Patent Publication Number: US-6216655-B1

Title: Valve operating control system for internal combustion engine

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a valve operating control system for an internal combustion engine, including a cam change-type valve operating characteristic changing mechanism, and a control unit for controlling the valve operating characteristic changing mechanism in a feedback manner and in a feed-forward manner. 
     2. Description of the Prior Art 
     Internal combustion engines, which include a cam phase changing-type valve operating characteristic changing mechanism constructed to continuously control the timing of the opening and closing of an intake valve or an exhaust valve, are known from Japanese Patent Application Laid-open No. 59-93964 and Japanese Patent Publication No. 5-43847. 
     In carrying out the control for converging a deviation between an actual cam phase and a target cam phase to zero in such valve operating characteristic changing mechanism, if the feedback control is carried out when the deviation is large, a responsiveness can be ensured, but there is a possibility that the actual cam phase overshoots the target cam phase, whereby the convergence cannot be ensured. In such a case, it is conceived that while the deviation is large, a feed-forward control is carried out to ensure the convergence, and after the deviation becomes small, feedback control is carried out, thereby enabling the responsiveness and the convergence to be reconciled. 
     When the feedback control and the feed-forward control are used in combination with each other, the effect can be exhibited in a particular operational state of the internal combustion engine, however, there is a possibility that a sufficient effect cannot be obtained depending on the operational state of the internal combustion engine over a wide range of an operational condition, e.g., the level of the engine temperature. 
     SUMMARY OF THE INVENTION 
     The present invention has been accomplished with the above circumstance in view, and it is an object of the present invention to ensure that when the valve operating characteristic changing control for converging the deviation between the actual cam phase and the target cam phase of the internal combustion engine to zero, is carried out, the responsiveness and the convergence can be reconciled independent of the operational state of the internal combustion engine. 
     To achieve the above object, there is provided a valve operating system for an internal combustion engine, comprising a cam phase changing-type valve operating characteristic changing mechanism capable of continuously changing a cam phase in the internal combustion engine. A control means controls the valve operating characteristic changing mechanism in a feedback manner and in a feed-forward manner, based on the deviation between a target cam phase set in accordance with the operational state of the internal combustion engine and an actual detected cam phase to converge the deviation to zero. The control means controls the valve operating characteristic changing mechanism in the feedback manner, when the deviation is equal to or smaller than a feed-forward determining threshold value, and controls the valve operating characteristic changing mechanism in the feed-forward manner with a basic operational amount, when the deviation exceeds the feed-forward determining threshold value. The control means is arranged so that as the engine temperature is higher, or as the deviation is larger, the basic operational amount is increased more. 
     With the above arrangement, by controlling the valve operating characteristic changing mechanism in the feed-forward manner with the basic operational amount, when the deviation between the target cam phase and the actual cam phase exceeds the feed-forward determining threshold value, it is possible to prevent a reduction in convergence due to the occurrence of overshooting feared when the feedback control is carried out. In addition, by controlling the valve operating characteristic changing mechanism in the feedback manner, when the deviation becomes equal to or smaller than the feed-forward determining threshold value to eliminate the occurrence of the overshooting, the actual cam phase can be converged into the target cam phase with a high responsiveness and a high convergence. Moreover, in carrying out the feed-forward control, as the engine temperature becomes higher, or as the deviation becomes larger, the basic operational amount is increased more. Therefore, it is possible to further enhance the convergence in the feed-forward control. 
     The feed-forward determining threshold value in the present invention corresponds to a second feed-forward control determining value #DCAINFFR in the disclosed embodiment; the basic operational amount in the present invention corresponds to a highest limit value #DVLMTH2 in the disclosed embodiment, and the engine temperature in the present invention corresponds to a cooling-water temperature TW in the disclosed embodiment. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The mode for carrying out the present invention will now be described by way of an embodiment shown in the accompanying drawings. 
     FIGS. 1 to  14  show an embodiment of the present invention. 
     FIG. 1 is a perspective view of an internal combustion engine having a valve operating system of the present invention. 
     FIG. 2 is an enlarged view taken in the direction of arrow  2  in FIG.  1 . 
     FIG. 3 is a sectional view taken along line  3 — 3  in FIG.  2 . 
     FIG. 4 is a sectional view taken along line  4 — 4  in FIG.  2 . 
     FIG. 5 is a sectional view taken along line  5 — 5  in FIG.  3 . 
     FIG. 6 is a sectional view taken along line  6 — 6  in FIG.  2 . 
