Abstract:
Factors affecting the response time of a transfer system from the combustion of injected fuel to the detection of its oxygen concentration include a stroke delay time due to an engine speed, the dependence of an LAF sensor response time on an exhaust gas flow rate, a response time change of the LAF sensor due to its deterioration with time, and the like. If a hyperplane of the sliding mode is fixed without considering the above-mentioned factors affecting the response time of the transfer system, an overshoot or oscillation of a feedback system may occur at low speeds of the engine even if preferable feedback responsiveness can be achieved, for example, at high speeds of the engine. This results in aggravated exhaust emissions, degraded drivability due to torque fluctuations, and fluctuations in idle speed. 
     A hyperplane used in a control system for providing feedback control of an air-fuel ratio through sliding mode control is varied based on the factors affecting the response time of the control system within a range in which the control system can be stabilized.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    1. Field of the Invention 
         [0002]    The present invention relates to a fuel control apparatus of an engine and more particularly to control an air-fuel ratio using sliding mode control. 
         [0003]    2. Description of the Related Art 
         [0004]    When a target air-fuel ratio is in a rich range, variations of an actual air-fuel ratio relative to the target air-fuel ratio become greater. A known technique as disclosed in JP-A-2007-247426 thus makes the limit amount of a feedback factor from the sliding mode control greater than that during the state of the stoichiometric air-fuel ratio by setting the inclination of a switching function (a switching hyperplane according to an aspect of the present invention) to a value smaller than that during a time period other than the rich mode. 
       SUMMARY OF THE INVENTION 
       [0005]    It is an object of the present invention to achieve through the sliding mode control an appropriate feedback gain for a transfer system based on changes in a delay time of the transfer system during the period from the injection of fuel to the detection of its oxygen concentration. 
         [0006]    A range of a hyperplane in which the transfer system can be maintained in a stable state (converging on a target without oscillating or diverging) is first determined, and then the hyperplane is made variable within that range. The transfer system is to have a delay time as affected by stroke delay due to an engine speed (delay of an exhaust gas in reaching an LAF sensor), the dependence of the LAF sensor response on a flow rate of the exhaust gas, and changes in response time of the LAF sensor due to deterioration with time or the like. The rising speed and convergence of the sliding mode control at the time of a target change can be determined based on the magnitude relation between elements constituting the hyperplane (designated as S 1  and S 2  in the present application) within a range in which the stability of the transfer system can be maintained. An optimum transient response can therefore be achieved by determining the elements constituting the hyperplane based on the factors affecting the delay time of the transfer system. 
         [0007]    Since an optimum transient response can be achieved in each operating range of the engine (low to high engine speed and small to large intake air amount), an overshoot of an air-fuel ratio with respect to a target air-fuel ratio and delay of the air-fuel ratio in reaching that target air-fuel ratio can be suppressed, whereby exhaust emissions can be prevented from being aggravated. In addition, a phenomenon in which the actual air-fuel ratio somewhat oscillates with respect to the target air-fuel ratio can be prevented, so that a driver can drive the vehicle without feeling torque fluctuations. Further, fluctuations in idle speed due to variations in air-fuel ratio convergence can be suppressed. 
         [0008]    Since feedback response is changed according to the response delay time of the LAF sensor, deterioration of exhaust emissions due to deterioration of the LAF sensor with time or the like can also be suppressed. 
         [0009]    An aspect of the present invention thus provides a control apparatus for an engine, comprising: means for detecting the oxygen concentration of an exhaust gas of the engine; means for calculating a target air-fuel ratio according to the operating state of the engine; means for providing feedback control by sliding mode control to achieve the target air-fuel ratio using the output from the means for detecting the oxygen concentration; means for considering a transfer system during the time interval between when injected fuel is burned and when the oxygen concentration is detected; means for storing in advance a range of a hyperplane in which the sliding mode control is stable; and means for varying a hyperplane according to the state of the transfer system. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0010]      FIG. 1  is a typical control block diagram of a fuel control apparatus according to an embodiment of the present invention. 
           [0011]      FIG. 2  shows an example of an engine and its surrounding components controlled by the fuel control apparatus according to the embodiment of the present invention. 
           [0012]      FIG. 3  shows another example of the engine and its surrounding components controlled by the fuel control apparatus according to the embodiment of the present invention. 
           [0013]      FIG. 4  is a typical internal configuration of the fuel control apparatus according to the embodiment of the present invention. 
