5        (       λ   /   15     -   1     )     ×   0.032     +     47   ×   0.028        (     λ   /   15     )                 +     T   0       )     ×     ɛ     κ   -   1                              (   16   )                 =       (       1216         c   p          (     1   +   β     )            (     0.114   +     0.916        (     λ   /   15     )         )         +     T   0       )     ×     ɛ     κ   -   1                              (   17   )                               
 
         [0085]    Cp: average specific heat at constant pressure (kcal/kg° C.),  
         [0086]    To: intake air temperature (K),  
         [0087]    κ: polytropic index.  
         [0088]    Here, the average specific heat at constant pressure Cp is approximated by the following formula (18), 
         c p =0.518-0.219(λ/15)+0.0521(λ/15) 2   (18) 
         [0089]    Accordingly, the flame temperature T is expressed by the following formulas (19) and (20),  
             T   =       (       1216           (     0.518   -     0.219        (     λ   /   15     )       +                       (     λ   /   15     )     2     )          (     1   +   β     )          (     0.114   +     0.916        (     λ   /   15     )         )               +     T   0       )     ×     ɛ     κ   -   1                 (   19   )                            =       [       1216        (     1   -   β     )          {     3.305   -     0.5346        (     λ   /   15     )         }       +     T   0       ]     ×                ɛ     κ   -   1                   (   20   )                               
 
         [0090]    If the formula (20) is substituted for the above formula (14), there is obtained the following formula (21),  
               G   noT     =     6.88   ×     10   17     ×       (       [       1216        (     1   -   β     )          {     3.305   -     0.5346        (     λ   /   15     )         }       +     T   0       ]     ×     ɛ     κ   -   1         )         -   1     /   2       ×     exp        (     -     64900       [       1216        (     1   -   β     )          {     3.305   -     0.5346        (     λ   /   15     )         }       +     T   0       ]     ×     ɛ     κ   -   1             )       ×       {       (       λ   /   15     -   1     )          (     4.5   +     59.5        (     λ   /   15     )         )       }       1   /   2       ×                G   f     ×     ɛ     3   /   2       ×     P     3   /   2       ×       T   0         -   3     /   2       ×   C                   (     kg   /   s     )               (   21   )                               
 
         [0091]    The formula (21) can be further approximated as expressed by the following formulas (22) to (24), 
           G   noT   =f (λ) g (β) h (ε) i ( TO ) ×P   3/2   ×G   f   ×C   (22) 
         =14.7×10 17    
         ×(−1.839×10 −7 +4.2374×10 −8 λ−3.9847×10 −9 λ 2   
         +1.9701×10 −10 λ 3 −5.415×10 −12 λ 4 +7.8535×10 −14 λ 5 −4.698×10 −16 λ 6 ) 
         ×(1−14.27β+69.16β 2 −110.97 β 3 ) 
         ×(1.693−0.004644T 0 +7.776×10 −6 T 0   2 ) 
         ×(−6.26+1.98ε) ×P   3/2   ×G   f   ×C   (23) 
           G   noT   =f (λ) g (β) h (ε) i ( TO ) ×P   3/2   ×G   f   ×C    
         =(−1.839×10 −7 +4.2374×10 −8 λ−3.9847×10 −9 λ 2   
         +1.9701×10 −10 λ 3 −5.415×10 −12 λ 4 +7.8535×10 −14 λ 5 −4.698×10 −16 λ 6 ) 
         ×(1−14.27β+69.16β 2 −110.97β 3 ) 
         ×(1.693−0.004644T 0 +7.776×10 −6 T 0   2 ) 
         ×(−6.26+1.98ε) ×P   3/2   ×G   f   ×C   0   (24) 
         [0092]    In the formulas (22) to (24), C and C 0  are correction coefficients which vary depending upon the model of the engine  1  and the combustion mode (stratified combustion, homogeneous combustion).  
         [0093]    The amount of NOx emitted per a unit time is calculated based on the formula (21), (23) or (24) from the thus detected air-fuel ratio λ, EGR rate β, intake air pressure Pb and intake air temperature To, and is integrated to estimate the total amount of NOx emission QNT as expressed by the following formula (25) and (26), 
         QNT=∫G noT dt  (25) 
         =ΣG noT Δt  (26) 
         [0094]    Next, the procedure for processing NOx according to the embodiment 1 of the invention will be described with reference to a flowchart of FIG. 2.  
         [0095]    In FIG. 2, first, operating conditions (accelerator opening degree α, EGR rate β, air-fuel ratio γ, engine rotational speed Ne, intake pipe pressure Pb, intake air amount Qa, intake air temperature To, etc.) of the engine  1  are detected from various sensor means (step S 1 ).  
         [0096]    Then, depending upon the operating conditions, a target torque Tqo is set (step S 2 ), a target air-fuel ratio λo is set (step S 3 ), and a target EGR opening degree βo is set (step S 4 ).  
         [0097]    Next, the NOx (NO) concentration [NO], oxygen concentration [O2] and nitrogen concentration [N2] in the combustion gas of the engine  1  are estimated in compliance with the above formulas (6) to (10), and a maximum adiabatic flame temperature T of when there is no heat loss is estimated as the temperature of the combustion gas in compliance with the formulas (19) and (20) (step S 5 ).  
         [0098]    Thereafter, the amount of NOx emission QNT in the exhaust gas is estimated in compliance with the above formulas (22) to (26) based on the oxygen concentration [O2], nitrogen concentration [N2] and the combustion gas temperature T (step S 6 ), and the air-fuel ratio λ is controlled and the NOx purifying catalyst  17  is controlled to purify the amount of NOx emission QNT (step S 7 ).  
         [0099]    By using the theoretical formula and empirical formula based upon the air-fuel ratio λ, EGR rate β, intake air pressure Pb and intake air temperature To from various sensor means, it is allowed to operate the amount of NOx emission QNT within short periods of time and highly precisely without increasing the memory capacity.  
         [0100]    That is, there is no need of forming a great amount of data to meet various operation modes, and the adjustment may be effected depending upon the combustion mode (stratified combustion, homogeneous combustion) and by using several correction coefficients (e.g., see C of the formula 23)) corresponding to a change in the model of the engine  1 . Thus, the control operation can be executed depending upon the individual engines  1  easily and in short periods of time.  
         [0101]    Therefore, the NOx purifying catalyst  17  is effectively controlled depending upon the amount of NOx emission QNT that is highly precisely estimated within a short period of time thereby to decrease the amount of NOx emission QNT.  
         [0102]    The NOx purifying catalyst  17  was controlled above depending upon the amount of NOx emission QNT. It is, however, also allowable to control the combustion condition operation quantities of the engine  1  so as to decrease the amount of NOx emission QNT.  
         [0103]    In this case, the combustion condition operation quantities controlled by the ECU  30  include a fuel injection amount, a fuel injection timing, an ignition timing and an EGR rate shown in FIG. 1.  
         [0104]    Further, the air-fuel ratio sensor  25  provided in the exhaust pipe  15  on the upstream of the NOx purifying catalyst  17  was used as the air-fuel ratio detector means. The operation, however, may be executed by using the intake air amount Qa from the air flow sensor  22  provided in the intake pipe  9  and the fuel injection quantity controlled by the ECU  30 A.  
         [0105]    In this case, the air-fuel ratio λ is estimated in the ECU  30 A from the air flow rate detection value Qa and the fuel injection amount (control quantity of the ECU  30 A).  
         [0106]    Further, the NOx absorbing agent  17  was used as the NOx purifying catalyst. It is, however, also allowable to use any other NOx purifying catalyst.