Abstract:
There is provided a method for starting a spark ignition engine having multiple cylinders. The method may comprise supplying air and fuel for restart into a first cylinder before said engine completely stops, and igniting the mixture of said air and said fuel in said first cylinder in response to an engine restart request, wherein said first cylinder is on an expansion stroke when said engine stops. The method may also include, after said piston in said first cylinder starts moving, injecting fuel into a second cylinder that is on a compression stroke when said engine stops, on a compression stroke where a piston of said second cylinder is moving in a direction opposite to an operative direction of said piston in said first cylinder.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    The present application is a continuation of U.S. Ser. No. 11/533,040, titled “Method of Starting Spark Ignition Engine without Using Starter Motor”, filed Sep. 19, 2006, the entire contents of which are incorporated herein by reference. 
     
    
     BACKGROUND 
       [0002]    The present description relates to a method of starting an internal combustion engine, more particularly to a method of starting a spark ignition engine without using a starter motor. 
         [0003]    In recent years, to improve fuel economy of vehicle engines, particularly for city driving, there has been the development of so called idle stop control. This method automatically stops the vehicle&#39;s engine when stop conditions are met, for example when the vehicle is stopping at a traffic light. The engine is automatically restarted when a restart condition is met or upon a restart request, such as when the driver operates the accelerator pedal for the vehicle launch from the traffic light. 
         [0004]    A method of the idle stop control is presented such as in European Patent Application publications EP1403511A1 and EP1544456A2. This method does not use a conventional electric starter for automatically restarting the engine because of starter motor durability concerns and because electric power consumption may be excessive due to the potential frequent use of the electric starter during idle stop control. Instead, the method first injects fuel directly in a cylinder, which is on the compression stroke when the engine stops and is referred to as “compression stroke cylinder”. Then, it ignites the mixture of air and fuel in the compression stroke cylinder. As a result, combustion of the ignited mixture generates higher pressure in the compression stroke cylinder and, moves the piston downward. The downward movement of the piston moves the crankshaft in reverse direction for a short interval, because the piston is in the compression stroke and it is supposed to move upward during four cycle engine operation. 
         [0005]    The reverse rotation of the crankshaft causes movement of pistons in other cylinders as well. A piston in a cylinder, which is on the expansion stroke when the engine stops and is referred to as “expansion stroke cylinder”, is moved upward by the reverse rotation of the crankshaft. The upward moving piston compresses the air in the expansion stroke cylinder. Then, fuel is directly injected in the expansion stroke cylinder and, the mixture is ignited and combusted to generate a higher pressure in the expansion stroke cylinder. The higher pressure pushes down the piston to move the crankshaft in the forward direction, thereby initiating the forward or normal rotation of the crankshaft. Movement of the piston also causes the other pistons to move because the pistons are linked together through the crankshaft. The piston in the compression stroke cylinder ascends and approaches the compression top dead center (hereafter referred to as “first compression top dead center”). Then, generally, the mixture in the compression stroke cylinder is already combusted or used up and does not make energy to crank the crankshaft. So, a cylinder that makes torque after the expansion stroke cylinder is a cylinder that is on the intake stroke when the engine stops and is therefore referred to as “intake stroke cylinder”. 
         [0006]    As the crankshaft continues to rotate, a piston in the intake stroke cylinder now moves into the compression stroke from the intake stroke. The molar mass of air contained in the intake stroke cylinder is close to the molar mass of air that the cylinder contained when the piston passed through bottom-dead-center, cylinder pressure was near intake manifold pressure, and when the cylinder volume was greatest. On the other hand, the compression stroke cylinder and the expansion stroke cylinder contained less air molar mass than some other cylinders, because some air may leak from the cylinder over time during the engine stop due to the pressure difference between the inside and outside of the cylinder. Then, the piston in the intake stroke cylinder compresses the full molar mass of the air and the cylinder pressure therein rises, as the crank shaft rotates forward on the inertia exerted by the combustion in the expansion stroke cylinder. When the piston in the intake stroke cylinder approaches the compression top dead center (hereafter referred to as “second top dead center), the pressure in the intake stroke cylinder might be so high that the piston does not pass the second compression top dead center. If the piston passes the second compression top dead center, the mixture in the intake stroke cylinder may be ignited and combustion may generate enough energy for subsequent continuous rotation of the crankshaft. So, for an engine restart, it is desirable that the rotational inertia on the crankshaft overcomes the counterforce exerted by the pressure in the intake stroke cylinder at the second top dead center. 
         [0007]    To increase the inertia of the crankshaft at the second compression top dead center, the EP1403511 publication presents a method of combusting air and fuel mixture in the compression stroke cylinder following the first combustion in the expansion stroke cylinder. Specifically, it leaves some fresh air in the compression stroke cylinder after the combustion for the reverse rotation by setting the initial air fuel ratio lean of the stoichiometry and injects additional fuel afterwards. Then, the mixture is of remaining air and the additional fuel just is ignited just after the first compression top dead center, thereby deriving additional energy to crank the engine from the compression stroke cylinder. Alternatively, the &#39;511 publication presents a method to open the intake valve of the compression stroke cylinder at the late stage of the reverse rotation and close it at the early stage of the forward rotation so that some fresh air is inducted into the compression stroke cylinder. The mixture of newly inducted air and remaining or newly injected fuel in the compression stroke cylinder can be ignited after the top dead center, thereby deriving the additional energy to crank the engine from the compression stroke cylinder to increase the inertia of the crankshaft at the second top dead center. 
         [0008]    For the same purpose, the EP1544456A2 publication presents a method of reducing pressure in the compression stroke cylinder at the first compression top dead center to reduce the counterforce acting against the inertia of the crankshaft. Specifically, it injects additional fuel into the compression stroke cylinder after the combustion for the reverse rotation in the compression stroke cylinder so that evaporative latent heat of the additional fuel cools down the combusted gas and decreases the pressure in the compression stroke cylinder. The decrease of the pressure in the compression stroke cylinder leads to a decrease of the counterforce acting against the inertia of the crankshaft. 
         [0009]    Although the above prior methods may improve the success rate of the engine starting, the inventors herein have recognized that there is still need to increase the rotational inertia of the crankshaft at the second top dead center for a more reliable engine restart, more specifically there is still room to increase the torque exerted by a first combustion after a restart request. 
       SUMMARY 
       [0010]    Accordingly, there is provided, in one aspect of the present description, a method of starting a spark ignition engine having multiple cylinders. The method comprises supplying air and fuel for restart into a first cylinder before the engine completely stops, and igniting the mixture of the air and the fuel in the first cylinder in response to an engine start request. 
         [0011]    In accordance with the method, by supplying air and fuel into the first cylinder before the engine completely stops, the mixture of air and fuel in the first cylinder may be homogeneous at the time of the engine start request. Also, there may be less mixture turbulence and combustion may propagate better within the cylinder. These conditions may reduce the rate of combustion in the first cylinder after a start request is initiated. The slower combustion rate may decrease temperature of the combusted gas while the cylinder wall temperature is relatively low because the engine has stopped. As a result, the slower combustion may reduce heat loss in the first cylinder because of the smaller difference between the temperatures of the combusted gas and the cylinder wall. Consequently, more energy may be directed from the first cylinder to the crankshaft. Then if the first cylinder is on the compression stroke when the engine stops, as the compression stroke cylinder described above, the crankshaft may rotate more in reverse so that the expansion stroke cylinder described above may ascend more and compress more air therein and exert more reaction force from the compression. It also may combust greater molar mass of air in the cylinder and may generate more combustion energy from the expansion stroke cylinder. Consequently, the additional compressive reaction force and the additional combustion energy may work together to increase the inertia of the crankshaft at the second top dead center of the engine, so that the engine restart becomes more reliable. 
         [0012]    In an embodiment, the restart fuel may be injected after a last exhaust stroke before the engine stops. Therefore, the fuel may be prevented from flowing out of the first cylinder. If the restart fuel is injected in a last intake stroke before the engine stops, the fuel may be mixed well with the air inducted into the first cylinder so that the rate of combustion during a subsequent restart is reduced. 
         [0013]    In an embodiment, the engine may be controlled to stop the piston of the first cylinder at more than 90° crank angle above the bottom dead center when the engine stops. Therefore, the piston of the first cylinder may descend for more distance and may transmit more energy derived from the slower combustion to the crankshaft. If the first cylinder is the compression stroke cylinder described above, additional fuel may be injected into the first cylinder after a last bottom-dead-center before the engine stops, so that evaporative latent heat of the additional fuel may reduce the pressure in the cylinder and pull up the piston position at the engine stopping for the more distance of the piston descend in the first cylinder. 
         [0014]    In an embodiment, additional fuel may be injected into the first cylinder in response to the restart request in accordance with a certain condition, for example, if certain time period has passed since the injection of the restart fuel. Thereby, the mixture which was formed before the engine stops may be prevented at the time of restart from being diluted too much to be ignited. 
         [0015]    In an embodiment, the combustion in the first cylinder, such as the compression stroke cylinder described above, may cause reverse rotation of the engine, and a valve for the first cylinder, such as an intake valve, may be opened during the reverse rotation of the engine. Thereafter, mixture of air and fuel in a second cylinder, such as the expansion stroke cylinder described above, may be ignited, thereby rotating the engine forward. Then, the valve for the first cylinder may be closed and the compressed mixture may be ignited again for the forward rotation. Consequently, the mixture in the first cylinder may contain some fresh air inducted while the valve is opened and may be used for the forward rotation in addition to the reverse rotation, so that the rotational inertia of the crankshaft at the second compression top dead center of the engine may be significantly increased. In this embodiment, additional fuel, may be injected when the valve is opened, so that the additional fuel may be well mixed with the fresh air. Considering mass of the fresh air in this instance, mass of the additional fuel may be less than mass of fuel injected before the engine completely stops. 
         [0016]    In an embodiment, the first cylinder may be on an expansion stroke when the engine stops, as the expansion stroke cylinder described above. The crankshaft may be rotated forward by igniting the mixture in response to the start request so that more energy may be derived from the expansion stroke cylinder to the crankshaft. 
         [0017]    In a second aspect of the present description, there is provided a method comprising combusting mixture of air and fuel in a first cylinder to rotate the engine in reverse in response to an engine start request, thereby compressing air in a second cylinder, and combusting mixture of the compressed air and fuel in the second cylinder to rotate the engine in forward, the combustion in the second cylinder being faster than that in the first cylinder. 
         [0018]    In accordance with the method, the combustion in the second cylinder such as the expansion stroke cylinder described above to rotate the engine in forward is faster than the combustion in the first cylinder such as the compression stroke cylinder described above to rotate the engine in reverse. In other words, the rate of combustion in the first cylinder is slower than that in the second cylinder. The slower combustion rate may derive more energy from the first cylinder to the crankshaft, as described above. By rotating the engine in reverse with the more energy, the air in the second cylinder may be more compressed, so that more compressive reaction force against the piston of the second cylinder may be exerted. This reaction force may accelerate the forward rotation of the engine, while there was no such a force for the reverse rotation at the first cylinder. Therefore, optimal time period for combustion of the second cylinder, which is between the reversal of the rotation and the bottom dead center of the second cylinder, may be shorter than that of the first cylinder. In this regard, the faster combustion is made in the second cylinder so that it may be completed within the shorter time period for combustion, thereby reducing loss of heat which the slower combustion could increase if the combustion occurred after the bottom dead center of the second cylinder. Consequently, the additional reaction force and the additional combustion energy may be exerted at the second cylinder for the forward rotation and eventually may turn into more rotational inertia at the second top dead center of the engine, so that the engine restart becomes more reliable. 
         [0019]    In an embodiment, a time difference between the fuel injection and the ignition for the first cylinder may be longer than that for the second cylinder, so that the mixture in the second cylinder may be more stratified than the mixture in the first cylinder and the combustion in the second cylinder may be faster. In another embodiment, the mixture in the first cylinder may be ignited with a single spark, while the mixture in the second cylinder may be ignited with simultaneous multipoint sparks, so that the combustion in the second cylinder may be faster due to multipoint flame propagations. 
