Patent Publication Number: US-10760519-B2

Title: Control device of compression-ignition engine

Description:
TECHNICAL FIELD 
     The technology disclosed herein relates to a control device of a compression-ignition engine. 
     BACKGROUND OF THE DISCLOSURE 
     It is known that combustion by compressed self-ignition, in which a mixture gas combusts instantly without flame propagation, maximizes fuel efficiency since the combustion period is minimal. However, various problems must be solved for automobile engines with regard to combustion by compressed self-ignition. For example, since the operating states and the environmental conditions vary greatly in automotive applications, stabilizing compressed self-ignition is a major problem. The combustion by compressed self-ignition has not been put to practical use for the automobile engine yet. In order to solve the problem, for example, JP4,082,292B2 proposes that an ignition plug ignites the mixture gas, when compressed self-ignition hardly occurs because of a low combustion-chamber temperature. By igniting the mixture gas immediately before the compression top dead center, the pressure around the ignition plug increases to facilitate the compressed self-ignition. 
     Unlike the technology disclosed in JP4,082,292B2 in which the compressed self-ignition is assisted by the ignition of the ignition plug, the present applicant rather proposes SPCCI (SPark Controlled Compression Ignition) combustion which is a combination of SI (Spark Ignition) combustion and CI (Compression Ignition) combustion. The SI combustion is combustion accompanied by the flame propagation initiated by forcibly igniting the mixture gas inside the combustion chamber. The CI combustion is combustion initiated by the mixture gas inside the combustion chamber carrying out the compressed self-ignition. The SPCCI combustion is combustion in which, when the mixture gas inside the combustion chamber is forcibly ignited to start the combustion by flame propagation, the unburnt mixture gas inside the combustion chamber combusts by the compression-ignition because of a pressure buildup due to the heat generation and the flame propagation of the SI combustion. Since the SPCCI combustion includes the CI combustion, it is one form of “the combustion by compression-ignition.” 
     The CI combustion takes place, when the in-cylinder temperature reaches an ignition temperature defined by the composition of the mixture gas. Fuel efficiency can be maximized, if the in-cylinder temperature reaches the ignition temperature near a compression top dead center and the CI combustion takes place. The in-cylinder temperature increases according to the increase in the in-cylinder pressure. The in-cylinder pressure in the SPCCI combustion is a result of two pressure buildups of a pressure buildup by the compression work of the piston in a compression stroke, and a pressure buildup caused by the heat generation of the SI combustion. 
     Here, if the CI combustion takes place near a compression top dead center because of a high in-cylinder temperature at a compression starting timing due to a high ambient temperature, etc., the in-cylinder pressure excessively increases to create excessive combustion noise. In this case, combustion noise can be reduced if the ignition timing is retarded. However, if the ignition timing is retarded, since the CI combustion takes place when the piston falls considerably in the expansion stroke, fuel efficiency is decreased. Since the pressure buildup caused by the heat generation of the SI combustion can be utilized in the SPCCI combustion, for example, it is effective to lower the effective compression ratio and to reduce the pressure buildup by the compression work of the piston in order to achieve both the reduction of combustion noise and improvement in fuel efficiency. Thus, combustion noise can be kept suitable, without decreasing fuel efficiency. 
     In order to put to practical use the engine which performs the SPCCI combustion, it is necessary to take into consideration other control factors relevant to the in-cylinder temperature, other than effective compression ratio. However, since the SPCCI combustion is a new combustion system, no one has found other control factors until now. 
     Since the SPCCI combustion is compression-ignition combustion, combustion noise tends to be increased. The present inventors found that it was necessary to adjust the temperature inside the combustion chamber at the start timing of the CI combustion to a suitable temperature, in order to achieve a stable SPCCI combustion, while reducing combustion noise. If the temperature inside the combustion chamber is low, the ignitability of the CI combustion falls. Combustion noise increases as the temperature inside the combustion chamber goes up. 
     The temperature inside the combustion chamber mainly depends on the geometric compression ratio of the engine, and the temperature and/or amount of gas introduced into the combustion chamber. Properties related to the gas introduced into the combustion chamber depend on the supercharging pressure of the supercharger, and the valve timing of the intake valve, especially when boosting. The optimal supercharging pressure was unknown so far. 
     SUMMARY OF THE DISCLOSURE 
     The present inventors succeeded in finding a relation between the supercharging pressure and the close timing of the intake valve, which appropriately causes SPCCI combustion, as a result of repeated and diligent examinations of SPCCI combustion. The present inventors came to invent a control device of a compression-ignition engine based on this knowledge. 
     Specifically, the technology disclosed herein relates to a control device of a compression-ignition engine. 
     The engine includes a fuel injection part configured to inject fuel to be supplied in a combustion chamber, a variable valve operating mechanism configured to change a valve timing of an intake valve, an ignition part configured to ignite a mixture gas inside the combustion chamber, a supercharger configured to boost gas introduced into the combustion chamber, a measurement part configured to measure a parameter related to an operating state of the engine, and a control part configured to perform a calculation according to a control logic corresponding to the operating state of the engine, in response to the measurement of the measurement part, and output a signal to the fuel injection part, the variable valve operating mechanism, the ignition part, and the supercharger. 
     The control part outputs the signal to the fuel injection part, the variable valve operating mechanism and the supercharger so that a gas-fuel ratio (G/F) that is a weight ratio of the entire gas of the mixture gas inside the combustion chamber to the fuel becomes leaner than a stoichiometric air fuel ratio, and an air-fuel ratio (A/F) that is a weight ratio of air contained in the mixture gas to the fuel becomes the stoichiometric air fuel ratio or richer than the stoichiometric air fuel ratio, while causing the supercharger to boost, and outputs the signal to the ignition part so that the unburnt mixture gas combusts by self-ignition after the ignition part ignites the mixture gas inside the combustion chamber. 
     The control part determines a supercharging pressure P by the supercharger, and determines a close timing IVC of the intake valve. The control part determines, according to the control logic, the close timing IVC (deg.aBDC) so that the supercharging pressure P (kPa) satisfies the following expression.
 
P≥8.0×10 −11 IVC 6 −1.0×10 −8 IVC 5 3.0×10 −7 IVC 4 −4.0×10 −6 IVC 3 +0.0068IVC 2 −0.3209IVC+116.63   (A)
 
     The ignition part ignites the mixture gas inside the combustion chamber in response to the signal from the control part. The combustion starts by flame propagation and then the unburnt mixture gas combusts by self-ignition to complete the combustion. That is, this engine performs the SPCCI (SPark Controlled Compression Ignition) combustion. 
     With this engine, the G/F of the mixture gas is made leaner than the stoichiometric air fuel ratio and the A/F is made to be the stoichiometric air fuel ratio or richer than the stoichiometric air fuel ratio. By making the G/F lean, fuel efficiency of the engine improves, and by making the A/F the stoichiometric air fuel ratio, emission performance improves by using a catalyst device. 
     In addition, the boost by the supercharger results in keeping the G/F of the mixture gas leaner than the stoichiometric air fuel ratio. This is advantageous in improving the fuel efficiency of the engine. 
     When controlling the engine, the control part first determines the supercharging pressure P by the supercharger. When the supercharging pressure P is set, the control part determines the close timing IVC of the intake valve so that the expression (A) is satisfied. By setting the close timing so as to satisfy the expression (A), the engine can perform a stable SPCCI combustion which is a combination of SI (Spark Ignition) combustion and CI (Compression Ignition) combustion while keeping combustion noise within the allowable range and the G/F lean environment, even under various conditions with different situations of the combustion chamber. 
     The index for determining the close timing IVC of the intake valve, which is available when controlling the engine for performing the SPCCI combustion, has been unknown until now. 
     The controlling method defines the relationship between the supercharging pressure P and the close timing IVC of the intake valve in order to achieve a suitable SPCCI combustion. When operating the engine, the control part can set the close timing IVC of the intake valve within the range in which the relationship is satisfied. Accordingly, the engine for performing the SPCCI combustion can put to practical use. 
     The supercharging pressure (kPa) may be determined so as to satisfy the following expression.
 
P≥150   (B)
 
     This is advantageous in using a comparatively small sized supercharger. 
     The control part may determine a target supercharging pressure corresponding to the operating state of the engine. The control part may determine the close timing IVC (deg.aBDC) so that, when the target supercharging pressure is used as the supercharging pressure P (kPa), the supercharging pressure P (kPa) satisfies the expression. 
     For example, when the engine load increases and the fuel amount supplied into the combustion chamber increases, by performing the boost by the supercharger, the G/F of the mixture gas is leaner than the stoichiometric air fuel ratio and the A/F is the stoichiometric air fuel ratio or richer than the stoichiometric air fuel ratio, which is advantageous in improving fuel efficiency. 
     The close timing IVC of the intake valve may change as the operating state of the engine changes, and the close timing IVC (deg.aBDC) may be determined for each operating state so that one of the expressions (A) and (B) is satisfied. 
     Thus, the engine can stably perform the SPCCI combustion in various operating states. 
     The engine may operate in a high-load operating state at a given load or higher. 
     In general CI combustion, since the pressure fluctuation at the ignition is relatively large, the combustion noise becomes too large when the engine load is high, and may exceed the allowable range. In this regard, in the SPCCI combustion, the SI combustion is performed at the start of the combustion and the pressure fluctuation at the ignition in the SI combustion is small. Thus, combustion noise can be reduced even when the engine load is high. 
     The engine may operate in a maximum load operating state. That is the engine may perform the SPCCI combustion in the maximum load operating state. 
     A geometric compression ratio ε of the engine may be set so as to satisfy 10≤ε&lt;21. In this way, the geometric compression ratio can be set suitably. 
     The engine may be provided with an exhaust gas recirculation (EGR) system configured to introduce exhaust gas into the combustion chamber. The control part may output the signal to the EGR system and the ignition part so that a heat amount ratio used as an index related to a ratio of an amount of heat generated when the mixture gas inside the combustion chamber combusts by flame propagation to the entire amount of heat generated when the mixture gas combusts, becomes a target heat amount ratio defined corresponding to the operating state of the engine. 
     The heat amount ratio of the SPCCI combustion is less than 100%. The heat amount ratio of the combustion mode where the combustion completes only by flame propagation without the combustion by compression ignition (i.e., SI combustion) is 100%. 
     If the heat amount ratio is increased in the SPCCI combustion, the ratio of the SI combustion increases, which is advantageous in reducing combustion noise. Whereas, if the heat amount ratio is lowered in the SPCCI combustion, the ratio of the CI combustion increases, which is advantageous in improving fuel efficiency. The heat amount ratio changes by changing the temperature of the combustion chamber and/or the ignition timing. For example, when the temperature inside the combustion chamber is high, the CI combustion starts at an early timing, and the heat amount ratio becomes low. Further, when the ignition timing is advanced, the SI combustion starts at an early timing, and the heat amount ratio becomes high. By the control part outputting signals to the EGR system and the ignition part so that the heat amount ratio becomes the target heat amount ratio defined in accordance with the operating state of the engine, both the reduction of combustion noise and the improvement of fuel efficiency can be achieved. 
     The control part may output a signal to the EGR system and the ignition part so that the heat amount ratio becomes higher when the load of the engine is higher. 
     When the engine load increases, the amount of fuel supplied into the combustion chamber increases and the temperature inside the combustion chamber becomes high. By increasing the heat amount ratio of the SPCCI combustion when the engine load is high, the combustion noise is reduced. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a view illustrating a configuration of an engine. 
         FIG. 2  is a view illustrating a configuration of a combustion chamber, where an upper figure corresponds to a plan view of the combustion chamber, and a lower figure is a cross-sectional view taken along a line II-II. 
         FIG. 3  is a plan view illustrating a configuration of the combustion chamber and an intake system. 
         FIG. 4  is a block diagram illustrating a configuration of an engine control device. 
         FIG. 5  is a graph illustrating a waveform of SPCCI combustion. 
         FIG. 6  illustrates maps of the engine, where an upper figure is a map when the engine is warm, a middle figure is a map when the engine is half warm, and a lower figure is a map when the engine is cold. 
         FIG. 7  illustrates the details of the map when the engine is warm. 
         FIG. 8  illustrates charts of a fuel injection timing, an ignition timing, and a combustion waveform in each operating range of the map of  FIG. 7 . 
         FIG. 9  illustrates a layer structure of the engine map. 
         FIG. 10  is a flowchart illustrating a control process according to a layer selection of the map. 
       An upper figure of  FIG. 11  is a graph illustrating a relation between an engine load and an open timing of an intake valve in Layer  2 , and a lower figure thereof is a graph illustrating a relation between an engine speed and the open timing of the intake valve in Layer  2 . 
       An upper figure of  FIG. 12  is a graph illustrating a relation between the engine load and the open timing of the intake valve in Layer  3 , a middle figure thereof is a graph illustrating a relation between the engine load and a close timing of an exhaust valve in Layer  3 , and a lower figure thereof is a graph illustrating a relation between the engine load, and an overlap period of the intake valve and the exhaust valve in Layer  3 . 
         FIG. 13  is a flowchart illustrating a process of an operation control of the engine executed by an ECU. 
         FIG. 14  illustrates a relation between the engine load and a target SI ratio. 
         FIG. 15  is a graph illustrating an occurring range of the SPCCI combustion versus an exhaust gas recirculation (EGR) rate in Layer  2 . 
         FIG. 16  is one example of a matrix image utilized in order to determine a relation between a geometric compression ratio and a close timing of the intake valve where the SPCCI combustion is possible in Layer  2 . 
       An upper figure of  FIG. 17  illustrates a relation between the geometric compression ratio and the close timing of the intake valve where the SPCCI combustion is possible in Layer  2  when high octane fuel is used, and a lower figure thereof illustrates a relation between the geometric compression ratio and the close timing of the intake valve where the SPCCI combustion is possible in Layer  2  when low octane fuel is used. 
         FIG. 18  is a graph illustrating a range where the SPCCI combustion is stabilized versus a gas-fuel ratio (G/F) in Layer  3 . 
         FIG. 19  is one example of a matrix image utilized in order to determine the relation between the geometric compression ratio and the close timing of the intake valve where the SPCCI combustion is possible in Layer  3 . 
       An upper figure of  FIG. 20  illustrates a relation between the geometric compression ratio and the close timing of the intake valve where the SPCCI combustion is possible in Layer  3  when high octane fuel is used, and a lower figure thereof illustrates a relation between the geometric compression ratio and the close timing of the intake valve where the SPCCI combustion is possible in Layer  3  when low octane fuel is used. 
       An upper figure of  FIG. 21  illustrates a relation between the geometric compression ratio and the close timing of the intake valve where the SPCCI combustion is possible in Layer  2  and Layer  3  when high octane fuel is used, and a lower figure thereof illustrates a relation between the geometric compression ratio and the close timing of the intake valve where the SPCCI combustion is possible in Layer  2  and Layer  3  when low octane fuel is used. 
         FIG. 22  is a flowchart illustrating a procedure of controlling a compression-ignition engine. 
       An upper figure of  FIG. 23  illustrates a relation between a supercharging pressure and the close timing of the intake valve where a G/F lean SPCCI combustion is possible in Layer  2  when the geometric compression ratio is set relatively high, and a lower figure thereof illustrates a relation between a supercharging pressure and the close timing of the intake valve where the G/F lean SPCCI combustion is possible in Layer  2  when the geometric compression ratio is set relatively low. 
         FIG. 24  is a flowchart illustrating a procedure of controlling the compression-ignition engine. 
     
    
    
