Abstract:
There is provided a method of starting an internal combustion engine having a combustion chamber and an intake valve which opens during an intake stroke of an engine cycle to allow air to be inducted into the combustion chamber. The method comprises cranking the internal combustion engine with advanced closing timing and a reduced lift of the intake valve without combustion of air and fuel in the combustion chamber from a stroke of the engine cycle prior to a first intake stroke of the combustion chamber since an engine start request, starting combustion of air and fuel in the combustion chamber after the first intake stroke, and retarding closing timing of said intake valve from the advanced closing timing and increasing the valve lift after the combustion is started. Accordingly, air charge in the combustion chamber may increase properly conforming to the engine speed increase caused by the combustion. Therefore, the torque derived from the combustion of the charged and fuel may increase the engine speed moderately after the beginning of the combustion.

Description:
BACKGROUND 
   The present description relates to an internal combustion engine, more particularly relates to a method of starting an internal combustion engine without excessive engine speed increase. 
   There is shown and presented, for example in Japanese patent application publication no. 2004-308570A, a method of starting an engine of a hybrid electric vehicle. Generally, the hybrid electric vehicle more frequently stops and restarts the engine, and therefore, when restarting the engine, it requires smoother engine start. Particularly, the method of &#39;570 publication seeks suppression of a vibration caused by compression of air in the combustion chamber during motoring the engine (without supplying fuel). When starting the engine, an electric machine first cranks the engine at an engine speed with advanced intake valve timing in order to purge the air in a surge tank of the engine. Then, it motors the engine at an increased speed with retarded intake valve timing in order to reduce an effective compression ratio by reducing air charge in the combustion chamber with the retarded intake valve timing. 
   According to the method, at the second stage of the motoring the engine, the reduced effective compression ratio may suppress the vibration caused by the compression of air. However, in supplying fuel and starting combustion of the fuel after the second stage, the engine speed may increase excessively. In theory, if the closing timing of the intake valve is constant after a bottom dead center of an intake stroke of an engine cycle, the amount of air charged into the combustion chamber increases as the engine speed increases. According to the prior art method, after the combustion has begun, the engine speed increases so as to increase the air charge and engine torque derived from the combustion of the increased air charge. The increased torque may further increase the engine speed, and eventually the excessive engine speed increase may occur. It may cause a torque disturbance or require a complex control of the electric machine to suppress the torque shock. 
   SUMMARY 
   Accordingly, there is provided, in one aspect of the present description, a method of starting an internal combustion engine having a combustion chamber and an intake valve which opens during an intake stroke of an engine cycle to allow air to be inducted into the combustion chamber. The method comprises cranking the internal combustion engine with advanced closing timing of the intake valve without combustion of air and fuel in the combustion chamber from a stroke of the engine cycle prior to a first intake stroke of the combustion chamber since an engine start request, starting combustion of air and fuel in the combustion chamber after the first intake stroke, and retarding closing timing of said intake valve from the advanced closing timing after the combustion is started. 
   According to the first aspect, by transitioning the closing timing of the intake valve from the advanced timing to the retarded timing after the start of the combustion of air and fuel in the combustion chamber, air charge in the combustion chamber may increase properly conforming to the engine speed increase caused by the combustion. Therefore, the torque derived from the combustion of the charged and fuel may increase the engine speed moderately after the beginning of the combustion. 
   There is provided, in a second aspect of the present description, a method of starting the internal combustion engine, comprising cranking the engine with a reduced valve lift of the intake valve without combustion of air and fuel in the combustion chamber from a stroke of the engine cycle prior to a first intake stroke of the combustion chamber since an engine start request, starting combustion of air and fuel in the combustion chamber after the first intake stroke, and increasing the lift of the intake valve from the reduced valve lift after the combustion is started. Accordingly, by transitioning the lift of the intake valve from the reduced lift to the increased lift after the combustion is started, the air charge in the combustion chamber may increase conforming to the engine speed increase caused by the combustion of the inducted air and fuel so that the torque derived from the combustion may increase the engine speed moderately after the beginning of the combustion. 
   The lift of the intake valve may be a maximum valve lift or duration of valve lifting or opening. In the latter case, if the opening timing of the valve is substantially constant, the closing timing is advanced as the lift is reduced. 
   There is provided, in a third aspect of the present description, a power-train system comprising an internal combustion engine with a plurality of combustion chambers having intake valves each of which opens during an intake stroke of an engine cycle to allow air to be inducted into each of the combustion chambers, a variable valve lift mechanism capable of variably setting lifts of said intake valves, a fuel supply system configured to supply fuel individually to the combustion chambers, a first rotational machine capable of converting rotational power from first energy and rotationally coupled to the internal combustion engine, and a controller. The controller is configured to control the variable valve mechanism to reduce the lift of the intake valves, adjust the first energy to crank the internal combustion engine upon an engine start request, control the fuel supply system to start supplying fuel so that a first combustion of the supplied fuel and air takes place in one of the combustion chambers, which has been cranked from a stroke of an engine cycle prior to its intake stroke, after the intake stroke, and control the variable valve mechanism to increase the lift of said intake valves after the first combustion. 
   According to the third aspect, by transitioning the lift of the intake valve from the reduced lift to the increased lift after the combustion is started, the air charge in the combustion chamber may increase conforming to the engine speed increase caused by the combustion of the inducted air and fuel so that the torque derived from the combustion may increase the engine speed moderately after the beginning of the combustion. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The advantages described herein will be more fully understood by reading an example of embodiments in which the above aspects are used to advantage, referred to herein as the Detailed Description, with reference to the drawings wherein: 
       FIG. 1  is a schematic diagram illustrating a series-parallel hybrid electric (HEV) power-train system according to an embodiment of the present description; 
       FIG. 2  shows collinear diagrams of a planetary gear set of the HEV power-train of  FIG. 1 , illustrating relationships between rotational speeds of three rotational elements of the planetary gear sets in an engine running state (A) and an engine stopping and starting state (B); 
       FIG. 3  is a schematic diagram illustrating an internal combustion engine consisting part of the HEV power-train of  FIG. 1 ; 
       FIG. 4  shows a perspective view of an intake valve drive mechanism including a variable cam timing mechanism and a variable valve lift mechanism in accordance with the embodiment; 
       FIG. 5  shows a side view of the variable valve lift mechanism for a valve open state ( 1 ) and a valve closed state ( 2 ) with a greater valve lift in accordance with the embodiment; 
       FIG. 6  shows a side view of the variable valve lift mechanism for a valve open state ( 1 ) and a valve closed state ( 2 ) with a smaller valve lift in accordance with the embodiment; 
       FIG. 7  is explanatory diagrams for the greater valve lift (A) and the smaller valve lift (B) respectively illustrated in  FIGS. 4 and 5 ; 
       FIG. 8  shows various valve lift profiles generated by the variable valve lift mechanism in accordance with the embodiment; 
       FIG. 9  shows a change of the valve lift profile in accordance with changes of control signals θ VCT  and θ VVL ; 
       FIG. 10  shows a flowchart of a routine RH 1  for operational mode selection of the HEV power-train which a HEV controller executes; 
       FIG. 11  shows a flowchart of a routine RH 2  for an engine running mode of the HEV power-train which the HEV controller executes; 
       FIG. 12  shows a flowchart of a routine RH 3  for an electric mode of the HEV power-train which the HEV controller executes; 
       FIG. 13  shows a flowchart of a routine RH 4  for an engine stopping mode of the HEV power-train which the HEV controller executes; 
       FIG. 14  shows a flowchart of a routine RH 5  for an engine starting mode of the HEV power-train which the HEV controller executes; 
       FIG. 15  shows a flowchart of a routine RE 6  which an engine controller executes during the engine stopping mode of the HEV power-train; 
       FIG. 16  shows a flowchart of a routine RE 7  which the engine controller executes during the engine starting mode of the HEV power-train; 
       FIG. 17  is a time chart illustrating an operation of the HEV power-train during the engine stopping mode; 
       FIG. 18  is a time chart illustrating an operation of the HEV power-train during the engine starting mode; and 
       FIG. 19  is a time chart illustrating the operation of the HEV power-train during the engine running mode, the engine stopping mode, the electric mode, the engine starting mode and again the engine running mode. 
   

   DETAILED DESCRIPTION 
   Embodiments of the present description will now be described with reference to the drawings, starting with  FIG. 1 , which illustrates a schematic diagram of an entire system of a series-parallel hybrid electric vehicle (HEV) power-train  1 . The series-parallel HEV power-train  1  comprises an internal combustion engine  2 , a first electric machine  3 , and a second electric machine  4 . These three rotational machines  2  through  4  are rotationally connected to a power transmission mechanism  5 . 
   The power transmission mechanism  5  comprises a planetary gear set  501 , a driven gear  502 , and a second driving gear  503 . The planetary gear set  501  comprises a sun gear  511 , a ring gear  512 , and a planetary carrier  513  carrying planetary pinions  514  thereon, all of which are engaged with each other in the known manner. The ring gear  512  has not only inner teeth that engage with the planetary pinions  514 , but also outer teeth that engage with the driven gear  502 . The driven gear  502  is also engaged with the second driving gear  503 . The power transmission mechanism does not have any clutch so that the all rotational elements are permanently engaged with each other. 
   The crankshaft  21  of the engine  2  is permanently coupled to the planetary carrier  513 . A rotational shaft of the first electric machine  3  is permanently coupled to the sun gear  511  which functions as a driving gear for the first electric machine  3 . A rotational shaft of the second electric machine  4  is permanently coupled to the second driving gear  503 . The driven gear  502  is permanently coupled through a final drive-train, for example, including a propeller shaft  6 , a differential gear set  7  and drive shafts  8 , as known in the art, to driving wheels  9 . In the illustrated embodiment, the driving wheels  9  are vehicle rear wheels, but they may be vehicle front wheels for front wheel drive vehicles. 