         [0020]    In a third aspect of the present description, there is provided a method comprising combusting mixture of air and fuel in a first cylinder for reverse rotation of the engine in response to an engine start request, thereby compressing air in a second cylinder, injecting fuel for forward rotation of the engine into the second cylinder during the reverse rotation of the engine, thereby causing turbulence of mixture of air and fuel in the second cylinder, and igniting the mixture of air and fuel in the second cylinder by the time when the turbulence of mixture is substantially diminished in the second cylinder. 
         [0021]    In accordance with the method, the engine is rotated in reverse by the combustion in the first cylinder, thereby compressing the air in the second cylinder. As described above, the time period for combustion in the second cylinder is shorter than that for the first cylinder, because of the compressive reaction force against the piston in the second cylinder and the acceleration of the forward rotation by the compression reaction force. By igniting the mixture in the second cylinder by the time when the turbulence of mixture is substantially diminished in the second cylinder, the mixture with some turbulence may be ignited so that the flame propagation may be faster and the combustion may be fast enough to finish within the time period for combustion in the second cylinder, thereby reducing loss of heat which the slower combustion could increase if the combustion occurred after the bottom dead center of the second cylinder. Consequently, the additional reaction force and the additional combustion energy may be exerted at the second cylinder for the forward rotation and eventually may turn into more rotational inertia at the second top dead center of the engine, so that the engine restart becomes more reliable. 
         [0022]    In an embodiment, the fuel may be injected into the second cylinder with higher pressure, such as 4 MPa, and may comprise first and second parts of the injection, the first part being injected before 90° crank angle after bottom dead center during the reverse rotation of the engine and the second part being injected after the first part, for example 75 ms or 10° crank angle before the reversal of the rotation of the engine, so that the first part may be injected relatively early and the fuel may be well mixed with air at the time of the second part being injected. Therefore, the combustion may be completed within the time period for combustion in the second cylinder because of the faster combustion accelerated by the turbulence caused by the second part of the fuel injected later and remaining at the time of ignition, while more fuel may be combusted thanks to the first par of fuel injected earlier. Consequently, more energy can be derived from the second cylinder 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0023]    The advantages described herein will be more fully understood by reading an example of embodiments in which the above aspects are used to advantage, referred to herein as the Detailed Description, with reference to the drawings wherein: 
           [0024]      FIG. 1  is a schematic diagram of an engine system according to embodiments of the present description; 
           [0025]      FIG. 2  is a schematic diagram of a variable system according to the embodiments; 
           [0026]      FIG. 3  is another schematic diagram of the engine system showing an exhaust recirculation passage according to the present embodiments; 
           [0027]      FIG. 4  is a diagram showing changes of crank angle sensor signals according to the embodiments; 
           [0028]      FIG. 5  is a flowchart showing a control routine for detecting a position of a piston or a crankshaft of the engine according to the embodiments; 
           [0029]      FIG. 6  is a flowchart showing a first stage of engine stop control of idle stop control of a reverse rotational type according to an embodiment of the present description; 
           [0030]      FIG. 7  is a flowchart showing a second stage of the engine stop control of  FIG. 6 ; 
           [0031]      FIG. 8  is a flowchart showing a third stage of the engine stop control of  FIG. 6 ; 
           [0032]      FIG. 9  is a flowchart showing a fourth stage of the engine stop control of  FIG. 6 ; 
           [0033]      FIG. 10  is a flowchart showing a fifth stage of the engine stop control of  FIG. 6 ; 
           [0034]      FIG. 11  is a flowchart showing a sixth stage of the engine stop control of  FIG. 6 ; 
           [0035]      FIG. 12  is a flowchart showing a seventh stage of the engine stop control of  FIG. 6 ; 
           [0036]      FIG. 13  is a diagram showing changes of parameters during the engine stop control according to the embodiments of the present description; 
           [0037]      FIG. 14  is a diagram showing an operation of the engine system and the change of parameters, particularly during the last stage of the engine stop control; 
           [0038]      FIG. 15  are diagrams illustrating a preferred stop range R for the idle stop control according to the embodiments of the present description; 
           [0039]      FIG. 16  is a graph depicting a change of temperature in a cylinder after an engine stop; 
           [0040]      FIG. 17  is a flowchart showing a first stage of an engine restart control of the idle stop control of the reverse rotational type according to the embodiment of the present description; 
           [0041]      FIG. 18  is a flowchart showing a second stage of the engine restart control of  FIG. 17 ; 
           [0042]      FIG. 19  is a flowchart showing a third stage of the engine restart control of  FIG. 17 ; 
           [0043]      FIG. 20  is a flowchart showing a fourth stage of the engine restart control of  FIG. 17 ; 
           [0044]      FIG. 21  is a flowchart showing a fifth stage of the engine restart control of  FIG. 17 ; 
           [0045]      FIG. 22  is a diagram showing operations and changes of parameters of the engine system during the engine restart control according to the embodiment of the present description; 
           [0046]      FIG. 23  illustrates graphs depicting characteristics of combustions in the cylinder; 
           [0047]      FIG. 24  illustrates graphs depicting characteristics in the cylinder when fuel injection timing is changed; 
           [0048]      FIG. 25  illustrates states in the cylinder when fuel injection timing is changed; 
           [0049]      FIG. 26  is a sectional view of an engine cylinder according to another embodiment of the present description; 
           [0050]      FIG. 27  is a plain view of the cylinder head showing three spark plugs according the embodiment of  FIG. 26 ; 
           [0051]      FIG. 28  illustrates three different spark patterns of the embodiment of  FIG. 26 ; 
           [0052]      FIG. 29  is a sectional view of an engine cylinder according to another embodiment of the present description; 
           [0053]      FIG. 30  is a sectional view of an engine cylinder according to further another embodiment of the present description; 
           [0054]      FIG. 31  is a plain view of the cylinder head according to the embodiment of  FIG. 30 ; 
           [0055]      FIG. 32  is a diagram similar to  FIG. 14 , but depicting fuel injection during engine stop control of a forward rotational type of engine stop control according to another embodiment of the present description; 
           [0056]      FIG. 33  is a flowchart showing a first stage of engine restart control of the forward rotational type of idle stop control; and 
           [0057]      FIG. 34  is a diagram similar to  FIG. 22  for the engine restart control of the forward rotational type of idle stop control. 
       
    
    
     DETAILED DESCRIPTION 
       [0058]    The embodiments of the present description will now be described with reference to the drawings, starting with  FIG. 1 , which shows an overview of an engine system of an internal combustion engine  1 . In the embodiments, the engine  1  is onboard of an automotive vehicle and drives wheels of the vehicle through a drive-train including a transmission, as is well known in the art. 
         [0059]    In the embodiment of  FIG. 1 , the engine  1  is a direct injection spark ignition engine, although a port injection type spark ignition engine may be employed. The engine  1  comprises a cylinder head  10  and a cylinder block  11  to form four cylinders  12 A- 12 D therein, although only one cylinder is shown in  FIG. 1 . A piston  13  is arranged is inserted to the cylinder  12  to form a combustion chamber  14  and connected to a crankshaft  3 , as is well known in the art. An engine control unit (ECU)  2  controls various actuators of the engine  2  based on various signals from sensors detecting engine operating conditions. The ECU  2  is a microcomputer based controller which comprises a memory storing computer program and data, a microprocessor executing the computer program and data, and input and output (I/O) busses inputting and outputting the signals, as is well known in the art. There are a fuel control section  41  and other sections shown within the ECU  2 . In this embodiment, those sections are not physically separated but integrated in the computer program stored in the ECU  2 , although some of the sections may be physically separated from the rest of the sections, for example, by using two microcomputers or more for the ECU  2 . 
         [0060]    A spark plug  15  is arranged at the top of the combustion chamber with its electrode located in the combustion chamber  14 . The spark plug  15  is made to spark by an ignition device  27  well known in the art, which is controlled by an ignition control section  42  of the ECU  2  so as to set proper ignition timing for each of the cylinders  12 A- 12 D. 
         [0061]    A fuel supply system  16  supplies fuel to the engine  1 . Fuel that may be used in the fuel supply system  16  includes gasoline, ethanol, hydrogen, any other fuel suitable for spark ignition and mix of them. The fuel supply system  16  includes a fuel injector  16   a  which is arranged at a side of the combustion chamber  14  on the cylinder head  10  to directly inject fuel into the combustion chamber  14 . The fuel supply system  16  also includes high pressure fuel pump not shown. The fuel pump supplies fuel from a fuel tank through a fuel delivery pipe to the injector  16   b  with a higher pressure. The fuel control section  41  of the ECU  2  may control the pressure of the fuel pump for example between 3 and 13 MPa. 
         [0062]    The fuel injector  16   a  includes therein a needle valve and a solenoid to drive the needle valve. The solenoid is exerted to open the needle valve for a time period corresponding to a pulse width of a pulse signal input from the fuel control section  41  of the ECU  2 . While the needle valve is open, fuel is injected toward proximity of the electrode of the spark plug  15  in the combustion chamber  14 . The fuel injector  16   a  has a plurality of injection holes, and is of a so called multiple hole type. 
         [0063]    There are arranged at the cylinder head  10 , an intake port  17  and an exhaust port  18  opening into the combustion chamber  14 . open and close the intake port  17  and the exhaust port  18  are respectively opened and closed by an intake valve  19  and an exhaust valve  20  which are driven by a valve driving mechanism.  FIG. 2  shows an example of the valve driving mechanism. The intake valve  19  is reciprocally actuated by a tappet  19   a  which is arranged above the valve stem. The tappet  19   a  is contacted and pushed by an intake cam  19   b  which is formed with and rotationally driven by an intake camshaft  191 . Likewise, the exhaust valve  20  is reciprocally actuated by a tappet  20   a  which is contacted and pushed by an exhaust cam  20   b  formed with an exhaust cam shaft  201 . The camshafts  191  and  201  are connected to and rotationally driven by the crankshaft  3  through a chain or belt, as is well known in the art. In this embodiment for the four cylinder four cylinder engine, all of the four cylinders  12 A through  12 D have the same valves  19  and  20  associated with the camshafts  191  and  201 . Engine cycles take place sequentially in the order of the first cylinder  12 A, the third cylinder  12 C, the fourth cylinder  12 D and the second cylinder  12 B (see  FIG. 3  for a physical arrangement of the cylinders within the cylinder block  11 ) with a phase difference of 180 degree crank angle (° CA), as is common in the four cycle four cylinder engines. 
         [0064]    In this embodiment, there is provided a variable valve mechanism  190  for the intake cam shaft  191 . The variable valve mechanism  190  is controlled by a valve control section  49  of the ECU  2  to change a phase of the intake camshaft  191  so that open and closing timing of the intake valve  19  thereby achieving valve timing (VVT) function. Although the VVT function is only available for the intake valve  19 , the exhaust valve  20  may be provided with it. Further, in addition to the VVT function, variable valve lift (VVL) function may be provided for either of the intake valve  19  and the exhaust valve  20  by a VVL mechanism which may vary, preferably, continuously a valve lift, preferably, from zero to a maximum stroke defined by a cam profile. Further, the valve driving mechanism and the variable valve mechanism for either of the intake valve  19  and the exhaust valve  20  may be substituted with an electromagnetic or electro-hydraulic valve drive mechanism or other valve mechanism which may open and close the valve free of correlation with a rotational angle or phase of the crankshaft  3 . 
         [0065]    As shown in  FIG. 3 , an intake passage  21  and an exhaust passage  22  are respectively connected to the intake ports  17  and the exhaust ports  18 . The intake passage  21  consists of a surge tank  21   a  at its upstream side, branch passages  21   b  communicating between the surge tank  21   a  and the respective intake ports  17  and a common intake passage  21   c  upstream of the surge tank  21   b . A throttle valve  23  is arranged in the common intake passage  21   c  and actuated by an actuator  24 , for example, an electric motor, which changes an opening of the throttle valve  23  according to a control signal computed by a throttle control section  43  of the ECU  2 . When stopping the engine, a change of opening of the throttle valve  23  may correspond to an individual air amount or mass within a particular cylinder, particularly just before a complete stop of the engine  1 . That eventually may affect a stop position of the engine or a position of the piston  13  when the engine stops, as a result of a difference of the individual air amount within the individual cylinders. 