     DETAILED DESCRIPTION OF THE DISCLOSURE 
     Hereinafter, one embodiment of a method of implementing control logic of a compression-ignition engine will be described in detail with reference to the accompanying drawings. The following description is one example of the engine and the method of implementing the control logic. 
       FIG. 1  is a view illustrating a configuration of the compression-ignition engine.  FIG. 2  is a view illustrating a configuration of a combustion chamber of the engine.  FIG. 3  is a view illustrating a configuration of the combustion chamber and an intake system. Note that in  FIG. 1 , an intake side is the left side in the drawing, and an exhaust side is the right side in the drawing. In  FIGS. 2 and 3 , the intake side is the right side in the drawings, and the exhaust side is the left side in the drawings.  FIG. 4  is a block diagram illustrating a configuration of a control device of the engine. 
     An engine  1  is a four-stroke engine which operates by a combustion chamber  17  repeating an intake stroke, a compression stroke, an expansion stroke, and an exhaust stroke. The engine  1  is mounted on an automobile with four wheels. The automobile travels by operating the engine  1 . Fuel of the engine  1  is gasoline in this example. The fuel may be a liquid fuel containing at least gasoline. The fuel may be gasoline containing, for example, bioethanol. 
     (Engine Configuration) 
     The engine  1  includes a cylinder block  12  and a cylinder head  13  placed thereon. A plurality of cylinders  11  are formed inside the cylinder block  12 . In  FIGS. 1 and 2 , only one cylinder  11  is illustrated. The engine  1  is a multi-cylinder engine. 
     A piston  3  is slidably inserted in each cylinder  11 . The pistons  3  are connected with a crankshaft  15  through respective connecting rods  14 . Each piston  3  defines the combustion chamber  17 , together with the cylinder  11  and the cylinder head  13 . Note that the term “combustion chamber” may be used in a broad sense. That is, the term “combustion chamber” may refer to a space formed by the piston  3 , the cylinder  11 , and the cylinder head  13 , regardless of the position of the piston  3 . 
     As illustrated in the lower figure of  FIG. 2 , a lower surface of the cylinder head  13 , i.e., a ceiling surface of the combustion chamber  17 , is comprised of a slope  1311  and a slope  1312 . The slope  1311  is a rising gradient from the intake side toward an injection axial center X 2  of an injector  6  which will be described later. The slope  1312  is a rising gradient from the exhaust side toward the injection axial center X 2 . The ceiling surface of the combustion chamber  17  is a so-called “pent-roof” shape. 
     An upper surface of the piston  3  is bulged toward the ceiling surface of the combustion chamber  17 . A cavity  31  is formed in the upper surface of the piston  3 . The cavity  31  is a dent in the upper surface of the piston  3 . The cavity  31  has a shallow pan shape in this example. The center of the cavity  31  is offset at the exhaust side with respect to a center axis X 1  of the cylinder  11 . 
     A geometric compression ratio ε of the engine  1  is set so as to satisfy 1≤ε&lt;30, and preferably satisfy 10≤ε&lt;21. The engine  1  which will be described later performs SPCCI (SPark Controlled Compression Ignition) combustion that is a combination of SI (Spark Ignition) combustion and CI (Compression Ignition) combustion in a part of operating ranges. The SPCCI combustion controls the CI combustion using a heat generation and a pressure buildup by the SI combustion. The engine  1  is the compression-ignition engine. However, in this engine  1 , temperature of the combustion chamber  17 , when the piston  3  is at a compression top dead center (i.e., compression end temperature), does not need to be increased. In the engine  1 , the geometric compression ratio can be set comparatively low. The low geometric compression ratio becomes advantageous in reduction of cooling loss and mechanical loss. For engines using regular gasoline (a low octane fuel of which octane number is about 91), the geometric compression ratio of the engine  1  is 14-17, and for those using high octane gasoline (high octane fuel of which octane number is about 96), the geometric compression ratio is 15-18. 
     An intake port  18  is formed in the cylinder head  13  for each cylinder  11 . As illustrated in  FIG. 3 , each intake port  18  has a first intake port  181  and a second intake port  182 . The intake port  18  communicates with the corresponding combustion chamber  17 . Although the detailed illustration of the intake port  18  is omitted, it is a so-called “tumble port.” That is, the intake port  18  has such a shape that a tumble flow is formed in the combustion chamber  17 . 
     Each intake valve  21  is disposed in the intake ports  181  and  182 . The intake valve  21  opens and closes a channel between the combustion chamber  17  and the intake port  181  or  182 . The intake valves  21  are opened and closed at given timings by a valve operating mechanism. The valve operating mechanism may be a variable valve operating mechanism which varies the valve timing and/or valve lift. In this example, as illustrated in  FIG. 4 , the variable valve operating mechanism has an intake-side electric S-VT (Sequential-Valve Timing)  23 . The intake-side electric S-VT  23  continuously varies a rotation phase of an intake cam shaft within a given angle range. The open timing and the close timing of the intake valve  21  vary continuously. Note that the electric S-VT may be replaced with a hydraulic S-VT, as the intake valve operating mechanism. 
     An exhaust port  19  is also formed in the cylinder head  13  for each cylinder  11 . As illustrated in  FIG. 3 , each exhaust port  19  also has a first exhaust port  191  and a second exhaust port  192 . The exhaust port  19  communicates with the corresponding combustion chamber  17 . 
     Each exhaust valve  22  is disposed in the exhaust ports  191  and  192 . The exhaust valve  22  opens and closes a channel between the combustion chamber  17  and the exhaust port  191  or  192 . The exhaust valves  22  are opened and closed at a given timing by a valve operating mechanism. The valve operating mechanism may be a variable valve operating mechanism which varies the valve timing and/or valve lift. In this example, as illustrated in  FIG. 4 , the variable valve operating mechanism has an exhaust-side electric SVT  24 . The exhaust-side electric S-VT  24  continuously varies a rotation phase of an exhaust cam shaft within a given angle range. The open timing and the close timing of the exhaust valve  22  change continuously. Note that the electric S-VT may be replaced with a hydraulic S-VT, as the exhaust valve operating mechanism. 
     The intake-side electric S-VT  23  and the exhaust-side electric S-VT  24  adjust the length of an overlap period where both the intake valve  21  and the exhaust valve  22  are open. If the length of the overlap period is made longer, the residual gas in the combustion chamber  17  can be purged. Moreover, by adjusting the length of the overlap period, internal EGR (Exhaust Gas Recirculation) gas can be introduced into the combustion chamber  17 . An internal EGR system is comprised of the intake-side electric S-VT  23  and the exhaust-side electric S-VT  24 . Note that the internal EGR system may not be comprised of the S-VT. 
     The injector  6  is attached to the cylinder head  13  for each cylinder  11 . Each injector  6  directly injects fuel into the combustion chamber  17 . The injector  6  is one example of a fuel injection part. The injector  6  is disposed in a valley part of the pent roof where the slope  1311  and the slope  1312  meet. As illustrated in  FIG. 2 , the injection axial center X 2  of the injector  6  is located at the exhaust side of the center axis X 1  of the cylinder  11 . The injection axial center X 2  of the injector  6  is parallel to the center axis X 1 . The injection axial center X 2  of the injector  6  and the center of the cavity  31  are in agreement with each other. The injector  6  faces the cavity  31 . Note that the injection axial center X 2  of the injector  6  may be in agreement with the center axis X 1  of the cylinder  11 . In such a configuration, the injection axial center X 2  of the injector  6  and the center of the cavity  31  may be in agreement with each other. 
     Although detailed illustration is omitted, the injector  6  is comprised of a multi nozzle-port type fuel injection valve having a plurality of nozzle ports. As illustrated by two-dot chain lines in  FIG. 2 , the injector  6  injects fuel so that the fuel spreads radially from the center of the combustion chamber  17 . The injector  6  has ten nozzle ports in this example, and the nozzle port is disposed so as to be equally spaced in the circumferential direction. 
     The injectors  6  are connected to a fuel supply system  61 . The fuel supply system  61  includes a fuel tank  63  configured to store fuel, and a fuel supply passage  62  which connects the fuel tank  63  to the injector  6 . In the fuel supply passage  62 , a fuel pump  65  and a common rail  64  are provided. The fuel pump  65  pumps fuel to the common rail  64 . The fuel pump  65  is a plunger pump driven by the crankshaft  15  in this example. The common rail  64  stores fuel pumped from the fuel pump  65  at a high fuel pressure. When the injector  6  is opened, the fuel stored in the common rail  64  is injected into the combustion chamber  17  from the nozzle ports of the injector  6 . The fuel supply system  61  can supply fuel to the injectors  6  at a high pressure of 30 MPa or higher. The pressure of fuel supplied to the injector  6  may be changed according to the operating state of the engine  1 . Note that the configuration of the fuel supply system  61  is not limited to the configuration described above. 
     An ignition plug  25  is attached to the cylinder head  13  for each cylinder  11 . The ignition plug  25  forcibly ignites a mixture gas inside the combustion chamber  17 . The ignition plug  25  is disposed at the intake side of the center axis X 1  of the cylinder  11  in this example. The ignition plug  25  is located between the two intake ports  181  and  182  of each cylinder. The ignition plug  25  is attached to the cylinder head  13  so as to incline downwardly toward the center of the combustion chamber  17 . As illustrated in  FIG. 2 , the electrode of the ignition plug  25  faces to the inside of the combustion chamber  17  and is located near the ceiling surface of the combustion chamber  17 . Note that the ignition plug  25  may be disposed at the exhaust side of the center axis X 1  of the cylinder  11 . Moreover, the ignition plug  25  may be disposed on the center axis X 1  of the cylinder  11 . 
     An intake passage  40  is connected to one side surface of the engine  1 . The intake passage  40  communicates with the intake port  18  of each cylinder  11 . Gas introduced into the combustion chamber  17  flows through the intake passage  40 . An air cleaner  41  is disposed in an upstream end part of the intake passage  40 . The air cleaner  41  filters fresh air. A surge tank  42  is disposed near the downstream end of the intake passage  40 . Part of the intake passage  40  downstream of the surge tank  42  constitutes independent passages branched from the intake passage  40  for each cylinder  11 . The downstream end of each independent passage is connected to the intake port  18  of each cylinder  11 . 
     A throttle valve  43  is disposed between the air cleaner  41  and the surge tank  42  in the intake passage  40 . The throttle valve  43  adjusts an introducing amount of the fresh air into the combustion chamber  17  by adjusting an opening of the throttle valve. 
     A supercharger  44  is also disposed in the intake passage  40 , downstream of the throttle valve  43 . The supercharger  44  boosts gas to be introduced into the combustion chamber  17 . In this example, the supercharger  44  is a mechanical supercharger driven by the engine  1 . The mechanical supercharger  44  may be a root, Lysholm, vane, or a centrifugal type. 
     An electromagnetic clutch  45  is provided between the supercharger  44  and the engine  1 . The electromagnetic clutch  45  transmits a driving force from the engine  1  to the supercharger  44  or disengages the transmission of the driving force between the supercharger  44  and the engine  1 . As will be described later, an ECU  10  switches the disengagement and engagement of the electromagnetic clutch  45  to switch the supercharger  44  between ON and OFF. 
     An intercooler  46  is disposed downstream of the supercharger  44  in the intake passage  40 . The intercooler  46  cools gas compressed by the supercharger  44 . The intercooler  46  may be of a water cooling type or an oil cooling type, for example. 
     A bypass passage  47  is connected to the intake passage  40 . The bypass passage  47  connects an upstream part of the supercharger  44  to a downstream part of the inter cooler  46  in the intake passage  40  so as to bypass the supercharger  44  and the inter cooler  46 . An air bypass valve  48  is disposed in the bypass passage  47 . The air bypass valve  48  adjusts a flow rate of gas flowing in the bypass passage  47 . 
     The ECU  10  fully opens the air bypass valve  48  when the supercharger  44  is turned OFF (i.e., when the electromagnetic clutch  45  is disengaged). The gas flowing through the intake passage  40  bypasses the supercharger  44  and is introduced into the combustion chamber  17  of the engine  1 . The engine  1  operates in a non-supercharged state, i.e., a natural aspiration state. 
     When the supercharger  44  is turned ON, the engine  1  operates in a supercharged state. The ECU  10  adjusts an opening of the air bypass valve  48  when the supercharger  44  is turned ON (i.e., when the electromagnetic clutch  45  is engaged). A portion of the gas which passed through the supercharger  44  flows back toward upstream of the supercharger  44  through the bypass passage  47 . When the ECU  10  adjusts the opening of the air bypass valve  48 , a supercharging pressure of gas introduced into the combustion chamber  17  changes. Note that the term “supercharging” as used herein refers to a situation where the pressure inside the surge tank  42  exceeds an atmospheric pressure, and “non-supercharging” refers to a situation where the pressure inside the surge tank  42  becomes below the atmospheric pressure. 
     In this example, a supercharging system  49  is comprised of the supercharger  44 , the bypass passage  47 , and the air bypass valve  48 . 
     The engine  1  has a swirl generating part which generates a swirl flow inside the combustion chamber  17 . As illustrated in  FIG. 3 , the swirl generating part has a swirl control valve  56  attached to the intake passage  40 . Among a primary passage  401  coupled to the first intake port  181  and a secondary passage  402  coupled to the second intake port  182 , the swirl control valve  56  is disposed in the secondary passage  402 . The swirl control valve  56  is an opening control valve which is configured to choke a cross section of the secondary passage  402 . When the opening of the swirl control valve  56  is small, since an intake flow rate of air flowing into the combustion chamber  17  from the first intake port  181  is relatively large, and an intake flow rate of air flowing into the combustion chamber  17  from the second intake port  182  is relatively small, the swirl flow inside the combustion chamber  17  becomes stronger. On the other hand, when the opening of the swirl control valve  56  is large, since the intake flow rates of air flowing into the combustion chamber  17  from the first intake port  181  and the second intake port  182  become substantially equal, the swirl flow inside the combustion chamber  17  becomes weaker. When the swirl control valve  56  is fully opened, the swirl flow will not occur. Note that the swirl flow circulates counterclockwise in  FIG. 3 , as illustrated by white arrows (also see white arrows in  FIG. 2 ). 
     An exhaust passage  50  is connected to the other side surface of the engine  1 . The exhaust passage  50  communicates with the exhaust port  19  of each cylinder  11 . The exhaust passage  50  is a passage through which exhaust gas discharged from the combustion chambers  17  flows. Although detailed illustration is omitted, an upstream part of the exhaust passage  50  constitutes independent passages branched from the exhaust passage  50  for each cylinder  11 . The upper end of the independent passage is connected to the exhaust port  19  of each cylinder  11 . 
     An exhaust gas purification system having a plurality of catalytic converters is disposed in the exhaust passage  50 . Although illustration is omitted, an upstream catalytic converter is disposed inside an engine room. The upstream catalytic converter has a three-way catalyst  511  and a GPF (Gasoline Particulate Filter)  512 . The downstream catalytic converter is disposed outside the engine room. The downstream catalytic converter has a three-way catalyst  513 . Note that the exhaust gas purification system is not limited to the illustrated configuration. For example, the GPF may be omitted. Moreover, the catalytic converter is not limited to those having the three-way catalyst. Further, the order of the three-way catalyst and the GPF may suitably be changed. 
     Between the intake passage  40  and the exhaust passage  50 , an EGR passage  52  which constitutes an external EGR system is connected. The EGR passage  52  is a passage for recirculating part of the exhaust gas to the intake passage  40 . The upstream end of the EGR passage  52  is connected between the upstream catalytic converter and the downstream catalytic converter in the exhaust passage  50 . The downstream end of the EGR passage  52  is connected to an upstream part of the supercharger  44  in the intake passage  40 . EGR gas flowing through the EGR passage  52  flows into the upstream part of the supercharger  44  in the intake passage  40 , without passing through the air bypass valve  48  of the bypass passage  47 . 
     An EGR cooler  53  of a water cooling type is disposed in the EGR passage  52 . The EGR cooler  53  cools the exhaust gas. An EGR valve  54  is also disposed in the EGR passage  52 . The EGR valve  54  adjusts a flow rate of the exhaust gas flowing through the EGR passage  52 . By adjusting the opening of the EGR valve  54 , an amount of the cooled exhaust gas, i.e., a recirculating amount of external EGR gas can be adjusted. 
     In this example, an EGR system  55  is comprised of the external EGR system and the internal EGR system. The external EGR system can supply the exhaust gas to the combustion chamber  17  that is lower in temperature than the internal EGR system. 
     The control device of the compression-ignition engine includes the ECU (Engine Control Unit)  10  for operating the engine  1 . The ECU  10  is a controller based on a well-known microcomputer, and as illustrated in  FIG. 4 , includes a central processing unit (CPU)  101  which executes a computer program, memory  102  which, for example, is comprised of a RAM (Random Access Memory) and/or a ROM (Read Only Memory), and stores the program and data, and an input/output bus  103  which inputs and outputs an electrical signal. The ECU  10  is one example of the control part. 
     As illustrated in  FIGS. 1 and 4 , various kinds of sensors SW 1 -SW 17  are connected to the ECU  10 . The sensors SW 1 -SW 17  output signals to the ECU  10 . The sensors include the following sensors: 
     Airflow sensor SW 1 : Disposed downstream of the air cleaner  41  in the intake passage  40 , and measures a flow rate of fresh air flowing through the intake passage  40 ; 
     First intake-air temperature sensor SW 2 : Disposed downstream of the air cleaner  41  in the intake passage  40 , and measures the temperature of fresh air flowing through the intake passage  40 ; 
     First pressure sensor SW 3 : Disposed downstream of the connected position of the EGR passage  52  in the intake passage  40  and upstream of the supercharger  44 , and measures the pressure of gas flowing into the supercharger  44 ; 
     Second intake-air temperature sensor SW 4 : Disposed downstream of the supercharger  44  in the intake passage  40  and upstream of the connected position of the bypass passage  47 , and measures the temperature of gas flowed out of the supercharger  44 ; 
     Second pressure sensor SW 5 : Attached to the surge tank  42 , and measures the pressure of gas downstream of the supercharger  44 ; 
     Pressure indicating sensors SW 6 : Attached to the cylinder head  13  corresponding to each cylinder  11 , and measures the pressure inside each combustion chamber  17 ; 
     Exhaust temperature sensor SW 7 : Disposed in the exhaust passage  50 , and measures the temperature of the exhaust gas discharged from the combustion chamber  17 ; 
     Linear O 2  sensor SW 8 : Disposed upstream of the upstream catalytic converter in the exhaust passage  50 , and measures the oxygen concentration of the exhaust gas; 
     Lambda O 2  sensor SW 9 : Disposed downstream of the three-way catalyst  511  in the upstream catalytic converter, and measures the oxygen concentration of the exhaust gas; 
     Water temperature sensor SW 10 : Attached to the engine  1  and measures the temperature of coolant; 
     Crank angle sensor SW 11 : Attached to the engine  1  and measures the rotation angle of the crankshaft  15 ; 
     Accelerator opening sensor SW 12 : Attached to an accelerator pedal mechanism and measures the accelerator opening corresponding to an operating amount of the accelerator pedal; 
     Intake cam angle sensor SW 13 : Attached to the engine  1  and measures the rotation angle of an intake cam shaft; 
     Exhaust cam angle sensor SW 14 : Attached to the engine  1  and measures the rotation angle of an exhaust cam shaft; 
     EGR pressure difference sensor SW 15 : Disposed in the EGR passage  52  and measures a pressure difference between the upstream and the downstream of the EGR valve  54 ; 
     Fuel pressure sensor SW 16 : Attached to the common rail  64  of the fuel supply system  61 , and measures the pressure of fuel supplied to the injector  6 ; and 
     Third intake-air temperature sensor SW 17 : Attached to the surge tank  42 , and measures the temperature of gas inside the surge tank  42 , i.e., the temperature of intake air introduced into the combustion chamber  17 . 
     The ECU  10  determines the operating state of the engine  1  based on the signals of the sensors SW 1 -SW 17 , and calculates a control amount of each device according to the control logic defined beforehand. The control logic is stored in the memory  102 . The control logic includes calculating a target amount and/or the control amount by using a map stored in the memory  102 . 
     The ECU  10  outputs electrical signals according to the calculated control amounts to the injectors  6 , the ignition plugs  25 , the intake-side electric S-VT  23 , the exhaust-side electric S-VT  24 , the fuel supply system  61 , the throttle valve  43 , the EGR valve  54 , the electromagnetic clutch  45  of the supercharger  44 , the air bypass valve  48 , and the swirl control valve  56 . 
     For example, the ECU  10  sets a target torque of the engine  1  based on the signal of the accelerator opening sensor SW 12  and the map, and determines a target supercharging pressure. The ECU  10  then performs a feedback control for adjusting the opening of the air bypass valve  48  based on the target supercharging pressure and the pressure difference before and after the supercharger  44  obtained from the signals of the first pressure sensor SW 3  and the second pressure sensor SW 5  so that the supercharging pressure becomes the target supercharging pressure. 
     Moreover, the ECU  10  sets a target EGR ratio (i.e., a ratio of the EGR gas to the entire gas inside the combustion chamber  17 ) based on the operating state of the engine  1  and the map. The ECU  10  then determines a target EGR gas amount based on the target EGR ratio and an intake air amount based on the signal of the accelerator opening sensor SW 12 , and performs a feedback control for adjusting the opening of the EGR valve  54  based on the pressure difference before and after the EGR valve  54  obtained from the signal of the EGR pressure difference sensor SW 15  so that the external EGR gas amount introduced into the combustion chamber  17  becomes the target EGR gas amount. 
     Further, the ECU  10  performs an air-fuel ratio feedback control when a given control condition is satisfied. For example, the ECU  10  adjusts the fuel injection amount of the injector  6  based on the oxygen concentration of the exhaust gas which is measured by the linear O 2  sensor SW 8  and the lambda O 2  sensor SW 9  so that the air-fuel ratio of the mixture gas becomes a desired value. 
     Note that the details of other controls of the engine  1  executed by the ECU  10  will be described later. 
     (Concept of SPCCI Combustion) 
     The engine  1  performs combustion by compressed self-ignition under a given operating state, mainly to improve fuel consumption and emission performance. The combustion by self-ignition varies largely at the timing of the self-ignition, if the temperature inside the combustion chamber  17  before a compression starts is nonuniform. Thus, the engine  1  performs the SPCCI combustion which is a combination of the SI combustion and the CI combustion. 
     The SPCCI combustion is combustion in which the ignition plug  25  forcibly ignites the mixture gas inside the combustion chamber  17  so that the mixture gas carries out the SI combustion by flame propagation, and the temperature inside the combustion chamber  17  increases by the heat generation of the SI combustion and the pressure inside the combustion chamber  17  increases by the flame propagation so that the unburnt mixture gas carries out the CI combustion by self-ignition. 
     By adjusting the heat amount of the SI combustion, the variation in the temperature inside the combustion chamber  17  before a compression starts can be absorbed. By the ECU  10  adjusting the ignition timing, the mixture gas can be self-ignited at a target timing. 
     In the SPCCI combustion, the heat release of the SI combustion is slower than the heat release in the CI combustion. As illustrated in  FIG. 5 , the waveform of the heat release rate of the SI combustion in the SPCCI combustion is smaller in the rising slope than the waveform in the CI combustion. In addition, the SI combustion is slower in the pressure fluctuation (dp/dθ) inside the combustion chamber  17  than the CI combustion. 
     When the unburnt mixture gas self-ignites after the SI combustion is started, the waveform slope of the heat release rate may become steeper. The waveform of the heat release rate may have an inflection point X at a timing of starting the CI combustion. 
     After the start in the CI combustion, the SI combustion and the CI combustion are performed in parallel. Since the CI combustion has larger heat release than the SI combustion, the heat release rate becomes relatively large. However, since the CI combustion is performed after a compression top dead center, the waveform slope of the heat release rate does not become too steep. The pressure fluctuation in the CI combustion (dp/dθ) also becomes comparatively slow. 
     The pressure fluctuation (dp/dθ) can be used as an index representing combustion noise. As described above, since the SPCCI combustion can reduce the pressure fluctuation (dp/dθ), it is possible to avoid excessive combustion noise. Combustion noise of the engine  1  can be kept below the tolerable level. 
     The SPCCI combustion is completed when the CI combustion is finished. The CI combustion is shorter in the combustion period than the SI combustion. The end timing of the SPCCI combustion becomes earlier than the SI combustion. 
     The heat release rate waveform of the SPCCI combustion is formed so that a first heat release rate part Q SI  formed by the SI combustion and a second heat release rate part Q CI  formed by the CI combustion continue in this order. 
     Here, a SI ratio is defined as a parameter indicative of a characteristic of the SPCCI combustion. The SI ratio is defined as an index related to a ratio of the amount of heat generated by the SI combustion to the entire amount of heat generated by the SPCCI combustion. The SI ratio is a ratio of heat amount generated by the two different combustion modes. If the SI ratio is high, the ratio of the SI combustion is high, and if the SI ratio is low, the ratio in the CI combustion is high. Alternatively, the SI ratio may be defined as a ratio of the amount of heat generated by the SI combustion to the amount of heat generated by the CI combustion. That is, in a waveform  801  illustrated in  FIG. 5 ,
 