     FIG. 7 is a hydraulic pressure circuit diagram of a valve operating characteristic changing mechanism. 
     FIG. 8 is a vertical sectional view of a second hydraulic pressure control valve. 
     FIG. 9 is a first portion of a flow chart of a target cam phase calculating routine of the present invention. 
     FIG. 10 is a second portion of the flow chart of the target cam phase calculating routine. 
     FIG. 11 is a first portion of a feedback control routine for a second valve operating characteristic changing mechanism of the present invention. 
     FIG. 12 is a second portion of the feedback control routine for the second valve operating characteristic changing mechanism. 
     FIG. 13 is a diagram showing a map for searching a water-temperature correcting factor KTWCI based upon a cooling water temperature TW. 
     FIG. 14 is a diagram showing a map for searching an upper-limit value #DVLMTH2 based upon the cooling water temperature TW or a deviation DCAINCMD. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     As shown in FIG. 1, a 4-cylinder DOHC type internal combustion engine E includes a crankshaft  3  to which four pistons  1  are connected through connecting rods  2 . A driving sprocket  4 . mounted at an end of the crankshaft  3  and follower sprockets  7  and  8  mounted at ends of an intake cam shaft  5  and an exhaust cam shaft  6 , respectively, are connected to each other through a timing chain  9 , so that the intake cam shaft  5  and the exhaust cam shaft  6  are driven in rotation at a ratio of one rotation per two rotations of the crankshaft  3 . 
     Two intake valves  10 ,  10  driven by the intake cam  5  and two exhaust valves  11 ,  11  driven by the exhaust cam shaft  6  are provided for each of four cylinders. First valve operating characteristic changing mechanisms V 1 , V 1  for changing the valve lifts and the opening angles of the intake valves  10 ,  10  and the exhaust valves  11 ,  11  at two stages, are provided between the intake cam shaft  5  and the intake valves  10 ,  10  and between the exhaust cam shaft  6  and the exhaust valves  11 ,  11 , respectively. A second valve operating characteristic changing mechanism V 2  is provided at the end of the intake cam shaft  5  for continuously advancing and retarding the opening and closing timing for the intake valves  10 ,  10 . 
     The first valve operating characteristic changing mechanism Vfor the intake valves  10 ,  10  and the second valve operating characteristic changing mechanism V 1  for the exhaust valves  11 ,  11  are of substantially the same structure and hence, only the structure of the first valve operating characteristic changing mechanism V 1  for the intake valves  10 ,  10  will be described with reference to FIGS. 2 to  5 . 
     The intake cam shaft  5  is provided with a pair of low-speed cams  14 ,  14  and a high-speed cam  15  sandwiched between both of the low-speed cams  14 ,  14  in correspondence to each of the cylinders. A first rocker arm  17 , a second rocker arm  18  and a third rocker arm  19  are swingably carried on a rocker shaft  16  fixed in parallel to and below the intake cam  5  in correspondence to the low-speed cam  14 , the high-speed cam  15  and the low-speed cam  14 , respectively. 
     Each of the pair of low-speed cams  14 ,  14  is comprised of a cam lobe  14   1  protruding a relatively small amount in the radial direction of the intake cam shaft  5 , and a base-circle portion  14   2 . The high-speed cam  15  is comprised of a cam lobe  15   1  protruding an amount larger than that of the cam lobes  14   1 ,  14   1  of the low-speed cams  14 ,  14  and in a wider range of angle, and a base-circle portion  15   2 . 
     Collars  21 ,  21  are provided at upper ends of valve stems  20 ,  20  of the intake valves  10 ,  10 , respectively, and the intake valves  10 ,  10  are biased in a closing direction by valve springs  23 ,  23  mounted in compressed states between a cylinder head  22  and the collars  21 ,  21 , respectively. The first and third rocker arms  17  and  19  swingably carried at one end thereof on the rocker shaft  16 , have cam slippers  17   1  and  19   1  formed at their intermediate portions which abut against the pair of low-speed cams  14 ,  14 , respectively. Tappet screws  24 ,  24  are mounted at the other ends of the first and third rocker arms  17  and  19  for advancing and retracting movements to abut against the upper ends of the valve stems  20 ,  20  of the intake valves  10 ,  10 , respectively. 