         [0066]    Along the intake passage  21 , there are arranged an airflow sensor  25  detecting intake airflow, an intake air temperature sensor  29  detecting a temperature of the intake air and an ambient pressure sensor SW 1  detecting a pressure of the atmosphere upstream of the throttle valve  23 , and an intake air pressure sensor  26  downstream of the throttle valve  23 , all of which output signals to the ECU  2 , while these sensors are not shown in  FIG. 3 , but only in  FIG. 1 . 
         [0067]    As shown in  FIGS. 1 and 3 , downstream of a converging portion of the exhaust passage  22 , there is arranged a catalyst converter  37  for purifying the exhaust gas. The catalyst  37  may comprise, in its can, a so called three way catalyst (TWC) which has higher purification ratios of HC, CO and NOx when an air fuel ratio of the exhaust gas is near the stoichiometry and has an oxygen storage capacity to adsorb oxygen in an oxygen excess atmosphere where an oxygen concentration in the exhaust gas is higher than the stoichiometry and releases the adsorbed oxygen to react it with HC, CO when the oxygen concentration is lower than the stoichiometry. The catalyst is not limited to TWC, but it may be one having the oxygen storage capacity and, for example, may be a so called lean NOx catalyst which can purify NOx in an excess oxygen atmosphere. 
         [0068]    As shown in  FIG. 3 , there is arranged an exhaust gas recirculation (EGR) passage  38  which communicates between the intake passage  21  downstream of the throttle valve  23  and the exhaust passage  22  upstream of the catalyst converter  37  for re-circulating the exhaust gas to the engine  1 . In the EGR passage  38 , there is arranged an EGR valve  39  which is controlled by an EGR control section  48  of the ECU  2  to regulate an amount of the re-circulated exhaust gas. 
         [0069]    Referring back to  FIG. 1 , there is provided an alternator  28  which is connected through a belt to and driven by the crankshaft  3  to generate electricity while the engine  1  is running. The alternator  28  has a regulator circuit  28   a  which adjusts an electric generation amount by adjusting a field current to a field coil of the alternator  28 , as is known in the art. The regulator circuit  28   a  is controlled by a signal from an alternator control section  44  of the ECU  2  to adjust the field current. The alternator control section  44  computes the signal to the regulator circuit based on various operating conditions such as electric load of the vehicle and a voltage of a battery onboard. Further it may change the load on the engine  1  by varying the field current of the alternator  28 . As a result, it may help to stop the engine  1  at a desired position or prevent too much spin up of the engine just after an engine start. 
         [0070]    There is arranged a cam angle sensor  32  around a wheel which is affixed to and rotates with the exhaust camshaft  201  and has one tooth at its periphery. The cam angle sensor  32  outputs a signal to the ECU  2 . The cam angle signal gives a falling or rising edge as a rotational reference signal once per rotation of the camshaft  191  or  201  or two rotations of the crankshaft  3  which is 720° CA. Around a wheel which is affixed to and rotates with the crankshaft  3  and has equally spaced tooth at its periphery, there are arranged two crank angle sensors  30  and  31  which detect change of magnetic field depending on the rotation of the tooth wheel and output crank angle signals CA 1  and CA 2  respectively to the ECU  2 . The ECU  2  may compute an engine speed N E  by counting number of edges of either of the rotational reference signal and the crank angle signal CA 1  or CA 2  per unit of time, although the crank angle signal is more accurate because of more number of teeth the tooth wheel has. In addition to the engine speed N E , the ECU  2 , specifically a crank angle computation section  45  therein, may compute an angular position of the crankshaft  3  or a position of each of the pistons  13  in the first through fourth cylinders  12 A through  12 D based on the rotational reference signal and the crank angle signal CA 1  or CA 2  by counting number of edges from the crank angle signal since a last edge of the rotational reference signal, as is known in the art. 
         [0071]    Further in the present embodiment, a crank angle determination section  45  of the ECU  2  can compute a position of the piston  13 , not only during normal rotation of the engine  1 , but also when the engine  1  stops, reverses or repeats forward and reverse rotation, using the two crank angle sensors  30  and  31 . They are so arranged around the tooth wheel that the crank angle signals CA 1  and CA 2  have a phase difference, for example by a half of the pulse width, as shown in  FIG. 4 . Based on a difference between the crank angle signals CA 1  and CA 2  during a forward rotation of the crankshaft  2  shown in  FIG. 4(A)  and during a reverse rotation in  FIG. 4(B) , the ECU  2  can determine a rotational direction of the crankshaft  2 . 
         [0072]    Specifically, a flowchart of  FIG. 5  shows a crank angle determination routine C run by the crank angle determination section  45  of the ECU  2 . After the start, the routine proceeds to a step SP 1  where it is determined whether a reference signal from the cam angle sensor  32  is detected or not. If it is detected that at the step SC 1 , the routine proceeds to a step SC 2 , where a crank angle counter CA in the crank angle determination section  45  is reset to be zero. If the reference signal is not detected at the step SC 1 , the routine proceeds to a step SC 3  where it is determined whether a rising edge of the crank angle signal CA 1  is detected or not. If a rising edge of CA 1  is detected (YES) at the step SC 3 , the routine proceeds to a step SC 4 . There it is determined whether the crank angle signal CA 2  is low or not. If the CA 2  is low (YES) at the step SC 4 , it means that the crankshaft  3  is in a forward rotation as can be seen in  FIG. 4(A) . Then, the routine proceeds to a step SC 5  where the counter CA that is initially zero at the step SC 2  is counted up by one. On the other hand, if the CA 2  is high (NO) at the step SC 4 , it means that the crankshaft  3  is in a reverse rotation as can be seen in  FIG. 4(B) . In this case, the routine proceeds to a step SC 6  and counts down the counter CA by one. 
         [0073]    If a rising edge of CA 1  is not detected at the step SP 4 , the routine proceeds to a step PP 7  and determines whether a falling edge of CA 1  is detected. If it is not detected, the routine returns to the step SP 3  and waits for a rising edge of CA 1 . If the falling edge of CA 1  is detected, the routine proceeds to a step SP 8  and determines whether or not the signal CA 2  is high. If the CA 2  is high (YES) at the step SP 8 , it means that the crankshaft  3  is in a forward rotation as can be seen in  FIG. 4(A) . Then the routine proceeds to the step SP 5  and counts up the counter CA by one. If the CA 2  is low (NO) at the step SP 8 , it means that the crankshaft  3  is in a reverse rotation as can be seen in  FIG. 4(B)  and the routine proceeds to the step SP 6  and counts up the counter CA by one. 
         [0074]    After the step SP 5  or SP 6 , the routine proceeds to a step SP 9  and reads out a count number from the counter CA. The count number shows number of rising and falling edges of the crank angle signal CA 1  which corresponds to number of tooth of the tooth wheel of the crankshaft  3  from the reference rotational position of the engine  1  that is derived from the reference signal from the cam angle sensor  32 . Eventually, the count number shows an absolute angular position CA of the crankshaft  3 . Consequently, an angular position of the crankshaft  3  or a piston position can be determined even after repeated back and forth movements of the crankshaft  3  just before the engine completely stops. 
         [0075]    Referring back to  FIG. 1 , there are provided an engine temperature sensor  33  which detects a temperature of engine coolant in the cylinder block  11  and a driver operation sensor  34  which detects operations of a vehicle driver such as a position of an accelerator pedal, a position of a brake pedal or a gear position or shift range of the vehicle transmission. These sensors output signals to the ECU  2  as well. 
         [0076]    There is also provided within the ECU  2  an in-cylinder temperature estimation section  46 , which estimates air temperatures of the respective cylinders  12 A- 12 D based on an engine temperature detected by the engine temperature sensor  33 , an intake air temperature detected by the intake air temperature sensor  29  and others, using a map predetermined through an experiment. Particularly in this embodiment, when restarting the engine  1 , the section  46  consider a time period of the engine  1  stopping for an in-cylinder temperature estimation at the time of restarting the engine  1 . 
         [0077]    Further there is provided within the ECU  2  an air density estimation section  47  which estimates an air density of the atmosphere based on intake air temperature sensor  29  and the ambient air pressure sensor SW 1 . The estimated air density may be used for determining engine control parameters at the time of restarting the engine  1 . 
       Reverse Rotational Type of Idle Stop Control 
       [0078]    Now, an operation of a reverse rotational type of idle stop control will be described. In this reverse rotational type, engine stop control attempts to stop the engine at an crank angle CA within a preferred stop range R which is described in greater detail later with reference to  FIG. 15 . At the time of restarting the engine  1 , fuel may already exist in a cylinder which has stopped in its compression stroke (hereafter may be referred to as “compression stroke cylinder”) and the number one cylinder (cylinder # 1 ) in an example of  FIG. 22 . Then, a spark is made in the compression stroke cylinder, thereby initiating combustion. This combustion raises the cylinder pressure, pushes down the piston  13  of the compression stroke cylinder and rotates the crankshaft  3  in reverse. 
         [0079]    Then, the crankshaft  3  in the reverse rotation raises the piston  13  of a cylinder which has stopped in its expansion stroke (hereafter referred to as “expansion stroke cylinder) and the number two cylinder (cylinder # 3 ) in the case of  FIG. 22 . The piston  13  of the expansion stroke cylinder compresses the air inside and receives a counterforce from the compressed air. This counterforce may help to reverse the rotation of the crankshaft  3 . Before the reversal of the rotation or change of the rotational direction, fuel is injected into the expansion stroke cylinder, and then around the rotational reversal, a spark is made in the expansion stroke cylinder, thereby initiating combustion. This combustion accelerates the forward rotation of the crankshaft  2 . This puts rotational inertia or energy to pass a first top dead center TDC 1  and a second top dead center TDC 2 , because a next substantial combustion is made after the second top dead center in a cylinder which has stopped in its intake stroke and is the number three cylinder (cylinder # 3 ) in the case of  FIG. 22 . 
         [0080]    At first, the engine stop control part of the reverse rotational type of the idle stop control is described below, mainly with reference to flowcharts illustrated in  FIGS. 6 through 12 . 
       Engine Stop Control 
       [0081]    The ECU  2  processes the engine stop control by running a computer program, which is stored in its memory, particularly control routines illustrated by the flowcharts of  FIGS. 6 through 12 . The engine stop control is comprised of first through seventh stages or seven control routines S 1  through S 7 . The first stage in particular is a preliminary stage of the engine stop control. 
         [0082]    After a start of the first stage or the routine S 1  shown in  FIG. 6 , it determines at a step SS 101  whether a flag F 1  is High or not. The flag F 1  is set High, when it is determined possible to initiate the first stage of the engine stop control or if several predetermined conditions are met. The conditions include that a speed of the vehicle is faster than a reference speed such as 10 km/h, that a steering angle of the vehicle is less than a reference angle, that a voltage of a vehicle battery is more than a reference voltage and that an air conditioner of the vehicle is OFF. All of these conditions are met, it can be determined that the engine stop can be desired and the engine  1  can be restarted. If the flag F 1  is High, the routine determines at a step SS 102  whether the accelerator pedal is fully released and the brake pedal is depressed more than a reference level or not from the driver operation sensor  34 . If it is determined that the accelerator pedal is fully released and the brake pedal is depressed more than the reference level (YES) at the step SS 102 , which means that the engine  1  is in an engine deceleration condition and not in a coasting condition and that the vehicle is more likely to stop, the routine proceeds to a step SS 103 , and otherwise returns. 
         [0083]    At the step SS 103 , the routine determines whether an engine speed N E  is higher than a first reference engine speed for fuel cut (N FC1 ), such as 1100 rpm. If it is determined that the engine speed N E  is higher than the first reference value N FC1  (YES) at the step SS 103 , it means the engine speed is relatively high in the deceleration condition and it is beneficial to cut off the fuel supply to the engine for a fuel economy improvement, and the routine proceeds to a step SS 104  and stops the fuel supply as is known in the art, then returns. If it is determined that the engine speed N E  is lower than the first reference value N FC1  (NO) at the step SS 103 , the routine proceeds to a step SS 105  and determines whether the engine speed N E  is lower than a second reference engine speed for fuel cut (N FC2 ), such as 900 rpm, or not. If it is determined that the engine speed N E  is higher than the second reference speed N FC2  (YES) at the step SS 105 , the routine proceeds to a step SS 106  and determines whether the fuel is already cut off or not. If it is determined that the fuel is already cut off (YES) at the step SS 106 , the routines proceeds to the step SS 104  and continues to stop the fuel supply, while if NO at the step SS 106 , the routine returns because a substantial fuel saving benefit can not be expected. If it is determined at the step SS 105  that the engine speed Ne is lower than the second reference speed N FC2 , the routine does not cut off the fuel and proceeds to a step SS 108 . 