SI ratio= Q   SI   /Q   CI .
 
Here,
 
     Q SI : Area of SI combustion; and 
     Q CI : Area of CI combustion. 
     The engine  1  generates a strong swirl flow inside the combustion chamber  17  when performing the SPCCI combustion. The term “strong swirl flow” may be defined as a flow having a swirl ratio of four or higher, for example. The swirl ratio can be defined as a value obtained by dividing an integrated value of intake flow lateral angular velocities by an engine angular velocity, where the intake flow lateral angular velocity is measured for every valve lift, and the measured values are integrated to obtain the integrated value. Although illustration is omitted, the intake flow lateral angular velocity can be obtained based on measurement using known rig test equipment. 
     When the strong swirl flow is generated in the combustion chamber  17 , the swirl flow is stronger in an outer circumferential part of the combustion chamber  17  and is relatively weaker in a central part. By the whirlpool resulting from a velocity gradient at the boundary between the central part and the outer circumferential part, turbulence energy becomes higher in the central part. When the ignition plug  25  ignites the mixture gas in the central part, the combustion speed of the SI combustion becomes higher by the high turbulence energy. 
     Flame of the SI combustion is carried by the strong swirl flow inside the combustion chamber  17  and propagates in the circumferential direction. The CI combustion is performed from the outer circumferential part to the central part in the combustion chamber  17 . 
     When the strong swirl flow is generated in the combustion chamber  17 , the SI combustion can fully be performed before the start in the CI combustion. Thus, the generation of combustion noise can be reduced, and the variation in the torque between cycles can be reduced. 
     (Engine Operating Range) 
       FIGS. 6 and 7  illustrate maps according to the control of the engine  1 . The maps are stored in the memory  102  of the ECU  10 . The maps include three kinds of maps, a map  501 , a map  502 , and a map  503 . The ECU  10  uses a map selected from the three kinds of maps  501 ,  502 , and  503  according to a wall temperature of the combustion chamber  17  and an intake air temperature, in order to control the engine  1 . Note that the details of the selection of the three kinds of maps  501 ,  502 , and  503  will be described later. 
     The first map  501  is a map when the engine  1  is warm. The second map  502  is a map when the engine  1  is half warm. The third map  503  is a map when the engine  1  is cold. 
     The maps  501 ,  502 , and  503  are defined based on the load and the engine speed of the engine  1 . The first map  501  is roughly divided into three areas depending on the load and the engine speed. For example, the three areas include a low load area A 1 , a middle-to-high load area (A 2 , A 3 , and A 4 ), and a high speed area A 5 . The low load area A 1  includes idle operation, and covers areas of a low engine speed and a middle engine speed. The middle-to-high load area (A 2 , A 3 , and A 4 ) are higher in the load than the low load area A 1 . The high speed area A 5  is higher in the engine speed than the low load area A 1  and the middle-to-high load area (A 2 , A 3 , and A 4 ). The middle-to-high load area (A 2 , A 3 , and A 4 ) is divided into a middle load area A 2 , a high-load middle-speed area A 3  where the load is higher than the middle load area A 2 , and a high-load low-speed area A 4  where the engine speed is lower than the high-load middle-speed area A 3 . 
     The second map  502  is roughly divided into two areas. For example, the two areas include a low-to-middle speed area (B 1 , B 2 , and B 3 ) and a high speed area B 4  where the engine speed is higher than the low-to-middle speed area (B 1 , B 2 , and B 3 ). The low-to-middle speed area (B 1 , B 2 , and B 3 ) is divided into a low-to-middle load area B 1  corresponding to the low load area A 1  and the middle load area A 2 , a high-load middle-speed area B 2 , and a high-load low-speed area B 3 . 
     The third map  503  has only one area Cl, without being divided into a plurality of areas. 
     Here, the low speed area, the middle speed area, and the high speed area may be defined by substantially equally dividing the entire operating range of the engine  1  into three areas in the engine speed direction. In the example of  FIGS. 6 and 7 , the engine speed is defined to be a low speed if the engine speed is lower than the engine speed N 1 , a high speed if the engine speed is higher than or equal to the engine speed N 2 , and a middle speed if the engine speed is higher than or equal to the engine speed N 1  and lower than the engine speed N 2 . For example, the engine speed N 1  may be about 1,200 rpm, and the engine speed N 2  may be about 4,000 rpm. 
     Moreover, the low load area may be an area including an operating state with the light load, the high load area may be an area including an operating state with full load, and the middle load area may be an area between the low load area and the high load area. Moreover, the low load area, the middle load area, and the high load area may be defined by substantially equally dividing the entire operating range of the engine  1  into three areas in the load direction. 
     The maps  501 ,  502 , and  503  in  FIG. 6  illustrate the states and combustion modes of the mixture gas in the respective areas. A map  504  in  FIG. 7  corresponds to the first map  501 , and illustrates the state and combustion mode of the mixture gas in each area of the map, the opening of the swirl control valve  56  in each area, and a driving area and a non-driving area of the supercharger  44 . The engine  1  performs the SPCCI combustion in the low load area A 1 , the middle load area A 2 , the high-load middle-speed area A 3 , the high-load low-speed area A 4 , the low-to-middle load area B 1 , the high-load middle-speed area B 2 , and the high-load low-speed area B 3 . The engine  1  performs the SI combustion in other areas, specifically, in the high speed area A 5 , the high speed area B 4 , and the area C 1 . 
     (Operation of Engine in Each Area) 
     Below, the operation of the engine  1  in each area of the map  504  in  FIG. 7  will be described in detail with reference to the fuel injection timing and the ignition timing which are illustrated in  FIG. 8 . The horizontal axis in  FIG. 8  is a crank angle. Note that the reference numerals  601 ,  602 ,  603 ,  604 ,  605 , and  606  in  FIG. 8  correspond to the operating states of the engine  1  indicated by the reference numerals  601 ,  602 ,  603 ,  604 ,  605 , and  606  in the map  504  of  FIG. 7 , respectively. 
     (Low load Area) 
     The engine  1  performs the SPCCI combustion when the engine  1  operates in the low load area A 1 . 
     The reference numeral  601  in  FIG. 8  indicates fuel injection timings (reference numerals  6011  and  6012 ), an ignition timing (reference numeral  6013 ), and a combustion waveform (i.e., a waveform indicating a change in the heat release rate with respect to the crank angle: reference numeral  6014 ), when the engine  1  operates in the operating state  601  in the low load area A 1 . The reference numeral  602  indicates fuel injection timings (reference numerals  6021  and  6022 ), an ignition timing (reference numeral  6023 ), and a combustion waveform (reference numeral  6024 ), when the engine  1  operates in the operating state  602  in the low load area A 1 . The reference numeral  603  indicates fuel injection timings (reference numerals  6031  and  6032 ), an ignition timing (reference numeral  6033 ), and a combustion waveform (reference numeral  6034 ), when the engine  1  operates in the operating state  603  in the low load area A 1 . The operating states  601 ,  602 , and  603  have the same engine speed, but different loads. The operating state  601  has the lowest load (i.e., light load), the operating state  602  has the second lowest load (i.e., low load), and the operating state  603  has the maximum load among these states. 
     In order to improve the fuel efficiency of the engine  1 , the EGR system  55  introduces the EGR gas into the combustion chamber  17 . For example, the intake-side electric S-VT  23  and the exhaust-side electric S-VT  24  are provided with a positive overlap period where both the intake valve  21  and the exhaust valve  22  are opened near an exhaust top dead center. Part of the exhaust gas discharged from the combustion chamber  17  into the intake port  18  and the exhaust port  19  is re-introduced into the combustion chamber  17 . Since the hot exhaust gas is introduced into the combustion chamber  17 , the temperature inside the combustion chamber  17  increases. Thus, it becomes advantageous to stabilize the SPCCI combustion. Note that the intake-side electric S-VT  23  and the exhaust-side electric S-VT  24  may be provided with a negative overlap period where both the intake valve  21  and the exhaust valve  22  are closed. 
     Moreover, the swirl generating part forms the strong swirl flow inside the combustion chamber  17 . The swirl ratio is four or higher, for example. The swirl control valve  56  is fully closed or at a given opening (closed to some extent). As described above, since the intake port  18  is the tumble port, an inclined swirl flow having a tumble component and a swirl component is formed in the combustion chamber  17 . 
     The injector  6  injects fuel into the combustion chamber  17  a plurality of times during the intake stroke (reference numerals  6011 ,  6012 ,  6021 ,  6022 ,  6031 , and  6032 ). The mixture gas is stratified by the multiple fuel injections and the swirl flow inside the combustion chamber  17 . 
     The fuel concentration of the mixture gas in the central part of the combustion chamber  17  is denser or richer than the fuel concentration in the outer circumferential part. For example, the air-fuel ratio (A/F) of the mixture gas in the central part is 20 or higher and 30 or lower, and the A/F of the mixture gas in the outer circumferential part is 35 or higher. Note that the value of the A/F is a value when the mixture gas is ignited, and the same applies to the following description. Since the A/F of the mixture gas near the ignition plug  25  is set 20 or higher and 30 or lower, generation of raw NO x  during the SI combustion can be reduced. Moreover, since the A/F of the mixture gas in the outer circumferential part is set to 35 or higher, the CI combustion stabilizes. 
     The A/F of the mixture gas is leaner than the stoichiometric air fuel ratio throughout the combustion chamber  17  (i.e., excess air ratio λ&gt;1). For example, the A/F of the mixture gas is 30 or higher throughout the combustion chamber  17 . Thus, the generation of raw NO x  can be reduced to improve the emission performance. 
     When the engine load is low (i.e., in the operating state  601 ), the injector  6  performs the first injection  6011  in the first half of an intake stroke, and performs the second injection  6012  in the second half of the intake stroke. The first half of the intake stroke may be a first half of an intake stroke when the intake stroke is equally divided into two, and the second half of the intake stroke may be the rest. Moreover, an injection amount ratio of the first injection  6011  to the second injection  6012  may be 9:1, for example. 
     In the operating state  602  where the engine load is higher, the injector  6  initiates the second injection  6022  which is performed in the second half of an intake stroke at a timing advanced from the second injection  6012  in the operating state  601 . By advancing the second injection  6022 , the mixture gas inside the combustion chamber  17  becomes more homogeneous. The injection amount ratio of the first injection  6021  to the second injection  6022  may be 7:3 to 8:2, for example. 
     In the operating state  603  where the engine load is even higher, the injector  6  initiates the second injection  6032  which is performed in the second half of an intake stroke at a timing further advanced from the second injection  6022  in the operating state  602 . By further advancing the second injection  6032 , the mixture gas inside the combustion chamber  17  becomes further homogeneous. The injection amount ratio of the first injection  6031  to the second injection  6032  may be 6:4, for example. 
     After the fuel injection is finished, the ignition plug  25  ignites the mixture gas in the central part of the combustion chamber  17  at a given timing before a compression top dead center (reference numerals  6013 ,  6023 , and  6033 ). The ignition timing may be during a final stage of the compression stroke. The compression stroke may be equally divided into three, an initial stage, a middle stage, and a final stage, and this finale stage may be used as the final stage of the compression stroke described above. 
     As described above, since the mixture gas in the central part has the relatively high fuel concentration, the ignitability improves and the SI combustion by flame propagation stabilizes. By the SI combustion being stabilized, the CI combustion begins at a suitable timing. Thus, the controllability in the CI combustion improves in the SPCCI combustion. Further, the generation of combustion noise is reduced. Moreover, since the A/F of the mixture gas is made leaner than the stoichiometric air fuel ratio to perform the SPCCI combustion, fuel efficiency of the engine  1  can be significantly improved. Note that the low load area A 1  corresponds to Layer  3  described later. Layer  3  extends to the light load operating range and includes a minimum load operating state. 
     (Middle-to-High Load Area) 
     When the engine  1  operates in the middle-to-high load area, the engine  1  also performs the SPCCI combustion, similar to the low load area. 
     The reference numeral  604  in  FIG. 8  indicates, in the middle-to-high load area, fuel injection timings (reference numerals  6041  and  6042 ), an ignition timing (reference numeral  6043 ), and a combustion waveform (reference numeral  6044 ), when the engine  1  operates in the operating state  604  in the middle load area A 2 . The reference numeral  605  indicates a fuel injection timing (reference numeral  6051 ), an ignition timing (reference numeral  6052 ), and a combustion waveform (reference numeral  6053 ), when the engine  1  operates in the operating state  605  in the high-load low-speed area A 4 . 
     The EGR system  55  introduces the EGR gas into the combustion chamber  17 . For example, the intake-side electric S-VT  23  and the exhaust-side electric S-VT  24  are provided with a positive overlap period where both the intake valve  21  and the exhaust valve  22  are opened near an exhaust top dead center. Internal EGR gas is introduced into the combustion chamber  17 . Moreover, the EGR system  55  introduces the exhaust gas cooled by the EGR cooler  53  into the combustion chamber  17  through the EGR passage  52 . That is, the external EGR gas with a lower temperature than the internal EGR gas is introduced into the combustion chamber  17 . The external EGR gas adjusts the temperature inside the combustion chamber  17  to a suitable temperature. The EGR system  55  reduces the amount of the EGR gas as the engine load increases. The EGR system  55  may not recirculate the EGR gas containing the internal EGR gas and the external EGR gas during the full load. 
     Moreover, in the middle load area A 2  and the high-load middle-speed area A 3 , the swirl control valve  56  is fully closed or at a given opening (closed to some extent). In the combustion chamber  17 , the strong swirl flow with the swirl ratio of four or higher is formed. On the other hand, in the high-load low-speed area A 4 , the swirl control valve  56  is open. 
     The air-fuel ratio (A/F) of the mixture gas is the stoichiometric air fuel ratio (A/F≈14.7:1) throughout the combustion chamber  17 . Since the three-way catalysts  511  and  513  purify the exhaust gas discharged from the combustion chamber  17 , the emission performance of the engine  1  is improved. The A/F of the mixture gas may be set within a purification window of the three-way catalyst. The excess air ratio λ of the mixture gas may be 1.0±0.2. Note that when the engine  1  operates in the high-load middle-speed area A 3  including the full load (i.e., the maximum load), the A/F of the mixture gas may be set at the stoichiometric air fuel ratio or richer than the stoichiometric air fuel ratio (i.e., the excess air ratio λ of the mixture gas is λ≤1) throughout the combustion chamber  17 . 
     Since the EGR gas is introduced into the combustion chamber  17 , the G/F which is a weight ratio of the entire gas to the fuel in the combustion chamber  17  becomes leaner than the stoichiometric air fuel ratio. The G/F of the mixture gas may be 18:1 or higher. Thus, a generation of a so-called “knock” is avoided. The G/F may be set 18:1 or higher and 30:1 or lower. Alternatively, the G/F may be set 18:1 or higher and 50:1 or lower. 
     When the engine  1  operates in the operating state  604 , the injector  6  performs a plurality of fuel injections (reference numerals  6041  and  6042 ) during an intake stroke. The injector  6  may perform the first injection  6041  in the first half of the intake stroke and the second injection  6042  in the second half of the intake stroke. 
     Moreover, when the engine  1  operates in the operating state  605 , the injector  6  injects fuel in an intake stroke (reference numeral  6051 ). 
     The ignition plug  25  ignites the mixture gas at a given timing near a compression top dead center after the fuel is injected (reference numerals  6043  and  6052 ). The ignition plug  25  may ignite the mixture gas before the compression top dead center when the engine  1  operates in the operating state  604  (reference numeral  6043 ). The ignition plug  25  may ignite the mixture gas after the compression top dead center when the engine  1  operates in the operating state  605  (reference numeral  6052 ). 
     Since the A/F of the mixture gas is set to the stoichiometric air fuel ratio and the SPCCI combustion is performed, the exhaust gas discharged from the combustion chamber  17  can be purified using the three-way catalysts  511  and  513 . Moreover, the fuel efficiency of the engine  1  improves by introducing the EGR gas into the combustion chamber  17  and making the mixture gas leaner. Note that the middle-to-high load areas A 2 , A 3 , and A 4  correspond to Layer  2  described later. Layer  2  extends to the high load area and includes the maximum load operating state. 
     (Operation of Supercharger) 
     Here, as illustrated in the map  504  of  FIG. 7 , the supercharger  44  is OFF in part of the low load area A 1  and part of the middle load area A 2  (see S/C OFF). In detail, the supercharger  44  is OFF in an area on the lower engine speed side in the low load area A 1 . In an area on the higher speed side in the low load area A 1 , the supercharger  44  is ON in order to secure a required intake filling amount for the increased speed of the engine  1 . Moreover, the supercharger  44  is OFF in a partial area on the lower load and lower engine speed side in the middle load area A 2 . In the area on the higher load side in the middle load area A 2 , the supercharger  44  is ON in order to secure a required intake filling amount for the increased fuel injection amount. Moreover, the supercharger  44  is ON also in the area on the higher speed side in the middle load area A 2 . 
     Note that in each area of the high-load middle-speed area A 3 , the high-load low-speed area A 4 , and the high speed area A 5 , the supercharger  44  is entirely ON (see S/C ON). 
     (High Speed Area) 
     When the speed of the engine  1  increases, a time required for changing the crank angle by 1° becomes shorter. Thus, it becomes difficult to stratify the mixture gas inside the combustion chamber  17 . When the speed of the engine  1  increases, it also becomes difficult to perform the SPCCI combustion. 
     Therefore, the engine  1  performs not the SPCCI combustion but the SI combustion when the engine  1  operates in the high speed area A 5 . Note that the high speed area A 5  extends entirely in the load direction from the low load to the high load. 
     The reference numeral  606  of  FIG. 8  indicates a fuel injection timing (reference numeral  6061 ), an ignition timing (reference numeral  6062 ), and a combustion waveform (reference numeral  6063 ), when the engine  1  operates in the high speed area A 5  in the operating state  606  where the load is high. 
     The EGR system  55  introduces the EGR gas into the combustion chamber  17 . The EGR system  55  reduces the amount of the EGR gas as the load increases. The EGR system  55  may not recirculate the EGR gas during full load. 
     The swirl control valve  56  is fully opened. No swirl flow occurs in the combustion chamber  17 , but only a tumble flow occurs. By fully opening the swirl control valve  56 , it is possible to increase the filling efficiency, and reduce the pumping loss. 
     Fundamentally, the air-fuel ratio (A/F) of the mixture gas is the stoichiometric air fuel ratio (A/F≈14.7:1) throughout the combustion chamber  17 . The excess air ratio λ of the mixture gas may be set to 1.0±0.2. Note that the excess air ratio λ of the mixture gas may be lower than 1 when the engine  1  operates near full load. 
     The injector  6  starts the fuel injection during an intake stroke. The injector  6  injects the fuel all at once (reference numeral  6061 ). By starting the fuel injection in the intake stroke, the homogeneous or substantially homogeneous mixture gas is formed inside the combustion chamber  17 . Moreover, since a longer vaporizing time of the fuel can be secured, unburnt fuel loss can also be reduced. 
     After the fuel injection is finished, the ignition plug  25  ignites the mixture gas at a suitable timing before a compression top dead center (reference numeral  6062 ). 
     (Layer Structure of Map) 
     As illustrated in  FIG. 9 , the maps  501 ,  502 , and  503  of the engine  1  illustrated in  FIG. 6  are comprised of a combination of three layers, Layer  1 , Layer  2 , and Layer  3 . 
     Layer  1  is a layer used as a base layer. Layer  1  extends throughout the operating range of the engine  1 . Layer  1  corresponds to the entire third map  503 . 
     Layer  2  is a layer which is superimposed on Layer  1 . Layer  2  corresponds to part of the operating range of the engine  1 . For example, Layer  2  corresponds to the low-to-middle speed area B 1 , B 2 , and B 3  of the second map  502 . 
     Layer  3  is a layer which is superimposed on Layer  2 . Layer  3  corresponds to the low load area A 1  of the first map  501 . 
     Layer  1 , Layer  2 , and Layer  3  are selected according to the wall temperature of the combustion chamber  17  and the intake air temperature. 
     When the wall temperature of the combustion chamber  17  is higher than a given first wall temperature (e.g., 80° C.) and the intake air temperature is higher than a given first intake air temperature (e.g., 50° C.), Layer  1 , Layer  2 , and Layer  3  are selected, and the first map  501  is formed by piling up Layer  1 , Layer  2 , and Layer  3 . In the low load area A 1  in the first map  501 , the top Layer  3  therein becomes effective, in the middle-to-high load areas A 2 , A 3 , and A 4 , the top Layer  2  therein becomes effective, and in the high speed area A 5 , Layer  1  becomes effective. 
     When the wall temperature of the combustion chamber  17  is lower than the given first wall temperature and higher than a given second wall temperature (e.g., 30° C.), and the intake air temperature is lower than the given first intake air temperature and higher than a given second intake air temperature (e.g., 25° C.), Layer  1  and Layer  2  are selected. By superimposing the Layer  1  and Layer  2 , the second map  502  is formed. The low-to-middle speed area B 1 , B 2 , and B 3  in second map  502 , the top Layer  2  therein becomes effective, and in the high speed area B 4 , Layer  1  becomes effective. 
     When the wall temperature of the combustion chamber  17  is lower than the given second wall temperature and the intake air temperature is lower than the given second intake air temperature, only Layer  1  is selected to form the third map  503 . 
     Note that the wall temperature of the combustion chamber  17  may be replaced, for example, by temperature of the coolant of the engine  1  measured by the water temperature sensor SW 10 . Alternatively, the wall temperature of the combustion chamber  17  may be estimated based on the temperature of the coolant, or other measurements. The intake air temperature is measurable, for example, by the third intake-air temperature sensor SW 17  which measures the temperature inside the surge tank  42 . Alternatively, the temperature of the intake air introduced into the combustion chamber  17  may be estimated based on various kinds of measurements. 
     As described above, the SPCCI combustion is performed by generating the strong swirl flow inside the combustion chamber  17 . Since the flame propagates along the wall of the combustion chamber  17  during the SI combustion, the flame propagation of the SI combustion is influenced by the wall temperature. If the wall temperature is low, the flame of the SI combustion is cooled to delay the timing of compression-ignition. 
     Since the CI combustion of the SPCCI combustion is performed in the area from the outer circumferential part to the central part of the combustion chamber  17 , it is influenced by the temperature in the central part of the combustion chamber  17 . If the temperature in the central part is low, the CI combustion becomes unstable. The temperature in the central part of the combustion chamber  17  depends on the temperature of the intake air introduced into the combustion chamber  17 . That is, when the intake air temperature is higher, the temperature in the central part of the combustion chamber  17  becomes higher, and when the intake air temperature is lower, the temperature in the central part becomes lower. 
     When the wall temperature of the combustion chamber  17  is lower than the given second wall temperature and the intake air temperature is lower than the given second intake air temperature, a stable SPCCI combustion cannot be performed. Thus, only Layer  1  which performs the SI combustion is selected, and the ECU  10  operates the engine  1  based on the third map  503 . By the engine  1  performing the SI combustion in the entire operating range, the combustion stability can be secured. 
     When the wall temperature of the combustion chamber  17  is higher than the given second wall temperature and the intake air temperature is higher than the given second intake air temperature, the stable SPCCI combustion of the mixture gas having substantially stoichiometric air fuel ratio (i.e., λ=1) can be carried out. Thus, in addition to Layer  1 , Layer  2  is selected, and the ECU  10  operates the engine  1  based on the second map  502 . By the engine  1  performing the SPCCI combustion in the part of the operating ranges, the fuel efficiency of the engine  1  improves. 
     When the wall temperature of the combustion chamber  17  is higher than the given first wall temperature and the intake air temperature is higher than the given first the intake air temperature, the stable SPCCI combustion of the mixture gas leaner than the stoichiometric air fuel ratio can be carried out. Thus, in addition to Layer  1  and Layer  2 , Layer  3  is selected, and the ECU  10  operates the engine  1  based on the first map  501 . By the engine  1  performing the SPCCI combustion of the lean mixture gas in the part of the operating ranges, the fuel efficiency of the engine  1  further improves. 
     Next, one example of control related to the layer selection of the map executed by the ECU  10  will be described with reference to a flowchart of  FIG. 10 . First, at Step S 1  after the control is started, the ECU  10  reads the signals of the sensors SW 1 -SW 17 . At the following Step S 2 , the ECU  10  determines whether the wall temperature of the combustion chamber  17  is 30° C. or higher and the intake air temperature is 25° C. or higher. If the determination at Step S 2  is YES, the control shifts the process to Step S 3 , and on the other hand, if NO, the control shifts the process to Step S 5 . The ECU  10  selects only Layer  1  at Step S 5 . The ECU  10  operates the engine  1  based on the third map  503 . The control then returns the process. 
     At Step S 3 , the ECU  10  determines whether the wall temperature of the combustion chamber  17  is 80° C. or higher and the intake air temperature is 50° C. or higher. If the determination at Step S 3  is YES, the control shifts the process to Step S 4 , and on the other hand, if NO, the control shifts the process to Step S 6 . 
     The ECU  10  selects Layer  1  and Layer  2  at Step S 6 . The ECU  10  operates the engine  1  based on the second map  502 . The control then returns the process. 
     The ECU  10  selects Layer  1 , Layer  2 , and Layer  3  at Step S 4 . The ECU  10  operates the engine  1  based on the first map  501 . The control then returns the process. 
     (Valve Timing of Intake Valve and Exhaust Valve) 