   The first and second electric machines  3  and  4  are three-phase induction motor generators (MGs) known in the art. They are electrically connected to a high voltage battery  11  through first and second inverters  12  and  13  respectively. The first electric machine  3  can rotate and generate alternate current (AC), which is output through three AC power lines to the first inverter  12 . There, the electricity in the form of AC is converted to direct current (DC), and output to DC power lines. When the electricity is supplied to the first electric machine  3  in the opposite direction, it may generate torque to drive the engine  2 , such as for an engine start. 
   The second inverter  13  receives electricity in the form of DC from the DC power lines, and converts the electricity from DC to AC. The second electric machine  4  can generate torque with the AC electricity from the second inverter  13  through three AC power lines, and output the torque to the driving wheels  5  through the power transmission mechanism  5 , in particular the second driving gear  503  and the driven gear  502 , and the final drive-train. Also, such as when the vehicle is decelerating, rotational inertia on the driving wheels  5  can rotate the second electric machine  4 , which can generate electricity in the form of AC and output it to the second inverter  13  through the three AC power lines. 
   The first and second inverters  12  and  13  are connected with each other by the DC power lines, which are respectively connected to positive and negative terminals of the battery  11 , so that direct currents can flow in any directions between the three electrical elements  11  through  13  in dependence on their terminal voltages. 
   A HEV controller  14  controls first and second inverters  12  and  13 , and eventually the first and second electric machines  3  and  4 . Specifically, the HEV controller  14  is a microcomputer based controller having a central processing unit which executes programs using data, memories, such as RAM and ROM, storing the programs and data, and input/output (I/O) bus inputting and outputting electric signals, as is well known in the art. More specifically, the controller  14  computes desired amounts of the respective input/outputs of the first and second electric machines  12  and  13  based on various inputs. The inputs include signals from a speed sensor  31  for detecting a speed N MG2  of the second electric machine  4  corresponding to a vehicle speed VSP, an accelerator position sensor  32  for detecting a position α of an accelerator pedal  32   a , a brake switch  33  for detecting a depression of a brake pedal  33   a  by a vehicle operator, a battery voltage sensor  34  for detecting a terminal voltage V B  of the battery  11 , first through third current sensors (not shown) for respectively detecting electric currents flowing to/from the first inverter  12 , the second inverter  13  and the battery  5 , and other sensors. The HEV controller also communicates with an engine controller  15 , which is described in greater detail below. 
   There is shown, in  FIG. 2 , a collinear diagram of the planetary gear set  501  of the power transmission mechanism  5 . A speed N RING  of the ring gear  512  is fixedly in proportion to the vehicle speed VSP and the speed N MG2  of the second electric machine  4  through the driven gear  502  and the second driving gear  503 . Speeds N SUN  and N CARR  of the sun gear  511  and the planetary carrier  513  are fixedly in proportion respectively to speeds N ENG  and N MG1  of the engine  2  and the first electric machine  3 . As is well known in the art, the planetary gear set  501  puts those speeds N RING , N SUN  and N CARR  at crossing points between a collinear line L C  and vertically lines R, S and C respectively. The collinear line L C  varies its position and inclination (in other words, speed ratios between the three rotational elements) depending on torque applied on the three rotational elements of the planetary gear set  501 . 
   When the engine  2  is running as shown in  FIG. 2(A) , it applies torque TQ CARR  on the planetary carrier  513 , and the torque TQ CARR  is divided ring gear torque TQ RING  and sun gear torque TQ SUN  which are applied on the ring gear  512  and the sun gear  511  respectively and reaction torques of which are illustrated in  FIG. 2(A) . The ring gear torque TQ RING  reaches eventually at the driving wheels  9 . The sun gear torque drives the first electric machine  3 , which, under control of the HEV controller  14  through the first inverter  12 , generates electric power P MG1  in accordance with the speed N SUN  and the torque TQ SUN . The electric power P MG1  which the first electric machine  3  generates is supplied to the second electric machine  4  and/or to the battery  11  for its charging through the first and second inverters  12  and  13  under the control of the HEV controller  14 . 
   In a case where all the electric power P MG1  is supplied to the second electric machine  4 , all the power the engine  2  generates can be considered supplied to the driving wheels  9  if the power transmission loss is ignored. Then, the speed ratio between the engine  2  and the driving wheels  9  can be continuously varied depending on the torque relationship between the three rotational elements of the planetary gear set  501 . For example as shown in  FIG. 2(A) , the sun gear speed N SUN  is increased by decreasing the sun gear torque TQ SUN  while the other torque is constant and causing a torque imbalance until the equilibrium of torque is obtained as shown by a one-dotted line for the collinear line L C , and the carrier speed N CARR  is increased accordingly. Therefore, in that case, the power transmission mechanism  5  varies a speed ratio continuously, in other words, functions as a continuously variable transmission. 
   On the other hand, when, as shown by a solid line L C  of  FIG. 2(B) , the engine  2  is stopped and the second electric machine  4  solely drives the driving wheels  9  with the electric power from the battery  11 , the ring gear  512  rotates at a speed N RING  which corresponds to the vehicle speed VSP and the speed N MG2  of the second electric machine  4 . But, the engine  2  does not rotate at all due to resistive force that moving parts of the engine generate, and the carrier speed N CARR  is zero. While the ring gear  512  rotates and the carrier  513  does not, the sun gear  511  rotates in the opposite direction if no torque is applied, in other words, the torque TQ SUN  is zero. 
   From the condition of the solid line L C  of  FIG. 2(B) , by generating electricity from the first electric machine  3  and then supplying electricity to the first electric machine  3  after the rotation of the sun gear  511  changes its direction, the engine  2  is started to rotate as shown by a one-dotted line of the collinear line L C . When the vehicle is stopped, in other words the ring gear speed N RING  is zero, the engine can be rotated simply by supplying electric power to the first electric machine  3 . 
   The internal combustion engine  2  is a four cylinder four stroke engine in the present embodiment. Therefore, it has four cylinders  22  (#1 through #4 cylinders in  FIG. 1 ), although it may have any number of cylinders. Referring to  FIG. 3  for greater detail, the engine  2  comprises a cylinder block  23 , and a cylinder head  24 , which is arranged on the cylinder block  23 . The cylinder block  23  and cylinder head  24  integrally form the cylinders  22 . The cylinder  22  accommodates a piston  25  which slides therein. As is well known in the art, the cylinder block  22  rotationally supports a crankshaft  21  using journals, bearings and the like. Further, a connecting rod  26  links the crankshaft  21  and the piston  25 . The cylinder head  24 , the cylinder  22 , and the piston  25  collectively form a combustion chamber  27  inside. 
   Although only one is illustrated in  FIG. 1 , two intake ports  28  are formed in the cylinder head  24 , and respectively open to the combustion chamber  27 . Likewise, two exhaust ports  29  are formed in the cylinder head  23 , and respectively open to the combustion chamber  27 . Intake valves  41  and exhaust valves  42  are respectively capable of shutting the intake ports  28  and the exhaust ports  29  from the combustion chamber  27  as shown in  FIG. 2 . A valve drive mechanism  101  causes each of the intake valves  41  to make reciprocating movement at desired timing. Likewise, a valve drive mechanism  102  causes each of the exhaust valves  42  to make a reciprocating movement at desired timing. The valve drive mechanism  101  will be described later in greater detail. 
   A spark plug  43  is mounted to the cylinder head  24  in the well known manner such as threading. An ignition circuit or system  44  receives a control signal SA from the engine controller  15 , and provides electric current to the spark plug  43  so that it makes a spark at desired ignition timing. 
   A fuel injector  45  is mounted to the cylinder head  24  at one side of a cylinder center axis in a known manner such as using a mounting bracket. A tip end of the injector  45  faces the inside of the combustion chamber  27  from a space vertically below and horizontally between the two intake ports  28 . A fuel supply system  46  includes a high pressure pump and an injector driver circuit not shown, and supplies fuel from a fuel tank not shown as is well known in the art. Also, the fuel supply system  46 , particularly an injector driver circuit therein, activates a solenoid of the injector  45  to open the spray nozzles in accordance with a control signal corresponding to a fuel injection pulse FP from the engine controller  15 , in order to inject desired amount of fuel at desired timing. 
   The intake ports  28  connect in fluid communication to a surge tank  47   a  through intake passages  47   b  of an intake manifold  47 . Air flows from an air cleaner not shown to the surge tank  47   a  through a throttle body  48 , in which a throttle valve  49  is arranged. The throttle valve  49  pivots and regulates airflow to the surge tank  47   a , as is well known in the art. A throttle actuator  49   a  adjusts an opening of the throttle valve  49  in accordance with a control signal TVO from the engine controller  15 . 
   The exhaust ports  29  connect to an exhaust manifold  50 , and eventually are in fluid communication with an exhaust pipe in a manner known in the art. Downstream of the exhaust manifold  50  in an exhaust gas passage, an exhaust gas purification system having one or more of catalyst converters  51  is arranged. The catalyst converter  51  may comprise a conventional three way catalyst, a lean NOx trap, an oxidation catalyst or any other type of catalyst that conforms to exhaust gas purification needs of the specific fuel control strategy. 
   For exhaust gas recirculation, an EGR pipe  52  connects the intake manifold  47 , downstream of the throttle valve  49 , and the exhaust manifold  50  in fluid communication. Pressure at the exhaust side is higher than at the intake side, so that exhaust gas flows into the intake manifold  47  and mixes with the fresh air inducted from the intake manifold  47  into the combustion chamber  27 . An EGR valve  53  is arranged in the EGR pipe  52  and regulates the EGR flow. An EGR valve actuator  53   a  adjusts an opening of the EGR valve  53  in accordance with a control signal EGR OPENING  from the engine controller  15 . 