         [0084]    At the step SS 108 , the routine determines whether a target air fuel ratio for the engine  1  is set substantially leaner than the stoichiometric air fuel ratio or not. If it is determined that the target air fuel ratio is leaner than the stoichiometry (YES) at the step SS 108 , the routine proceeds to a step SS 109  and sets a first target speed of the engine  1  (N TARGET1 ) substantially higher than a normal idle speed (N IDLE ), such as 650 rpm. The first target speed in this case may be for example 750 rpm. On the other hand, if it is determined at the step SS 109  that the target air fuel ratio is the stoichiometry or richer than that, the routine proceeds to a step SS 110  and sets a second target speed N TARGET2  which is higher than the first target speed N TARGET1  and may be for example 800 rpm. From either of the steps SS 109  and SS 110 , the routine proceeds to a step SS 111  and initiates a feed back control of the target engine speed adjusting the throttle opening K, the fuel injection amount FP or mass or duration of opening of the fuel injector  16   a  or the ignition timing. Then the routine proceeds to a step SS 112  and sets the flag F 1  to be High and a flag F 2  to be Low. The flag F 2  indicates readiness of executing the second stage of the engine stop control. 
         [0085]    The engine idle speed is set higher than the normal idle speed at the step SS 109  or SS 110  and it is maintained at the step SS 111 . When the ECU  2  executes the second stage of the engine stop control afterward, the engine idle speed is relatively high and stable, so that more precise engine stop control can be made. Also it is not necessary to increase the engine speed from the normal speed for the more stable engine rotation after the vehicle really stops and requires the engine stop control, thereby reducing some discomfort of vehicle occupants and longer time period of the engine stop control which the increase of the engine speed for the longer gap may cause. 
         [0086]    Now the second stage of the engine stop control will be described with reference to a flow chart of  FIG. 7  which illustrates the second control routine S 2 . After the start, at a step SS 201 , the routine determines whether the flag F 2  is High or not. If it is OFF, the routine returns and waits for the flag F 2  high. If it is ON, it proceeds to a step SS 202  and determines whether or not a vehicle speed VSP is zero or the vehicle is completely stopped. If it is NO at the step SS 202 , the engine stop is not required yet, so the routine S 2  returns. If it is YES at the step SS 202 , the routine S 2  proceeds to a step SS 203  and determines whether or not the accelerator pedal is fully released and the brake pedal is depressed more than a reference level from the driver operation sensor  34 . If it is NO at the step SS 203 , that means the engine stop is not desired any more, and the routine proceeds to a step SS 204  and resets the flag F 2  to be Low so that the ECU  2  takes the normal engine control. Then the routine returns. If it is YES at the step SS 204 , the routine S 2  proceeds to a step SS 205  and starts a timer T 0 . Then the routine proceeds to a step SS 206  and determines whether or not a target air fuel ratio for the engine  1  is set substantially leaner than the stoichiometric air fuel ratio. If it is determined that the target air fuel ratio is leaner than the stoichiometry (YES) at the step SS 206 , the routine proceeds to a step SS 207  and sets a third target speed N TARGET3  which is a little bit of higher than the first target idle speed N TARGET1  and may be for example 810 rpm. Then the routine proceeds to a step S 208  and the EGR control section of the ECU 2  controls the EGR valve  39  for improving scavenging effect in the cylinders  12 A through  12 D. 
         [0087]    On the other hand, if it is determined at the step SS 206  that the target air fuel ratio is the stoichiometry or richer than that, the routine proceeds to a step SS 209  and sets a fourth target speed N TARGET4  which is even higher than the second target speed N TARGET2  and may be for example 860 rpm. Then it proceeds to a step SS 210  and sets a target intake air pressure Bt TARGET1  which is a relatively higher pressure even for the given fourth target engine speed N TARGET4  and may be for example −400 mm Hg. Therefore, to reduce the torque to maintain the target engine speed, the ignition timing is retarded heavily, so that the exhaust gas temperature becomes higher and activity of the catalyst  37  may be maintained or it may be regenerated if it is a NOx catalyst due to the greater amount or mass of the stoichiometric or rich exhaust gas. 
         [0088]    After the step SS 208  or SS 210 , the routine S 2  proceeds to a step SS 211  and the ECU  2  controls the transmission to be in a neutral range to make a no-load condition. Then the routine proceeds to a step SS 212  and the ECU  2  initiates feedback control of the fuel injection amount FP, the ignition timing and the throttle opening K to meet to the target values set at the steps SS 207  or SS 209  and SS 210 . Finally at a step S 213 , the routine resets the flag F 2  to be Low and sets a flag F 3  to be High, then it returns. The flag F 3  indicates a readiness to stop the fuel for finally stopping the engine  1 . 
         [0089]    As shown in  FIG. 13 , at time t 0  after the second stage of the engine stop control, the engine speed Ne starts to increase from the first to third or second to fourth target speeds by the feedback control initiated at the step SS 210 . At the time t 1  in  FIG. 13 , the engine speed is substantially at to the target speed (N TARGET4  in  FIG. 13 ). The smaller gap between the two target speeds set may substantially prevent the discomfort of the vehicle occupants described above. When the engine is determined to operate in a lean air fuel ratio at the step SS 204 , the airflow amount to the engine is greater, so that more scavenging effect within the cylinder can be expected and the engine speed can be put relatively low, thereby reducing the noise or the fuel consumption. 
         [0090]    Now the third stage of the engine stop control will be described with reference to a flow chart of  FIG. 8  which illustrates the third control routine S 3 . After the start, at a step SS 301 , the routine determines whether the flag F 3  is High or Low. If it is Low, the routine S 3  returns and waits for the flag F 3  High. If it is ON, it proceeds to a step SS 302  and determines whether the accelerator pedal is fully released and the brake pedal is depressed more than a reference level or not from the driver operation sensor  34 . If it is NO at the step SS 302 , which means that the engine stop is not desired any more, and the routine proceeds to a step SS 303  and resets the flag F 3  to be OFF so that the ECU  2  takes the normal engine control. Then the routine returns. If it is YES at the step SS 302 , the routine proceeds to a step SS 304  and determines whether or not the timer T 0  exceeds a predetermined threshold value t A , which may be for example one second. If it is determined the timer T 0  exceeds the threshold value (YES) at the step SS 304 , the routine proceeds to a step SS 305 , and otherwise it returns and waits for the count up of the timer T 0 . At the step SS 305  the routine determines whether a condition for cutting off the fuel is met or not. The fuel cut condition may include a stable engine speed Ne at the target speed N TARET3  or N TARGET4  and a stable boost pressure Bt at the target intake air pressure P 1 . If it is YES at the step SS 305 , which means that the predetermined time period t A  has passed since the time t 0  and it is now time t 1  in  FIG. 12 , the routine proceeds to a step SS 306  and resets the timer T 0  and starts another timer T 1 . Otherwise, the routine returns and waits for the fuel cut condition to be met. After the step SS 306 , the routine proceeds to a step SS 307  and stops the fuel supply. Then it proceeds to a step SS 308  and sets a target value Ge TARGET1  of a field current Ge of the alternator  28  to be 0 A, so that the alternator control section  44  controls the regulator circuit  28   a  to shut off the field current to the alternator  28 , thereby stopping the electric generation. 
         [0091]    After the step SS 308 , the routine proceeds to a step SS 309  and sets a target throttle valve opening K TARGET1  to be for example 80%, so that the throttle control section  43  of the ECU  2  controls the throttle actuator  24  to open the throttle valve  23  up to 80%, thereby increasing the intake air pressure Bt as shown in  FIGS. 13 and 14  between the time t 1  and time t 2 . Finally at a step SS 310 , the routine resets the flag F 3  to be Low and sets a flag F 4  to be High. The flag F 4  indicates that the fuel supply is already stopped but the engine is still running. 
         [0092]    Now the fourth stage of the engine stop control will be described with reference to a flow chart of  FIG. 9  which illustrates the fourth control routine S 4 . After the start, at a step SS 401 , the routine determines whether the flag F 4  is High or Low. If it is Low, the routine returns and waits for the flag F 4  to be High. If it is High, it proceeds to a step SS 402  and determines whether the timer T 1  counts exceeding a reference value t B , which corresponds to a time period of one engine cycle or two crankshaft rotations or 720° CA, as can be seen in  FIG. 13  between time t 1  and t 2 . The value t B  may be, for example, 32 ms, given that the engine speed is now 810 rpm as set at the step SS 207  of the second routine. 
         [0093]    If it is determined that the timer T 1  exceeds the predetermined value t B  (YES) at the step SS 402 , the last injected fuel is supposed to be combusted, and the routine proceeds to a step SS 403  and stops the ignition because it is not needed any more. If it is NO at the step SS 402 , the routine returns and waits for the count up of the timer T 1 . After the step SS 403 , the routine proceeds to a step SS 404  and determines whether the engine speed Ne is lower than a first reference speed N 1 . The reference speed N 1  is set lower than the third target speed N TARGET3  and the fourth target speed N TARGET4  which are respectively set at the steps SS 208  and SS 209  of the second routine and may be for example 760 rpm. If it is determined the engine speed Ne is lower than the reference speed N 1  at the step SS 404 , which means that the engine speed has started falling, as shown in  FIGS. 13 and 14  at time t 2 , the routine S 4  proceeds to a step SS 405  and sets a target throttle opening K TARGET2  to be zero so that the throttle control section  43  of the ECU  2  controls the throttle actuator  24  to fully close the throttle valve  23 . Therefore the intake air pressure Bt is falling, and a cylinder which takes an intake stroke later will hold less air therein at the time of complete engine stop. In the case of  FIG. 14 , the cylinder # 1  takes the intake stroke last before a last cylinder stroke or last compression stroke, specifically between the time t 3  and time t 4  and holds the least air therein and holds the least amount or mass of air at the compression stroke after the time t 4 . 
         [0094]    After the step SS 405 , the routine proceeds to a step SS 406  and sets a target generated electric current Ge TARGET2  in accordance to a target field current map M 1  stored in the ECU  2 . The map M 1  sets the target generated electric current Ge TARGET2  versus the engine speed Ne so that the Ge TARGET2  is set 60 A at 540 rpm or greater and set gradually falling to zero at 460 rpm. Based on the set target generated current Ge TARGET2 , the alternator control section  44  of the ECU  2  controls the regulator circuit  28   a  of the alternator  28 . 
         [0095]    Then, the routine S 4  proceeds to a step SS 407  and determines whether the engine speed Ne is lower than a second reference speed N 2 , which is significantly lower than the first reference speed N 1 . As shown in  FIG. 14 , the engine speed Ne is falling while oscillating with its lower peak at each top dead center. The second reference speed N 2  is set lower than a speed at which the engine  1  or the crankshaft  3  reaches a second last top dead center before the complete stopping (TDC LAST2 ) and may be for example 400 rpm. If it is determined at the step S 407  that the engine speed Ne is lower than the second reference speed N 2 , which means that the engine  2  reaches the second last top dead center TDC LAST2 , as shown in  FIG. 14  at the time t 3 , the routine proceeds to a step SS 408 , and otherwise it returns and waits for the engine speed Ne falling to N 2 . 
         [0096]    At the step SS 408 , the routine S 4  stores the engine speed Ne determined at the previous step SR 407  as a value N 2A  and an air intake pressure Bt detected by the intake air pressure sensor  25  in the memory of the ECU  2  as a value Bt 2  for a later use, specifically at the sixth stage of the engine stop control. Then the routine proceeds to a step SS 409  and resets the timer T 1  to be zero. Next at a step SS 410 , it resets the flag F 4  to be Low and sets another flag F 5  to be High, then returns. The flag F 5  indicates that the engine  2  reaches the second last top dead center or the time t 3  in  FIG. 14 . 