       FIG. 11  illustrates one example of a change in an open timing IVO of the intake valve  21  when the ECU  10  controls the intake-side electric S-VT  23  according to the control logic set for Layer  2 . An upper figure of  FIG. 11  (i.e., a graph  1101 ) illustrates a change of the open timing IVO of the intake valve  21  (vertical axis) versus the engine load (horizontal axis). The solid line corresponds to a case where the speed of the engine  1  is a relatively low first engine speed, and a broken line corresponds to a case where the speed of the engine  1  is a relatively high second engine speed (first engine speed&lt;second engine speed). 
     A lower figure of  FIG. 11  (i.e., a graph  1102 ) illustrates a change of the open timing IVO of the intake valve  21  (vertical axis) versus the speed of the engine  1  (horizontal axis). The solid line corresponds to a case where the engine load is a relatively low first load, and the broken line corresponds to a case where the engine load is a relatively high second load (first load &lt;second load). 
     In the graph  1101  and the graph  1102 , the open timing IVO of the intake valve  21  is advanced as it goes upward and the positive overlap period where both the intake valve  21  and the exhaust valve  22  open becomes longer. Therefore, the amount of the EGR gas introduced into the combustion chamber  17  increases. 
     In Layer  2 , the engine  1  operates with the A/F of the mixture gas at the stoichiometric air fuel ratio or the substantially stoichiometric air fuel ratio, and the G/F leaner than the stoichiometric air fuel ratio. When the engine load is low, the fuel supply amount decreases. As illustrated in the graph  1101 , when the engine load is low, the ECU  10  sets the open timing IVO of the intake valve  21  at a timing on the retard side. Thus, the amount of the EGR gas introduced into the combustion chamber  17  is regulated to secure the combustion stability. 
     Since the fuel supply amount increases when the engine load increases, the combustion stability improves. The ECU  10  sets the open timing of the intake valve  21  at a timing on the advance side. The pumping loss of the engine  1  can be lowered by increasing the amount of the EGR gas introduced into the combustion chamber  17 . 
     When the engine load further increases, the temperature inside the combustion chamber  17  further increases. Then, the amount of the internal EGR gas is reduced and the amount of the external EGR gas is increased so that the temperature inside the combustion chamber  17  does not become too high. Therefore, the ECU  10  sets the open timing of the intake valve  21  again at a timing on the retard side. 
     When the engine load further increases and the supercharger  44  starts boosting, the ECU  10  sets the open timing of the intake valve  21  again at a timing on the advance side. Since the positive overlap period where both the intake valve  21  and the exhaust valve  22  open is provided, the residual gas in the combustion chamber  17  can be purged. 
     Note that when the engine speed is high and low, the tendency of the change in the open timing of the intake valve  21  is almost the same. 
     As illustrated in the graph  1102 , when the engine speed is low, the flow inside the combustion chamber  17  becomes weaker. Since the combustion stability falls, the amount of the EGR gas introduced into the combustion chamber  17  is regulated. The ECU  10  sets the open timing of the intake valve  21  at a timing on the retard side. 
     Since the flow inside the combustion chamber  17  becomes strong when the engine speed increases, the amount of the EGR gas introduced into the combustion chamber  17  can be increased. The ECU  10  sets the open timing of the intake valve  21  at a timing on the advance side. 
     When the engine speed further increases, the ECU  10  sets the open timing of the intake valve  21  at a timing on the retard side according to the engine speed. Thus, the amount of gas introduced into the combustion chamber  17  is maximized. 
       FIG. 12  illustrates one example of a change in the open timing IVO of the intake valve  21 , a close timing EVC of the exhaust valve  22 , and an overlap period O/L of the intake valve  21  and the exhaust valve  22 , when the ECU  10  controls the intake-side electric S-VT  23  and the exhaust-side electric S-VT  24  according to the control logic set for Layer  3 . 
     An upper figure of  FIG. 12  (i.e., a graph  1201 ) illustrates a change in the open timing IVO of the intake valve  21  (vertical axis) versus the engine load (horizontal axis). The solid line corresponds to a case where the engine speed is a relatively low third engine speed, and the broken line corresponds to a case where the engine speed is relatively high fourth engine speed (third engine speed&lt;fourth engine speed). 
     A middle figure of  FIG. 12  (i.e., graph  1202 ) illustrates a change in the close timing EVC of the exhaust valve  22  (vertical axis) versus the engine load (horizontal axis). The solid line corresponds to a case where the engine speed is at the third engine speed, and the broken line corresponds to a case where the engine speed is at the fourth engine speed. 
     A lower figure of  FIG. 12  (i.e., graph  1203 ) illustrates a change in the overlap period O/L of the intake valve  21  and the exhaust valve  22  (vertical axis) versus the engine load (horizontal axis). The solid line corresponds to a case where the engine speed is at the third engine speed, and the broken line corresponds to a case where the engine speed is at the fourth engine speed. 
     In Layer  3 , the engine  1  operates by carrying out the SPCCI combustion of the mixture gas with the A/F leaner than the stoichiometric air fuel ratio. When the engine load is low, the fuel supply amount decreases. Thus, the ECU  10  regulates the amount of gas introduced into the combustion chamber  17  so that the A/F of the mixture gas does not become too low. As illustrated in the graph  1201 , the ECU  10  sets the open timing IVO of the intake valve  21  at a timing on the retard side of an exhaust top dead center. The close timing of the intake valve  21  becomes after an intake bottom dead center, so-called “late close”. Moreover, when the engine load is low, the ECU  10  regulates the amount of the internal EGR gas introduced into the combustion chamber  17 . As illustrated in the graph  1202 , the ECU  10  sets the close timing EVC of the exhaust valve  22  at a timing on the advance side. The close timing EVC of the exhaust valve  22  approaches an exhaust top dead center. 
     Since the fuel supply amount increases when the engine load increases, the ECU  10  does not regulate the amount of gas introduced into the combustion chamber  17 . Moreover, in order to stabilize the SPCCI combustion of the mixture gas leaner than the stoichiometric air fuel ratio, the ECU  10  increases the amount of the internal EGR gas introduced into the combustion chamber  17 . The ECU  10  sets the open timing IVO of the intake valve  21  at a timing on the advance side of an exhaust top dead center. Moreover, the ECU  10  sets the close timing EVC of the exhaust valve  22  at a timing on the retard side of the exhaust top dead center. As a result, as illustrated in the graph  1203 , when the engine load increases, the overlap period where both the intake valve  21  and the exhaust valve  22  open becomes longer. 
     When the engine load further increases, the ECU  10  reduces the amount of the internal EGR gas introduced into the combustion chamber  17  so that the temperature inside the combustion chamber  17  does not become too high. The ECU  10  brings the close timing EVC of the exhaust valve  22  closer to an exhaust top dead center. Thus, the overlap period of the intake valve  21  and the exhaust valve  22  becomes shorter. Moreover, when the engine load is high and the engine speed is high, the ECU  10  sets the open timing of the intake valve  21  on the retard side more than when the engine speed is low. Thus, the amount of gas introduced into the combustion chamber  17  is maximized. 
     Note that in the low load area surrounded by a one-dot chain line in  FIG. 12 , the engine  1  may perform a reduced-cylinder operation in order to improve fuel efficiency. When performing the reduced-cylinder operation, the amount of gas and the internal EGR gas introduced into the combustion chamber  17  are not regulated. As illustrated by a two-dot chain line in the graphs  1201  and  1202 , the ECU  10  may set the open timing of the intake valve  21  at a timing on the advance side and the close timing of the exhaust valve  22  at a timing on the retard side. 
     (Engine Control Logic) 
       FIG. 13  is a flowchart illustrating the control logic of the engine  1 . The ECU  10  operates the engine  1  according to the control logic stored in the memory  102 . For example, the ECU  10  determines the operating state of the engine  1  based on the signals of the sensors SW 1 -SW 17 , and performs calculations for adjusting properties in the combustion chamber  17 , the injection amount, the injection timing, and the ignition timing so that the combustion in the combustion chamber  17  becomes combustion at the SI ratio according to the operating state. 
     The ECU  10  first reads the signals of the sensors SW 1 -SW 17  at Step S 131 . Subsequently, at Step S 132 , the ECU  10  determines the operating state of the engine  1  based on the signals of the sensors SW 1 -SW 17 , and sets a target SI ratio (i.e., a target heat amount ratio). The target SI ratio is set according to the operating state of the engine  1 . 
       FIG. 14  schematically illustrates one example of a setting of the target SI ratio. When the engine load is low, the ECU  10  sets the target SI ratio low, and on the other hand, when the engine load is high, it sets the target SI ratio high. When the engine load is low, both the reduction of combustion noise and the improvement in fuel efficiency can be achieved by increasing the ratio in the CI combustion to the SPCCI combustion. When the engine load is high, it becomes advantageous for the reduction of the combustion noise by increasing the ratio of the SI combustion to the SPCCI combustion. 
     Returning to the flowchart of  FIG. 13 , the ECU  10  sets the target in-cylinder properties for achieving the target SI ratio setting based on the combustion model stored in the memory  102  at the following Step S 133 . For example, the ECU  10  sets a target temperature, a target pressure, and target properties in the combustion chamber  17 . At Step S 134 , the ECU  10  sets an opening of the EGR valve  54 , an opening of the throttle valve  43 , an opening of the air bypass valve  48 , an opening of the swirl control valve  56 , and phase angles of the intake-side electric S-VT  23 , and the exhaust-side electric S-VT  24  (i.e., a valve timing of the intake valve  21  and a valve timing of the exhaust valve  22 ), which are required for achieving the target in-cylinder properties. The ECU  10  sets the control amounts of these devices based on the map stored in the memory  102 . The ECU  10  outputs signals to the EGR valve  54 , the throttle valve  43 , the air bypass valve  48 , the swirl control valve (SCV)  56 , the intake-side electric S-VT  23 , and the exhaust-side electric S-VT  24  based on the control amount setting. By each device operating based on the signal of the ECU  10 , the properties in the combustion chamber  17  become the target properties. 
     The ECU  10  further calculates predicted values or estimated values of the properties in the combustion chamber  17  based on the control amount setting of each device. The predicted property value is a predicted value of the property in the combustion chamber  17  before the intake valve  21  is closed. The predicted property value is used for setting of the fuel injection amount during the intake stroke as will be described later. The estimated property value is an estimated value of the property in the combustion chamber  17  after the intake valve  21  is closed. The estimated property value is used for setting of the fuel injection amount during a compression stroke, and setting of the ignition timing, as will be described later. The estimated property value is also used for calculation of a property error of comparison with an actual combustion state. 
     At Step S 135 , the ECU  10  sets a fuel injection amount in the intake stroke based on the predicted property value. When performing a divided injection during the intake stroke, the ECU  10  sets the injection amount of each injection. Note that when fuel is not injected in the intake stroke, the injection amount of fuel is zero. At Step S 136 , the ECU  10  outputs a signal to the injector  6  so that the injector  6  injects fuel into the combustion chamber  17  at given injection timing(s). 
     At Step S 137 , the ECU  10  sets a fuel injection amount in a compression stroke based on the estimated property value and the injection result of the fuel in the intake stroke. Note that when fuel is not injected in the compression stroke, the injection amount of fuel is zero. At Step S 138 , the ECU  10  outputs a signal to the injector  6  so that the injector  6  injects fuel into the combustion chamber  17  at an injection timing based on the preset map. 
     At Step S 139 , the ECU  10  sets an ignition timing based on the estimated property value and the injection result of the fuel in the compression stroke. At Step S 1310 , the ECU  10  outputs a signal to the ignition plug  25  so that the ignition plug  25  ignites the mixture gas inside the combustion chamber  17  at the set ignition timing. 
     By the ignition plug  25  igniting the mixture gas, the SI combustion or the SPCCI combustion is performed inside the combustion chamber  17 . At Step S 1311 , the ECU  10  reads the change in the pressure inside the combustion chamber  17  measured by the pressure indicating sensor SW 6 , and based on the change, the ECU  10  determines a combustion state of the mixture gas inside the combustion chamber  17 . At Step S 1312 , the ECU  10  compares the measurement result of the combustion state with the estimated property values estimated at Step S 134 , and calculates an error between the estimated properties value and the actual properties. The calculated error is used for the estimation at Step S 134  in the subsequent cycles. The ECU  10  adjusts the openings of the throttle valve  43 , the EGR valve  54 , the swirl control valve  56 , and/or the air bypass valve  48 , and the phase angles of the intake-side electric S-VT  23  and the exhaust-side electric S-VT  24  so as to eliminate the property error. Thus, the amount of the fresh air and the EGR gas introduced into the combustion chamber  17  are adjusted. 
     If the ECU  10  estimates that the temperature inside the combustion chamber  17  will be lower than the target temperature again based on the estimated property values, it advances, at Step S 138 , the injection timing in the compression stroke more than the injection timing based on the map so that the advancing of the ignition timing becomes possible. On the other hand, if ECU  10  estimates that the temperature inside the combustion chamber  17  will be higher than the target temperature based on the estimated property values, it retards, at Step S 138 , the injection timing in the compression stroke more than the injection timing based on the map so that the retarding of the ignition timing becomes possible. 
     That is, if the temperature inside the combustion chamber  17  is low, a self-ignition timing θ CI  (see  FIG. 5 ) of the unburnt mixture gas is delayed after the SI combustion begins by jump-spark ignition, which deviates the SI ratio from the target SI ratio. In this case, an increase in the unburnt fuel and a fall in emission performance will be caused. 
     Thus, when the ECU  10  estimates that the temperature inside the combustion chamber  17  will be lower than the target temperature, it advances the injection timing, and advances the ignition timing at Step S 1310 . Since the heat release which is sufficient for the SI combustion becomes possible by an earlier start of the SI combustion, it can prevent that the self-ignition timing θ CI  of the unburnt mixture gas is delayed when the temperature inside the combustion chamber  17  is low. As a result, the SI ratio approaches the target SI ratio. 
     On the other hand, when the temperature inside the combustion chamber  17  is high, the unburnt mixture gas will carry out the self-ignition shortly after the SI combustion begins by the jump-spark ignition, which deviates the SI ratio from the target SI ratio. In this case, combustion noise increases. 
     Thus, when the ECU  10  estimates that the temperature inside the combustion chamber  17  will be higher than the target temperature, it retards the injection timing, and retards the ignition timing at Step S 1310 . Since the start of the SI combustion is delayed, when the temperature inside the combustion chamber  17  is high, the self-ignition timing θ CI  of the unburnt mixture gas becoming early can be prevented. As a result, the SI ratio approaches the target SI ratio. 
     The control logic of the engine  1  is configured to adjust the SI ratio by using a property setting device including the throttle valve  43 , the EGR valve  54 , the air bypass valve  48 , the swirl control valve  56 , the intake-side electric S-VT  23 , and the exhaust-side electric S-VT  24 . By adjusting the properties in the combustion chamber  17 , a rough adjustment of the SI ratio is possible. The control logic of the engine  1  is also configured to adjust the SI ratio by adjusting the injection timing and the ignition timing of the fuel. By adjusting the injection timing and the ignition timing, a difference between the cylinders can be corrected, and a fine adjustment of the self-ignition timing can be performed, for example. By adjusting the SI ratio by two steps, the engine  1  can achieve the target SPCCI combustion accurately corresponding to the operating state. 
     The ECU  10  also outputs signals to at least the EGR system  55  and the ignition plug  25  so that the actual SI ratio by combustion becomes the target SI ratio. Moreover, as described above, when the engine load is high, since the ECU  10  makes the target SI ratio higher than when the load is low, it then outputs the signals to at least the EGR system  55  and the ignition plug  25  when the engine load is high so that the SI ratio becomes higher than when the load is low. 
     Note that the control of the engine  1  executed by the ECU  10  is not limited to the control logic based on the combustion model described above. 
     (Method of Controlling Engine) 
     When controlling the engine  1  for performing the SPCCI combustion described above, the parameter related to the control amount of each device is set. For example, if the device is the ignition plug  25 , ignition energy and the ignition timing corresponding to the operating state of the engine  1  are set. If the device is the intake-side electric S-VT  23 , the valve timing of the intake valve  21  corresponding to the operating state of the engine  1  is set. Below, the setting of the valve timing of the intake valve  21  in the method of controlling the engine  1  will be described with reference to the drawings. 
     (1) Controlling Method According to Close Timing of Intake Valve 
     In the engine  1  for performing the SPCCI combustion, in order to reduce combustion noise and achieve the stable SPCCI combustion, the present inventors found out that it was necessary to adjust the temperature inside the combustion chamber  17  to a suitable temperature at a start timing in the CI combustion (θ CI : see  FIG. 5 ). That is, when the temperature inside the combustion chamber  17  is low, the ignitability in the CI combustion decreases. When the temperature inside the combustion chamber  17  is high, combustion noise increases. 
     The temperature inside the combustion chamber  17  at the start timing θ CI  in the CI combustion is mainly related to the effective compression ratio of the engine  1 . The effective compression ratio of the engine  1  is determined by the geometric compression ratio ε and the close timing IVC of the intake valve  21 . In order to put the engine for performing the SPCCI combustion in practical use, the present inventors newly found that a suitable IVC range existed within a range of the geometric compression ratio ε where the SPCCI combustion may occur. The technology disclosed herein is novel in that a given relation was found out between the geometric compression ratio ε and the close timing IVC of the intake valve  21 , where the given relation is required in order to put in practical use the engine which performs the unique combustion mode that is the SPCCI combustion. In addition, a relational expression between the geometric compression ratio ε and the close timing IVC of the intake valve  21 , which will be described later, is also novel. 
     Further, the technology disclosed herein is also novel in that, when controlling the engine  1  for performing the SPCCI combustion, the close timing IVC of the intake valve  21  is set based on the relation between the geometric compression ratio ε and the close timing IVC of the intake valve  21 . 
     The engine  1  switches between “Layer  2 ” where the SPCCI combustion is performed with the A/F of the mixture gas being made at the stoichiometric air fuel ratio or richer than the stoichiometric air fuel ratio and the G/F being made leaner than the stoichiometric air fuel ratio, and “Layer  3 ” where the SPCCI combustion is performed with the A/F of the mixture gas being made leaner than the stoichiometric air fuel ratio. The relation between the geometric compression ratio ε and the close timing IVC of the intake valve  21  in Layer  2  differs from the relation between the geometric compression ratio ε and the close timing IVC of the intake valve  21  in Layer  3 . 
     (1-1) Relation Between Geometric Compression Ratio and Close Timing of Intake Valve in Layer 
       FIG. 15  illustrates the characteristic of the SPCCI combustion. For example,  FIG. 15  illustrates the occurring range of the SPCCI combustion against the EGR ratio (horizontal axis) in a case where the engine  1  carries out the SPCCI combustion of the mixture gas of which the A/F is the stoichiometric air fuel ratio and the G/F is leaner than the stoichiometric air fuel ratio, similar to Layer  2 . The vertical axis in this graph is a crank angle corresponding to a combustion center of gravity, where the combustion center of gravity advances as it goes upward in this graph. 
     The occurring range of the SPCCI combustion is illustrated by a hatched range in this graph. The occurring range of the SPCCI combustion is located between a line of “advancing limit” and a line of “retarding limit.” If the combustion center of gravity advances beyond the “advancing limit” line, combustion becomes abnormal, which means that the SPCCI combustion does not occur. Similarly, if the combustion center of gravity retards beyond the “retarding limit” line, self-ignition does not occur, which means that the SPCCI combustion does not occur. 
     The one-dot chain line in this graph illustrates the combustion center of gravity of combustion corresponding to a MBT (Minimum advance for Best Torque). Here, the combustion center of gravity of combustion corresponding to the MBT is simply referred to as “MBT.” The MBT is advanced as the EGR ratio increases. 
     In terms of the improvement in fuel efficiency, it is desirable to bring the combustion center of gravity of the SPCCI combustion closer to the MBT. As the EGR ratio increases, the occurring range of the SPCCI combustion is advanced, but the interval between the “advancing limit” line and the “retarding limit” line becomes narrower, which narrows the occurring range of the SPCCI combustion. 
     When the engine load is low (when “light load”), the occurring range of the SPCCI combustion is on the advance side. Therefore, as illustrated by a both-ends arrow in  FIG. 15 , the SPCCI combustion corresponding to the MBT can be achieved by adjusting the EGR ratio within a certain width, and adjusting the combustion center of gravity to the advance side or the retard side. 
     When the engine load increases, the amount of air introduced into the combustion chamber  17  must be increased corresponding to the increase in the fuel supply amount. When the EGR ratio is increased corresponding to the increase in the air amount, a large amount of the EGR gas must be introduced into the combustion chamber  17 . However, because of the limit of the supercharging capability of the supercharger  44 , it is difficult to introduce both a large amount of air and a large amount of the EGR gas into the combustion chamber  17 . Therefore, when the engine load increases, the occurring range of the SPCCI combustion becomes on the retard side. If bringing the combustion center of gravity of the SPCCI combustion closest to the MBT when the engine load is high, the SPCCI combustion must be performed at a point Y in  FIG. 15 . The point Y corresponds to the operating state of the engine  1  with the maximum load where the SPCCI combustion of the mixture gas with the A/F being at the stoichiometric air fuel ratio is possible. When the engine  1  operates with the maximum load, it is difficult to achieve the SPCCI combustion corresponding to the MBT by adjusting the EGR ratio or the combustion center of gravity. 
     The engine  1  operates over a wide operating range from the low load to the high load in Layer  2 . In Layer  2 , the state where the engine  1  operates with the maximum load corresponds to the operating state at the limit where the SPCCI combustion can occur. In Layer  2 , upon determining the relation between ε and IVC so that the temperature of the combustion chamber  17  at the start timing (θ CI ) in the CI combustion becomes the given temperature, it is necessary to set the relation based on the temperature inside the combustion chamber  17  when the engine  1  operates with the maximum load. 
     In order to obtain the temperature inside the combustion chamber  17  when the engine  1  operates with the maximum load, the present inventors performed the SPCCI combustion in an actual engine  1 , and used measurements acquired from the engine  1 . For example, the present inventors measured various parameters when the engine  1  operates with the maximum load in Layer  2 , and estimated an actual temperature inside the combustion chamber  17  at θ CI  based on the measured parameter. The present inventors used an average value of a plurality of estimated temperatures as a reference temperature Tth 1 . If the temperature of the combustion chamber  17  at θ CI  is the reference temperature Tth 1 , the SPCCI combustion can be achieved in Layer  2 . 
     Here, as described above, θ CI  an be adjusted by adjusting the ignition timing in the SPCCI combustion. However, while the engine  1  operates with the maximum load in Layer  2 , it becomes impossible to adjust θ CI  even if the ignition timing is adjusted when the temperature inside the combustion chamber  17  at θ CI  exceeds the reference temperature Tth 1 . On the other hand, if the temperature inside the combustion chamber  17  at θ CI  is the reference temperature Tth 1  or lower, the ignition timing is adjusted (e.g., the ignition timing is advanced) to raise the temperature inside the combustion chamber  17  at θ CI  to the reference temperature Tth 1 , thereby achieving the SPCCI combustion. 
     Therefore, in order to achieve the SPCCI combustion in Layer  2 , the relation between ε and IVC is required so that the temperature of the combustion chamber  17  at θ CI  does not exceed the reference temperature Tth 1 . 
     Thus, as conceptually illustrated in  FIG. 16 , the present inventors performed an estimation of the temperature of the combustion chamber  17  at θ CI  by using a model of the engine  1 , while changing the values of the geometric compression ratio ε and the close timing IVC of the intake valve  21  in a matrix comprised of the two parameters of ε and IVC. A combination of and IVC where the temperature of the combustion chamber  17  becomes the reference temperature Tth 1  or lower can achieve the SPCCI combustion in Layer  2 . As illustrated in  FIG. 16 , when the geometric compression ratio ε is high and the close timing IVC of the intake valve  21  approaches an intake bottom dead center, the temperature of the combustion chamber  17  during the CI combustion exceeds the reference temperature Tth 1 . 
     Note that  FIG. 16  illustrates the matrix where IVC is set after the intake bottom dead center. Although illustration is omitted, the present inventors also acquired a combination of and IVC where the temperature becomes the reference temperature Tth 1  or lower, by performing an estimation of the temperature of the combustion chamber  17  at θ CI , similarly for the matrix where IVC is set before the intake bottom dead center. 
     A graph  1701  of the upper figure in  FIG. 17  illustrates approximations (I) and (II) calculated based on the combination of ε and IVC. The horizontal axis of the graph  1701  is the geometric compression ratio ε, and the vertical axis is the close timing IVC (deg.aBDC) of the intake valve  21 . Although illustration is omitted, the present inventors plotted on the graph  1701  the combination of ε and IVC where the temperature becomes the reference temperature Tth 1  or lower, and determined the approximations (I) and (II) based on the plots. 
     The graph  1701  corresponds to a case where the engine speed is 2,000 rpm. The approximations (I) and (II) are as follows.
 