     The second rocker arm  18  disposed between the pair of intake valves  10 ,  10  and swingably carried at one end thereof on the rocker shaft  16 , is biased by a resilient biasing means  25  which is mounted in a compressed state between the second rocker arm  18  and the cylinder head  22 , and a cam slipper  18   1  formed at the other end of the second rocker arm  18  abuts against the high-speed cam  15 . The resilient biasing means  25  is comprised of a bottomed cylindrical lifter  26  abutting at its closed end against the second rocker arm  18 , and a lifter spring  27  for biasing the lifter  26  toward the second rocker arm  18 . 
     As can be seen from FIG. 5, a connection switching mechanism  31  for switching the connected states of the first, second and third rocker arms  17 ,  18  and  19  includes a first switching pin  32  capable of connecting the third rocker arm  19  and the second rocker arm  18  to each other, a second switching pin  33  capable of connecting the second rocker arm  18  and the first rocker arm  17  to each other, a third switching pin  34  for limiting the movements of the first switching pin  32  and the second switching pin  33 , and a return spring  35  for biasing the switching pins  32 ,  33  and  34  in disconnecting directions. 
     A bottomed guide bore  19   2  parallel to the rocker shaft  16 , is defined in the third rocker arm  19  with its opened end turned toward the second rocker arm  18 . The first switching pin  32  is slidably fitted in the guide bore  19   2 , and a hydraulic pressure chamber  36  is defined between the first switching pin  32  and a closed end of the guide bore  19   2 . A communication passage  37  is defined in the third rocker arm  19  to communicate with the hydraulic pressure chamber  36 , and a hydraulic pressure supply passage  38  is defined in the rocker shaft  16 . The communication passage  37  and the hydraulic pressure supply passage  38  are normally in communication with each other through a communication passage  39  defined in a sidewall of the rocker shaft  16 , regardless of the swinging state of the third rocker arm  19 . 
     A guide bore  18   2  corresponding to the guide bore  19   2  and having the same diameter as the guide bore  19   2  is provided through the second rocker arm  18  in parallel to the rocker shaft  16 , and the second switching pin  33  is slidably fitted in the guide bore  18   2 . 
     A bottomed cylindrical guide bore  17   2  corresponding to the guide bore  18   2  and having the same diameter as the guide bore  18   2  is defined in the first rocker arm  17  in parallel to the rocker shaft  16  with its opened end turned toward the second rocker arm  18 , and the third switching pin  34  is slidably fitted in the guide bore  17   2 . Moreover, a shaft portion  34 , integrally formed on the third switching pin  34  is slidably guided in a guide portion  17   3  formed at a closed end of the guide bore  17   2 . The return spring  35  is mounted in the compressed state between the closed end of the guide bore  17   2  and the third switching pin  34  in such a manner that it is fitted over an outer periphery of the shaft portion  34   1  of the third switching pin  34 , so that the three switching pins  32 ,  33  and  34  are biased in disconnecting directions, i.e., toward the hydraulic pressure chamber  36  by the resilient force of the return spring  35 . 
     When hydraulic pressure supplied to the hydraulic pressure chamber  36  is released, the three switching pins  32 ,  33  and  34  are moved in the disconnecting directions by the resilient force of the return spring  35 . In this state, the abutting faces of the first switching pin  32  and the second switching pin  33  are between the third rocker arm  19  and the second rocker arm  18 , and the abutting faces of the second switching pin  33  and the third switching pin  34  are between the second rocker arm  18  and the first rocker arm  17 . Therefore, the first, second and third rocker arms  17 ,  18  and  19  are in their non-connected states. When hydraulic pressure is supplied to the hydraulic pressure chamber  36 , the three switching pins  32 ,  33  and  34  are moved in connecting directions against the resilient force of the return spring  35 , whereby the switching pin  32  is fitted into the guide bore  18   2 , and the second switching pin  33  is fitted into the guide bore  17   2 , thereby causing the first, second and third rocker arms  17 ,  18  and  19  to be connected integrally to one another. 
     The structure of the second valve operating characteristic changing mechanism V 2  provided at the end of the intake cam shaft  4  will be described below with reference to FIGS. 2 and 6. 