         [0097]    The fifth stage of the engine stop control will now be described with reference to a flow chart of  FIG. 10  which illustrates the fifth control routine S 5 . After the start, at a step SS 501 , the routine determines whether the flag F 5  is High or Low. If it is Low, the routine returns and waits for the flag F 5  to be High. If it is High, it proceeds to a step SS 502  and determines whether an air density ρ computed by the air density estimation section  47  of the ECU  2  is greater than a reference density ρ 1  or not. The reference density ρ 1  may be for example 1.08 kg/m 3 . It may be determined by considering a fact that, when the vehicle is at a higher altitude, for example, higher than 1500-1800 m above sea level, if fuel is injected at the engine restarting, the fuel is not evaporated enough by the ignition, the rate of combustion may be too fast and the start-ability might be deteriorated. Therefore, in such a case, the fuel injection beforehand is desired. 
         [0098]    If it is determined the air density ρ is less than the reference density ρ 1  (YES) at the step SS 502 , the routine proceeds to a step SS 503  and determines an amount of fuel (FP 1 ) for restarting the engine to be injected into a cylinder which is now in its intake stroke and the cylinder # 1  in  FIG. 14 . The fuel amount FP 1  is determined based on the actual engine speed N 2A  at the second last top dead center TDC LAST2  stored at the step SS 408  of the fourth stage of the engine stop control or at the time t 3 , so that the fuel amount FP 1  is greater as the speed N 2A  is greater, thereby more effectively utilizing the intake airflow during the intake stroke for the evaporation and atomization of fuel to be injected. 
         [0099]    The cylinder # 1  which is in its intake stroke at the step SS 503  or between the times t 3  and t 4  is supposed to be in its compression stroke when the engine  1  completely stops, as shown in  FIG. 14  after the time t 4 , so that in this case the cylinder # 1  is a compression stroke cylinder described above. Therefore, the injected fuel is trapped in the cylinder and then is evaporated and atomized, making a homogeneous mixture of air and fuel within the cylinder # 1  during the engine stop. Also, it cools the temperature and decreases the pressure inside of the combustion chamber  14 . After the step SS 503 , the routine S 5  proceeds to a step SS 504  and the fuel control section  41  of the ECU  2  controls the fuel supply system  16  to inject fuel of the amount FP 1  into the cylinder # 1  in  FIG. 14 . At the same time the routine S 5  sets a flag F 5   f  to be High for later use at the time of restarting the engine. 
         [0100]    If it is determined that the air density is greater than the reference density ρ 1  (NO) at the step SS 502 , the steps SS 503  and SS 504  are skipped and the fuel is not injected to that cylinder. Then, the routine S 5  proceeds to a step SS 505  and determines whether the engine speed Ne is lower than a third reference speed N 3 , which is significantly lower than the second reference speed N 2  and may be for example 260 rpm. If it is determined at the step SS 505  that the engine speed Ne is lower than the third reference speed N 3 , which means that the engine  2  reaches the last top dead center TDC LAST1 , as shown in  FIG. 14  at the time t 4 , the routine proceeds to a step SS 506 , and otherwise it returns and waits for the engine speed Ne falling to N 3 . At the step SS 506 , the routine resets the flag F 5  to be Low and sets another flag F 6  to be High, then returns. The flag F 6  indicates that the engine  2  reaches the last top dead center or the time t 4  in  FIG. 14 . 
         [0101]    The sixth stage of the engine stop control will now be described with reference to a flow chart of  FIG. 11  which illustrates the sixth control routine S 6 . After the start, at a step SS 601 , the routine determines whether the flag F 6  is High or Low. If it is Low, the routine returns and waits for the flag F 6  to be High. If it is High, it proceeds to a step SS 602  and determines whether or not the engine speed N 2A , which is a speed at the second last top dead center TDC LAST2  and stored in the memory of the ECU  2  at the step SS 408  of the routine R 4 , is higher than a fourth reference speed N 4 , which is lower than the third reference speed N 3  and may be for example 200 rpm which is lower than the N 3  by 60 rpm. 
         [0102]    If it is determined at the step SS 602  that the engine speed N 2A  is higher than a fourth reference speed N 4 , it can be considered that the crankshaft  3  has a greater rotational inertia at the last top dead center TDC LAST1  at the time t 4  of  FIG. 14 . Then, the routine S 6  proceeds to a step SS 603  and determines whether or not the intake air pressure Bt 2  at the second last top dead center TDC LAST2  which is stored at the step SS 408  of the fourth stage of the engine stop control and detected at the time t 3 , is less than a reference pressure Bt 2REF  such as −200 mm Hg. If it is determined that the intake air pressure Bt is lower than the reference pressure Bt 2  (YES) at the step SS 603 , an amount of air inducted into the cylinder (cylinder # 1  in the case of  FIG. 14 ), which was in its intake stroke at the time t 3  and is now in its compression stroke, is relatively small, and it can be assumed that the pressure inside of the cylinder # 1  is relatively low at the time of complete engine stop. Therefore if the both decisions at the steps SS 602  and SS 603  are YES, the rotational inertia is relatively great and the counterforce acting in the cylinder # 1  against the rotational inertia is relatively small so that the piston  13  in the cylinder # 1  may finally stop at 100° CA or farther from the bottom dead center. That stop position may be within a preferable range R of stop position for the engine restarting, which will be described with greater detail below with reference to  FIG. 15  and may be between 100 and 120° CA from the bottom dead center of a cylinder which is in its compression stroke at the time of complete stop. So, in this case, the throttle valve  23  needs to be positioned just for the restarting. Then, the routine S 6  proceeds to a step SS 604  and sets a throttle opening K during stopping K to be a value K STOP1  which may be for example 5% so that the throttle control section  43  of the ECU  2  controls the throttle actuator  24  to slightly open the throttle valve  23 . 
         [0103]    On the other hand, either of the decisions at the steps SS 602  and SS 603  is NO, the piston  13  in the cylinder # 1  may finally stop at 100° CA or closer to the bottom dead center which is out of the preferable stop range R in  FIG. 15 . Therefore, amount of intake air, which is now inducted into the cylinder # 4  that is now in its intake stroke, is increased by widely opening the throttle valve  23 , so as to reduce the resistance of the airflow and the decrease of the rotational inertia caused by the airflow resistance, thereby stopping the piston  13  in the cylinder # 1  within the preferable stop range R. Specifically, the routine S 6  proceeds to a step SS 605  and sets a target throttle valve opening K during the engine stop to be a value K STOP2  which may be for example 80%, so that the throttle control section  43  of the ECU  2  controls the throttle actuator  24  to open the throttle valve  23  up to 80%. 
         [0104]    After either of the routines SS 604  and SS 605 , the routine proceeds to a step SS 606  and resets the flag F 6  to be Low and another flag F 7  to be High. The flag F 7  indicates that the engine does not make any continuous rotation but oscillates in rotation. 
         [0105]    The seventh or final stage of the engine stop control will now be described with reference to a flow chart of  FIG. 12  which illustrates the seventh control routine S 7 . After the start, at a step SS 701 , the routine determines whether the flag F 7  is High or Low. If it is Low, the routine returns and waits for the flag F 7  to be High. If it is High, the routine S 7  proceeds to a step SS 702  and estimates a final engine stop position CA E     —     STOP , more particularly a final position of the piston  13  in the cylinder # 1  which is now in its compression stroke in the case of  FIG. 14 . Specifically, for the estimation, the crank angle determination section  45  of the ECU  2  continuously monitors the absolute position CA of the crankshaft  3  at the step SP 9  in the crank angle determination routine C 1  in  FIG. 5 . Based on the change of the absolute crankshaft position CA, the final stop position CA E     —     STOP  is estimated. 
         [0106]    After the step SS 702 , the routine S 7  proceeds to a step SS 703  and determines whether or not the estimated stop position CA E     —     STOP  is within the preferred stop range R shown in  FIG. 15 . If it is YES at the step SS 703 , nothing is supposedly to be done, so that the routine S 7  proceeds to a step SS 704  and determines whether or not the crankshaft  3  completely stops based on the change of the absolute crankshaft position CA and waits for the complete stop. 
         [0107]    On the other hand, if it is determined at the step SS 703  that the estimated stop position CA E     —     STOP  is out of the preferred stop range R or less than 100° from the bottom dead center of the cylinder # 1  which is in its compression stroke, the routine S 7  proceeds to a step SS 705  and determines an amount of fuel (FP 2 ) for restarting the engine to be additionally injected into a cylinder which is the cylinder # 1  in  FIG. 14 . The fuel amount FP 2  is determined based on the estimated stop position CA E     —     STOP  so that the amount is greater as the CAE STOP is farther away from the preferred range R or the cylinder # 1  is supposed to stop closer to its bottom dead center. The additional fuel decreases the temperature and pressure within the cylinder # 1  through the evaporative latent heat, thereby making it more likely to stop the piston  13  in the cylinder # 1  within the preferred stop range R. Then the routine S 7  proceeds to a step SS 706  and the fuel control section  41  of the ECU  2  controls the fuel supply system  16  to inject fuel of the amount FP 2  into the cylinder # 1  in  FIG. 14 . Next, the routine F 7  proceeds to the step SS 704 , and determines the engine  1  completely stops or not, as described above. 
         [0108]    After the engine  1  has completely stopped, the routine F 7  proceeds to a step SS 707  and starts a timer T 2 , which indicates the engine  1  is being stopped by the idle stop control. Then it proceeds to a step SS 708  and the ECU  2  controls the transmission to be shifted from the neutral range to a drive range for the engine restart and the following vehicle launch. Then, it proceeds to a step SS 709  and reset the flag F 7  to be Low, so that the engine stop control is completed. 
         [0109]    According to the engine stop control described above, the engine  1  is now stopped within the preferred stop range R shown in  FIG. 15 . In the case of  FIG. 14 , the cylinder # 1  is now in its compression stroke (therefore, hereafter referred to as compression stroke cylinder), the cylinder # 2  is in its expansion stroke (therefore, hereafter referred to as expansion stroke cylinder) and their rotational phases are offset by 180° CA, as shown in  FIG. 15(A) . Over time during the engine stop, even if the intake and exhaust valves are closed such as for the compression stroke cylinder and the expansion stroke cylinder, the pressure inside of the cylinder approaches an atmospheric pressure, because air inside of the cylinder somewhat communicates with the outside through a small gap, for example, between the cylinder wall or between the piston ring or the valve and the valve seat. 
         [0110]    As shown in a graph of  FIG. 16 , from the time of the engine stop, a temperature inside of the cylinder is predicted to change. When the engine  1  completely stops, flow of engine coolant stops as well, and it causes the temperature inside of the cylinder to rapidly rise and the pressure inside to rise as well. This pressure increase may help the air inside go out of the cylinder. 
         [0111]    In accordance with the above prediction, it can be said that, at the time of restarting the engine, the volume inside of the cylinder or the position of the piston shown in  FIG. 15  directly influences mass of the air inside. As can be seen from  FIG. 15(A) , the expansion stroke cylinder has more air mass than the compression stroke cylinder does. For restarting the engine  1 , the air in the compression stroke cylinder is used for temporary reverse rotation to compress the air in the expansion stroke cylinder, while the air in the expansion stroke cylinder is used for a start of a continuous rotation. In this instance, the expansion stroke cylinder needs more air than the compression stroke cylinder does, while excessively small amount or mass of the air in the compression stroke cylinder can not generate energy to rotate the crankshaft  3  in reverse. Therefore, the preferred range R of the stop position of the compression stroke cylinder is set between 100 and 120° CA from its bottom dead center, as shown in  FIG. 15 . 
       Engine Restart Control 
       [0112]    Now an operation of automatically restarting the engine  1  will be described. The ECU  2  processes the engine restart control by running a computer program stored therein, and comprised of first through fifth stages or four control routines R 1  through R 5  illustrated by the flowcharts of  FIGS. 17 through 21 . The engine restart control at first initiates the combustion in the compression stroke cylinder (or the cylinder # 1  in the diagrams of  FIGS. 14 and 22 ) to rotate the crankshaft  3  in reverse and compress air in a cylinder which stops in its expansion stroke (therefore, hereafter referred to as expansion stroke cylinder) and is the cylinder # 2  in  FIGS. 14 and 22 , and then initiates the combustion in the expansion stroke cylinder and the forward rotation of the crankshaft  3 . 