   Referring to  FIG. 4 , the valve drive mechanism  101  for the intake valves  11  will now be described in greater detail. Referring to  FIG. 3 , there is shown the valve drive mechanism  101  for the intake valves  41 . The valve drive mechanism  102  for the exhaust valves  12  has a same construction as for the intake in the present embodiment. Therefore the specific description for the mechanism  102  will be omitted. Alternatively, the valve drive mechanism  102  for the exhaust valves may be of a conventional overhead camshaft (OHC) type. The OHC type valve drive mechanism comprises a cam for pushing a valve stem, a camshaft integrally forming the cam, and a camshaft drive-train such as chain and sprocket for transmitting rotational movement of the crankshaft  6  to the camshaft, as is well known in the art. 
   The valve drive mechanism  101  has a variable cam timing (VCT) mechanism  103 , which is linked to the crankshaft  21  through a chain drive mechanism including a driven sprocket  104 , a drive sprocket at the crankshaft  21 , and a chain not shown and engagingly wounded around the drive and driven sprockets. The VCT mechanism  103  comprises a casing, which is affixed to the sprocket  104  to rotate with it, and a rotor, which is affixed to an inner shaft  105  and rotates with it. Between the casing and the rotor of the VCT mechanism  103 , there are formed a plurality of hydraulic chambers, which are circumferentially arranged around the rotational axis X. Fluid pressurized by a pump, such as engine oil, is selectively supplied to each of the hydraulic chambers to make a pressure difference between the opposing chambers. A VCT control system  201  including an electromagnetic valve  106  adjusts the hydraulic fluid supplied to the chambers. The electromagnetic valve  106  cyclically switches hydraulic acting directions to the chambers in a duty ratio in accordance with a control signal θ VCT  from the engine controller  100  and an actual phase difference between the sprocket  104  and the inner shaft  105 , thereby achieving a desired rotational phase of the inner shaft  105 , as is known in the art. 
   Still referring to  FIG. 4 , the inner shaft  105  has an eccentric disc-shaped cam  106  for each of the cylinders  22 . The eccentric cam  106  is formed integrally but not coaxially with the inner shaft  105  and rotates at a phase defined by the VCT mechanism  103 . Freely rotationally fitted around the eccentric disc  106  is an inner surface of a ring arm  107 . Therefore, the ring arm  107  can self rotate about a center axis Y of the eccentric cam  106  (only shown in  FIG. 6 ) and orbit around the rotational axis X, as the inner shaft  105  rotates about the rotational axis X. 
   Arranged around the inner shaft  105  is a rocker connector  110  for each of the cylinders  22 . The rocker connector  110  pivots coaxially with the inner shaft  105 , in other words, about the axis X, and integrally forms first and second rocker cams  111  and  112 . The rocker connector  110  forms a bearing journal at its outer circumferential surface, so that a bearing cap not shown arranged on the cylinder head  24  can rotationally support the rocker cam parts  110  through  112 . As shown in  FIG. 5 , each of the rocker cams  111  and  112  has a cam surface  111   a  and a basic circular surface  111   b , either of which contacts to an upper surface of a tappet  115 , as a conventional valve drive cam does, except that the rocker cams do not continuously rotate, but rocks. The tappet  115  is supported by a valve spring  116 , which is sustained between retainers  117  and  118 , as is known in the art. 
   Referring back to  FIG. 4 , arranged above and in parallel with the assembly of inner shaft  105  and the rocker cam parts  110  through  112  is a control shaft  120 , which is rotationally supported by bearings not shown. The control shaft  120  integrally forms a worm gear  121  coaxially at its outer peripherally. The worm gear  121  engages with a worm  122 , which is affixed to an output shaft of an electric motor  123 . Therefore, the motor  123  may rotate the control shaft  120  to its desired position, in accordance with a control signal θ VVL  from the engine controller  15 , and hereinafter is referred to as a VVL actuator. 
   Four control arms  131  for the respective cylinders  22  are attached to the control shaft  120 , so that the control arms  131  can pivot integrally with the control shaft  120 . A control link  132  couples each of the control arms  131  and the respective ring arm  107  through a control pivot  133  and a common pivot  134 . Then, a rocker link  135  couples the ring arm  107  and the first cam  111  through the common pivot  134  and a rocking pivot  136 . 
     FIG. 5  and  FIG. 7(A)  show a condition where a valve lift is greater. The control arm  131  is adjusted to define a VVL control angle θ VVL     —     A  between the horizontal plane shown by a dotted line in  FIG. 6(A)  and a line connecting the center axes of the control shaft  120  and the control pivot  133 . 
   When the inner shaft  105  rotates about the axis X clockwise on the sheet of Figures from a no-lift state ( 1 ) to a maximum-lift state ( 2 ) in  FIG. 5  or from a state shown by broken lines to a state shown by solid lines in  FIG. 7(A) , the common center Y of the eccentric cam  106  and the ring arm  107  orbits clockwise from points Y 1A  to Y 2A  about the axis X as shown in  FIG. 7(A) . The orbital movement of the ring arm  107  causes a rocking movement of the control link  132  by an angle θ 132A  about the control pivot  132  due to a first four-link relationship consisting of four pivots X, Y,  133  and  134  and the corresponding links. Therefore, the common pivot  134  rocks about the control pivot  133 . The common pivot  134  is at its rotational end positions when the axis X, the common center Y and the common pivot  134  are in line. One of the end positions of the common pivot  134  is shown by the solid lines in  FIG. 7(A) . 
   Four pivots  133 ,  134 ,  136  and X and corresponding links consist a second four-link relationship. It converts the rocking movement of the common pivot  134  by the angle θ 132A  to a rocking movement of the rocker cam  111  or  112  by an angle θ 111A  about the axis X. When the common center Y is located at Y A1 , the cam  111  is at one of its angular end positions because the common pivot is at its rotational end as described above and as shown in  FIG. 7(A) . 
   When the cam surface  111   a  of the rocker cam  111  or  112  contacts the tappet top surface  115   a  as in the state ( 2 ) of  FIG. 5  and as shown by the solid line in  FIG. 7(A) , the rocker cam  111  or  112  moves down the tappet  115  against the valve spring  116 . Then, the tappet  115  causes the intake valve  41  to move down to its maximum valve lift under the angle θ VVL     —     A  of the control arm  131  in  FIG. 7(A) . 
   On the other hand, when the basic circular surface  111   b  contacts the tappet top surface  115   a  as shown in the state ( 1 ) of  FIG. 5  and by the broken line in  FIG. 7(A) , the tappet  115  is not pushed down, because the basic circular surface  111   b  has a constant radius smaller than a distance between a point of the cam surface  111   a  and the axis X. Therefore, the angle θ VVL     —     A  or the angular position of the control arm  131  causes a valve lift h A  as shown in  FIG. 7(A) . 
     FIGS. 6 and 7(B)  show a condition of smaller valve lift h B . The control arm  131  is adjusted to define an angle θ 131B  between the horizontal plane shown by the dotted line and the line connecting the center axes of the control shaft  120  and the control pivot  133  as shown in  FIG. 7(B) . In this Figure, as the inner shaft  105  rotates clockwise, the common center Y orbits from points Y 1B  to Y 2B . For the illustrative purpose, the point Y 1B  is the same point as Y 1A  in  FIG. 7(A) . The position Y 2B  is one of angular end positions where the axis X, the common center Y and the common pivot  133  are in line. 
   The first four-link relationship consisting of the pivots X, Y,  133  and  134  and the others causes an angular movement of the control link  132  by an angle θ 132B . Then, the second four-link relationship consisting of the pivots  133 ,  134 ,  136  and X converts the angular movement of the control link  132  or the common pivot  134  into a rocking movement of the rocking cam  111  or  112  with an angle θ 111B . When the common center Y is located at Y B1 , the cam  111  is at one of its angular end positions because the common pivot Y is at its rotational end as described above and as shown in  FIG. 7(B) . 
   When the basic circular surface  111   b  contacts tappet top surface  115   a  as shown in the state ( 1 ) of  FIG. 6  and by the broken line in  FIG. 7(B) , the tappet  115  is not pushed down as in the case of  FIG. 7(A) . When the cam  111  is positioned as shown by the solid line in  FIG. 7(B) , the cam surface  111   a  contacts the tappet top surface  115   a  and pushes down the tappet  115  most under the angular position θ 131B  of the control arm  131 . As can be seen from  FIG. 7 , a valve lift h B  is much smaller than the valve lift h A . Therefore, as the angle θ VVL  is smaller, the peak valve lift h decreases. If the angle θ VVL  is further increased, the valve lift can be zero depending on the configuration of a variable valve lift (VVL) mechanism. 
   Further, as the angle θ VVL  is smaller, the rocking angle θ 111  decreases, and the angular position Y 2  of the common center Y, with which the maximum valve lift is obtained, shifts counterclockwise. These can be seen from valve lift curves in  FIG. 8 . A valve lift curve L A  illustrates the greater valve lift state with the angle θ VVL     —     A  shown in  FIGS. 5 and 7(A) , and a valve lift curve L B  illustrates the smaller valve lift state with the angle θ VVL     —     B  shown in  FIGS. 6 and 7(B) , for a case where only the VVL actuator  123  is operated with the VCT mechanism  103  setting the inner shaft  105  at a fixed angular phase with respect to the crankshaft  21 . 
   As can be seen from  FIG. 8 , the variable valve lift (VVL) mechanism has characteristics where valve opening duration increases, peak valve lift timing is retarded and valve closing timing is retarded as the maximum valve lift increases. Further it can be seen that the valve opening timing does not change so much as the valve closing timing does. 
   This valve lift profile is preferable for regulating air charge inducted into the combustion chamber  27 . When the throttle valve  49  is closed to regulate the air charge, it causes restriction of intake air flow to the combustion chamber  27 , and the kinetic energy of the engine moving parts, such as the piston  25  and the crankshaft  21 , are spent for pumping in the restricted air in an intake stroke of an engine cylinder cycle. This is called “pumping loss”. Rather, the valve lift characteristic shown in  FIG. 8  can regulate air charge with less throttling and less pumping loss. 