 IVC =− 0.4288ε 2 +31.518ε−379.88   Approximation (I)
 
 IVC=− 1.9163ε 2 −89.935ε+974.94   Approximation (II)
 
     In the graph  1701 , the combination of ε and IVC on the left side of the approximations (I) and (II) and ε=17, the temperature of the combustion chamber  17  during the CI combustion becomes the reference temperature Tth 1  or lower. In this combination, it is possible to carry out the SPCCI combustion of the mixture gas with the A/F being the stoichiometric air fuel ratio and the G/F being leaner than the stoichiometric air fuel ratio. 
     The relation between ε and IVC described above is a relation based on the maximum temperature of the combustion chamber  17  in Layer  2 . 
     On the other hand, in Layer  2 , also while the engine  1  operates with the light load, the relation between ε and IVC must be defined so that the temperature of the combustion chamber  17  becomes the given temperature. 
     The temperature of the combustion chamber  17  when the SPCCI combustion is performed is a result of two pressure buildups of a pressure buildup by the compression work of the piston  3  in a compression stroke, and the pressure buildup caused by the heat generation of the SI combustion. The compression work of the piston  3  is determined by the effective compression ratio. If the effective compression ratio is too low, the pressure buildup by the compression work of the piston  3  decreases. Unless the pressure buildup, which is caused by the heat generation of the SI combustion after the flame propagation in the SPCCI combustion progresses, increases considerably, the in-cylinder temperature cannot be raised to an ignition temperature. As a result, since the amount of the mixture gas which is ignited by the compressed self-ignition is little, and most of the mixture gas burn by the flame propagation, the combustion period becomes longer and fuel efficiency falls. In order to stabilize the CI combustion in the SPCCI combustion and maximize fuel efficiency, it is necessary to maintain the effective compression ratio above a certain value. Therefore, the relation between ε and IVC must be determined accordingly. 
     Similarly, the present inventors measured various parameters when the actual engine  1  operates with the light load, and estimated an actual temperature inside the combustion chamber  17  at θ CI  based on the measured parameters. The present inventors used an average value of a plurality of estimated temperatures as a reference temperature Tth 2 . 
     If the temperature inside the combustion chamber  17  at θ CI  is the reference temperature Tth 2  or higher while the engine  1  operates with the light load, the SPCCI combustion can be achieved by delaying the ignition timing. However, since the temperature of the combustion chamber  17  is too low if the temperature at θ CI  is lower than the reference temperature Tth 2 , the SPCCI combustion cannot be achieved even if the ignition timing is advanced. 
     Thus, in order to achieve the SPCCI combustion in Layer  2 , a relation between ε and IVC is required so that the temperature of the combustion chamber  17  at θ CI  becomes the reference temperature Tth 2  or higher. 
     The present inventors performed an estimation of the temperature of the combustion chamber  17  during the CI combustion by using a model of the engine  1 , while changing the values of the geometric compression ratio ε and the close timing IVC of the intake valve  21  in a matrix comprised of two parameters of ε and IVC, similarly to the matrix illustrated in  FIG. 16 . In this matrix, the combination of ε and IVC where the temperature of the combustion chamber  17  becomes the reference temperature Tth 2  or higher can achieve the SPCCI combustion in Layer  2 . 
     In the graph  1701  of  FIG. 17 , approximations (III) and (IV) calculated based on the combination of ε and IVC where the temperature becomes the reference temperature Tth 2  or higher are also illustrated. The approximations (III) and (IV) are as follows.
 