         [0113]    After a start of the first stage or the routine R 1  shown in  FIG. 17 , it determines at a step SR 101  whether a flag F 11  is High or Low. The flag F 11  is set High when there is one of conditions to restart the engine, which include that the accelerator pedal is depressed, that a voltage of the vehicle battery is less than the reference voltage and that the air condition of the vehicle is ON. If it is determined that the flag F 11  is High at the step SR 101 , the routine R 1  proceeds to a step SR 102 , or otherwise it returns and waits for the flag F 11  to be High. At the step SR 102 , the valve control section  49  of the ECU  2  controls the variable valve timing mechanism  190  so that the intake valve close timing is delayed to, for example, 100° CA after top dead center. Thereby, the intake valve  19  of the compression cylinder (# 1 ) will be slightly opened at the late stage of the reverse rotation and the early stage of the reverse rotation, as shown in  FIG. 22 , so that some of combusted gas is exchanged with fresh air in the intake passage  21 . 
         [0114]    After the step SR 102 , the routine R 1  proceeds to a step SR 103  and determines whether the flag F 5   f  is High or not. If the flag F 5   f  is High, the fuel FP 1  was injected to the compression stroke cylinder or the cylinder # 1  in  FIG. 14  at the step SS 503  of the fifth stage of the engine stop control shown in  FIG. 10 . If it is YES at the step SR 103 , the routine R 1  proceeds to a step SR 104  and resets the flag F 5   f  to be Low. Then, it proceeds to a step SR 105  and determines whether the timer T 2  counts exceeding a reference value t C . The timer T 2  was started at the step SS 706  of the engine stop control at the time of the complete stop of the engine. The reference value t C  is set corresponding to a time period for which the inside of the compression stroke cylinder gets diluted too much to achieve the desired combustion status. The dilution in the cylinder may be caused by the communication of the air in the cylinder to the outside described above. 
         [0115]    If it is determined that the timer T 1  exceeds the predetermined value t C  (YES) at the step SR 105 , it is considered that fuel needs to be injected to the compression stroke cylinder due to the dilution in the cylinder. Also if it is determined that the flag F 5   f  is Low (NO) at the step SR 103 , it is considered that fuel needs to be injected to the compression stroke cylinder, because there may be no fuel in the cylinder. On the other hand, if it is determined that the timer T 1  does not exceed the predetermined value t C  (NO) at the step SR 105 , it is considered that no more fuel is needed for the compression stroke cylinder, because the fuel was injected (YES at the step SR 102 ) and the time t c  to dilute the air fuel mixture is not passed. 
         [0116]    If it is considered fuel is needed for the compression stroke cylinder, the routine R 1  proceeds to a step SR 106 . Since the engine rotation during the engine stop control is adjusted to stop the engine  1  or the crankshaft  3  within the range R of  FIG. 15 , the decision of the step SR 106  is not likely to be YES, but even if it is smaller, the possibility of stopping outside of the range R can not be ignored. Therefore, the routine R 1  determines from a crank angle CA STOP  when the engine stops, which is derived from the routine shown in  FIG. 5  and stored in the memory of the ECU  2 , whether or not the compression stroke cylinder (cylinder # 1  in  FIGS. 14 and 22 ) is positioned at 100° CA or farther from its bottom dead center. That crank angle 100° CA of is the lower end of the preferred stop range R, as described above. 
         [0117]    If it is determined that the compression stroke cylinder is positioned at 100° CA or farther from its bottom dead center (YES) at the step SR 106 , it is considered an amount of air in the compression stroke cylinder is appropriate, the routine R 1  proceeds to a step SR 106  and sets a target air fuel ratio AF CMP     —     CYL1  to be stoichiometric or rich (λ≦1) so that the later combustion generates enough energy for the reverse rotation. A target air fuel ratio AF CMP     —     CYL1  is set in accordance with a map M 11  which defines the air fuel ratio as a function of the stop crank angle CA STOP  so that the air fuel ratio AF CMP     —     CYL1  is richer as the crank angle CA STOP  is closer to the top dead center of the compression stroke cylinder. On the other hand, it is determined NO at the step SR 106 , it is considered an amount of air in the compression stroke cylinder is too much, the routine R 1  proceeds to a step SR 108  and sets a target air fuel ratio AF CMP     —     CYL1  to be lean of the stoichiometry (λ&gt;1) so as to prevent the later combustion from generating too much energy for the reverse rotation and the piston of the expansion stroke cylinder from exceeding the top dead center. The lean target air fuel ratio is set in accordance with a map M 12  which also defines the air fuel ratio as a function of the crank angle CA STOP  in the same manner as the map M 11  does. 
         [0118]    After either of the steps SR 107  and SR 108 , the routine R 2  proceeds to a step SR 109  and the in-cylinder temperature estimation section  46  estimates a temperature T CMP     —     CYL  based on an engine coolant temperature from the engine temperature sensor  33 , the count of the timer T 2  which corresponding to elapsed time from the complete engine stop, and others in accordance with a map or mathematical formula which is determined from a prior experiment and generally in line with the graph of  FIG. 16 . Then the routine R 1  proceeds to a step SR 110  and determines a fuel injection amount FP CMP     —     CYL1 . It is computed based on the target air fuel ratio AF COM-CYL1  determined at the step SR 107  or SR 108  and an estimated amount of air in the compression stroke cylinder (AM CMP     —     CYL ). The air amount AM CMP     —     CYL  is estimated based on a volume in the compression stroke cylinder derived from the crank angle CA STOP , air density ρ derived from the air density estimation section  47  of the ECU  2  and the temperature T CMP-CYL  in the compression stroke cylinder. 
         [0119]    After the fuel amount FP CMP     —     CYL1  is determined at the step SR 110 , the routine R 1  proceeds to a step SR 110  and sets a flag F 11   f  to be High and starts a timer T 3  and the fuel control section  41  of the ECU  2  controls the fuel supply system  16  to inject fuel of the computed amount FP CMP     —     CYL1  into the compression stroke cylinder. 
         [0120]    After the step SR 111  or after the decision of the step SR 105  is N 0 , the routine R 1  proceeds to a step SR 112  where it stores the current count value of the timer T 2  into the memory of the ECU  2  for its later use, resets the timer T 2  to be zero, resets the flag F 11  to be Low and sets another flag F 12  to be High. The flag F 12  indicates the compression stroke cylinder is ready for ignition. 
         [0121]    The second stage of the engine restart control will now be described with reference to a flow chart of  FIG. 18  which illustrates the second control routine R 2 . After the start, at a step SR 201 , the routine determines whether the flag F 12  is High or Low. If it is Low, the routine returns and waits for the flag F 12  to be High. If it is ON, it proceeds to a step SR 202  and determines whether the flag F 12   f  is High or not. If the flag F 11   f  if is High, the fuel FP CMP     —     CYL1  is injected at the first stage of the restart control as described above and illustrated in  FIG. 16  at the step SR 109 , then the routine R 2  proceeds to a step SR 203  and determines whether the timer T 3  counts exceeding a reference value t F  or not. The value t F  is preset corresponding to a time period for which the fuel injected at the first stage of the restart evaporates. If it is determined that the timer T 3  count exceeds the value t F  (YES) at the step SR 203 , this means that it is ready to ignite the fuel in the compression stroke cylinder, then the routine R 2  proceeds to a step SR 204 . On the other hand, if it is NO at the step SR 203 , it is not ready to ignite and the routine R 2  returns and waits for the timer T 3  counts up to the value t F . At the step SR 204 , the routine R 2  resets the flag F 11   f  to be Low and the timer T 3  to be zero. 
         [0122]    After the step SR 204  or after the decision at the step SR 202  is NO, the routine R 2  proceeds to a step SR 205  and the ignition control section  42  of the ECU  2  controls the ignition system  27  to cause the spark plug  15  to make a spark in the compression stroke cylinder (cylinder # 1  in  FIG. 22 ). Then, the routine R 2  proceeds to step SR 206  and increments a counter C 1  by one, and waits at a step SR 207  for the counter C 1  counting up every predetermined counts which correspond to a predetermined time period, such as 50 ms. After the count up of the counter C 1 , the routine R 2  proceeds to a step SR 208  and determines whether or not a crankshaft angle CA is changed. If it is YES at the step SR 208 , the ignition made at the step SR 205  is successful, because the crankshaft is determined to rotate. Then, the routine R 2  proceeds to a step SR 209  and resets the counter C 1  to be zero, resets the flag F 12  to be Low, and sets another flag F 13 . The flag F 13  indicates that combustion in the compression stroke cylinder is successful and that the engine  1  or the crankshaft  3  rotates in reverse. 
         [0123]    If it is not determined that the crank angle CA is not changed (NO) at the step SR 208 , the ignition at the step SR 205  is failed and another ignition will be attempted. First, the routine R 2  determines at a step  210  whether or not the counter C 1  counts more than a reference count number C F1 . If it is YES at the step SR 210 , it is considered that too many attempts to ignite the air and fuel mixture in the compression stroke cylinder are made, and the routine proceeds to a step SR 211  and resets the counter C 1  to be zero, resets the flag F 12  to be OFF and sets a flag F FAIL . On the other hand, if it is NO at the step SR 210 , the routine R 2  returns and repeats ignition attempts at the step SR 205  until the crank angle change is detected at the step SR 208 . 
         [0124]    The third stage of the engine restart control will now be described with reference to a flow chart of  FIG. 19  which illustrates the second control routine R 3 . After the start, at a step SR 301 , the routine determines whether the flag F 13  is High or Low. If it is Low, the routine returns and waits for the flag F 13  to be High. If the flag F 13  is High at the step SR 301 , the routine R 3  proceeds to a step SR 302  and estimates a current temperature T EXP     —     CYL  in the expansion stroke cylinder. The in-cylinder temperature estimation may be made in the same manner as is done for the temperature T COM     —     CYL  of the expansion stroke cylinder at the step SR 108  of the first routine R 1  or the first stage of the restart control. Then the routine proceeds to a step SR 303  and determines an air amount in the expansion stroke cylinder (AM EXP     —     CYL ) based on the estimated in-cylinder temperature T EXP     —     CYL  and a cylinder volume. The cylinder volume may be computed based on the crank angle CA STOP  when the engine stops, which is derived from the routine shown in  FIG. 5  and stored in the memory of the ECU  2 . 
         [0125]    Then, the routine R 3  proceeds to a step SR 304  and determines a fuel injection amount for the expansion stroke cylinder (FP EXP     —     CYL ) based on the air amount AM EXP     —     CYL  and the stop crank angle CA STOP  so that an air fuel ratio in the compression stroke cylinder (AF EXP     —     CYL ) is stoichiometric or rich (λ≦1) for maximizing energy exerted from the first forward rotation of the engine  1  or the crankshaft  3 . Then, it proceeds to a step SR 305  and determines first and second halves split from the fuel amount FP EXP     —     CYL  based on the stop crank angle CA STOP  and the estimated in-cylinder temperature T EXP     —     CYL . The second half of the fuel amount FP EXP     —     CYL2  is set larger as the stop crank angle CA STOP  indicates the expansion stroke cylinder stopped closer to its bottom dead center, because more air exists in the cylinder and compression counterforce will be higher so that the evaporative latent heat from the second half fuel will be necessary to reduce the compression counterforce. Also, the second half of the fuel amount FP EXP     —     CYL2  is set larger as the in-cylinder temperature T EXP     —     CYL  is higher, because it promotes to evaporate the injected fuel to reduce need for the earlier injection and later injection promotes faster combustion intended for the expansion stroke cylinder. Then, the routine R 3  proceeds to a step SR 306  and determines second fuel injection timing to the expansion stroke cylinder. The second fuel injection timing is set based on the stop crank angle CA STOP  and the estimated in-cylinder temperature T EXP     —     CYL  so that evaporative latent heat of the second half of the fuel helps to compress the air in the expansion stroke cylinder in the reverse movement and the injected fuel can be evaporated enough until the ignition. Then, the routine R 3  proceeds to a step SR 307  and determines timing of an ignition for the expansion stroke cylinder or a delay time period of the ignition from the second injection timing so that the injected fuel evaporates enough. 