           [0014]      FIG. 5  is a typical control block diagram for air-fuel ratio feedback of the fuel control apparatus according to the embodiment of the present invention. 
           [0015]      FIG. 6  is a typical block diagram for determining a nonlinear gain of the fuel control apparatus according to the embodiment of the present invention. 
           [0016]      FIG. 7  is a typical block diagram for determining a hyperplane of the fuel control apparatus according to the embodiment of the present invention. 
           [0017]      FIG. 8  is a typical block diagram for finally determining the hyperplane of  FIG. 7 . 
           [0018]      FIG. 9  is a diagram showing an example of the time required for an exhaust gas to reach a sensor of the engine according to the embodiment of the present invention. 
           [0019]      FIG. 10  is a diagram showing an example of the dependence of the response time of an LAF sensor according to the embodiment of the present invention on an exhaust gas flow rate. 
           [0020]      FIG. 11  is a diagram showing a typical setting of a hyperplane of the fuel control apparatus according to the embodiment of the present invention. 
           [0021]      FIG. 12  is a diagram showing typical behaviors of a target air-fuel ratio and an actual air-fuel ratio of an engine including the fuel control apparatus according to the embodiment of the present invention. 
           [0022]      FIG. 13  is a flowchart showing typical general control of the fuel control apparatus according to the embodiment of the present invention. 
           [0023]      FIG. 14  is a flowchart showing details of the block diagram of  FIG. 5 . 
           [0024]      FIG. 15  is a flowchart showing details of the block diagram of  FIG. 6 . 
           [0025]      FIG. 16  is a flowchart showing details of the block diagram of  FIG. 7 . 
           [0026]      FIG. 17  is a flowchart showing details of the block diagram of  FIG. 8 . 
       
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0027]    1. First Embodiment 
         [0028]    Embodiments of the present invention will be described below with reference to the accompanying drawings.  FIG. 1  is a typical control block diagram of a fuel control apparatus employing a method for feedback controlling an air-fuel ratio of fuel, to which the present invention is applied. 
         [0029]    A block  101  is an engine speed calculation section. The block  101  counts the number of inputs of changes in electric signal per unit time, typically a pulse signal, of a crank angle sensor disposed at a predetermined angle in an engine. The block  101  then performs arithmetic operations of the count to find the engine speed per unit time. A block  102  calculates a basic fuel amount required by the engine in each operating range based on the engine speed calculated by the block  101  and an airflow rate drawn in by the engine. A block  103  calculates a correction factor of the basic fuel amount calculated in the block  102  in each operating range of the engine, using the engine speed calculated in the block  101  and the basic fuel amount as engine loads. A block  104  determines an optimum ignition timing in each operating range of the engine through map search or the like based on the engine loads of the engine speed and the basic fuel amount. A block  105  sets a target idle speed in order to maintain a predetermined level of the engine idle speed and calculates a target flow rate and an ISC ignition timing correction amount for an ISC valve control section. A block  106  determines an optimum target air-fuel ratio according to the engine operating range based on the engine loads of the engine speed and the basic fuel amount. A block  107  calculates a response delay based on an output from an air-fuel ratio sensor provided on an engine exhaust pipe and the behavior of an air-fuel ratio feedback factor to be described later, the response delay including a delay due to a deterioration of the air-fuel ratio sensor. A block  108  finds a hyperplane of a sliding mode control from the response delay of the air-fuel ratio sensor, the engine speed, an intake air amount, the target idle speed, a vehicle speed, an idle switch, and the like. A block  109  calculates, from the hyperplane found by the block  108 , the air-fuel ratio sensor output, and the target air-fuel ratio established by the block  106 , a feedback factor required for achieving a desirable air-fuel ratio with the sliding mode control as a core. A block  110  corrects the basic fuel amount calculated by the block  102 , using the correction factor calculated by the block  103 , a correction factor according to an engine coolant temperature, the air-fuel ratio feedback factor found by the block  109 , and the like. A block  111  corrects the basic ignition timing determined by the block  104 , using the ISC ignition timing correction amount of the block  105 , the correction factor according to the engine coolant temperature, and the like. Blocks  112  to  115  are fuel injectors that supply the engine with fuel based on the fuel amount calculated by the block  110 . Blocks  116  to  119  are igniters that ignite a fuel mixture flowing into a cylinder according to the required ignition timing of the engine corrected by the block  111 . A block  120  is an actuator that drives the ISC valve so as to achieve the target flow rate during idling calculated by the block  105 . In accordance with the embodiment of the present invention, the basic fuel amount calculated from the intake air amount represents the engine load; however, a negative pressure inside the intake pipe may represent the engine load. 