   Basically, the air charge will be decreased as the intake valve closing timing is advanced or retarded from certain timing. The certain timing is at the bottom dead center of the piston if the engine speed is extremely low because there is no inertia of the intake airflow. Practically, it retards as the inertia of the intake airflow increases. The inertia more heavily weights on the intake airflow rate or engine speed. Further, greater valve lift is required for greater airflow. Otherwise, flow restriction may occur at the intake port throat  28  and the intake valve  41  when the air flow increases in dependence on the increased airflow rate or air charge. The VVL mechanism described above has the characteristic where the valve closing timing is retarded as the valve lift is greater as shown in  FIG. 8  and described above. Therefore, it can meet to the requirement for regulating air charge into the combustion chamber  27  with less throttling. 
   Referring to  FIG. 9 , there is shown a change of the valve lift profile of the intake valve  41  in accordance with the VCT control signal θ VCT  and the VVL control signal θ VVL  the engine controller  15  sends respectively to the VCT control system  210  and the VVL actuator  123 . As the VCT control signal θ VCT  is greater, the crankshaft angle of the maximum valve lift is retarded. And as the VVL control signal θ VVL  is greater, the maximum valve lift is reduced and the valve closing timing is retarded. 
   The engine controller  15  is a microcomputer based controller having a central processing unit which runs programs using data, memories, such as RAM and ROM, storing the programs and data, and input/output (I/O) bus inputting and outputting electric signals, as is well known in the art. In the present embodiment, as shown in  FIG. 1 , the engine controller  15  is a separate unit from the HEV controller  14 . But, the two controllers may be integrated into a single unit. As shown in  FIG. 3 , the engine controller  15  receives various inputs including an airflow AF from a mass airflow meter  61 , an intake manifold pressure MAP from an intake air pressure sensor  62 , a crank angle pulse signal from a crank angle sensor  63 , based on which an engine speed N ENG  is computed, a cylinder identification signal SIG from a SIG sensor  64  which detects one pulse signal per rotation of the inner shaft  105  of the valve driving mechanism  101 , an oxygen concentration EGO in the exhaust gas from an exhaust gas oxygen sensor  65 , and other sensors as is known in the art. In addition to the conventional inputs, the engine controller  15  receives an operational engine torque signal TQ ENG     —     O  from the HEV controller  14 . On the other hand, the engine controller  15  outputs the computed engine speed N ENG  to the HEV controller  14 . 
   The crank angle sensor  63  has two sensor elements which are angularly spaced around the flywheel of the engine  2  and outputs two pulse signals with a fixed angular phase difference. The angular phase difference for the forward rotation of the crankshaft  21  is not same as that for the reverse rotation because of the angularly spaced arrangement of the two sensor elements. The reverse rotation of the crankshaft  21  may happen just before the angular movement of the crankshaft  21  completely stops. Based on the two pulse signals from the crank angle sensor  63 , the engine controller  15  identifies of the rotational direction of the crankshaft  21  and considers it when counting the pulses. Therefore, by considering the rotational direction of the crankshaft  21  as well as the pulse signal from the crank angle sensor  63  and the SIG signal from the SIG sensor  64 , the engine controller  15  can recognize the absolute angular position of the crankshaft  21  with regard to an engine cycle which consists of 720° CA (degree crank angle) until its angular movement completely stops. Then, the recognized absolute angular position of the crankshaft  21  is stored in the memory of the engine controller  15  for the future engine restarting. 
   The engine controller  15  computes operating parameters for the actuators, for example, including the throttle actuator  49   a , the fuel injectors  45 , the ignition system  44 , and the valve drive mechanism  101 , in accordance with the inputs described above. Then, the controller  15  outputs control signals, for example, including the desired throttle position signal TVO, the fuel injection pulse FP, and the VCT and VVL control signals θ VCT  and θ VVL . 
   Control in HEV Controller 
   The HEV controller  14  controls the overall HEV power-train  1 . It directly controls the first and second inverters  12  and  13 , and indirectly controls the engine  2  through the engine controller  15 . Control routines RH 1  through RH 5  which the HEV power-train controller  14  executes will now be described with reference to  FIGS. 10 through 14 . First, there is shown, in  FIG. 10 , a mode selection routine RH 1 . 
   After a start, the routine RH 1  proceeds to a step S 101 , and the HEV controller  14  reads data in its memory including the accelerator pedal position a from the accelerator position sensor  32 , the engine speed N ENG  derived from the engine controller  15 , the battery voltage V B  from the battery voltage sensor  34 , and signals indicating auxiliary loads such as a desired operation of a compressor for a vehicle air conditioner. Then, the routine RH 1  proceeds to a step S 102 , and the HEV controller  14  determines desired power P HEV     —     D  at the driving wheels  9 . The determination of P HEV     —     D  is based on the vehicle speed VSP detected by the vehicle speed sensor  31  and the accelerator position a and generally in proportion to a product of those two parameters at least in a part of the range. 
   After the step S 102 , the routine RH 1  proceeds to a step S 103  and determines desired auxiliary power P AUX     —     D , which is desired to charge the battery  11  or drive the other auxiliary load such as air conditioner compressor. Therefore, the determination of P AUX     —     D  is based on the battery voltage V B  and the other data relating to the auxiliary load read at the step S 101 . After the step S 103 , the routine RH 1  proceeds to a step S 104 , and the HEV controller  14  determines desired engine power P ENG     —     D , which is generally the sum of P HEV     —     D  and P AUX     —     D  because the engine  2  is the single source of power within the HEV power-train  1 . The determination of P ENG     —     D  may take into account the vehicle speed VSP in addition to those two parameters because the efficiency of the power transmission mechanism  5  varies depending on its speed. 
   After the step S 104 , the routine RH 1  proceeds to a step S 105  and determines whether an engine running flag F ENG     —     RUN  is high (=1) or not. If it is determined at the step S 105  the engine running flag F ENG     —     RUN  is high, which means that the engine is currently in operation and the HEV power-train  1  is in an engine running mode, the routine proceeds to a step S 106  and determines whether the desired engine power P ENG     —     D  determined at the step S 104  is greater than a first reference engine power P ENG     —     1  or not. If it is determined at the step S 106  that the desired engine power P ENG     —     D  is greater than the first reference engine power P ENG     —     1 , which means the engine  2  is still required to run in the engine running mode, the routine RH 1  returns. 
   On the other hand, if it is determined at the step S 106  that the desired engine power P ENG     —     D  is not greater than the first reference engine power P ENG     —     1 , which means the engine  2  is not required to run any more and the HEV power-train  1  is to be in an engine stopping mode, the routine RH 1  proceeds to a step S 107  and resets the engine running flag F ENG     —     RUN  to be low (=0). Then, the routine further proceeds to a step S 108  and sets a first engine stopping flag F ENG     —     STOP     —     1  is high (=1), and it returns. 
   When, at the step S 105  of the routine RH 1  in  FIG. 10 , it is determined that the engine running flag F ENG     —     RUN  is low (=0), which means that the engine is currently not in operation and the HEV power-train  1  is in an electric mode, the routine RH 1  proceeds to a step S 109  and determines whether the desired engine power P ENG     —     D  determined at the step S 104  is greater than a second reference engine power P ENG     —     2  that is greater than the first reference engine power P ENG     —     1 . If it is determined at the step S 109  that the desired engine power P ENG     —     D  is not greater the second reference engine power P ENG     —     2 , it means that the engine  2  is still not required to run and the HEV power-train  1  is to stay in the electric mode, and the routine RH 1  returns. On the other hand, if it is determined at the step S 109  that the desired engine power P ENG     —     D  is greater the second reference engine power P ENG     —     2 , which means that the engine  2  is now required to start running and the HEV power-train  1  is in an engine starting mode, then the routine RH 1  proceeds and sets the engine running flag F ENG     —     RUN  to be high (=1) at a step S 110  and a first engine starting flag F ENG     —     START     —     1  to be high (=1) and returns. 
   Referring to  FIG. 11 , there is shown a routine RH 2  for the engine running mode which the HEV controller  14  executes. After the start, the routine proceeds to a step S 201  and reads data in its memory such as the flags set and reset in the routine RH 1  described above in addition to those from the sensors as read at the step S 101  of the routine RH 1 . Then, the routine RH 2  proceeds to a step S 202  and determines whether the engine running flag F ENG     —     RUN  is high (=1) or not. If it is determined at the step S 202  that the engine running flag F ENG     —     RUN  is low (=0), it means that the engine  2  is not required to run and the HEV power-train  1  is not in the engine running mode, and the routine RH 2  returns. Otherwise, it proceeds to a step S 203  and determines whether the first engine starting flag F ENG     —     START     —     1  is high (=1) or not. 
   If it is determined at the step S 203  that the first engine starting flag F ENG     —     START     —     1  is high (=1), it means that the engine  2  is in the middle of the engine starting mode which will be described later with reference to  FIGS. 14 and 16  and the HEV power-train is transitioning from the electric mode to the engine running mode, and the routine RH 2  returns. Otherwise, it proceeds to a step S 204  and determines operational engine torque TQ ENG     —     O  and an operational engine speed N ENG     —     O  based on the desired engine power P ENG     —     D  determined at the step S 104  with reference to a table which contains combinations of torque and speed with the best efficiencies for the respective desired engine powers P ENG     —     D . Then, the routine proceeds to a step S 205  and determines an operational speed N MG1     —     O  of the first electric machine  3  based on the vehicle speed VSP and the engine speed N ENG  in consideration of the collinear diagram as shown in  FIG. 2 . After the step S 205 , the routine proceeds to a step S 206  and determines desired torque TQ MG2     —     D  of the second electric machine  4  primarily based on the vehicle speed VSP, the desired power P HEV     —     D  at the wheels  9 , the desired auxiliary power P AUX     —     D , the operational engine torque TQ ENG     —     O  and the current engine speed N ENG . Then, the routine RH 2  proceeds to a step S 207  and determines desired torque TQ MG1     —     D  of the first electric machine  3  primarily based on the operational engine torque TQ ENG     —     O  and the desired torque TQ MG2     —     D  of the second electric machine  4  in consideration of the collinear diagram as shown in  FIG. 2 . 