         [0126]    After the step SR 307 , the routine proceeds to a step SR 308  and determines a fuel injection amount for the compression stroke cylinder after a reversal of rotation (FP CMP     —     CYL2 ). When the intake valve  19  of the compression stroke is not expected to open at a later stage of the reverse rotation (such as when the intake valve closing timing set at the step SR 102  is relatively early), the fuel amount FP CMP     —     CYL2  is determined based on the air amount AM CMP     —     CYL  estimated at the step SR 109  and any of the fuel amounts FP 1 , FP 2  and FP CMP     —     CYL1  injected into the compression stroke cylinder. The fuel amount FP CMP     —     CYL2  is set so that the air fuel ratio in the compression stroke cylinder after the reversal is richer than the combustible limit (7.0 or 8.0 for a gasoline engine) and may be for example 6.0, thereby preventing self-ignition of the air fuel mixture therein and counterforce caused by it. 
         [0127]    On the other hand, when the intake valve  19  is expected to open at the later stage of the reverse rotation as shown in  FIG. 22 , amount of fresh air inducted into the compression stroke cylinder during the opening of the intake stroke cylinder (AM CMP     —     IN ) is estimated based on the stop crank angle CA STOP , intake air temperature detected by the intake air temperature sensor  25  and an engine coolant temperature detected by the engine temperature sensor  33 . Then, the fuel amount FP CMP     —     CYL2  is determined based on the intake air amount AM CMP     —     IN , the air amount AM CMP     —     CYL  estimated at the step SR 109  and any of the fuel amounts FP 1 , FP 2  and FP CMP     —     CYL1  injected into the compression stroke cylinder. In this case, the fuel amount FP CMP     —     CYL2  is set so that the air fuel ratio in the compression stroke cylinder after the reversal is richer than the stoichiometry and combustible by spark ignition. 
         [0128]    After the step SR 308 , the routine R 3  proceeds to a step SR 309  and the fuel control section  41  of the ECU  2  controls the fuel supply system  16  to inject fuel of the first half amount (FP EXP     —     CYL1 =FP EXP     —     CYL −FP EXP     —     CYL2 ) which is determined at the steps SR 304  and SR 305  into the expansion stroke cylinder. Then, the routine R 3  proceeds to a step SR 310  and waits for the second injection timing determined at the step SR 306 . At the second injection timing or at a step SR 311 , the fuel control section  41  of the ECU  2  controls the fuel supply system  16  to inject fuel of the first second half amount (FP EXP     —     CYL2 ) which is determined at the step SR 305  into the expansion stroke cylinder. 
         [0129]    After the fuel is injected into the expansion stroke cylinder, the routine R 3  proceeds to a step SR 312  and waits for the ignition timing which is determined at the step SR 307 . At the ignition timing or at a step SR 313 , the ignition control section  42  of the ECU  2  controls the ignition system  27  to cause the spark plug  15  to make a spark in the expansion stroke cylinder. 
         [0130]    On the other hand, for the compression stroke cylinder, the routine R 3  waits at a step SR 314  for injection timing of fuel of the amount FP CMP     —     CYL2  determined at the step SR 308 . This injection timing is after the reversal of the rotation and before the compression stroke reaches its top dead center. Then, at the injection timing, the routine R 3  proceeds to a step SR 315  and the fuel control section  41  of the ECU  2  controls the fuel supply system  16  to inject fuel of the amount FP CMP     —     CYL2  which is determined at the step SR 308  into the compression stroke cylinder. Finally, the routine R 3  proceeds to a step SR 316  and resets the flag F 13  to be Low and sets another flag F 14  to be High. The flag F 14  indicates the engine  1  has started a forward rotation. 
         [0131]    The fourth stage of the engine restart control will now be described with reference to a flow chart of  FIG. 20  which illustrates the fourth control routine R 4 . After the start, at a step SR 401 , the routine determines whether the flag F 14  is High or Low. If it is Low, the routine returns and waits for the flag F 14  to be High. If it is High, it proceeds to a step SR 402  and waits for ignition timing of the compression stroke cylinder. This timing is set just (for example a couple of degrees crank angle) before a top dead center of the compression stroke cylinder or a first top dead center of the forward rotation (TDC 1 ), so that the ignited air fuel mixture generates energy after the first top dead center TDC 1 , as shown in  FIG. 22 , thereby accelerating the forward rotation, if combustible gas exists in the compression stroke cylinder even after the combustion for the reverse rotation. Then, at the ignition timing, the routine R 4  proceeds to a step SR 403  and the ignition control section  42  of the ECU  2  controls the ignition system  27  to cause the spark plug  15  to make a spark in the compression stroke cylinder. 
         [0132]    The routine R 4  proceeds to a step SR 404  and determines whether of not the crank angle CA indicates the engine  1  or the crankshaft  3  has passed the first top dead center TDC 1 . If it is NO, the routine R 4  proceeds to a step SR 405  and increments a counter C 2  by one. Then, it proceeds to a step SR 406  and determines whether or not the counter C 2  exceeds a reference value C F2 . If it is determined that the counter C 2  exceeds the reference value C F2  (YES) at the step SR 407 , it indicates that the first top dead center could not be passed and this engine restart operation is failed. Then, the routine R 4  proceeds to a step SR 407  and resets the counter C 2  to be zero, resets the flag F 14  to be Low and sets the fail flag F FAIL  to be High. If it is NO at the step SR 406 , the step SR 404  is repeated until it determines the first top dead center TDC 1  is passed. 
         [0133]    After it is determined at the step SR 404  that the TDC 1  is passed, the routine R 4  proceeds to a step SR 408  and resets the counter C 2  to be zero. Then, it proceeds to a step SR 409  and determines amount of fuel to be injected into a cylinder which was stopped in its intake stroke (FP INT     —     CYL ). That cylinder is the cylinder # 3  in the case of  FIGS. 14 and 22  and hereafter referred to as intake stroke cylinder. The fuel amount FP INT-CYL  is determined based on air amount in the intake stroke cylinder and an air fuel ratio AF INT-CYL . The air amount may be derived from air density estimated by the air density estimation section  47  of the ECU  2  and the cylinder volume when the intake valve  19  is closed. The air fuel ratio AF INT     —     CYL  is set leaner than the stoichimetory so that self ignition of the air fuel mixture does not occur before a top dead center of the intake stroke cylinder or a second top dead center TDC 2 . If the self ignition occurred before the TDC 2 , the ignition would cause combustion energy to be generated and the piston  13  in the intake stroke cylinder would be pushed down thereby acting against the rotational inertia of the crankshaft (negative torque) so that it would be harder to pass the second top dead center TDC 2 . 
         [0134]    Then, the routine R 4  proceeds to a step SR 410  and waits for an injection timing of the fuel of the amount FP INT     —     CYL . This injection timing is set at a later stage of the compression stroke so that the evaporative latent heat will reduce the compression pressure and the energy to pass the second top dead center. Specifically, it may be determined based on count value of the timer T 2  at the step SR 104  of the first routine R 1  corresponding to a time period of the engine stopping, an intake air temperature detected by the intake air temperature sensor  25 , an engine coolant temperature detected by the engine coolant temperature sensor  33 , and others. 
         [0135]    If it is determined that the injection timing is reached at the step SR 410 , the routine R 4  proceeds to a step SR 411  and the fuel control section  41  of the ECU  2  controls the fuel supply system  16  to inject fuel of the amount FP INT     —     CYL  which is determined at the step SR 409  into the intake stroke cylinder. Therefore, the fuel is injected before the second top dead center TDC 2 . To prevent the generation of the combustion energy against the rotational inertia, ignition of the injected fuel is made after the second top dead center TDC 2 . 
         [0136]    After the fuel injection to the intake stroke cylinder at the step SR 411 , the routine proceeds to a step SR 412  and determines whether or not the crank angle CA indicates the engine  1  or the crankshaft  3  has passed the second top dead center TDC 2 . If it is NO, the routine R 4  proceeds to a step SR 413  and increments a counter C 3  by one. Then, it proceeds to a step SR 414  and determines whether or not the counter C 3  exceeds a reference value C F3 . If it is determined that the counter C 3  exceeds the reference value C F3  (YES) at the step SR 414 , it indicates that the second top dead center could not be passed and this engine restart operation is failed. Then, the routine R 4  proceeds to a step SR 415  and resets the counter C 3  to be zero, resets the flag F 14  to be Low and sets the fail flag F FAIL  to be High. If it is NO at the step SR 414 , the step SR 412  is repeated until it determines the second top dead center TDC 2  is passed. 
         [0137]    If it is determined at the step SR  412  that the second top dead center TDC 2  is passed, the step proceeds to a step SR 416  and waits for the ignition timing for the intake stroke cylinder. At the ignition timing, the routine R 4  proceeds to a step SR 417  and the ignition control section  42  of the ECU  2  controls the ignition system  27  to cause the spark plug  15  to make a spark in the intake stroke cylinder. Then, the routine R 4  proceeds to a step SR 418  and starts the normal fuel and ignition control. Finally, it resets the counter C 3  to be zero, resets the flag F 14  to be OFF and sets another flag F 15  to be ON at a step SR 419 . The flag F 15  indicates that the engine  1  has successfully passed the second top dead center TDC 2  and has started a continuous forward rotation and that the fuel control section  41  and ignition control section  42  of the ECU  2  have restarted the control for the normal engine operation. 
         [0138]    The fifth or final stage of the engine restart control will now be described with reference to a flow chart of  FIG. 21  which illustrates the fifth control routine R 5 . After the start, at a step SR 501 , the routine determines whether the flag F 15  is High or Low. If it is Low, the routine returns and waits for the flag F 15  to be High. If it is High, it proceeds to a step SR 502  and determines whether or not an intake air pressure Bt detected by the intake air pressure sensor  26  is greater than a reference intake air pressure Bt IDLE  which corresponds to an intake air pressure at a normal idle operation. If it is YES at the step SR 502 , it is supposed that there is too much air in the intake air passage  21  and the engine speed may increase too much. This may be unfavorable because it may cause an acceleration shock or cause a vehicle driver to feel uncomfortable. 
         [0139]    If it is determined at the step SR 502  that the intake air pressure Bt is greater than the reference value Bt IDLE , the routine R 5  proceeds to a step SR 503  and the throttle control section  43  of the ECU  2  controls the actuator  24  to close the throttle valve, for example, fully close it (throttle opening K=0), thereby decreasing the intake air pressure Bt and the air amount to be inducted into the cylinders. Then, the routine R 5  proceeds to a step SR 504  and the alternator control section  44  of the ECU  2  controls the regulator circuit  28   a  to increase the field current Ge of the alternator  28 , for example, to 60 A, thereby increasing the load on the engine  1  or the crankshaft. The steps SR 503  and SR 504  are continued until it is determined that the intake air pressure Bt is less than the reference value Bt IDLE  (NO) at the step SR 502 . 
         [0140]    After the step SR 504 , the routine R 5  proceeds to a step SR 505  and estimates a temperature of the catalyst  37  (T CAT ) from various parameters including the count value of the timer T 2  which is stored in the step SR 111  of the routine R 1  and is corresponding to the time period of the engine stopping, and determines whether the catalyst temperature T CAT  is lower than a reference value T CAT1 . If it is YES at the step SR 504 , it is considered the catalyst  37  is cooled down beyond a proper active temperature of the catalyst  37  during the engine stopping, then the routine R 5  proceeds to a step SR 506  and sets a target air fuel ratio to be the stoichiometry or richer than that (λ≦1) so that the fuel control section  41  of the ECU  2 , which has started the normal control operation at the step SR 418  of the routine R 4 , controls the fuel supply system  16  to inject fuel with the stoichiometric or rich air fuel ratio into the cylinders. Then, the routine R 5  proceeds to a step SR 507  and sets an ignition timing to be after the top dead center so that the ignition control section  42  of the ECU  2 , which has also started the normal control operation at the step SR 418  of the routine R 4 , controls the ignition system  27  to make a spark in the cylinder after the top dead center. Thereby, the exhaust gas temperature is raised so that the catalyst  37  is heated up while the generated torque is reduced, preventing too much increase of the engine speed. 