     A support bore  41   1  defined in the center of a substantially cylindrical boss member  41 , is coaxially fitted with the end of the intake cam shaft  5  and coupled to the end in a non-rotatable manner by a pin  42  and a bolt  43 . The follower sprocket  7 , around which the timing belt  9  is reeved, is formed into a substantially cup shape having a circular recess  7   1 , and sprocket teeth  7   2  are formed around an outer periphery of the follower sprocket  7 . An annular housing  44  fitted in the recess  7   1  of the follower sprocket  7  and a plate  45  superposed on an outer side of the housing  44  are coupled to the follower sprocket  7  by four bolts  46  passing through the housing  44  and the plate  45 . Therefore, the boss member  41  integrally coupled to the intake cam shaft  5 , is relatively rotatably accommodated in a space surrounded by the housing  44  and the plate  45 . A locking pin  47  is slidably fitted in a pin bore  41   2  provided axially through the boss member  41 . The locking pin  47  is biased in a direction to engage a locking bore  7   3  defined in the follower sprocket  7  by a spring  48  mounted in a compressed state between the locking pin  47  and the plate  45 . 
     Four fan-shaped recesses  44   1  are provided in the housing  44  at distances of 90° about the axis of the intake cam shaft  5 . Four vanes  49  protruding radiantly from the outer periphery of the boss member  41  are fitted in the recesses  44   1 , so that they can be relatively rotated in a range of a center angle of 30°. Four seal members  50  are mounted at tip ends of the four vanes  49  to abut against ceiling walls of the recesses  44   1  for sliding movement, and four seal members  51  are mounted in an inner peripheral surface of the housing  44  to abut against an outer peripheral surface of the boss member  41  for sliding movement, whereby an advancing chamber  52  and a retarding chamber  53  are defined on opposite sides of each of the vanes  49 . 
     An advancing oil passage  54  and a retarding oil passage  55  are defined in the intake cam shaft  5 . The advancing oil passages  54  communicate with the four advancing chambers  52  through four oil passages  56  provided radially through the boss member  41 , respectively. The retarding oil passages  55  communicate with the four retarding chambers  53  through four oil passages  57  provided radially through the boss member  41 , respectively. The locking bore  7   3  in the follower sprocket  7 , in which a head of the locking pin  47  is fitted, communicates with any of the advancing chambers  52  through an oil passage which is not shown. 
     Thus, when no hydraulic pressure is supplied to the advancing chambers  52 , the head of the locking pin  47  is fitted in the locking bore  7   3  in the follower sprocket  7  by the resilient force of a spring  48 , and the intake cam shaft  5  is locked in the most-retarded state (in a most-displaced basic position) in which it has been rotated in a counterclockwise direction relative to the follower sprocket  7 , as shown in FIG.  6 . When hydraulic pressure supplied to the advancing chambers  52  is increased from this state, the locking pin  47  is moved out of the locking bore  7   3  in the follower sprocket  7  against the resilient force of the spring  48  by the hydraulic pressure transmitted from any of the advancing chambers  52 , and pushed by the vanes  49  under the action of a difference in pressure between the advancing chambers  52  and the retarding chambers  53 . This causes the intake cam shaft  5  to be rotated relative to the follower sprocket  7  in a clockwise direction (in a direction opposite to a direction of rotation of the crankshaft  3  of the internal combustion engine E, as viewed in FIG.  1 ), whereby the phases of the low-speed cams  14 ,  14  and the high-speed cam  15  are advanced in unison with each other to change the timing of opening and closing of the intake valves  10 ,  10  in an advancing direction. Therefore, it is possible to continuously change the timings of opening and closing of the intake valves  10 ,  10  by controlling the hydraulic pressures in the advancing chambers  52  and the retarding chambers  53 . 
     A control system for the first and second valve operating characteristic changing mechanisms V 1  and V 2  will be described below with reference to FIG.  7 . 
     Oil pumped by an oil pump  61  from an oil pan  62  in the bottom of the crankcase through an oil passage L 1  is discharged to an oil passage L 2  as lubricating oil for parts or portions around the crankshaft of the internal combustion engine E and for the valve operating mechanism and as a working oil for the first and second valve operating characteristic changing mechanisms V 1  and V 2 . A first hydraulic pressure control valve  63  comprising an ON/OFF solenoid valve for switching the hydraulic pressure at two stages, is provided in an oil passage L 3  which is diverted from the oil passage L 2 , to communicate with the intake-side and exhaust-side first valve operating characteristic changing mechanisms V 1 , V 1 . A second hydraulic pressure control valve  64  comprising a duty solenoid valve for continuously controlling the hydraulic pressure is provided in an oil passage L 4  which is diverted from the oil passage L 2  to communicate with the second valve operating characteristic changing mechanism V 2 . 