   Following the determination of the torque and speeds of the engine  2  and the first and electric machines  3  and  4  at the steps S 204  through S 207 , the routine RH 2  determines operational power P MG1     —     O  and P MG2     —     O  of the first and second electric machines  3  and  4  respectively at steps S 208  and S 209 . Then, the routine proceeds to a step S 210 , and the HEV controller  14  outputs signals to the engine controller  15  and the first and second inverters  12  and  13 . For example, the HEV controller sends a signal corresponding to the operational engine torque TQ ENG     —     O  determined at the step S 204  to the engine controller  15 , which then controls actuators including the fuel system  46 , the throttle actuator  49   a , the VCT control system  210  and the VVL actuator  123  so that the engine  2  generates the operational engine torque TQ ENG     —     O . The fuel injection pulse FP output from the engine controller  15  to the fuel system  46  is generally in proportion with the operational engine torque, and the throttle control signal TVO, the VCT control signal θ VCT  and the VVL control signal θ VVL  are determined from two dimensional maps of the engine speed N ENG  and the operational engine torque TQ ENG     —     O  so that proper amount of air is inducted into the engine  1  and an air-fuel ratio in the combustion chamber  27  is a desired value such as the stoichiometric air fuel ratio. 
   Also at the step S 210 , the HEV controller  14  sends signals corresponding to the operational power P MG1     —     O  and P MG2     —     O  of the first and second electric machines  3  and  4  determined at the steps S 208  and S 209  to the first and second inverters  12  and  13  respectively to operate the first and second electric machines  3  and  4  accordingly. After the step S 210 , the routine RH 2  returns. 
   Referring to  FIG. 12 , there is shown a routine RH 3  for the electric mode which the HEV controller  14  executes. After the start, the routine proceeds to a step S 301  and reads data in its memory such as the flags set and reset at the steps S 107 , S 108 , S 110  and S 111  of the routine RH 1  described above in addition to those from the sensors as read at the step S 101 . Then, the routine RH 3  proceeds to a step S 302  and determines whether the engine running flag F ENG     —     RUN  is high (=1) or not. If it is determined at the step S 302  that the engine running flag F ENG     —     RUN  is high (=1), it means that the engine  2  is required to run and the HEV power-train  1  is not in the electric mode, and the routine RH 3  returns. Otherwise, it proceeds to a step S 303  and determines whether the engine stop flag F ENG     —     STOP     —     1  is high (=1) or not. 
   If it is determined at the step S 303  that the first engine starting flag F ENG     —     STOP     —     1  is high (=1), it means that the engine  2  is in the middle of the engine stopping mode which will be described later with reference to  FIGS. 13 and 15  and the HEV power-train is transitioning from the electric mode to the engine running mode, and the routine RH 3  returns. Otherwise, the routine RH 3  proceeds to a step S 304  and sets the operational engine torque TQ ENG     —     O  to be zero since the engine  2  is not required to run in the electric mode. Also, the routine RH 3  sets the operational power P MG1     —     O  of the first electric machine  3  to be zero at a step S 305  because it is required to generate neither of positive nor negative torque in the electric mode as described with reference to  FIG. 2(B) . 
   After the step S 305 , the routine RH 3  proceeds to a step S 306  and determines the operational power P MG2     —     O  of the second electric machine  4  based on the desired power P HEV     —     D  at the driving wheels  9  and the vehicle speed VSP. Then, the routine RH 3  proceeds to a step S 307  and outputs the signals to the engine controller  15  and the first and second inverters  12  and  13  as is done at the step S 210  of the routine RH 2 . 
   Referring to  FIG. 13 , there is shown a routine RH 4  for the engine stopping mode which the HEV controller  14  executes. After the start, the routine proceeds to a step S 401  and reads data in its memory such as the flags set and reset at the steps S 107 , S 108 , S 110  and S 111  of the routine RH 1  described above in addition to those from the sensors as read at the step S 101  of the routine RH 1 . Then, the routine RH 4  proceeds to a step S 402  and determines whether the engine running flag F ENG     —     RUN  is high (=1) or not. If it is determined at the step S 402  that the engine running flag F ENG     —     RUN  is high (=1), it means that the engine  2  is required to run and the HEV power-train  1  is not in the engine stopping mode, and the routine RH 4  returns. Otherwise, it proceeds to a step S 403  and determines whether the first engine stopping flag F ENG     —     STOP     —     1  is high (=1) or not. 
   If it is determined at the step S 403  that the first engine stopping flag F ENG     —     STOP     —     1  is low (=0), it means that the HEV power-train is in the electric mode, and the routine RH 4  returns. Otherwise, it proceeds to a step S 404  and sets the operational engine torque TQ ENG     —     O  to be zero since the engine  2  is not required to run any more. 
   After the step S 404 , the routine RH 4  proceeds to a step S 405  and determines whether or not a second engine stopping flag F ENG     —     STOP     —     2  is high (=1) or not. The flag F ENG     —     STOP     —     2  is set by a routine RE 6  executed by the engine controller  15  until it determines that the engine  2  has rotated enough to reduce air charged therein. If it is determined at the step S 405  that the second engine stopping flag F ENG     —     STOP     —     2  is high (=1), the routine RH 4  proceeds to a step S 406  and sets the operational engine speed N ENG     —     O  to be a pre-stop speed N ENG     —     STOP  which is predetermined to be 1000 rpm for example. Then, the routine proceeds to a step S 407  and determines the operational power P MG1     —     O  of the first electric machine  3  primarily based on the operational engine speed N ENG     —     O , the current engine speed N ENG  and the vehicle speed VSP so that the engine speed N ENG  to be feedback controlled to the pre-stop engine speed N ENG     —     STOP . 
   On the other hand, if it is determined at the step S 405  that the second engine stopping flag F ENG     —     STOP     —     2  is low (=0), it means that the engine controller  15  has determined the engine  2  has rotated enough to reduce air charged therein, and the routine RH 4  sets the operational engine speed N ENG     —     O  to be zero at a step  408  and then sets the operational power P MG1     —     O  of the first electric machine  3  to be zero at a step S 409 . Next, the routine proceeds to a step S 410  and reset the first engine stopping flag F ENG     —     STOP     —     1  (=0). 
   Following the step S 407  or S 410 , the routine RH 4  proceeds to a step S 411  and determines the operational power P MG2     —     O  of the second electric machine  4  primarily based on the desired power P HEV     —     D  at the driving wheels  9  and the vehicle speed VSP and additionally on the operational power P MG1     —     O  of the first electric machine  3  and the current engine speed N ENG . In the determination of P MG2     —     O , the operational power of the second electric machine  4  is determined greater as P MG1     —     O  of the first electric machine  3  is greater in consideration of the torque balance shown in  FIG. 2 . Then, the routine RH 4  proceeds to a step S 412  and outputs the signals to the engine controller  15  and the first and second inverters  12  and  13 , and it returns. 
   Referring to  FIG. 14 , there is shown a routine RH 5  for the engine starting mode which the HEV controller  14  executes. After the start, the routine proceeds to a step S 501  and reads data in its memory such as the flags set and reset at the steps S 107 , S 108 , S 110  and S 111  of the routine RH 1  described above in addition to those from the sensors as read at the step S 101  of the routine RH 1 . Then, the routine RH 5  proceeds to a step S 502  and determines whether the engine running flag F ENG     —     RUN  is high (=1) or not. If it is determined at the step S 502  that the engine running flag F ENG     —     RUN  is low (=0), it means that the engine  2  is not required to run and the HEV power-train  1  is not in the engine start mode, and the routine RH 5  returns. Otherwise, it proceeds to a step S 503  and determines whether the first engine starting flag F ENG     —     START     —     1  is high (=1) or not. 
   If it is determined at the step S 503  that the first engine starting flag F ENG     —     STOP     —     1  is low (=0), it means that the HEV power-train is in the engine running mode, and the routine RH 4  returns. Otherwise, it proceeds to a step S 504  and determines whether a second engine starting flag F ENG     —     START     —     2  is high (=1) or not. The flag F ENG     —     START     —     2  is set by a routine RE 7  executed by the engine controller  15  until it considers the engine  2  has exceeded a predetermined speed N ENG     —     START . 
   If it is determined at the step S 504  that the second engine starting flag F ENG     —     START     —     2  is high (=1), the routine RH 5  proceeds to a step S 505  and determines the operational power P MG1     —     O  of the first electric machine  3  based on the vehicle speed VSP and an angular position of the crankshaft  21  of the engine  2  which is computed in the engine controller  15  based on the crank angle position from the crank angle sensor  63  and the SIG signal from the SIG sensor  64 . 
   On the other hand, if the second engine starting flag F ENG     —     START     —     2  is low (=0), which means the engine  2  has competes the starting phase, the routine proceeds to a step S 506  and resets the first engine starting flag F ENG     —     START     —     1  to be low (=0) so that the HEV power-train will be in the engine running mode beginning in the next path of each of the routines RH 1  through RH 6 . 
   After the step S 505  or S 506 , the routine RH 5  proceeds to a step S 507  and determines the operational power P MG2     —     O  of the second electric machine  4  primarily based on the desired power P HEV     —     D  at the driving wheels  9  and the vehicle speed VSP and additionally on the operational power P MG1     —     O  of the first electric machine  3  and the current engine speed N ENG . In the determination of P MG2     —     O , the operational power of the second electric machine  4  is determined greater as P MG1     —     O  of the first electric machine  3  is greater in consideration of the torque balance shown in  FIG. 2 . Then, the routine RH 4  proceeds to a step  508  and outputs the signals to the engine controller  15  and the first and second inverters  12  and  13 , and it returns. 