 IVC=− 0.4234ε 2 +22.926ε−167.84   Approximation (III)
 
 IVC= 0.4234ε 2 −22.926ε+207.84   Approximation (IV)
 
     In the graph  1701 , the combination of ε and IVC on the right side of the approximations (III) and (IV), the temperature of the combustion chamber  17  during the CI combustion becomes the reference temperature Tth 2  or higher. In this combination, the SPCCI combustion of the mixture gas with the A/F being the stoichiometric air fuel ratio and the G/F being leaner than the stoichiometric air fuel ratio is possible. 
     As seen in  FIG. 17 , the relation between ε and IVC is substantially vertically symmetrical with respect to IVC=about 20 deg.aBDC. IVC=20 deg.aBDC corresponds to a close timing (i.e., the best IVC) at which the amount of gas introduced into the combustion chamber  17  becomes the maximum when the engine speed is 2,000 rpm. Moreover, IVC=120 deg.aBDC is a retarding limit of the close timing IVC of the intake valve  21 , and IVC=−80 deg.aBDC is an advancing limit of the close timing IVC of the intake valve  21 . 
     The combination of ε and IVC within a range surrounded by the approximations (I), (II), (III), and (IV) in  FIG. 17  is a combination which can put in practical use the engine  1  for performing the SPCCI combustion in Layer  2 . In other words, the combination of ε and IVC outside this range cannot put in practical use the engine  1  for performing the SPCCI combustion in Layer  2 . 
     The ECU  10  has to determine IVC within the ε-IVC valid range hatched in  FIG. 17 , upon determining the close timing IVC of the intake valve  21  when the engine  1  operates in Layer  2 . 
     For example, if the geometric compression ratio ε is set as 10≤ε&lt;17, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
0.4234ε 2 −22.926ε+207.84≤ IVC≤− 0.4234ε 2 +22.926ε−167.84   (1)
 
     Moreover, if the geometric compression ratio ε is set as 17≤ε&lt;20, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
−0.4288ε 2 +31.518ε−379.88≤ IVC ≤−0.4234ε 2 +22.926ε−167.84   (2)
 
or
 
0.4234ε 2 −22.926ε+207.84≤ IVC≤ 1.9163ε 2 −89.935ε+974.94   (3)
 
     Further, if the geometric compression ratio ε is set as 20≤ε≤30, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
−0.4288ε 2 +31.518ε−379.88≤ IVC≤ 120   (4)
 
or
 
−80≤ IVC≤ 1.9163ε 2 −89.935ε+974.94   (5)
 
     By setting the close timing IVC of the intake valve  21  based on the relational expressions (1) to (5), the SPCCI combustion of the mixture gas with the A/F being the stoichiometric air fuel ratio or richer than the stoichiometric air fuel ratio and the G/F being leaner than the stoichiometric air fuel ratio is achieved. Note that the close timing IVC is set for each operating state which is determined by the load and the engine speed in Layer  2 . The example illustrated by the solid line in  FIG. 17  is the ε-IVC valid range when the engine speed is 2,000 rpm, as described above. If the engine speed changes, the ε-IVC valid range also changes. As the engine speed increases, the best IVC is retarded. 
     For example, when the engine speed is 3,000 rpm, the best IVC is about 22 deg.aBDC. As illustrated by broken lines in  FIG. 17 , the ε-IVC valid range when the engine speed is 3,000 rpm can be obtained by parallelly translating the ε-IVC valid range when the engine speed is 2,000 rpm to the retard side by about 2 degrees. 
     Therefore, if the geometric compression ratio ε is set as 10≤ε&lt;17, when the engine speed is 3,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
0.4234ε 2 −22.926ε+209.84≤ IVC≤− 0.4234ε 2 +22.926ε−165.84   (1 −1 )
 
     Moreover, if the geometric compression ratio ε is set as 17≤ε&lt;20, when the engine speed is 3,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
−0.4288ε 2 +31.518ε−377.88≤ IVC≤− 0.4234ε 2 +22.926ε−165.84   (2 −1 )
 
or
 
0.4234ε 2 −22.926ε+209.84≤ IVC≤ 1.9163ε 2 −89.935ε+976.94   (3 −1 )
 
     Further, if the geometric compression ratio ε is set as 20≤ε≤&lt;30, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
−0.4288ε 2 +31.518ε−377.88≤ IVC≤ 120   (4 −1 )
 
or
 
−80≤ IVC≤ 1.9163ε 2 −87.935ε+976.94   (5 −1 )
 
     Moreover, when the engine speed is 4,000 rpm, the best IVC is about 28 deg.aBDC. As illustrated by one-dot chain lines in  FIG. 17 , the ε-IVC valid range when the engine speed is 4,000 rpm is obtained by parallelly translating the ε-IVC valid range when the engine speed is 2,000 rpm to the retard side by about 8 degrees. 
     Therefore, if the geometric compression ratio ε is set as 10≤ε&lt;17, when the engine speed is 4,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
0.4234ε 2 −22.926ε+215.84≤ IVC≤− 0.4234ε 2 +22.926ε−159.84   (1 −2 )
 
     Moreover, if the geometric compression ratio ε is set as 17≤ε&lt;20, when the engine speed is 4,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
−0.4288ε 2 +31.518ε−371.88≤ IVC≤− 0.4234ε 2 +22.926ε−159.84   (2 −2 )
 
or
 
0.4234ε 2 −22.926ε+215.84≤ IVC≤ 1.9163ε 2 −89.935ε+982.94   (3 −2 )
 
     Further, if the geometric compression ratio ε is set as 20≤ε≤30, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
−0.4288ε 2 +31.518ε−371.88≤ IVC≤ 120   (4 −2 )
 
or
 
−80≤ IVC≤ 1.9163ε 2 −89.935ε+982.94   (5 −2 )
 
     If the correction term C according to the engine speed NE (rpm) of the engine  1  is set as the following,
 
 C= 3.3×10 −   NE   3 −1.0×10 −6   NE   3 +7.0×10 −4   NE  
 
the relational expression of ε and IVC in Layer  2  can be expressed as follows. If the geometric compression ratio ε is 10≤ε&lt;17,
 
0.4234ε 2 −22.926ε+207.84+ C≤IVC≤− 0.4234ε 2 +22.926ε−167.84+ C    (1 −3 )
 
If the geometric compression ratio ε is 17≤ε&lt;20,
 
0.4288ε 2 +31.518ε−379.88+ C≤IVC≤− 0.4234ε 2 +22.926ε−167.84+ C    (2 −3 )
 
or
 
0.4234ε 2 −22.926ε+207.84+ C≤IVC≤ 1.9163ε 2 −89.935ε+974.94+ C    (3 −3 )
 
If the geometric compression ratio ε is 20≤ε≤30,
 
−0.4288ε 2 +31.518ε−379.88+ C≤IVC≤ 120   (4 −3 )
 
or
 
−80≤ IVC≤ 1.9163ε 2 −89.935ε+974.94+ C    (5 −3 )
 
The ECU  10  determines the close timing IVC based on the ε-IVC valid range determined for every engine speed of the engine  1 . As a result, the ECU  10  can set the valve timing of the intake valve  21  in Layer  2  as illustrated in  FIG. 11 .
 
(1-2) Change in ε-IVC Valid Range by Difference of Octane Number
 
     The graph  1701  in  FIG. 17  is a relation between ε and IVC when the fuel is high octane fuel (octane number is about 96). A graph  1702  illustrated in the lower figure is a relation between ε and IVC when the fuel is low octane fuel (octane number is about 91). According to the examination of the present inventors, when the fuel was the low octane fuel, it was found that the ε-IVC valid range shifts by 1.3 compression ratios toward the lower compression ratio from the ε-IVC valid range of the high octane fuel. 
     Accordingly, upon determining the close timing IVC in the engine  1  of the low octane fuel, if the geometric compression ratio ε is set as 10≤ε&lt;15.7, when the engine speed is 2,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
0.4234ε 2 −21.826ε+178.75≤ IVC≤− 0.4234ε 2 +21.826ε−138.75   (6)
 
     Moreover, if the geometric compression ratio ε is set as 15.7≤ε&lt;18.7 in the engine  1  of the low octane fuel, when the engine speed is 2,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
−0.5603ε 2 +34.859ε−377.22≤ IVC≤− 0.4234ε 2 +21.826ε−138.75   (7)
 
or
 
0.4234ε 2 −21.826ε+178.75≤ IVC≤ 1.9211ε 2 −85.076ε+862.01   (8)
 
     Further, if the geometric compression ratio ε is set as 18.7≤ε≤30 in the engine  1  of the low octane fuel, when the engine speed is 2,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
0.5603ε 2 +34.859ε−377.22≤ IVC≤ 120   (9)
 
or
 
−80≤ IVC≤ 1.9211ε 2 −85.076ε+862.01   (10)
 
     The cross-hatched range in the graph  1702  of  FIG. 17  is an overlapping range of the ε-IVC valid range of the high octane fuel and the ε-IVC valid range of the low octane fuel. The ECU  10  can set the control logic which suits both the engine  1  using the high octane fuel and the engine  1  using the low octane fuel, if IVC is determined within the overlapping range of the two valid ranges. Even if the octane number of the fuel differs for every destination of this product, the ECU  10  can collectively use the engine control logic. 
     Note that although illustration is omitted, the ε-IVC valid range is parallelly translated to the retard side also in the engine  1  of the low octane fuel, when the engine speed increases. If the geometric compression ratio ε is set as 10≤ε&lt;15.7 in the engine  1  of the low octane fuel, when the engine speed is 3,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
0.4234ε 2 −21.826ε+180.75≤ IVC≤− 0.4234ε 2 +21.826ε−136.75   (6 −1 )
 
     Moreover, if the geometric compression ratio ε is set as 15.7≤ε&lt;18.7 in the engine  1  of the low octane fuel, when the engine speed is 3,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
−0.5603ε 2 +34.859ε−375.22≤ IVC≤− 0.4234ε 2 +21.826ε−136.75   (7 −1 )
 
or
 
0.4234ε 2 −21.826ε+180.75≤ IVC≤ 1.9211ε 2 −85.076ε+864.01   (8 −1 )
 
     Further, if the geometric compression ratio ε is set as 18.7≤ε&lt;30 in the engine  1  of the low octane fuel, when the engine speed is 3,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
−0.5603ε 2 +34.859ε−375.22≤ IVC≤ 120   (9 −1 )
 
or
 
−80≤ IVC≤ 1.9211ε 2 −85.076ε+864.01   (10 −1 )
 
     Moreover, if the geometric compression ratio ε is set as 10≤ε&lt;15.7 in the engine  1  of the low octane fuel, when the engine speed is 4,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
0.4234ε 2 −21.826ε+186.75≤ IVC≤− 0.4234ε 2 +21.826ε−130.75   (6 −2 )
 
     Moreover, if the geometric compression ratio ε is set as 15.7≤ε&lt;18.7 in the engine  1  of the low octane fuel, when the engine speed is 4,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
−0.5603ε 2 +34.859ε−369.22≤ IVC≤− 0.4234ε 2 +21.826ε−130.75   (7 −2 )
 
or
 
0.4234ε 2 −21.826ε+186.75≤ IVC≤ 1.9211ε 2 −85.076ε+870.01   (8 −2 )
 
     Further, if the geometric compression ratio ε is set as 18.7≤ε&lt;30 in the engine  1  of the low octane fuel, when the engine speed is 4,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
0.5603ε 2 +34.859ε−369.22≤ IVC≤ 120   (9 −2 )
 
or
 
−80≤ IVC≤ 1.9211ε 2 −77.076ε+870.01   (10 −2 )
 
     If the correction term C according to the engine speed NE (rpm) of the engine  1  is used similar to the above, the relational expression of ε and IVC in Layer  2  in the engine  1  of the low octane fuel can be expressed as follows. 
     If the geometric compression ratio ε is 10≤ε≤15.7,
 
0.4234ε 2 −21.826ε+178.75+ C≤IVC≤− 0.4234ε 2 +21.826ε−138.75+ C    (6 −3 )
 
If the geometric compression ratio ε is 15.7≤ε&lt;18.7,
 
−0.5603ε 2 +34.859ε−377.22+ C≤IVC≤− 0.4234ε 2 +21.826ε−138.75+ C    (7 −3 )
 
or
 
0.4234ε 2 −21.826ε+178.75+ C≤IVC≤ 1.9211ε 2 −85.076ε+862.01+ C    (8 −3 )
 
If the geometric compression ratio ε is 18.7≤ε≤30,
 
−0.5603ε 2 +34.859ε−377.22+ C≤IVC≤ 120   (9 −3 )
 
or
 
−80≤ IVC≤ 1.9211ε 2 −85.076ε+862.01+ C    (10 −3 )
 
(1-3) Relation Between Geometric Compression Ratio and Close Timing of Intake Valve in Layer  3 
 
       FIG. 18  illustrates the characteristic of the SPCCI combustion when the engine  1  carries out the SPCCI combustion of the mixture gas where the A/F is leaner than the stoichiometric air fuel ratio, similar to Layer  3 .  FIG. 18  illustrates a range where the SPCCI combustion is stable with respect to the G/F (horizontal axis). The vertical axis in this graph is a crank angle corresponding to a combustion center of gravity, and the combustion center of gravity is advanced as it goes upward in this graph. 
     The range where the SPCCI combustion is stabilized is a range surrounded by a curve in this graph. When the engine load is low, the range where the SPCCI combustion is stabilized is located at upper left in  FIG. 18 . When the engine load increases, the range where the SPCCI combustion is stabilized moves downwardly in  FIG. 18 . 
       FIG. 18  also illustrates a range where discharge of raw NO x  can be reduced. The range where the discharge of raw NO x  can be reduced is located at lower right in  FIG. 18 . This range has a triangular shape in  FIG. 18 . If the A/F is leaner than the stoichiometric air fuel ratio, raw NO x  cannot be purified by the three-way catalyst. In Layer  3 , the engine  1  must satisfy both securing of the stability of the SPCCI combustion and reduction of the discharge of raw NO x . 
     As seen in this graph, if the engine load is high, an overlapping area of the range where the combustion stability is secured and the range where the discharge of raw NO x  can be reduced increases. On the other hand, if the engine load is low, the overlapping area of the range where the combustion stability is secured and the range where the discharge of raw NO x  can be reduced decreases. 
     Regarding Layer  3 , the state where the engine  1  operates with the light load corresponds to a limit of the operating state where the SPCCI combustion can occur. Regarding Layer  3 , upon determining the relation between ε and IVC so that the temperature of the combustion chamber  17  at the start timing (θ CI ) of the CI combustion becomes the given temperature, it is necessary to be set based on the temperature inside the combustion chamber  17  when the engine  1  operates with the light load. 
     Similar to the above, using the actual engine  1 , the present inventors measured various parameters when operating the engine  1  with the light load in Layer  3 , and estimated an actual temperature inside the combustion chamber  17  at θ CI  based on the measured parameters. Then, an average value of a plurality of estimated temperatures was determined as a reference temperature Tth 3 . If the temperature of the combustion chamber  17  at θ CI  is the reference temperature Tth 3 , the SPCCI combustion can be achieved in Layer  3 . This reference temperature Tth 3  corresponds to the minimum temperature. If the temperature inside the combustion chamber  17  at θ CI  is the reference temperature Tth 3  or higher while the engine  1  operates with the light load, the SPCCI combustion can be achieved by delaying the ignition timing. However, if the temperature inside the combustion chamber  17  at θ CI  is lower than the reference temperature Tth 3 , SPCCI combustion cannot be achieved even if the ignition timing is advanced. 
     Therefore, in order to achieve the stable SPCCI combustion in Layer  3 , the relation between ε and IVC is required so that the temperature inside the combustion chamber  17  at θ CI  becomes the reference temperature Tth 3  or higher. 
     Thus, as conceptually illustrated in  FIG. 19 , the present inventors estimated the temperature of the combustion chamber  17  during the CI combustion by using the model of the engine  1 , while changing the values of IVC and O/L in a matrix of the close timing IVC of the intake valve  21  and the overlap period O/L of the intake valve  21  and the exhaust valve  22 , for every geometric compression ratio ε (ε 1 , ε 2  . . . ) (a reference numeral  1901 ). As hatched in the matrix of the reference numeral  1901 , a combination of IVC and O/L where the temperature becomes the reference temperature Tth 3  or higher can achieve the SPCCI combustion in Layer  3 . 
     Moreover, in order to reduce the discharge of raw NO x , the G/F of the mixture gas must be made a given value or higher. As illustrated by a reference numeral  1902  in  FIG. 19 , the present inventors estimated the G/F by using the model of the engine  1 , while changing the values of the close timing IVC and the overlap period O/L in the matrix comprised of the two parameters of IVC and O/L. As oblique lines are drawn in the matrix of the reference numeral  1902 , the combination of IVC and O/L where the G/F becomes the given value or higher can reduce the discharge of raw NO x . 
     Then, the present inventors determined the relation between ε and IVC which can achieve both the stability of the SPCCI combustion and the reduction of raw NO x  discharge, by overlapping the combination of IVC and O/L where the temperature becomes the reference temperature Tth 3  or higher which is illustrated by the reference numeral  1901 , and the combination of IVC and O/L where the G/F becomes the given value or higher which is illustrated by the reference numeral  1902 . That is, in the matrix of a reference numeral  1903 , a cross-hatched range is the combination of ε and IVC which can achieve both the stability of the SPCCI combustion and the reduction of NO x  discharge. 
     Note that although illustration is omitted, the present inventors acquired a combination of IVC and O/L where the temperature becomes the reference temperature Tth 3  or higher and a combination of IVC and O/L where the G/F becomes the given value or higher by estimating the temperature of the combustion chamber  17  and the G/F during the CI combustion, similarly for the matrix where the close timing of the intake valve  21  is set before the intake bottom dead center. 
       FIG. 20  illustrates approximations (V) and (VI) calculated based on the combinations of ε and IVC. The horizontal axis in  FIG. 20  is the geometric compression ratio ε, and the vertical axis is the close timing IVC (deg. aBDC) of the intake valve  21 . 
     An upper  figure 2001  of  FIG. 20  corresponds to a case when the engine speed is 2,000 rpm. The approximations (V) and (VI) are as follows.
 