     An electronic control unit U is provided as a control means which receives a signal from a cam shaft sensor S 1  for detecting the phase of the intake cam shaft  5 , a signal from a TDC sensor S 2  for detecting top dead centers of the pistons  1  based on the phase of the exhaust cam shaft  6 , a signal from an intake negative-pressure sensor S 4  for detecting an intake negative pressure, a signal from a cooling-water temperature sensor S 5  for detecting the temperature of cooling water, and a signal from an engine rotational-speed sensor S 7  for detecting the rotational speed of the engine. The electronic control unit U controls the operation of the first hydraulic pressure control valve  63  for the first valve operating characteristic changing mechanisms V 1 , V 1  and the operation of the second hydraulic pressure control valve  64  for the second valve operating characteristic changing mechanisms V 2 . 
     The structure of the second hydraulic pressure control valve  64  for the second valve operating characteristic changing mechanisms V 2  will be described below with reference to FIG.  8 . 
     The second hydraulic pressure control valve  64  includes a cylindrical sleeve  65 , a spool  66  slidably fitted in the sleeve  65 , a duty solenoid  67  fixed to the sleeve  65  for driving the spool  66 , and a spring  68  for biasing the spool  66  toward the duty solenoid  67 . The axial position of the spool  66  slidably fitted in the sleeve  65  can be varied continuously by duty-controlling the current in the duty solenoid  67  by a command from the electronic control unit U. 
     Defined in the sleeve  65  are a central input port  69 , a retarding port  70  and an advancing port  71  located on the opposite sides of the input port  69 , and a pair of drain ports  72  and  73  located on the opposite sides of the retarding port  70  and the advancing port  71 . The spool  66  slidably fitted in the sleeve  65 , is provided with a central groove  74 , a pair of lands  75 ,  75  located on opposite sides of the groove  74 , and a pair of grooves  77  and  78  located on opposite sides of the lands  75  and  76 . The input port  69  is connected to the oil pump  61 ; the retarding port  70  is connected to the retarding chambers  53  in the second valve operating characteristic changing mechanism V 2 , and the advancing port  71  is connected to the advancing chambers  52  in the second valve operating characteristic changing mechanism V 2 . 
     The operation of the first valve operating characteristic changing mechanism V 1  will be described below. 
     During rotation of the internal combustion engine E at a low speed, the first hydraulic pressure control valve  63  comprising an ON/OFF solenoid valve is turned off by a command from the electronic control unit U, thereby cutting off the hydraulic pressure supplied from the oil pump  61  to the connection switching mechanism  31  of the first valve operating characteristic changing mechanism V 1 . At this time, hydraulic pressure is not applied to the hydraulic pressure chamber  36  connected to the hydraulic pressure supply passage  38  within the rocker shaft  16 , and the first, second and third switching pins  32 ,  33  and  34  are moved to the disconnecting positions shown in FIG. 5 by the resilient force of the return spring  35 . As a result, the first, second and third rocker arms  17 ,  18  and  19  are disconnected from one another, and the two intake valves  10 ,  10  are opened and closed by the first and third rocker arms  17  and  19  having the cam slippers  17   1  and  19   1  abutting against the two low-speed cams  14 ,  14 . At this time, the second rocker arm  18  having the cam slipper  18   1  abutting against the high-speed cam  15  is raced independently of the operation of intake valves  10 ,  10 . 
     During rotation of the internal combustion engine E at a high speed, the first hydraulic pressure control mechanism  63  comprising the ON/OFF solenoid valve is turned on by a command from the electronic control unit U, and the hydraulic pressure is supplied from the oil pump  61  to the connection switching mechanism  31  of the first valve operating characteristic changing mechanism V 1  and transmitted from the hydraulic pressure supply passage  38  within the rocker shaft  16  to the hydraulic pressure chamber  36 . As a result, the first, second and third switching pins  32 ,  33  and  34  are moved to the connecting positions against the resilient force of the return spring  35 , and the first, second and third rocker arms  17 ,  18  and  19  are connected integrally to one another by the first and second switching pins  32  and  33 . Therefore, the swinging movement of the second rocker arm  18  having the cam slipper  18   1  abutting against the high-speed cam  15  including the cam lobe  15   1  having large ranges of height and angle is transmitted to the first and third rocker arms  17  and  19  connected integrally to the second rocker arm  18 , whereby the two intake valves  10 ,  10  are opened and closed. At this time, the cam lobes  14   1 ,  14   1  of the low-speed cams  14 ,  14  are moved away from the cam slippers  17   1  and  19   1  of the first and third rocker arms  17  and  19  and thus raced. 