         [0030]      FIG. 2  shows an example of the engine and its surrounding components controlled by the fuel control apparatus employing the method for feedback controlling the air-fuel ratio of fuel, to which the present invention is applied. 
         [0031]    An engine  201  includes a thermal air flow meter  202 , a throttle valve  203 , an idle speed control valve  204 , a fuel injection valve  206 , a cam angle sensor  207 , an ignition module  208 , a coolant temperature sensor  209 , an air-fuel ratio sensor  210 , an ignition key switch  211 , and an engine control unit  212 . Specifically, the thermal air flow meter  202  measures the amount of air drawn in. The throttle valve  203  regulates the rate of an airflow drawn into the engine. The idle speed control valve  204  controls the engine idle speed by controlling the area of a flow path that bypasses the throttle valve  203  and connects to an intake pipe  205 . The fuel injection valve  206  supplies a fuel of a particular amount requested by the engine  201 . The cam angle sensor  207  is disposed at a predetermined cam angle of the engine  201 . The ignition module  208  supplies an ignition plug that ignites a fuel mixture supplied into an engine cylinder with ignition energy based on an ignition signal of the engine control unit  212 . The coolant temperature sensor  209  is provided on a cylinder block of the engine  201  to detect an engine coolant temperature. The air-fuel ratio sensor  210  is disposed upstream of a catalyst of an engine exhaust pipe. The air-fuel ratio sensor  210  outputs an electric signal that is linear relative to the oxygen concentration of an exhaust gas. The ignition key switch  211  serves as a main switch for running and stopping the engine  201 . The engine control unit  212  controls auxiliaries of the engine  201 . The idle speed control valve  204 , which controls the engine idle speed, is not necessary if the throttle valve  203  is to be controlled by a motor or the like. In accordance with the first embodiment of the present invention, fuel control is accomplished by detecting the amount of air drawn into the engine  201 ; however, the fuel control can also be achieved by detecting an intake pipe pressure. 
         [0032]      FIG. 3  shows a second example of the engine and its surrounding components controlled by the fuel control apparatus employing the feedback control method for controlling the air-fuel ratio of fuel, to which the present invention is applied. 
         [0033]    The second example shown in  FIG. 3  differs from the first example shown in  FIG. 2  in that a fuel injection valve  306  is not disposed upstream of an intake valve but connected to an engine cylinder. The fuel injection valve  306  thereby injects fuel directly into the cylinder. Because of this arrangement, the second example additionally includes a high pressure fuel pump  307  for boosting a fuel pressure and a fuel pressure sensor  308 . 
         [0034]      FIG. 4  is a typical internal configuration of the fuel control apparatus employing the feedback control method for controlling the air-fuel ratio of fuel, to which the present invention is applied. A CPU  401  includes an I/O section  402  that converts electric signals of the sensors provided in the engine  201  to corresponding signals for digital arithmetic operations and the digital arithmetic operation control signals to corresponding actual actuator drive signals. The I/O section  402  receives inputs from a coolant temperature sensor  403 , a cam angle sensor  404 , an air-fuel ratio sensor  405 , an intake airflow rate sensor  406 , a throttle opening sensor  407 , a vehicle speed sensor  408 , and an ignition switch  409 . Output signals are transmitted from the CPU  401  to fuel injection valves  411  to  414 , ignition coils  415  to  418 , and an ISC opening command value  419  for an ISC valve via an output signal driver  410 . 
         [0035]    Basic equations for finding an air-fuel ratio feedback control factor (air-fuel ratio feedback factor) of the engine that employs the feedback control method for controlling the air-fuel ratio of fuel according to the first embodiment of the present invention will be given below. Expression 1 represents a transfer function of the air-fuel ratio sensor. A fuel-air ratio of a fuel injection amount and a fuel-air ratio detected by the air-fuel ratio sensor may be represented by Expression 1 that includes the transfer function of the air-fuel ratio sensor. It is to be noted that the fuel-air ratio is a normalized value, given by the fuel amount divided by the air amount, the divided amount further multiplied by the stoichiometric air-fuel ratio (about 14.5) (which is referred to as the fuel-air ratio). 