 IVC=− 0.9949ε 2 +41.736ε−361.16   Approximation (V)
 
IVC=0.9949ε 2 −41.736ε+401.16   Approximation (VI)
 
     In  FIG. 20 , the combinations of ε and IVC on the right side of the approximations (V) and (VI) have the temperature of the combustion chamber  17  during CI combustion becoming the reference temperature Tth 3  or higher, thereby achieving the SPCCI combustion of the mixture gas with the A/F being leaner than the stoichiometric air fuel ratio. 
     In Layer  3 , the relation between ε and IVC described above is a relation based on the minimum temperature of the combustion chamber  17  which can achieve the SPCCI combustion when the engine  1  operates with the light load. 
     On the other hand, if the temperature inside the combustion chamber  17  is too high, the CI combustion begins before the start of the SI combustion and the SPCCI combustion cannot be performed, regardless of Layer  2  or Layer  3 . 
     Here, the concept of the SPCCI combustion is such that, as described above, when the ignition plug  25  ignites the mixture gas, the mixture gas around the ignition plug  25  starts the SI combustion, and, after that, the surrounding mixture gas carries out the CI combustion. From examinations by experiments, etc. which the present inventors conducted until now, it was found that the self-ignition of the mixture gas occurred when the surrounding temperature of the mixture gas which self-ignites exceeds a given reference temperature Tth 4 , and this reference temperature Tth 4  was not necessarily in agreement with a mean temperature of the entire combustion chamber  17 . From this knowledge, if the mean temperature inside the combustion chamber  17  at a compression top dead center reaches the reference temperature Tth 4 , it is thought that the CI combustion will begin before the SI combustion begins, and in this case, the SPCCI combustion cannot be performed. 
     Thus, the present inventors estimated the temperature of the combustion chamber  17  at the compression top dead center by using the model of the engine  1 , while changing the values of the close timing IVC and the overlap period O/L in the matrix of the close timing IVC of the intake valve  21 , and the overlap period O/L of the intake valve  21  and the exhaust valve  22 , for every geometric compression ratio ε (ε 1 , ε 2  . . . ), similar to the matrix of the reference numeral  1901  of  FIG. 19 . The combination of IVC and O/L where the temperature inside the combustion chamber  17  at the compression top dead center exceeds the reference temperature Tth 4  cannot achieve the SPCCI combustion, but the combination of IVC and O/L being the reference temperature Tth 4  or lower can achieve the SPCCI combustion. 
       FIG. 20  illustrates approximations (VII) and (VIII) calculated based on the combination of ε and IVC where the temperature inside the combustion chamber  17  at the compression top dead center becomes the reference temperature Tth 4  or lower. The approximations (VII) and (VIII) are as follows.
 
 IVC=− 4.7481ε 2 +266.75ε−3671.2   Approximation (VII)
 
and
 
 IVC= 4.7481ε 2 −266.75ε+3711.2   Approximation (VIII)
 
     In  FIG. 20 , the combination of ε and IVC on the left side the approximations (VII) and (VIII) can avoid that the CI combustion begins before the SI combustion, and achieves the SPCCI combustion. 
     As seen in  FIG. 20 , also in Layer  3 , the relation between ε and IVC is substantially vertically symmetrical with respect to IVC=20 deg.aBDC. Moreover, IVC=75 deg.aBDC is a retarding limit of the close timing of the intake valve  21  set in consideration of the amount of gas introduced into the combustion chamber  17  when the engine  1  operates in Layer  3 . Similarly, IVC=−35 deg.aBDC is an advancing limit of the close timing of the intake valve  21  set in consideration of the amount of gas introduced into the combustion chamber  17 . 
     When determining the close timing IVC of the intake valve  21  in the case where the engine  1  operates in Layer  3 , the ECU  10  must determine IVC within the ε-IVC valid range surrounded by the approximations (V), (VI), (VII), and (VIII) in  FIG. 20  (the hatched range in  FIG. 20 ). 
     For example, if the geometric compression ratio ε is set as 10≤ε&lt;20, when the engine speed is 2,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
0.9949ε 2 −41.736ε+401.16≤ IVC≤ −0.9949ε 2 +41.736ε−361.16   (11)
 
     Moreover, if the geometric compression ratio ε is set as 20≤ε&lt;25, when the engine speed is 2,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
−35≤ IVC≤ 75   (12)
 
     Further, if the geometric compression ratio ε is set as 25≤ε≤30, when the engine speed is 2,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
−4.7481ε 2 +266.75ε−3671.2≤ IVC≤ 75   (13)
 
or
 
−35≤ IVC≤ 4.7481ε 2 −266.75ε+3711.2   (14)
 
     By setting the close timing IVC of the intake valve  21  based on the relational expressions (11) to (14), the SPCCI combustion is achieved of the mixture gas with a A/F leaner than the stoichiometric air fuel ratio. Note that the close timing IVC is set for each operating state which is determined by the load and the engine speed in Layer  3 . 
     The example illustrated by a solid line in  FIG. 20  is the ε-IVC valid range when the engine speed is 2,000 rpm, as described above. If the engine speed changes, the ε-IVC valid range also changes. When the engine speed increases, the ε-IVC valid range is also parallelly translated to the retard side, similarly in  FIG. 20 . Therefore, if the geometric compression ratio is set as 10≤ε&lt;20, when the engine speed is 3,000 rpm (see a broken line), the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
0.9949ε 2 −41.736ε+403.16≤ IVC≤− 0.9949ε 2 +41.736ε−359.16   (11 −1 )
 
     If the geometric compression ratio ε is set as 20≤ε&lt;25, when the engine speed is 3,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
−33≤ IVC ≤77   (12 −1 )
 
     Further, if the geometric compression ratio ε is set as 25≤ε≤30, when the engine speed is 3,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
−4.7481ε 2 +266.75ε−3669.2≤ IVC≤ 77   (13 −1 )
 
or
 
−33≤ IVC≤ 4.7481ε 2 −266.75ε+3713.2   (14 −1 )
 
     If the geometric compression ratio ε is set as 10≤ε≤20, when the engine speed is 4,000 rpm (see one-dot chain line), the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
0.9949ε 2 −41.736ε+409.16≤ IVC≤− 0.9949ε 2 +41.736ε−353.16   (11 −2 )
 
     If the geometric compression ratio ε is set as 20≤ε≤25, when the engine speed is 4,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
−27≤ IVC≤ 83   (12 −2 )
 
     Further, if the geometric compression ratio ε is set as 25≤ε≤30, when the engine speed is 4,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
−4.7481ε 2 +266.75ε−3663.2≤ IVC≤ 83   (13 −2 )
 
or
 
−27≤ IVC≤ 4.7481ε 2 −266.75ε+3719.2   (14 −2 )
 
     If the correction term C according to the engine speed NE (rpm) of the engine  1  is used similar to the above, the relational expression of ε and IVC in Layer  3  can be expressed as follows. If the geometric compression ratio ε is 10≤ε&lt;20,
 
0.9949ε 2 −41.736ε+401.16+ C≤IVC≤− 0.9949ε 2 +41.736ε−361.16+ C    (11 −3 )
 
If the geometric compression ratio ε is 20≤ε≤25,
 
−35+ C≤IVC≤ 75+ C    (12 −3 )
 
If the geometric compression ratio ε is 25≤ε≤30,
 
−4.7481ε 2 +266.75ε−3671.2+ C≤IVC≤ 75+ C    (13 −3 )
 
or
 
−35+ C≤IVC≤ 4.7481ε 2 −266.75ε+3711.2+ C    (14 −3 )
 
     The ECU  10  determines the close timing IVC based on the ε-IVC valid range determined for every engine speed of the engine  1 . As a result, the ECU  10  can set the valve timing of the intake valve  21  in Layer  3  as illustrated in  FIG. 12 . 
     Moreover, a lower  figure 2002  of  FIG. 20  is a relation between ε and IVC when the fuel is the low octane fuel. 
     Upon determining the close timing IVC in the engine  1  of the low octane fuel, if the geometric compression ratio ε is set as 10≤ε&lt;18.7, when the engine speed is 2,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
0.9949ε 2 −39.149ε+348.59≤ IVC≤− 0.9949ε 2 +39.149ε−308.59   (15)
 
     Moreover, if the geometric compression ratio ε is set as 18.7≤ε&lt;23.7 in the engine  1  of the low octane fuel, when the engine speed is 2,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
−35≤ IVC≤ 75   (16)
 
     Further, if the geometric compression ratio ε is set as 23.7≤ε≤30 in the engine  1  of the low octane fuel, when the engine speed is 2,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
−3.1298ε 2 +172.48ε−2300≤ IVC≤ 75   (17)
 
or
 
−35≤ IVC≤ 3.1298ε 2 −172.48ε+2340   (18)
 
     The cross-hatched range in the lower  figure 2002  of  FIG. 20  is an overlapping range of the ε-IVC valid range of the high octane fuel and the ε-IVC valid range of the low octane fuel. Similar to the above, the control logic which suits both the engine  1  using the high octane fuel and the engine  1  using the low octane fuel is set by determining IVC within the overlapping range of the two occurring ranges. 
     Note that although illustration is omitted, if the engine speed increases, the ε-IVC valid range is parallelly translated to the retard side also in the engine  1  of the low octane fuel. If the geometric compression ratio ε is set as 10≤ε&lt;18.7 in the engine  1  of the low octane fuel, when the engine speed is 3,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
0.9949ε 2 −39.149ε+350.59≤ IVC≤− 0.9949ε 2 +39.149ε−306.59   (15 −1 )
 
     Moreover, if the geometric compression ratio ε is set as 18.7≤ε&lt;23.7 in the engine  1  of the low octane fuel, when the engine speed is 3,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
−33≤ IVC≤ 77   (16 −1 )
 
     Further, if the geometric compression ratio ε is set as 23.7≤ε≤30 in the engine  1  of the low octane fuel, when the engine speed is 3,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
−3.1298ε 2 +172.48ε−2298≤ IVC≤ 77   (17 −1 )
 
or
 
−33≤ IVC≤ 3.1298ε 2 −172.48ε 2 +2342   (18 −1 )
 
     If the geometric compression ratio ε is set as 10≤ε&lt;18.7 in the engine  1  of the low octane fuel, when the engine speed is 4,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
0.9949ε 2 −39.149ε+356.59≤ IVC≤− 0.9949ε 2 +39.149ε−300.59   (15 −2 )
 
     Moreover, if the geometric compression ratio ε is set as 18.7≤ε&lt;23.7 in the engine  1  of the low octane fuel, when the engine speed is 4,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
−27≤ IVC≤ 83   (16 −2 )
 
     Further, if the geometric compression ratio ε is set as 23.7≤ε≤30 in the engine  1  of the low octane fuel, when the engine speed is 4,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
−3.1298ε 2 +172.48ε−2292≤ IVC≤ 83   (17 −2 )
 
or
 
−27≤ IVC≤ 3.1298ε 2 −172.48ε+2348   (18 −2 )
 
     If the correction term C according to the engine speed NE (rpm) of the engine  1  is used similar to the above, the relational expression of ε and IVC in Layer  3 , in the engine  1  of the low octane fuel can be expressed as follows. If the geometric compression ratio ε is 10≤ε&lt;18.7,
 
0.9949ε 2 −39.149ε+348.59+ C≤IVC≤− 0.9949ε 2 +39.149ε−308.59+ C    (15 −3 )
 
If the geometric compression ratio ε is 18.7≤ε&lt;23.7,
 
−35+ C≤IVC≤ 75+ C    (16 −3 )
 
If the geometric compression ratio ε is 23.7≤εε30,
 
−3.1298ε 2 +172.48ε−2300+ C≤IVC≤ 75+ C    (17 −3 )
 
or
 
−35+ C≤IVC ≤3.1298ε 2 −172.48ε+2340+ C    (18 −3 )
 
(1-4) Relation Between Geometric Compression Ratio and Close Timing of Intake Valve in Layers  2  and  3 
 
       FIG. 21  illustrates a relation between the geometric compression ratio ε and the close timing IVC of the intake valve  21  where the SPCCI combustion is possible in both Layer  2  and Layer  3 . This relational expression is obtained from the ε-IVC valid range of  FIG. 17  and the ε-IVC valid range of  FIG. 20 . 
     When the ECU  10  selects Layer  3  according to the temperature, etc. of the engine  1 , the low-load operating range of the engine  1  is switched from Layer  2  to Layer  3 . If the close timing IVC of the intake valve  21  is set so that the SPCCI combustion is possible in both Layer  2  and Layer  3 , it is possible to continuously perform the SPCCI combustion even when the map of the engine  1  is switched from Layer  2  to Layer  3 . 
     An upper  figure 2101  of  FIG. 21  is a relation between ε and IVC when the fuel is the high octane fuel. A lower  figure 2102  is a relation between ε and IVC when the fuel is the low octane fuel. 
     If the geometric compression ratio ε is set as 10≤ε&lt;17 in the engine  1  of the high octane fuel, when the engine speed is 2,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
0.9949ε 2 −41.736ε+401.16≤IVC≤− 0 . 9949 ε 2 +41.736ε−361.16   (19)
 
     If the geometric compression ratio ε is set as 17≤ε≤30 in the engine  1  of the high octane fuel, when the engine speed is 2,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
−0.4288ε 2 +31.518ε−379.88≤ IVC≤− 0.9949ε 2 +41.736ε−361.16   (20)
 
or
 
0.9949ε 2 −41.736ε+401.16≤ IVC≤ 1.9163ε 2 −89.935ε+974.94   (21)
 
     By setting the close timing IVC of the intake valve  21  based on the relational expressions (19) to (21), the SPCCI combustion of the mixture gas with the A/F being leaner than the stoichiometric air fuel ratio can be carried out, and the SPCCI combustion of the mixture gas with the A/F being the stoichiometric air fuel ratio or richer than the stoichiometric air fuel ratio, and the G/F being leaner than the stoichiometric air fuel ratio can be carried out. 
     Note that the close timing IVC is set for each operating state which is determined by the load and the engine speed in Layer  2  and Layer  3 . 
     As illustrated by a broken line, if the geometric compression ratio ε is set as 10≤ε&lt;17 in the engine  1  of the high octane fuel, when the engine speed is 3,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
0.9949ε 2 −41.736ε+403.16≤ IVC≤− 0.9949ε 2 +41.736ε−359.16   (19 −1 )
 
     If the geometric compression ratio ε is set as 17≤ε≤30 in the engine  1  of the high octane fuel, when the engine speed is 3,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
−0.4288ε 2 +31.518ε−377.88≤ IVC≤− 0.9949ε 2 +41.736ε−359.16   (20 −1 )
 
or
 
0.9949ε 2 −41.736ε+403.16≤ IVC≤ 1.9163ε 2 −89.935ε+976.94   (21 −1 )
 
     Similarly, as illustrated by a one-dot chain line, if the geometric compression ratio ε is set as 10≤ε&lt;17 in the engine  1  of the high octane fuel, when the engine speed is 4,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
0.9949ε 2 −41.736ε+409.16≤ IVC≤− 0.9949ε 2 +41.736ε−353.16   (19 −2 )
 
     If the geometric compression ratio ε is set as 17≤ε≤30 in the engine  1  of the high octane fuel, when the engine speed is 4,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
−0.4288ε 2 +31.518ε−371.88≤ IVC≤− 0.9949ε 2 +41.736ε−353.16   (20 −2 )
 
or
 
0.9949ε 2 −41.736ε+409.16≤ IVC≤ 1.9163ε 2 −89.935ε+982.94   (21)
 
     If the correction term C according to the engine speed NE (rpm) of the engine  1  is used similar to the above, the relational expression of ε and IVC in Layer  2  and Layer  3  can be expressed as follows. If the geometric compression ratio ε is 10≤ε&lt;17,
 
0.9949ε 2 −41.736ε+401.16+ C≤IVC≤− 0.9949ε 2 +41.736ε−361.16+ C    (19 −3 )
 
If the geometric compression ratio ε is 17≤ε≤30,
 
−0.4288ε 2 +31.518ε−379.88+ C≤IVC≤− 0.9949ε 2 +41.736ε−361.16+ C    (20 −3 )
 
or
 
0.9949ε 2 −41.736ε+401.16+ C≤IVC≤ 1.9163ε 2 −89.935ε+974.94+ C    (21 −3 )
 
     Here, if the geometric compression ratio ε determined to be lower than 17, the ECU  10  can determine IVC based on the relational expression (19 −3 ). Since the selection range of IVC is wide, a degree of freedom in the design becomes high. 
     Moreover, as illustrated in the lower  figure 2102  of  FIG. 21 , if the geometric compression ratio ε is set as 10≤ε&lt;15.7 in the engine  1  of the low octane fuel, when the engine speed is 2,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
0.9949ε 2 −39.149ε+348.59≤ IVC≤− 0.9949ε 2 +39.149ε−308.59   (22)
 
     Moreover, if the geometric compression ratio ε is set as 15.7≤ε≤30 in the engine  1  of the low octane fuel, when the engine speed is 2,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
−0.5603ε 2 +34.859ε−377.22≤ IVC≤− 0.9949ε 2 +39.149ε−308.59   (23)
 
or
 
0.9949ε 2 −39.149ε+348.59≤ IVC≤ 1.9211ε 2 −85.076ε+862.01   (24)
 
     Although illustration is omitted, if the geometric compression ratio ε is set as 10≤ε&lt;15.7 in the engine  1  of the low octane fuel, when the engine speed is 3,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
0.9949ε 2 −39.149ε+350.59≤ IVC≤− 0.9949ε 2 +39.149ε−306.59   (22 −1 )
 
     Moreover, if the geometric compression ratio ε is set as 15.7≤ε≤30 in the engine  1  of the low octane fuel, when the engine speed is 3,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
−0.5603ε 2 +34.859ε−375.22≤ IVC≤− 0.9949ε 2 +39.149ε−306.59   (23 −1 )
 
or
 
0.9949ε 2 −39.149ε+350.59≤ IVC≤ 1.9211ε 2 −85.076ε+864.01   (24 −1 )
 
     Although illustration is similarly omitted, if the geometric compression ratio ε is set as 10≤ε&lt;15.7 in the engine  1  of the low octane fuel, when the engine speed is 4,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
0.9949ε 2 −39.149ε+356.59≤ IVC≤− 0.9949ε 2 +39.149ε−300.59   (22 −2 )
 
     Moreover, if the geometric compression ratio ε is set as 15.7≤ε≤30 in the engine  1  of the low octane fuel, when the engine speed is 4,000 rpm, the ECU  10  determines the close timing IVC (deg.aBDC) so that the following expression is satisfied.
 