     Thus, during rotation of the internal combustion engine E at the low speed, the intake valves  10 ,  10  can be driven at a low valve lift and at a small opening angle, and during rotation of the internal combustion engine E at the high speed, the intake valves  10 ,  10  can be driven at a high valve lift and at a large opening angle. The valve lift and opening angle of the exhaust valves  11 ,  11  are also controlled in the same manner as the intake valves  10 ,  10  by the corresponding first valve operating characteristic changing mechanism V 1 . 
     The operation of the second valve operating characteristic changing mechanism V 2  will be described below. 
     At the time of stopping of the internal combustion engine E, the second valve operating characteristic changing mechanism V 2  is in a state shown in FIG. 6 in which each of the retarding chambers  53  is maximum in volume and each of the advancing chambers  52  is zero in volume, and the locking pin  47  is maintained in a most retarded state in which it has been fitted into the locking bore  7   3  in the follower sprocket  7 . When the internal combustion engine E is started, the oil pump  61  is operated. When the hydraulic pressure transmitted through the second hydraulic pressure control valve  64  to the advancing chambers  52  exceeds a predetermined value (e.g., 1 kg/cm 2 ), the locking pin  47  is moved out from the locking bore  7   3  by the hydraulic pressure, thereby bringing the second valve operating characteristic changing mechanism V 2  into an operable state. 
     If the duty ratio of the duty solenoid  67  is increased, for example, to 50% or more from this state, the spool  66  is moved to a left side of a neutral position as viewed in FIG. 8 against the resilient force of the spring  68 , so that the input port  69  connected to the oil pump  61  communicates with the advancing port  71  through the groove  74 , and the retarding port  70  communicates with the drain port  72  through the groove  77 . As a result, hydraulic pressure is applied to the advancing chambers  52  in the second valve operating characteristic changing mechanism V 2  and hence, the intake cam shaft  5  is rotated in the clockwise direction relative to the follower sprocket  7 , whereby the cam phase of the intake shaft  5  is changed continuously in the advancing direction. When a target cam phase is obtained, the duty ratio of the duty solenoid  67  is set at a value (e.g., 50%) corresponding to the high-speed valve timing which will be described hereinafter. Thus, the follower sprocket  7  and the intake cam shaft  5  can be connected integrally to maintain the cam phase by stopping the spool  66  of the second hydraulic pressure control valve  64  in the neutral position shown in FIG. 8, closing the input port  69  between the pair of lands  75  and  76  and closing the retarding port  70  and the advancing port  71  by the lands  75  and  76 , respectively. 
     To continuously change the cam phase of the intake cam shaft  5  in the retarding direction, the duty ratio of the duty solenoid  67  may be decreased to 50% or less to move the spool  66  rightwards from the neutral position, thereby permitting the input port  69  connected to the oil pump  61  to communicate with the retarding port  70  through the groove  74  and permitting the advancing port  71  to communicate with the drain port  73 . When the target phase is obtained, if the duty ratio of the duty solenoid  67  is set at 50%, whereby the spool  66  is stopped in the neutral portion shown in FIG. 8, the input port  69 , the retarding port  70  and the advancing port  71  can be closed to maintain the cam phase. 
     Thus, the timing of the opening and closing of the intake valves  10 ,  10  can be advanced and retarded continuously over a range of a rotational angle of 30° of the intake cam shaft  5  (over a range of 60°, if it is converted into a rotational angle of the crankshaft  3 ). 
     When the internal combustion engine E is in an extremely low load and a high-speed rotating state, the first valve operating characteristic changing mechanism V 1  is controlled to a high-speed valve timing state, and the second valve operating characteristic changing mechanism V 2  is controlled to a most-retarded state. To set the second valve operating characteristic changing mechanism V 2  in the most-retarded state, the duty ratio of the duty solenoid  67  of the second hydraulic pressure control valve  64  may be decreased to 0% to move the spool  66  rightwards as viewed in FIG. 8, thereby permitting the oil from the oil pump  61  to be supplied to the retarding chambers  53 . However, if this is done, there is a possibility that the amount of oil supplied from the oil pump  61  via the first hydraulic pressure control valve  63  to the first valve operating characteristic changing mechanism V 1  is reduced due to the leakage of the oil from the retarding chambers  53 , because the first valve operating characteristic changing mechanism V 1  and the second valve operating characteristic changing mechanism V 2  are adapted to receive the hydraulic pressure from the common oil pump  61 , and hence, the establishment of the high-speed valve timing state of the first valve operating characteristic changing mechanism V 1  is unstable, if the volume of the oil pump  61  is set at a sufficiently large value. 