         [0000]    
       
         
           
             
               
                 
                   
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         [0036]    u(z): Injection fuel-air ratio 
         [0037]    y(z): LAF sensor output fuel-air ratio 
         [0038]    Expressions 2 represent a state space of the air-fuel ratio sensor. Expression 2-(1) is a state equation, and Expression 2-(2) is an output equation. Expressions 2-(1) and 2-(2) are derived from the above-referenced equation 1. Further, x 1  and x 2  represent internal status variables. 
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         [0039]    x 1 ,x 2 : Internal status variables 
         [0040]    Expressions 3 represent a hyperplane, a linear element, a nonlinear element, and a switching hyperplane of the sliding mode control used in the first embodiment of the present invention. Expression 3-(1) defines the hyperplane, given by two numeric values of S 1  and S 2 . Expression 3-(2) represents the linear element, and Expression 3-(3) represents the nonlinear element, both derived from the state space of the above-referenced Expressions 2 and the switching hyperplane to be described later. Expression 3-(4) represents the switching hyperplane. An evaluation value multiplied by the hyperplane is the difference between a current value of the internal status variable and a convergence value of the internal status variable. 
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         [0041]    η: Nonlinear gain 
         [0000]      δ( n )= S·e ( n ) 
         [0000]    When e(n)=(x(n)−  x (n)), the above δ(n) is then given by 
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         [0042]    Expressions 4 represent a final output (air-fuel ratio feedback factor) of the sliding mode control used in the first embodiment of the present invention. Expression 4-(1) adds the above-referenced linear element to the nonlinear element to find the air-fuel ratio feedback factor. Expression 4-(2) is a relational expression between S 1  and S 2  of the hyperplane for stabilizing the sliding mode control according to the first embodiment of the present invention. In a relational area of S 1  and S 2 , in which the Expression 4-(2) holds true, divergence or oscillation of the air-fuel ratio feedback factor does not occur. The stabilization area can be found using the Expression 2-(1) and a switching function, details of which will, however, be omitted. 
         [0000]        u   total   =u   eq ( n )+ u   nl    Expression 4-(1) 
       Stable Convergence Condition 
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         [0044]      FIG. 5  is a typical control block diagram for air-fuel ratio feedback by the sliding mode control of the engine that employs the feedback control method for controlling the air-fuel ratio of fuel according to the first embodiment of the present invention. An adder  501  adds the air-fuel ratio feedback factor from a preceding sliding mode control process to the difference between a target fuel-air ratio and an actual fuel-air ratio, and the result is applied to an LAF sensor state space of a block  502 . The state variables of the LAF sensor are outputted from the LAF sensor state space. A block  503  determines a hyperplane from the intake air amount, the engine speed, an LAF sensor response time constant, the vehicle speed, the target idle speed, and the idle switch. A block  504  determines a nonlinear gain from the target fuel-air ratio and the actual fuel-air ratio. A block  505  calculates a linear element using the LAF sensor state variables and the hyperplane determined by the block  503 . A block  506  calculates a nonlinear element using the LAF sensor state variables, the hyperplane, and the nonlinear gain. An adder  507  adds the linear element to the nonlinear element and outputs the result as the air-fuel ratio feedback factor. 
         [0045]      FIG. 6  is a typical block diagram for determining the nonlinear gain by the sliding mode control of the engine that employs the feedback control method for controlling the air-fuel ratio of fuel according to the first embodiment of the present invention. 
         [0046]    An adder  601  and a block  602  calculate the absolute value of the difference between the target fuel-air ratio and the actual fuel-air ratio. A block  603  finds the nonlinear gain from the absolute value of the difference through table search. 
         [0047]      FIG. 7  is a typical block diagram for determining the hyperplane by the sliding mode control of the engine that employs the feedback control method for controlling the air-fuel ratio of fuel according to the first embodiment of the present invention. A block  701  performs a table search for S 1  for the hyperplane from the engine speed. A block  702  performs a table search for S 2  for the hyperplane from the engine speed. A block  703  performs a table search for intake air amount correction from the intake air amount. This correction is based on the dependence of the LAF sensors responsiveness on an exhaust gas flow rate. A block  704  performs a table search for a response delay correction amount from an LAF sensor response delay index. The LAF sensor response delay index may be obtained from system identification, response to the fuel amount inputted, and the like, details of which will, however, be omitted. A multiplier  705  corrects the SI for the intake air amount correction and the response delay correction. In this example, the correction is made for the S 1 ; however, the S 2  or both the S 1  and S 2  may be corrected. A block  706  is a hyperplane final determination section determining the final hyperplane using the corrected S 1 , the S 2 , the engine speed, the target idle speed, the idle switch, the vehicle speed, and the like. 