−0.5603ε 2 +34.859ε−369.22≤ IVC≤− 0.9949ε 2 +39.149ε−300.59   (23 −2 )
 
or
 
0.9949ε 2 −39.149ε+356.59≤ IVC≤ 1.9211ε 2 −85.076ε+870.01   (24 −2 )
 
     If the correction term C according to the engine speed NE (rpm) of the engine  1  is used similar to the above, the relational expression of ε and IVC in Layer  2  and Layer  3  in the engine  1  of the low octane fuel can be expressed as follows. If the geometric compression ratio ε is 10≤ε&lt;15.7,
 
0.9949ε 2 −39.149ε+348.59+ C≤IVC≤− 0.9949ε 2 +39.149ε−308.59+ C    (22 −3 )
 
If the geometric compression ratio ε is 15.7≤ε≤30,
 
−0.5603ε 2 +34.859ε−377.22+ C≤IVC≤− 0.9949ε 2 +39.149ε−308.59+ C    (23 −3 )
 
or
 
0.9949ε 2 −39.149ε+348.59+ C≤IVC&lt; 1.9211ε 2 −85.076ε+862.01+ C    (24 −3 )
 
     Note that although illustration is omitted, the ECU  10  may determine IVC within an overlapping range of the ε-IVC valid range of the upper  FIG. 2101  and the ε-IVC valid range of the lower  figure 2102  of  FIG. 21 . Similar to the above, the ECU  10  can set the control logic which suits both the engine  1  using the high octane fuel and the engine  1  using the low octane fuel by determining IVC within the overlapping range of the two occurring ranges. 
     (1-5) Procedure of Method of Implementing Control Logic 
     Next, a procedure of the method of controlling the engine  1  for performing the SPCCI combustion will be described with reference to a flowchart illustrated in  FIG. 22 . The ECU  10  can execute each step and stores information on the ε-IVC valid range illustrated in  FIGS. 17, 20 , and  21 . 
     At Step S 221  after the procedure starts, the ECU  10  first sets the geometric compression ratio ε. The set value of the geometric compression ratio ε may be inputted from an exterior device into the ECU  10 . 
     At the following Step S 222 , the ECU  10  sets the valve opening angle of the intake valve  21 , and the valve opening angle of the exhaust valve  22 . This corresponds to determining the cam shapes of the intake valve  21  and the exhaust valve  22 . The set values of the valve opening angles of the intake valve  21  and the exhaust valve  22  may be inputted from an exterior device into the ECU  10 . Thus, a hardware configuration of the engine  1  can be identified at Steps S 221  and S 222 . 
     At Step S 223 , the ECU  10  sets the operating state comprised of the load and the engine speed, and at the following Step S 224 , the ECU  10  selects IVC based on the stored ε-IVC valid range ( FIGS. 17, 20, and 21 ). 
     Then, at Step S 225 , the computer determines whether the SPCCI combustion can be achieved based on IVC set at Step S 224 . If the determination at Step S 225  is YES, this procedure shifts to Step S 226 , and the ECU  10  controls the engine  1  according to the control logic corresponding to the engine operating state so that the SPCCI combustion is performed in the operating state set at Step S 223 . On the other hand, if the determination at Step S 225  is NO, this procedure shifts to Step S 227 , and the ECU  10  controls the engine  1  according to the control logic corresponding to the engine operating state so that the SI combustion is performed in the operating state set at Step S 223 . Note that at Step S 227 , the ECU  10  may again set the close timing IVC of the intake valve  21  in consideration of performing the SI combustion. 
     As described above, the control device of the compression-ignition engine disclosed herein can set the close timing IVC of the intake valve  21  within the range where the relation between the engine geometric compression ratio ε and the close timing IVC of the intake valve  21  is satisfied. 
     (2) Method of Controlling Supercharging Pressure 
     As described above, the close timing IVC of the intake valve  21  can be set based on the relation between the geometric compression ratio ε and the close timing IVC of the intake valve  21 . 
     As a result of further repeated and diligent examinations, the present inventors further found that, in order to put in practical use the engine  1  for performing the SPCCI combustion with a lean G/F in Layer  2 , another relation was required between a supercharging pressure P of the engine  1  and the close timing IVC of the intake valve  21 . The present inventors further found a control method based on such another relation, after the implementing method was utilized. 
     (2-1) Relation Between Supercharging Pressure and Close Timing of Intake Valve in Layer  2   
     As described above, the engine  1  operates, while making the A/F of the mixture gas the stoichiometric air fuel ratio or a substantially stoichiometric air fuel ratio in Layer  2 , and making the G/F leaner than the stoichiometric air fuel ratio. Here, the G/F can be controlled through the amount of gas supplied into the combustion chamber  17 , and a control factor for controlling the amount of gas includes the supercharging pressure P of the supercharger  44 , in addition to an overlap period O/V. 
     For example, since the fuel supply amount is large when operating the engine  1  in the high-load operating state including the maximum load operating state, a larger amount of gas is required to be supplied into the combustion chamber  17 . Therefore, in order to maintain the G/F lean in Layer  2 , it may be necessary to set the supercharging pressure P (especially, a target supercharging pressure of the supercharger  44 ) at a given pressure or higher. That is, in Layer  2 , a lower limit of the supercharging pressure P can be determined. Moreover, an actual amount of gas sent into the combustion chamber  17  from the intake passage  40  among the gas supercharged by the supercharger  44  depends also on the close timing IVC of the intake valve  21 . 
     Therefore, as a condition for maintaining the G/F at lean in Layer  2 , a relation between the lower limit of the supercharging pressure P and the close timing IVC can be determined. 
     Therefore, the present inventors estimated the G/F by using the model of the engine  1  also in consideration of an inertia effect of air, while changing the values of the two parameters of the supercharging pressure P and the close timing IVC. Then, the present inventors acquired a combination of the lower limit of the supercharging pressure P and the close timing IVC so that the G/F becomes the given value or higher. 
       FIG. 23  illustrates an approximation (A) calculated from the combination of the lower limit of P and IVC. The horizontal axis of  FIG. 23  is the close timing IVC (deg. aBDC) of the intake valve  21 , and the vertical axis is the supercharging pressure P (kPa) of the engine  1 . In  FIG. 23 , “E −n ” (n is an integer) indicates “10 −n .” For example, “8E-11IVC 6 ” means “8×10 −11 ×IVC 6 .” 
     An upper figure of  FIG. 23  corresponds to a case where the engine speed of the engine  1  is 2000 rpm or higher. The approximation (A) corresponds to a solid line in  FIG. 23 .
 
 P= 8.0×10 −11   IVC   6 −1.0×10 −8   IVC   5 +3.0×10 −7 IVC 4 −4.0×10 −6 IVC 3 +0.0068 IVC   2 −0.3209 IVC+ 116.63   Approximation (A)
 
     In  FIG. 23 , the combination of P and IVC above the approximation (A) can achieve the SPCCI combustion, while maintaining the G/F at lean, because the G/F becomes the given value or higher. 
     As seen in  FIG. 23 , the relation between P and IVC is substantially laterally symmetrical with respect to IVC=20 deg.aBDC. IVC=20 deg.aBDC corresponds to a close timing (best IVC) at which the amount of gas introduced into the combustion chamber  17  becomes the maximum. 
     That is, at IVC=20 deg.aBDC, a large amount of gas can be supplied into the combustion chamber  17 , even if the supercharging pressure P is set relatively low. Therefore, the supercharging pressure P is the minimum at IVC=20 deg.aBDC. Moreover, in order to maintain the G/F at a given value or higher, it is required to set the supercharging pressure P relatively high as the G/F deviates from this minimum. Therefore, as IVC deviates from 20 deg.aBDC, it is necessary to increase the supercharging pressure P. 
     Note that the close timing IVC is set for each operating state which is defined by the load and the engine speed in Layer  2 . The example of  FIG. 23  is a P-IVC valid range when the engine speed of the engine  1  is 2000 rpm, as described above. If the engine speed of the engine  1  changes, the P-IVC valid range also changes. The ECU  10  determines the close timing IVC based on the P-IVC valid range defined for every engine speed of the engine  1 . 
     The supercharging pressure P described above may also be a target supercharging pressure of the supercharger  44  in Layer  2 . 
     Moreover, it is generally thought that, as for the supercharging pressure P which can be set to the supercharger  44 , an upper limit (a so-called supercharger limit) due to its hardware configuration exists. Therefore, in Layer  2 , the upper limit can be provided to the supercharging pressure P. 
       FIG. 23  also illustrates the approximation (B) indicative of the upper limit of P. The approximation (B) corresponds to the reference character P 1  in  FIG. 23 , and in the illustrated example,
 
P=150.   Approximation (B)
 
     In  FIG. 23 , the combination of P and IVC below the approximation (B) permits the supercharging pressure P to be set within a range without exceeding the supercharger limit. Moreover, although the supercharger limit indicated by the approximation (B) varies according to the hardware configuration of the supercharger  44 , the limit may be set so as to at least exceed the minimum of the supercharging pressure P in the approximation (A). 
     Moreover, other than the upper limit of P based on the approximation (B), an upper limit (second upper limit) of P in consideration of the fuel efficiency may be provided. Thus, the loss of work caused by excessive supercharging pressure can be reduced, and this becomes advantageous to improve the fuel efficiency of the engine. Although illustration is omitted, this second upper limit can be set to, for example,
 
P=250.
 
     As illustrated in the above equation, the second upper limit can be set higher than the upper limit illustrated in the approximation (B). 
     Moreover, in order to achieve the SPCCI combustion in Layer  2 , the relation between ε and IVC is required in the first place so that the temperature of the combustion chamber  17  at θCI becomes the reference temperature Tth 2  or higher. Such a requirement is satisfied by, for example, the combination of ε and IVC on the right side of the approximations (III) and (IV) in  FIG. 17 . 
     That is, in order to achieve the SPCCI combustion in Layer  2 , IVC needs to fall within a given range. That is, an upper limit and a lower limit can be set to IVC. 
     Thus, when estimating the G/F, the present inventors set the upper limit and the lower limit of IVC according to the value of the geometric compression ratio ε. 
     In  FIG. 23 , an approximation (C) indicative of the upper limit of IVC and an approximation (D) indicative of the lower limit of IVC are also illustrated. The approximation (C) is determined based on the approximation (III) in  FIG. 17 , and corresponds to a reference character Ir in  FIG. 23 . On the other hand, the approximation (D) is determined based on the approximation (IV) in  FIG. 17 , and corresponds to a reference character Il in  FIG. 23 . In the illustrated example, the approximations (C) and (D) are as follows.
 
IVC=90   Approximation (C)
 
IVC=−50   Approximation (D)
 
     In  FIG. 23 , the combination of P and IVC on the left side of the approximation (C) and on the right side of the approximation (D) can stably achieve SPCCI combustion. 
     Note that the approximations (C) and (D) in the upper figure of  FIG. 23  correspond to a case where the geometric compression ratio ε is set to around  16  as can be seen in  FIG. 17 . If ε is set smaller than this, as illustrated in the lower figure of  FIG. 23 , the upper limit and the lower limit of IVC both approach IVC=20 deg.aBDC. Moreover, the approximations (C) and (D) vary according to the octane number of the fuel. 
     Note that the approximation (A) in the lower figure of  FIG. 23  is made the same as that of the upper figure for the convenience of illustration, but the details of the approximation (A) may vary in fact according to the geometric compression ratio ε. 
     The combination of P and IVC within a range surrounded by the approximations (A), (B), (C), and (D) in  FIG. 23  is the combination which can achieve the SPCCI combustion, while maintaining the G/F in Layer  2  at the given value or higher. In other words, the combination of P and IVC outside this range cannot achieve the G/F-lean SPCCI combustion in Layer  2 . 
     The ECU  10  must determine IVC within the P-IVC valid range which is hatched in  FIG. 23 , when operating the engine  1  in Layer  2  and determining the close timing IVC of the intake valve  21 . 
     Specifically, in the configuration example illustrated in the upper figure of  FIG. 23 , the ECU  10  determines the close timing IVC (deg.aBDC) so that the supercharging pressure P (kPa) satisfies the following expression.
 
 P≥ 8.0×10 −11   IVC   6 −1.0×10 −8   IVC   5 +3.0×10 −7   IVC   4 −4.0×10 −6   IVC   3 +0.0068IVC 2 −0.3209 IVC+ 116.63   (25)
 
     Moreover, the ECU  10  determines the close timing IVC (deg.aBDC) so that the supercharging pressure P (kPa) satisfies the following expression.
 
P≤150   (26)
 
     Moreover, the ECU  10  determines the close timing IVC (deg.aBDC) so as to satisfy the following expression.
 
−50≤ IVC≤ 90   (27)
 
(2-2) Procedure of Control Method
 
     Next, a procedure of the method of controlling the engine  1  for performing the SPCCI combustion will be described with reference to a flowchart illustrated in  FIG. 24 . The ECU  10  can execute each of the following steps. The ECU  10  stores information on the P-IVC valid range illustrated in  FIG. 23 . 
     At Step S 241  after the procedure starts, the ECU  10  first sets the geometric compression ratio ε. A preset value of the geometric compression ratio ε may be inputted into the ECU  10  from an exterior device. 
     At the subsequent Step S 242 , the ECU  10  sets a valve opening angle of the intake valve  21 , and a valve opening angle of the exhaust valve  22 . This corresponds to determining cam shapes of the intake valve  21  and the exhaust valve  22 . The preset values of the valve opening angles of the intake valve  21  and the exhaust valve  22  may be inputted into the ECU  10  from an exterior device. A hardware configuration of the engine  1  can be specified at Steps S 241  and S 242 . 
     At Step S 243 , the ECU  10  sets the operating state comprised of the load and the engine speed of the engine  1 , and at the subsequent Step S 244 , the ECU  10  sets a target supercharging pressure as the supercharging pressure P based on the operating state set at Step S 243 . 
     At the subsequent Step S 245 , the ECU  10  determines IVC based on the prestored P-IVC valid range ( FIG. 23 ). 
     Then, at Step S 246 , the ECU  10  determines whether SPCCI combustion can be achieved based on IVC set at Step S 245 . If the determination of Step S 246  is YES, the procedure shifts to Step S 247 , where the ECU  10  controls the engine  1  according to the control logic corresponding to this operating state so that the SPCCI combustion is performed in the operating state set at Step S 243 . On the other hand, if the determination of Step S 246  is NO, the procedure shifts to Step S 248 , where the ECU  10  controls the engine  1  according to the control logic corresponding to this operating state so that the SI combustion is performed in the operating state set at Step S 243 . Note that at Step S 245 , the ECU  10  may again set the close timing IVC of the intake valve  21  in consideration of performing the SI combustion. 
     As described above, in the control device of the compression-ignition engine disclosed herein, the relation between the supercharging pressure P of the engine  1  and the close timing IVC of the intake valve  21  is defined beforehand, and the ECU  10  can set the close timing IVC of the intake valve  21  within a range where this relation is satisfied. 
     (Other Embodiments) 
     Note that the application of the technology disclosed herein is not limited to the engine  1  having the configuration described above. The engine  1  may adopt various configurations. 
     For example, the engine  1  may be provided with a turbocharger, instead of the mechanical supercharger  44 . 
     It should be understood that the embodiments herein are illustrative and not restrictive, since the scope of the invention is defined by the appended claims rather than by the description preceding them, and all changes that fall within metes and bounds of the claims, or equivalence of such metes and bounds thereof, are therefore intended to be embraced by the claims. 
     DESCRIPTION OF REFERENCE CHARACTERS 
       1  Engine 
       10  ECU (Control Part) 
       17  Combustion Chamber 
       23  Intake-side Electric S-VT (Variable Valve Operating Mechanism) 
       25  Ignition Plug (Ignition Part) 
       44  Supercharger 
       55  EGR System 
       6  Injector (Fuel Injection Part) 
     SW 1  Airflow Sensor (Measurement Part) 
     SW 2  First Intake-air Temperature Sensor (Measurement Part) 
     SW 3  First Pressure Sensor (Measurement Part) 
     SW 4  Second Intake-air Temperature Sensor (Measurement Part) 
     SW 5  Second Pressure Sensor (Measurement Part) 
     SW 6  Pressure Indicating Sensor (Measurement Part) 
     SW 7  Exhaust Temperature Sensor (Measurement Part) 
     SW 8  Linear O 2  Sensor (Measurement Part) 
     SW 9  Lambda O 2  Sensor (Measurement Part) 
     SW 10  Water Temperature Sensor (Measurement Part) 
     SW 11  Crank Angle Sensor (Measurement Part) 
     SW 12  Accelerator Opening Sensor (Measurement Part) 
     SW 13  Intake Cam Angle Sensor (Measurement Part) 
     SW 14  Exhaust Cam Angle Sensor (Measurement Part) 
     SW 15  EGR Pressure Difference Sensor (Measurement Part) 
     SW 16  Fuel Pressure Sensor (Measurement Part) 
     SW 17  Third Intake-air Temperature Sensor (Measurement Part)