   Control in Engine Controller 
   The engine controller  15  controls the actuators of the engine  2 , such as the ignition system  44 , the fuel system  46  including the fuel injector  45 , the throttle actuator  49 , the VCT control system  210  and the VVL actuator  123 . In the engine running mode which is taken when it is determined in the mode selection routine RH 1  of  FIG. 10  that the engine running flag F ENG     —     RUN  is high but neither of the first engine stop flag F ENG     —     STOP  and the first engine starting flag F ENG     —     START  is high, the engine controller  15  computes, under a normal engine control strategy, control signals for those actuators mainly based on the operational engine torque TQ ENG     —     O  which is computed at the step S 204  of the routine RH 2  and the current engine speed N ENG  which is computed based on the crank angle pulse signal detected by the crank angle sensor  63 . The fuel injection pulse FP output from the engine controller  15  to the fuel system  46  is generally in proportion with the operational engine torque TQ ENG     —     O , and the throttle control signal TVO, the VCT control signal θ VCT  and the VVL control signal θ VVL  are determined from two dimensional maps of the engine speed N ENG  and the operational engine torque TQ ENG     —     O  so that proper amount of air is inducted into the engine  1  and an air-fuel ratio in the combustion chamber  27  is a desired value such as the stoichiometric air fuel ratio. 
   In the electric mode which is taken when it is determined in the mode selection routine RH 1  of  FIG. 10  that the engine running flag F ENG     —     RUN  is low and neither of the first engine stop flag F ENG     —     STOP  and the first engine starting flag F ENG     —     START  is high, the operational engine torque is set to be zero. Then, the engine controller  15  determines the fuel injection pulse FP to be zero, and no fuel is injected from the fuel injector  45 . But, the VCT control signal θ VCT  and the VVL control signal θ VVL  are held, and the valve lift profile set in the engine stopping mode is maintained. 
   Referring to  FIG. 15 , there is shown a engine stopping mode routine RE 6  which the engine controller  15  executes during the engine stopping mode in which the HEV controller  14  executes the routine RH 4  shown in  FIG. 13 . After the start, the routine RE 6  proceeds to a step S 601 , and the engine controller  15  reads data in its memory such as the flags set and reset in the routine RH 1  described above with reference to  FIG. 9 , executed by and input from the HEV controller  14  in addition to the signals from the various sensors. 
   Then, the routine RE 6  proceeds to a step S 602  and determines whether the first engine stopping flag F ENG     —     STOP     —     1 , which the HEV controller  14  may set in the mode selection routine RH 1 , is high (=1) or not. If it is determined at the step S 602  that the first engine stop flag F ENG     —     STOP     —     1  is low (=0), it means that the engine  2  is not in the engine stopping mode, and the routine RE 6  returns. Otherwise, the routine proceeds to a step S 603  and determines whether the second engine stop flag F ENG     —     STOP     —     2  is high (=1) or not. In the first path of the engine stopping mode, the flag F ENG     —     STOP     —     2  is low (=0). 
   When the first path of the engine stopping mode takes place, the routine RE 6  proceeds to a step S 604  and sets the second engine stop flag F ENG     —     STOP     —     2  to be high (=1), which causes the routine RH 4  to determine the operational engine speed N ENG     —     O  to be the pre-stop engine speed N ENG     —     STOP  at its step S 406  instead of zero at the step S 408 . Then, the routine RE 6  proceeds to a step S 605  and determines an initial counter value C 1     —     INI  of a first counter C 1  based on the current VCT control signal θ VCT  for the VCT control system  210  and the current VVL control signal θ VVL  for the VVL actuator  123 . The value C 1     —     INI  is determined in consideration of responses of the VCT control system  210  and the VVL actuator  123  so that the value C 1     —     INI  is greater as the signals θ VCT  and θ VVL  indicate that the closing timing of the intake valve  41  is more retarded and the intake valve lift is greater. Then, the routine RE 6  proceeds to a step S 606  and initialize the first counter C 1  with the initial value C 1     —     INI  determined at the step S 605 . 
   After the step S 606 , the routine RE 6  proceeds to a step S 607  and sets the fuel injection pulse FP to be zero to shut off fuel injected from the fuel injector  45 . Then, the routine proceeds to steps S 608  and S 609  and sets the VCT and VVL control signals θ VCT  and θ VVL  to be predetermined values θ VCT     —     ST     —     1  and θ VVL     —     ST     —     1  for engine stopping and starting. The values θ VCT     —     ST     —     1  and θ VVL     —     ST     —     1  are predetermined so that the closing timing of the intake valve  41  is greatly advanced from a bottom dead center of an intake stroke, for example by 100° CA (crank angle) and a maximum valve lift is greatly reduced, for example, to be 20% of the greatest valve lift. 
   After the step S 609 , the routine RE 6  proceeds to a step S 610 , and the engine controller  15  outputs the control signals which are set during the process of the routine RE 6  to the actuators and the HEV controller  14 . For example, the fuel injection pulse FP set at the step S 607  is output to the fuel system  46 , the VCT control signal θ VCT  is output to the VCT control system  210 , and the VVL control signal θ VVL  is output to the VVL actuator  123 . 
   When it is determined at the step S 603  that the second engine stop flag F ENG     —     STOP     —     2  is high (=1), it means that the engine  2  is already in the engine stopping mode, and the routine RE 6  proceeds to a step S 611  and determines whether a third engine stop flag F ENG     —     STOP     —     3  is high (=1) or not. If it is high, the routine proceeds to a step S 612  and decrements the counter C 1  for example by one. Then, the routine proceeds to a step S 613  and determines whether the counter C 1  reaches zero or not. If no, the routine proceeds to the step S 610 , and the engine controller  15  outputs the control signals to the actuators. 
   If it is determined at the step S 613  that the counter C 1  counts down and reaches zero, it means that the actual positions of the VCT actuator  103  and the VVL actuator  123  are supposed to correspond to the values θ VCT     —     ST     —     1  and θ VVL     —     ST     —     1  set at the steps S 608  and S 609 . In other words, the valve lift profile for the engine stopping is supposedly obtained because the response of the actuators are taken account of based on the valve lift profile at the first path of the routine RE 6 . 
   Then, the routine RE 6  proceeds to the step S 614  and sets the third engine stop flag F ENG     —     STOP     —     3  to be high (=1). Then, it proceeds to a step S 615  and initializes a first crank angle counter C CRK     —     1  to be zero. The first crank angle counter C CRK     —     1  counts up by the angle of rotation of the crankshaft  21  detected by the crank angle sensor  63  during one path of this routine. After the step S 606 , the routine proceeds to the step S 610  described above. 
   When it is determined at the step S 611  that the third engine stop flag F ENG     —     STOP     —     3  is high (=1), it means that the first counter C 1  has counted the initial value C 1     —     INI  determined at the step S 605 . Then, the routine RE 6  proceeds to a step S 616  and increments the first crank angle counter C CRK     —     1  by an angle of rotation of the crankshaft  21  during the last path of the routine. After the step S 616 , the routine RE 6  proceeds to a step S 617  and determines whether the first crank angle counter C CRK     —     1  exceeds a predetermined value, for example 720° CA, in other words, two rotations of the crankshaft  21  or one engine cycle. 
   If it is determined at the step S 617  that the first crank angle counter C CRK     —     1  does not exceed the predetermined value, the routine RE 6  proceeds to the step S 610  described above. On the other hand, if it is determined the first crank angle counter C CRK     —     1  exceeds the predetermined value, it means that the engine  2  has rotated by the predetermined amount since it is determined at the step S 613  that the actual positions of the VCT actuator  103  and the VVL actuator  123  are supposed to correspond to the values θ VCT     —     ST     —     1  and θ VVL     —     ST     —     1 . Then, the routine proceeds to a step S 618  and resets the third engine stop flag F ENG     —     STOP     —     3  to be low (=0). Further, it resets at a step S 619  the second engine stop flag F ENG     —     STOP     —     2  to be low (=0), which causes the routine RH 4  to sets the operational engine speed N ENG     —     O  to be zero at the step S 408  of the routine RH 4  the HEV controller  14  executes. 
   Referring to  FIG. 16 , there is shown an engine stop routine RE 7  which the engine controller  15  executes during the engine starting mode in which the HEV controller  14  executes the routine RH 5  shown in  FIG. 14 . After the start, the routine RE 7  proceeds to a step S 701 , and the engine controller  15  reads data in its memory such as the flags set and reset in the routine RH 1  described above with reference to  FIG. 9 , executed by and input from the HEV controller  14  in addition to the signals from the various sensors. 
   Then, the routine RE 7  proceeds to a step S 702  and determines whether the first engine starting flag F ENG     —     START     —     1  is high (=1) or not. If it is determined at the step S 702  that the first engine starting flag F ENG     —     START     —     1  is low (=0), it means that the engine  2  is not in the engine starting mode, and the routine RE 7  returns. Otherwise, the routine proceeds to a step S 703  and determines whether the second engine stop flag F ENG     —     START     —     2  is high (=1) or not. In the first path of the engine starting mode, the flag F ENG     —     START     —     2  is low (=0). 
   When the first path of the engine starting mode takes place, the routine RE 7  proceeds to a step S 704  and sets the second engine starting flag F ENG     —     START     —     2 . Then, it proceeds to a step S 705  and identifies cylinders, specifically determines which of the #1 through #4 cylinders  22  is in an intake stroke from data which is computed from the crank angle signal CA from the crank angle sensor  63  and the SIG signal from the SIG sensor  64  and stored in the memory of the engine controller  15  when the engine  1  previously stopped completely. Then, the routine RE 7  proceeds to a step S 706  and identifies the current angular position of the crankshaft  21  also stored in the memory. 
   After the step S 706 , the routine RE 7  proceeds to a step S 707  and determines whether change ΔP ENG     —     D  of the desired engine power P ENG     —     D  exceeds a predetermined change Δ 1  or not. The desired engine power P ENG     —     D  is determined at the step S 104  of the routine RH 1  the HEV controller  14  executes, and the change ΔP ENG     —     D  is computed by differentiating the desired engine power P ENG     —     D . 