         [0048]      FIG. 8  is a typical detailed control block configuration of the hyperplane final determination section shown in  FIG. 7 . Blocks  801  and  802  calculate an absolute value of S 2 /S 1 . A comparator  803  determines if the absolute value is smaller than a predetermined value or not. The predetermined value is a value obtained by an adder  805  subtracting from the stability limit 1 of the Expression 4-(2) the value of Hys found through a table search at a block  806  based on an engine speed. If the comparator  803  determines that the absolute value is more than the predetermined value, output for S 2  is a value obtained by multiplying the value of (1−Hys) by S 1  with a multiplier  807  and a switch  808 . An adder  809  and a block  810  calculate the absolute value of the difference between the engine speed and the target idle speed. If a comparator  812  determines that the absolute value is smaller than a predetermined value  811 , and if a comparator  814  determines that the vehicle speed is smaller than a predetermined value  813 , and further if the idle switch is ON, switches  817  and  819  select, as values during idling, preferentially a predetermined value  816  and  818  for S 1  and S 2 , respectively, which have been determined by blocks  801  through  808 . 
         [0049]      FIG. 9  is a diagram showing the time it takes an exhaust gas to reach the LAF sensor (stroke delay time) with respect to the engine speed in the engine according to the embodiment of the present invention. The delay time exhibits a tendency as shown in  FIG. 9  and is represented by Expression  901 . 
         [0050]      FIG. 10  is a diagram showing an example of the dependence of the time constant of the LAF sensor provided on the engine according to the first embodiment of the present invention on an exhaust gas flow rate. The time constant shows the tendency as shown in  FIG. 10 , ranging roughly between 150 ms and 200 ms in an ordinary range as indicated by reference numeral  1001 . The time becomes longer in a range with a low exhaust gas flow rate. 
         [0051]      FIG. 11  is a diagram showing a typical setting tendency of S 1  of the hyperplane of the sliding mode control of the engine that employs the feedback control method for controlling the air-fuel ratio of fuel according to the first embodiment of the present invention. S 1  is set so as to be greater at smaller engine speeds or with smaller intake air amounts. 
         [0052]      FIG. 12  is a diagram showing typical behavior of the actual air-fuel ratio with changing target air-fuel ratios of the engine that employs the feedback control method for controlling the air-fuel ratio of fuel according to the first embodiment of the present invention. A chart  1201  represents the target air-fuel ratio varied in a stepwise fashion at a time  1202 . A chart  1203  shows the actual air-fuel ratio that follows the target air-fuel ratio when the engine speed is high and the intake air amount is great. A chart  1204  shows the behavior of the actual air-fuel ratio when the engine speed is lower and the intake air amount is smaller than with the chart  1203  and when no correction is made for the hyperplane of the chart  1203 . As is known from the chart  1204 , there is noted a large overshoot relative to the target air-fuel ratio, and the behavior is relatively oscillatory. A chart  1205  shows fluctuations of the actual air-fuel ratio when the hyperplane correction according to the first embodiment of the present invention is made for the hyperplane of the chart  1204 . The chart  1205  shows that the overshoots of the chart  1204  are eliminated and the behavior stably follows the target air-fuel ratio. 
         [0053]      FIG. 13  is a flowchart showing typical control of the fuel control apparatus that employs the feedback control method for controlling the air-fuel ratio of fuel according to the first embodiment of the present invention. In step  1301 , the number of inputs of changes in electric signal per unit time, typically a pulse signal, of the crank angle sensor is counted, and the engine speed is calculated through arithmetic operations. In step  1302 , the output voltage of the thermal air flow meter is translated to a corresponding airflow rate through voltage-flow rate conversion, and the resultant airflow rate is read. In step  1303 , the basic fuel amount is calculated from the engine speed and the intake air amount. In step  1304 , a map search is performed for the basic fuel correction factor based on the engine speed and the basic fuel amount. In step  1305 , the output voltage of the LAF sensor is subjected to voltage-to-air-fuel-ratio conversion, and the corresponding actual air-fuel ratio is read. In step  1306 , a map search is performed for the target air-fuel ratio using the engine speed and the basic fuel amount (load). In step  1307 , a response delay including a delay due to a deterioration of the LAF sensor and the like is detected. In step  1308 , the hyperplane of the sliding mode control is selected (calculated). In step  1309 , the air-fuel ratio feedback factor is obtained through the sliding mode control. In step  1310 , the basic fuel amount is corrected using the basic fuel correction factor and the air-fuel ratio feedback factor. In step  1311 , the corrected basic fuel amount is set as the fuel injection amount. In step  1312 , the target idle speed is set. In step  1313 , the target flow rate that can achieve the target idle speed is calculated. In step  1314 , an ignition correction amount for suppressing fluctuations in the idle speed is calculated. In step  1315 , the target flow rate is outputted to an ISC flow rate control section. In step  1316 , a map search is performed for the basic ignition timing using the engine speed and the basic fuel amount (load). In step  1317 , the basic ignition timing is corrected using correction factors of the ISC ignition timing, engine coolant temperature, and the like. In step  1318 , the ignition timing is set. 