     Therefore, in the present embodiment, when the first valve operating characteristic changing mechanism V 1  is controlled to the high-speed valve timing state, the duty ratio of the duty solenoid  67  of the second hydraulic pressure control valve  64  is set at the predetermined value (e.g., 50%) corresponding to the high-speed valve timing to fix the second valve operating characteristic changing mechanism V 2  in the most-retarded state. In other words, the spool  66  is moved rightwards as viewed in FIG. 8 by setting the duty ratio at 0% to supply the hydraulic pressure to the retarding chambers  53 , thereby controlling the second valve operating characteristic changing mechanism V 2  to the most-retarded state. Thereafter, the duty ratio is maintained at 50% to return the spool  66  to the neutral position, thereby closing the input port  69  in the second hydraulic pressure control valve  64  connected to the oil pump  61 , and closing the advancing port  71  connected to the advancing chambers  52  and the retarding port  70  connected to the retarding chambers  53 . 
     When the second valve operating characteristic changing mechanism V 2  is in the most-retarded state by the above-described control, the hydraulic pressure from the oil pump  61  can be shut off by the second hydraulic pressure control valve  64 , whereby the leakage of the oil in the second valve operating characteristic changing mechanism V 2  can be prevented. Therefore, hydraulic pressure for establishing the high-speed valve timing state can be ensured in the second valve operating characteristic changing mechanism V 2  without increasing the volume of the oil pump  61  to guarantee the reliability of the valve operating characteristic changing control. Moreover, the duty ratio of the duty solenoid  67  of the second hydraulic pressure control valve  64  is set at 50% to maintain the spool in the neutral state and hence, in changing the cam phase of the second valve operating characteristic changing mechanism V 2  in the advancing direction from the most-retarded state, the hydraulic pressure in the advancing chambers  52  can be raised quickly to enhance the responsiveness. 
     The operation of the second valve operating characteristic changing mechanism V 2  will be described below in further detail with reference to the flow chart. 
     The flow chart in FIGS. 9 and 10 show a routine for calculating a target cam phase CAINCMD. This routine is carried out at every predetermined time interval. First, when the internal combustion engine E is in a starting mode at Step S 11 , an after-start cam phase changing control prohibiting timer TMCAAST is set at a predetermined time #TMCAAST (e.g., 5 sec) at Step S 12 . A second valve operating characteristic changing mechanism operating delay timer TMCADLY is set at a predetermined time #TMCADLY (e.g., 500 msec) at Step S 13 , and the target cam phase CAINCMD is set at 0 at Step S 14 . A second valve operating characteristic changing mechanism control permitting flag F_VTC for indicating whether the operation of the second valve operating characteristic changing mechanism V 2  is permitted, is set “0” (which indicates the prohibition of the operation of the second valve operating characteristic changing mechanism V 2 ) at Step S 15 . 
     After the internal combustion engine E begins to come out of the starting mode at Step S 11  into a basic mode, the processing is advanced to Steps S 13  to S 15  to prohibit the operation of the second valve operating characteristic changing mechanism V 2 , before the counting of the after-start cam phase changing control prohibiting timer TMCAAST is completed. When the counting of the after-start cam phase changing control prohibiting timer TMCAAST has completed, and 5 seconds have lapsed after the starting, the processing is advanced to Step S 17 . If a second valve operating characteristic changing mechanism failure flag F_VTCNG has been set at “1” (which indicates a failure) at Step S 17 , or another failure has been produced at Step S 18 , the processing is advanced to Steps S 13  to S 15  to prohibit the operation of the second valve operating characteristic changing mechanism V 2 . 
     If no failure has been produced at Steps S 17  and S 18 , an idle flag F_IDLE is referred to at Step S 19 . When the idle flag F_IDLE has been set at “1” to indicate that the internal combustion engine E is in an idling state, for example, when the throttle opening degree TH detected by a throttle opening degree sensor S 6  is a value corresponding to a full opening state, and the engine rotational speed NE detected by the engine rotational speed sensor S 7  is near 700 rpm, the processing is advanced to Steps S 13  to S 15  to prohibit the operation of the second valve operating characteristic changing mechanism V 2 . 