   When it is determined at the step S 707  that the desired engine power change ΔP ENG     —     D  is not greater than the predetermined change Δ 1  (NO), which means that the engine  2  is not required to so rapidly ramp up its output, the routine RE 7  proceeds to steps S 708  and  709  and sets the VCT control signal θ VCT  and the VVL control signal θ VVL  to be first predetermined values θ VCT     —     ST     —     1  and θ VVL     —     ST     —     1 , which are the same as set at the step S 608  of the routine RE 6  during the engine stopping mode. During the electric mode, the valve lift profile set in the engine stopping mode is maintained as described above, and in this case, it is not changed at all for the engine starting mode. 
   Then, the routine proceeds to a step S 710  and sets the fuel injection pulse FP to be a first start fuel injection pulse FP START     —     1 . After the step S 710 , the routine RE 7  proceeds to a step S 711 , and the engine controller  15  outputs the control signals which are set during the process of the routine RE 7  to the actuators and the HEV controller  14 . For example, the VCT control signal θ VCT  is output to the VCT control system  210 , the VVL control signal θ VVL  is output to the VVL actuator  123 , and the fuel injection pulse FP set at the step S 710  is output to the fuel system  46 . After the step S 711 , the routine RE 7  returns. 
   When it is determined at the step S 707  that the desired engine power change ΔP ENG     —     D  is greater than the predetermined change Δ 1  (YES), which means that the engine  2  is required to rapidly ramp up its output, the routine RE 2  proceeds to steps S 712  and  713  and sets the VCT control signal θ VCT  and the VVL control signal θ VVL  to be second predetermined values θ VCT     —     ST     —     2  and θ VVL     —     ST     —     2 , which are predetermined so that the closing timing of the intake valve  41  is advanced from a bottom dead center of an intake stroke, but retarded from the closing timing caused by the first values θ VCT     —     ST     —     1  and θ VVL     —     ST     —     1 , and a lift of the intake valve  41  is greater than that of the first values. Then, the routine proceeds to a step S 714  and sets the fuel injection pulse FP to be a second start fuel injection pulse FP START     —     2 , which is greater than the first pulse FP START     —     1  set at the step S 710 . Then, the routine RE 7  proceeds to a step S 715 , and the engine controller  15  sets a control signal for the fuel supply system  46  to inject fuel into one of the cylinders  22  which is in an intake stroke as identified at the step S 705 . After the step S 715 , the routine RE 7  proceeds to the step S 711 , and the engine controller  15  outputs the control signals including that set at the step S 715  as described above. Therefore, if the desired engine power change ΔP ENG     —     D  is greater than the predetermined change Δ 1 , the engine  2  inducts more air into the combustion chambers  27  and gets more fuel. After the step S 715 , the routine proceeds to the step S 716 , and the engine controller  15  outputs signals as described above. 
   When it is determined at the step S 703  that the second engine starting flag F ENG     —     START     —     2  is high (=1), it means that the engine  2  is already in the engine starting mode, and the routine RE 7  proceeds to a step S 716  and determines whether the current engine speed N ENG  is greater than a predetermined reference speed N ENG     —     START , which is set, for example, 1000 rpm. If it is determined at the step S 716  that the current engine speed N ENG  is not greater than the predetermined reference speed N ENG     —     START  (NO), it means that the engine  2  is not completely started up yet, and the routine RE 7  proceeds to a step S 717  and determines whether the crankshaft  21  of the engine  2  has passed a first dead center, which is at every 180° CA in the case of the four cylinder four stroke engine in this embodiment, based on the initial angular position of the crankshaft  21  that is identified at the step  705  and the current angular position of the crankshaft  21  detected from the crank angle sensor  63 . If NO, it means that the engine has barely rotated, and the routine directly proceeds to the step S 711  described above. 
   When it is determined at the step S 717  that the crankshaft has passed the first dead center (YES), which means a first intake stroke has started, the routine RE 7  proceeds to a step S 718  and determines whether fuel start flag F FUEL     —     ST  is high (=1) or not. If NO at the step S 717 , the routine sets the flag F FUEL     —     ST  to be high at a step S 719  and proceeds to a step S 720 . Otherwise, the routine RE 7  directly proceeds to the step S 720 , where the engine controller  15  sets a control signal for the fuel system  46  to inject fuel to a cylinder which is in the first intake stroke and after a top dead center by a predetermined crank angle (e.g. 100° ATDC). Then, the routine proceeds to a step S 721 , and the engine controller  15  sets a control signal for the ignition system  44  to make a spark in a cylinder which is in a compression stroke and before a top dead center by a predetermined crank angle (e.g. 20° BTDC). Then, the routine proceeds to the step S 711  described above, and output signals including the control signals set at the steps S 720  and S 721 . 
   When it is determined at the step S 716  that the current engine speed N ENG  is greater than the predetermined reference speed N ENG     —     START  (NO), it means that the engine  2  is completely started up, and the routine RE 7  proceeds to a step S 722  and resets the second engine starting flag F ENG     —     START     —     2  to be low (=0) so that the first engine starting flag F ENG     —     START     —     1  is reset at the step S 506  of the routine RH 5  the HEV controller  14  executes. The reset flag F ENG     —     START     —     1  causes at the step S 702  the routine RH 7  not to run. Finally, the routine RE 7  proceeds to a step S 723  and resets the fuel starting flag F FUEL     —     ST  to be low (=0), and then it returns. After the engine  2  is completely started under the engine starting mode routine RE 7 , the engine controller  15  controls the actuators of the engine  2  under the normal engine control strategy executed in the engine running mode of the HEV power-train  1 . 
   The operation of the HEV power-train  1  will be described below. As described above, the operation is controlled by the HEV power-train controller  14  executing the control routines RH 1  through RH 5  and by the engine controller  15  executing the control routines RE 6  and RE 7 . 
   Operation in Engine Stopping Mode 
   Referring to  FIGS. 17 and 19 , there are shown changes of the various parameters processed during the engine stopping mode and described above with reference to  FIGS. 10 ,  13  and  15 . At time t 1 , the desired engine power P ENG     —     D  is determined not greater than the first reference engine power P ENG     —     1  at the step S 106  of the routine RH 1  executed by the HEV controller  14  and shown in  FIG. 10 , and the engine running flag F ENG     —     RUN  is reset a the step S 107  and the first engine stop flag F ENG     —     STOP     —     1  is set high at the step S 108 . At the same time, the second engine stop flag F ENG     —     STOP     —     2  is set high at the step S 604  of the routine RE 6  executed by the engine controller  15  and shown in  FIG. 15 . As a result, the HEV power-train  1  has entered the engine stopping mode from the engine running mode at the time t 1 . 
   During the engine running mode before the time t 1 , the first electric machine  3  generates electricity to brake the engine  2  and achieve the operational engine speed N ENG     —     O  determined at the step S 204  of the routine RH 2  executed by the HEV power-train controller  14  and shown in  FIG. 11 . Therefore, the operational power P MG1     —     O  of the first electric machine  3  is at the negative side before the time t 1  as shown in  FIGS. 17 and 19 . 
   After the time t 1 , the operational engine torque TQ ENG     —     O  is set to be zero at the step S 404  of the routine RH 4  executed by the HEV power-train controller  14  and shown in  FIG. 13 , and the engine speed tends to be reduced, but the operational engine speed N ENG     —     O  is set to be the pre-stop engine speed N ENG     —     STOP  at the step S 406 . Therefore, the operational power P MG1     —     O  of the first electric machine  3  will be at the positive side as can be seen from the collinear diagram of  FIG. 2(B) . The operational power P MG1     —     O  of the first electric machine  3  is adjusted to feedback control the engine speed N ENG  to be the pre-stop engine speed N ENG     —     STOP  at the step S 407  so that engine speed N ENG  converges within a range from the N ENG     —     STOP  as shown in  FIG. 17 . Through the time t 1 , the operational power P MG1     —     O  of the first electric machine  3  varies from the negative to positive side, and the operational power P MG2     —     O  of the second electric machine  4  varies corresponding to the change of the first electric machine as determined at the step S 410  of the routine RH 4  so that the P MG2     —     O  increases as the P MG1     —     O  increases in the positive side. 
   At the time t 1 , the fuel pulse FP is set to be zero at the step S 606  of the routine RE 6  shown in  FIG. 15 , and, as shown in  FIG. 17 , fuel injection is shut off starting with a next cylinder to be fueled after the time t 1 , in this case, the cylinder #4. Although fuel is shut off, but spark ignition is continued as long as the engine rotates. 
   Also at the time t 1 , the VCT and VVL control signals θ VCT  and θ VVL  are set to be the predetermined values θ VCT     —     ST     —     1  and θ VVL     —     ST     —     1  for engine stopping and starting which correspond to advanced closing timing and reduced maximum lift of the intake valves  41  at the steps S 608  and S 609  of the routine RE 6  shown in  FIG. 15 . This valve lift profile reduces air charged in the combustion chamber  27  to, for example, 15% of the displacement of the cylinder  22  (cylinder charging efficiency is 15%). Before the time t 1 , the HEV power-train  1  is in the engine running mode, and the cylinder charging efficiency is greatly reduced by advancing the closing timing and reducing the maximum valve lift through the time t 1  as can be seen from  FIG. 19 . 
   At the same time, the counter C 1  is initialized to be the initial value C 1     —     INI  which corresponds to the actual state of the intake valves  41  at the time t 1  and is determined at the step S 605 , and started to be counted down. Then, at time t 3  of  FIG. 17 , the counter C 1  reaches zero and the actual state of the intake valves  41  is supposed to reach the advanced closing timing and the reduced lift corresponding to the predetermined values θ VCT     —     ST     —     1  and θ VVL     —     ST     —     1 . 
   At the time t 3 , the first crank angle counter C CRK     —     1  is started at the step S 615  of the routine RE 6  shown in  FIG. 15 . It counts the predetermined crank angle, for example 720° CA, at time t 4  in  FIGS. 17 and 19 . In other words, at the time t 4 , the engine  2  is supposed to have rotated one engine cycle since the state of the intake valves reached the advanced closing timing and the reduced lift at the time t 3 . That is, all the four cylinders  22  have had respective intake strokes take place since the time t 3 . Therefore, at the time t 4 , air charged in the four cylinders  22  is significantly reduced. 