         [0054]      FIG. 14  is a typical flowchart showing details of the block diagram of  FIG. 5 . In step  1401 , the target fuel-air ratio, the actual fuel-air ratio, and the previous air-fuel ratio feedback factor are read. In step  1402 , the previous air-fuel ratio feedback factor is added to the difference between the target fuel-air ratio and the actual fuel-air ratio. In step  1403 , the resultant sum is inputted to the LAF sensor state space to calculate the LAF sensor state variable. In step  1404 , the hyperplane is determined from the intake air amount, the engine speed, the LAF sensor response delay time constant, the vehicle speed, the target idle speed, and the idle switch. In step  1405 , a table search is performed for the nonlinear gain using the absolute value of the difference between the target fuel-air ratio and the actual fuel-air ratio. In step  1406 , a linear element is calculated from the state variable and the hyperplane. In step  1407 , a nonlinear element is calculated from the state variable, the hyperplane, and the nonlinear gain. In step  1408 , the linear element and the nonlinear element are added up to calculate the air-fuel ratio feedback factor. 
         [0055]      FIG. 15  is a typical flowchart showing details of the block diagram of  FIG. 6 . In step  1501 , the target fuel-air ratio and the actual fuel-air ratio are read. In step  1502 , the difference between the target fuel-air ratio and the actual fuel-air ratio is calculated. In step  1503 , the absolute value of the difference is calculated. In step  1504 , a table search is performed for a nonlinear gain from the absolute value of the difference. 
         [0056]      FIG. 16  is a typical flowchart showing details of the block diagram of  FIG. 7 . In step  1601 , the engine speed, the intake air amount, and the LAF sensor response delay index are read. In step  1602 , a table search is performed for S 1  and S 2  of the hyperplane using the engine speed. In step  1603 , a table search is performed for the intake air amount correction value using the intake air amount. In step  1604 , a table search is performed for the response delay correction using the LAF sensor response delay index. In step  1605 , the intake air amount correction and the response delay correction are made for S 1 . In step  1606 , the target idle speed, the idle switch, and the vehicle speed are read. In step  1607 , S 1  and S 2  are finally fixed for the final hyperplane based on the corrected S 1  and S 2 , the engine speed, the target idle speed, the idle switch, and the vehicle speed. 
         [0057]      FIG. 17  is a typical flowchart showing details of the block diagram of  FIG. 8 . In step  1701 , the engine speed, the target idle speed, the state of the idle switch, and the vehicle speed are read. In step  1702 , the absolute value of the difference between the target idle speed and the engine speed is calculated. In steps  1703 ,  1704 , and  1705 , it is determined whether the absolute value of the difference is less than a predetermined value of 1, whether the vehicle speed is less than a predetermined value of 2, and whether the idle switch is ON. If all of these are true, S 1 IDLE is set for S 1  and S 2 IDLE is set for S 2  in steps  1712  and  1713 , respectively. If any of the foregoing conditions is false, the operation branches to steps  1706  to  1711 . In step  1706 , the absolute value of a value obtained from S 2  divided by the corrected S 1  is calculated. In step  1707 , a table search is performed for Hys using the engine speed. In step  1708 , it is determined whether the absolute value of the divided value is smaller than 1−Hys. If it is determined that the absolute value is greater than (or equal to) 1−Hys, it is determined in step  1709  whether S 1  is positive or negative. If it is determined that S 1  is negative, −S 1 ×(1−Hys) is substituted for S 2  in step  1711 , and if it is determined that the S 1  is positive, S1×(1−Hys) is substituted for S 2  in step  1710 .