         [0141]    On the other hand, if it is determined at the step SR 505  that the catalyst temperature T CAT  is lower than a reference value T CAT1 , it is considered the catalyst  37  is not cooled down during the engine stopping, then the routine proceeds to a step SR 507  and sets the target air fuel ratio to be lean of the stoichiometry (λ&gt;1). Thereby, fuel consumption is reduced while the generated torque is reduced, preventing too much increase of the engine speed. 
         [0142]    If it is determined that the intake air pressure MAP is less than the reference pressure Bt IDLE  (NO) at the step SR 502 , it is considered that there is not too much air in the intake air passage  21  and any special control is needed. Then, the routine R 5  proceeds to a step SR 508 , the throttle control section  43  starts its normal control operation. And, the routine R 5  proceeds to a step SR 509  and the alternator control section  44  starts its normal operation. Finally, the routine R 5  proceeds to a step SR 510  and resets the flag F 15 , finishing the engine restart control. 
       Slower Combustion for the Compression Stroke Cylinder and Faster Combustion for the Expansion Stroke Cylinder 
       [0143]    According to this embodiment of the reverse rotational type of the idle stop control, when the compression stroke cylinder (cylinder # 1 ) is in its intake stroke during the engine stop control, as show in  FIG. 14  between the times t 3  and t 4 , the fuel is injected into the compression stroke cylinder, specifically at the step SS 504  of the routine S 5  shown in  FIG. 10 . This fuel injected during the intake stroke is mixed well with the intake airflow, so that it is evaporated and atomized, thereby promoting the homogenization of the air fuel mixture. 
         [0144]    In the engine restart control, specifically at the time zero in  FIG. 22 , the air fuel mixture in the compression stroke cylinder (# 1 ) is ignited, specifically at the step SR 205  of the routine R 2  shown in  FIG. 18 . Then, the ignited mixture exerts the slower combustion, which may take, for example, 28 ms. Referring to  FIG. 23 , solid lines PL 1 , J 1  and Q 2  show a physical characteristic of the slower combustion in the present embodiment, and broken lines PL 2 , J 2  and Q 1  show a physical characteristic of the faster combustion for which fuel is injected into the compression stroke cylinder just before the ignition. 
         [0145]    The slower combustion in the compression stroke cylinder may moderate the heat loss, which is caused by the cylinder wall absorbing the heat generated by the combustion, thereby enabling conversion of larger amount of the energy into the movement energy of the crankshaft  3  rotating in reverse. This movement energy in the reverse rotation turns into movement energy in the forward rotation through the reversal of the rotation or the change of rotational direction. 
         [0146]    On the other hand, as shown in  FIG. 22 , the fuel ( FPEXP     —     CYL1  and FP EXP     —     CYL2 ) is injected to the cylinder # 2  (expansion stroke cylinder), specifically at the steps SR 306  and SR 311  of the routine R 3  shown in  FIG. 19 , and relatively shortly after it the spark is made, specifically at the steps SR 313 , thereby initiating the combustion. The rate of this combustion may be greater and the combustion may take shorter time period than that in the compression stroke cylinder (28 ms). So, the combustion time may be, for example, 15 ms, more preferably 11 ms. 
         [0147]    The time difference between the last fuel injection and the ignition in the expansion stroke cylinder (# 2  in  FIG. 22 ) is set, specifically at the steps SR 306  and SR 307  of the routine R 3  shown in  FIG. 19 , so that turbulence of the air fuel mixture caused by the fuel injection in the cylinder remains at the time of ignition. Therefore, the air fuel mixture is ignited when the turbulence remains, thereby making the combustion faster. The faster combustion enables the expansion stroke cylinder to generate larger energy within a limited piston stroke. 
         [0148]    It will now be described how to set the injection timing to the expansion stroke cylinder in accordance with a specific engine configuration. The inventors herein have simulated several factors which may affect the combustion in the expansion stroke cylinder for a specific engine configuration. 
         [0149]    As shown in a graph (A) of  FIG. 24 , a pressure in the expansion stroke cylinder at the reversal of the rotation is at an acceptable level, when the fuel is injected between 105 degree crank angle before top dead center (° CA BTDC) and 45° CA BTDC during the reverse rotation. That acceptable level is preferred for making a piston stroke of the compression stroke cylinder after the reversal of the rotation to be longer. Further if the fuel is injected between 100 and 55° CA BTDC as shown by a preferred range R 1 , it is supposed that penetration of the injected fuel mist is reduced so that the fuel is less likely to adhere the cylinder wall thereby promoting evaporation and atomization of the fuel and further decreasing the pressure in the expansion stroke cylinder. 
         [0150]    As show in a graph (B) of  FIG. 24 , energy of turbulence of the fuel mist increases as the injection timing is closer to the top dead center. The energy of turbulence means energy of random flow of the injected fuel mist. It is supposed that the combustion is faster as the energy of turbulence is greater. 
         [0151]    As show in a graph (C) of  FIG. 24 , an air fuel ratio around the spark plug  15  is constant when the fuel is injected between 105 and 45° CA BTDC. When the fuel is injected after 45° CA BTDC, the air fuel ratio becomes too rich, so that the combustion may be slower. In this instance, the fuel injection timing is preferably 45° CA BTDC or before. 
         [0152]    As show in a graph (C) of  FIG. 24 , a distribution of the mixture is evener when the fuel is injected before 45° CA BTDC. If it is injected after 40° CA BTDC, the mixture distribution becomes radically uneven and it is supposed that air usage ratio at the combustion is too low to combust the fuel appropriately. In this instance, the fuel injection timing is preferably 40° CA BTDC or earlier. 
         [0153]      FIG. 25  shows velocity contours of the air fuel mixtures and distribution of air fuel ratio in the expansion stroke cylinder when the piston is located relatively close to the top dead center after the fuel is injected respectively at 90, 70 and 45° CA BTDC. It can be seen from  FIG. 25 , within the preferable range R 1  (the fuel injection between 100 and 55° CA BTDC), the turbulence is smaller and the air fuel ratio is relatively even. On the other hand, the fuel injection timing is relatively later (45° CA BTDC), the turbulence is larger and the air fuel ratio is relatively uneven. 
         [0154]    From the foregoing, the inventors herein have reached a conclusion that if the fuel is dividedly injected between 90 and 60° CA BTDC, combination of preferable characters at the respective fuel injection timing can be obtained. For example, a first half of the fuel may be injected at 80° CA BTDC and the second half may be injected at 65° CA BTDC Then, the fuel mist may be ignited 30 ms after the second half, while the turbulence of the mist remains. Thereby, the first half fuel has a low penetration character because the piston is located relatively low at the injection timing and causes relatively even mixture distribution as shown in the graph (D) of  FIG. 24 , so that the first half fuel can effectively cool the air in the expansion stroke cylinder and effectively reduce the final in-cylinder pressure and increase a piston stroke. The second half fuel causes relatively higher energy of turbulence as shown in the graph (B) and is injected into the evenly distributed mixture of the first half fuel with relatively even air fuel ratio around the spark plug as shown in the graphs (C) and (D), so that relatively great turbulence energy may be generated. As a result of the greater piston stroke and the greater turbulence energy will make greater movement energy from the combustion in the expansion stroke cylinder. 
         [0155]    The fuel injection to the expansion stroke cylinder may be divided into three, instead of two, and the timings may be 90, 75 and 60° CA BTDC. 
         [0156]    Further in the case of the fuel injection divided into two, the injection timing for the first half may be between 90 and 70° CA BTDC, and that for the second half may be between 70° CA BTDC and the top dead center. In this case, there should be an interval of at least 2° CA or 1.5 ms, so that the reduced pressure by the in-cylinder cooling and the rapid homogeneous combustion described above can be achieved, thereby deriving the greater movement energy from the expansion stroke cylinder. 
       Engine Configurations for the Faster Combustion 
       [0157]    A different engine configuration may be employed for the faster combustion for the expansion stroke cylinder than for the compression stroke cylinder. At first, as shown in  FIGS. 26 and 27 , a multipoint spark ignition may be employed. Specifically, three spark plugs  15 A through  15 C are arranged on the cylinder head  10  and face the inside of the combustion chamber  14 . The spark plug  15 A is arranged at a center of the combustion chamber  14 , while the spark plugs  15 B and  15 C are at a periphery of the combustion chamber  14 . The ignition control section  42  of the ECU  2  may independently control the spark of the three spark plugs  15 A through  15 C through the ignition system  27 . The injector  16   a  of the multi-hole type may inject fuel toward each of the three spark plugs  15 A through  15 C. 
         [0158]    When the compression stroke cylinder is ignited at the step SR 205  in  FIG. 18 , as shown in  FIG. 22  at the time zero, only one or two of the three plugs  15 A through  15 C may spark, as shown in a diagram (A) or (B) of  FIG. 28 , thereby causing slower combustion. On the other hand, when the expansion stroke cylinder is ignited at the step SR 312 , all of the three spark plugs may spark simultaneously, as shown in a diagram (C) of  FIG. 28 , thereby exerting multipoint flame and shortening the flame propagation distance. Consequently, the shorter distance of flame propagation makes combustion at the expansion stroke cylinder faster than the combustion at the compression stroke cylinder. 
         [0159]    Further,  FIGS. 22 through 24  show other configurations of the engine  1  for the faster combustion at the expansion stroke cylinder. An additional injector  160  is arranged and faces the inside of the combustion chamber  14 . The additional injector  160  injects fuel which is easier to ignite than the fuel injected from the fuel injector  16   a . For example, in the case of gasoline injected from the injector  16   a , the additional injector  160  may inject hydrogen or mixture of gasoline and hydrogen. By only using the fuel injector  16   a  for the compression stroke cylinder, and only using the additional injector  160  for the expansion stroke cylinder, the combustion at the expansion stroke cylinder may be faster than that at the compression stroke cylinder, because of the difference of the ignitability levels. 
       Forward Rotational Type of Idle Stop Control 
       [0160]    Now, a forward rotational type of idle stop control will be described. At the time of restarting the engine  1 , fuel may already exist in a cylinder which has stopped in its expansion stroke (expansion stroke cylinder). Then, a spark is made in the expansion stroke cylinder, thereby initiating combustion. The first combustion for restarting the engine is for the forward rotation, rather than the reverse rotation in the case of the reverse rotational type of idle stop control described above. However, a piston stroke of the expansion stroke cylinder is limited and there is no force acting on the crankshaft  3  such as the rotational inertia and the compressive counterforce, so that the first combustion should be slower than the following combustions. 
         [0161]    The idle stop control of the forward rotation type consists of an engine stop control and an engine restart control. For the engine stop control, similar control routines to those of the engine stop control of the reverse rotational type are employed, except that the fuel injection at the step SS 504  of the routine S 5  is made to the expansion stroke cylinder or the cylinder # 2 , as shown in  FIG. 32 . Further, the steps SS 702 , SS 703 , SS 705  and SS 706  are not needed for the forward rotation type of the idle stop control. 
         [0162]    For the engine restart control, similar control routines to those of the reverse rotational type are employed. For example, the first stage of the engine restart control, a routine R 11  is run, as shown in  FIG. 33 . The routine R 11  is similar to the routine R 1  of the reverse rotational type, except for the steps SR 106 , SR 107  and SR 108  shown in  FIG. 17 . Further, fuel FP EXP     —     CYL  is injected into the expansion stroke cylinder or the cylinder # 3 , as shown in  FIG. 34 . 
         [0163]    After the first stage of the engine restart control or the routine R 11 , control routines similar to the routines R 2  through R 5  are taken, in which fuel injection and spark ignition are made in a sequence as shown in  FIG. 34 . Especially, amount of fuel injection and timing to the compression stroke cylinder are determined in the routine R 3 , in the same manner as for the reverse rotational type of the idle stop control, taking into account of the combustion rate described above. So, the combustion made in the compression stroke is faster than the combustion made in the expansion stroke. 
         [0164]    It is needless to say that the invention is not limited to the illustrated embodiments and that various improvements and alternative designs are possible without departing from the substance of the invention as claimed in the attached claims.