   At the time t 4 , the first through third engine stop flags F ENG     —     STOP     —     1  through F ENG     —     STOP     —     3  are all reset at the step S 410  of the routine RH 4  and the steps S 618  and S 619  of the routine RE 6 , and the engine stopping mode is exited to the electric mode. Then, the operational power P MG1     —     O  of the first electric machine  3  are set to be zero at the step S 409  of the routine RH 4  executed by the HEV controller  14  and shown in  FIG. 13 , the engine  2  is not driven any more, and the engine speed N ENG  is falling as shown in  FIGS. 17 and 19 . 
   During the engine speed falling, as can be seen from the bottom graph of  FIG. 17 , fluctuation of the engine speed corresponding to the dead centers is reduced due to the significantly reduced air charge in the cylinders  22  and accompanying reduced compression pressure. The reduced fluctuation of the engine speed can greatly suppress a vibration of the HEV power-train  1 , especially, because the engine  2  is permanently coupled to the driving wheels through the power transmission mechanism  5 . 
   From the time t 4 , the engine  2  or the crankshaft  21  will still rotate by about two cycles or 1440° CA in the forward rotation while decreasing the speed. Then, the crankshaft  21  will repeat forward and reverse angular movement for a while. Even during the reverse angular movement, the engine controller  15  can recognize the angular position of the crankshaft based on the signal from crank angle sensor  63  as is known in the art. Therefore, the engine controller  15  can recognize the exact angular position of the crankshaft  21  at the time of the complete stop of the engine  2  and stores the position in its memory for usage at the time of engine restarting, particularly at the step S 717  of the routine RE 7  shown in  FIG. 16 . 
   Operation in Engine Starting Mode 
   Referring to  FIGS. 18 and 19 , there are shown changes of the various parameters processed during the engine starting mode described above with reference to  FIGS. 10 ,  14  and  16 . At time t 1 , the desired engine power P ENG     —     D  is determined greater than the first reference engine power P ENG     —     2  at the step S 109  of the routine RH 1  executed by the HEV controller  14  and shown in  FIG. 10 , and the engine running flag F ENG     —     RUN  is set a the step S 110  and the first engine stop flag F ENG     —     START     —     1  is set high at the step S 108 . At the same time, the second engine stop flag F ENG     —     START     —     2  is set high at the step S 704  of the routine RE 7  executed by the engine controller  15  and shown in  FIG. 16 . As a result, the HEV power-train  1  has enter the engine starting mode from the electric mode at the time t 11 . 
   At the time t 11 , the operational power P MG1     —     O  is supplied to the first electric machine  3  through the first inverter  12  as determined at the step S 505  of the routine RH 5  executed by the HEV controller  14  and shown in  FIG. 14 . The operational power P MG1     —     O  is set in consideration of the vehicle speed VSP and the speed ratio of the power transmission mechanism  5  so as to rotate the engine  2  at a target engine speed, for example 300 rpm. At the same time, as determined at the step S 507  of the routine RH 5 , the operational power P MG2     —     O  is increased corresponding to the increase of P MG1     —     O , and it balances the torques TQ SUN  and TQ RING  between the sun gear and the ring gear of the planetary gear set  501  as can be seen in  FIG. 2 . 
   Also at the time t 11 , the engine controller  15  identifies the absolute angular position of the crankshaft  21  with regard to an engine cycle at the step S 706  of the routine RE 7  executed by the engine controller  15  and shown in  FIG. 16 . After the time t 11 , the ignition system  44  makes a spark at every spark timing no matter whether fuel is supplied or not as shown in  FIG. 18  where the cylinder #3 gets a spark at first. 
   If the engine  2  is required to rapidly ramp up its output as determined at the step S 707  of the routine RE 7  shown in  FIG. 16 , the fuel injector  45  injects fuel to a cylinder which is in an intake stroke at the time t 11 , for example, the cylinder #4 in  FIG. 18 . During the electric mode before the time t 11 , the intake valve  41  of the cylinder #4 is closed, but a pressure therein becomes equal to the atmospheric pressure over time due to a gap between the piston ring and the cylinder wall as known in the art. Therefore, air charged in the cylinder #4 will depend on its piston position, for example it is 45% of the cylinder displacement, in other words, charging efficiency is 45%, in the case of  FIG. 18 . 
   Otherwise, the first fuel injection is made for a cylinder which is in an exhaust stroke at the time t 11 , for example, the cylinder #2 in  FIG. 18 . The engine controller  15  identifies a first dead center at time t 12  as determined at the step S 717  of the routine RE 7  and set the fuel starting flag F FUEL     —     ST  to be high at the step S 719 . After the time t 12 , the engine controller  15  controls the fuel injector  45  and the fuel system  46  to inject fuel in an intake stroke as processed at the step S 720 . Therefore, the fuel is injected into a cylinder which is in an intake stroke, in this case the cylinder #2. The intake valve  41  of the cylinder #2 closes in accordance with the control signals θ VCT  and the VVL control signal θ VVL  as determined at the steps S 709  and S 710  so that the reduced lift and the advanced closing timing take place and charging efficiency of the cylinder #2 is much less than that of the cylinder #4, for example 15%. The supplied fuel is ignited by the spark made at the step S 721  and combusted. The combustion in the cylinder #2 generates less energy due to the reduced charging efficiency. But, torque derived from the combustion energy in the cylinder #2 causes the engine speed N ENG  to increase. As shown in  FIG. 18 , the HEV controller  14  reduces the operational power P MG1     —     O  of the first electric machine after the combustion as determined based on the crank angle at the step S 505  of the routine RH 5  shown in  FIG. 14  to prevent the excessive engine speed increase. Corresponding to the decrease of the operational power P MG1     —     O  of the first electric machine, the second electric machine&#39;s operational power P MG2     —     O  is decreased accordingly as determined at the step S 506  of the routine RH 5 . 
   Following the cylinder #2, the cylinder #1 goes through the same process, and then the cylinders #3 and #4 do thereby continuing until the engine speed N ENG  exceeds the predetermined reference speed N ENG     —     START  at time t 13  (only shown in  FIG. 19 ) as determined at the step S 716  of the routine RE 7  executed by the engine controller  15  and shown in  FIG. 16 . The operational powers P MG1     —     O  and the corresponding P MG2     —     O  are reduced in a prescribed manner, for example, in the stepped manner until the prescribed crank angle has passed as shown in  FIG. 18 . 
   At the time t 13 , the first and second engine starting flags F ENG     —     START     —     1  and F ENG     —     START     —     2  are reset at the step S 506  of the routine RH 5  and the step S 722  of the routine RE 7 , and the engine starting mode is exited to the engine running mode. After the time t 13  in the engine running mode, the engine controller  15  controls the actuators of the engine  1  in accordance with the operational engine torque TQ ENG     —     O  which is determined at the step S 204  of the routine RH 2  executed by the HEV controller  14  and shown in  FIG. 11 . The operational engine torque TQ ENG     —     O  is achieved basically by adjusting the fuel injection pulse FP. For exhaust gas emission control and other reasons, the air inducted into the engine  2  needs to be regulated corresponding to the fuel injection pulse FP usually so as to make stoichiometric air fuel mixture. The inducted air can be regulated by adjusting the control signals θ VCT  and θ VVL  for the VCT actuator  103  and the VVL actuator  123  so as to vary the maximum valve lift and the closing timing of the intake valves  41  as shown in  FIG. 9 . Therefore, the maximum valve lift of the intake valves  41  is increased and the closing timing of the intake valves  41  is advanced before a bottom dead center as the operational engine torque TQ ENG     —     O  is increased, as shown in  FIG. 19 . 
   Before the time t 13 , the control signals θ VCT  and θ VVL  for the VCT actuator  103  and the VVL actuator  123  are set to be the values θ VCT     —     ST     —     1  and θ VVL     —     ST     —     1  or θ VCT     —     ST     —     2  and θ VVL     —     ST     —     2  for starting the engine  2 , which correspond to the reduced maximum lift and the advanced closing timing of the intake valves  41  compared to the control signals during the engine running mode. In other words, after the time t 13 , the maximum valve lift is greater and the closing timing is retarded compared to before the time t 13  as can be seen in  FIG. 19 . The change of the maximum valve lift and the closing timing also conform to the increase of the engine speed N ENG  so that a moderate transition of the intake valve setting and engine speed increase it derives can be achieved from the transition from the engine starting mode to the engine running mode. 
   It is needless to say that the invention is not limited to the illustrated embodiment and that various improvements. Therefore, alternative designs are possible without departing from the substance of the invention as claimed in the attached claims, as described below. 
   Although the engine  2  is part of the HEV power-train  1  which couples the engine  2 , the first electric machine  3 , the second electric machine  4  and the driving wheels  9  through the power transmission mechanism  5  including the planetary gear set  501  in the above embodiment, the engine  2  may be coupled with a rotational machine through any power transmission apparatus, for example those two are directly coupled to each other through, for example, gears, a chain and sprockets, a belt and pulleys, and the like. 
   Although the first and second electric machines  3  and  4  are powered with electricity, they may be replaced with any rotational machines such as hydraulic machines and the like. 
   Although the fuel injector  41  of the engine  2  is arranged to inject fuel directly to the combustion chamber  27  (direct injection), it may be arranged to inject fuel in the intake port  28  (port injection). In that case, the fuel injection during the engine starting mode needs to be completed well before the closing of the intake valve  41 . 
   The intake valve drive mechanism  101  is not limited to the type described above, but it may be of any type as long as the valve lift profile including the maximum valve lift and the closing timing can be arranged, and it may be, for example, electromagnetic valve actuators which drive the valve(s) of the respective cylinders individually by using electromagnetic force through solenoids.