     If the idle flag F_IDLE has been set at “0” to indicate that the internal combustion engine E is not in the idling state, it is determined at Step S 20  whether the temperature of cooling water detected by the cooling-water temperature sensor S 5  is between a lowest limit value #TWVTCL (e.g., 0° C.) and a highest limit value #TWVTCH (e.g., 110° C.), and whether the engine rotational speed detected by the engine rotational speed sensor S 7  is smaller than a lowest limit value #NEVTCL (e.g., 1,500 rpm). If any of the above-described conditions is not established, the processing is advanced to Steps S 13  to S 15  to prohibit the operation of the second valve operating characteristic changing mechanism V 2 . 
     If all of the conditions at Steps S 11  and S 16  to S 20  are established, the processing is advanced to Step S 21  to operate the second valve operating characteristic changing mechanism V 2 . If the first valve operating characteristic changing mechanism control permitting flag F_VTEC is at “0” at Step S 21  to indicate that the first valve operating characteristic changing mechanism V 1  has established the low-speed valve timing, a target cam phase #CICMD_L corresponding to the low-speed valve timing is searched from a map at Step S 22 . On the other hand, if the first valve operating characteristic changing mechanism control permitting flag F_VTEC is at “1” to indicate that the first valve operating characteristic changing mechanism V 1  has established the high-speed valve timing, a target cam phase #CICMD_H corresponding to the high-speed valve timing is searched from a map at Step S 23 . The maps used at Steps S 22  and S 23  are established with the intake negative pressure PBA detected by the intake negative pressure sensor S 4  and the engine rotational speed NE detected by the engine rotational speed sensor S 7  being used as parameters. 
     At subsequent Step S 24 , the target cam phases #CICMD_L and #CICMD_H which are map values detected at Step S 22  and S 23  are determined as a target cam phase CAINCMDX. Then, at Step S 25 , an absolute value of a deviation resulting from the subtraction of the last value CAINCMD(n−1) of the target cam phase from the target cam phase CAINCMDX is compared with a cam phase operation-amount limit value #DCACMDX (e.g., 2° in terms of a crank angle). As a result, when the relation, |CAINCNIDX−CAINCMD(n−1)|&lt;#DCACMDX is established, i.e., the absolute value of the deviation is relatively small, the target cam phase CAINCMDX is determined as a current value CAINCMD(n) of the target cam phase at Step S 26 . 
     On the other hand, when the relation, |CAINCMDX−CAINCMD(n−1)|&lt;#DCACMDX is not established, i.e., the absolute value of the deviation is relatively large at Step S 25 , the sign of the deviation CAINCMDX−CAINCMD(n−1) is determined at Step S 27 . As a result, if the deviation CAINCMDX−CAINCMD(n−1)&gt;0 is established, a value resulting from the addition of the cam phase operation-amount limit value #DCACMDX to the last value CAINCMD(n−1) of the target cam phase is determined as the current value CAINCMD(n) of the target cam phase at Step S 28  to stepwise change the cam phase in the advancing direction. On the other hand, if the deviation CAINCMDX−CAINCMD(n−1)&gt;0 is not established, a value resulting from the subtraction of the cam phase operation-amount limit value #DCACMDX from the last value CAINCMD(n−1) of the target cam phase is determined as the current value CAINCMD(n) of the target cam phase at Step S 29  to stepwise change the cam phase in the retarding direction. 
     If the deviation between the current value CAINCMD(n) and the last value CAINCMD(n−1) of the target cam phase exceeds the cam phase operation-amount limit value #DCACMDX, the target cam phase is changed gradually rather than quickly, thereby making it possible to prevent an overshoot from being caused during feedback control of the cam phase due to the quick changing of the cam phase, and to prevent the unnecessary changing of the cam phase, when the engine rotational speed is increased instantaneously and returned immediately to the original value, for example, during shift-changing or the like. 
     At subsequent Step S 30 , the current value CAINCMD(n) of the target cam phase is corrected by multiplying the current value CAINCMD(n) by the water temperature correcting factor KTWCI. The water temperature correcting factor KTWCI searched using the cooling-water temperature TW detected by the cooling-water temperature sensor S 5  as a parameter, is set so that it is equal to 1, when the cooling-water temperature TW is equal to or higher than a predetermined value, and it is decreased linearly from 1, when the cooling-water temperature TW is lower than the predetermined value. 
     Then, at Step S 31 , the current value CAINCMD(n) of the target cam phase is compared with a control-executed cam phase #CAINL0 (e.g., 3° or 5° in terms of the crank angle) from the most-retarded position. If the current value CAINCMD(n) of the target cam phase is smaller than the control-executed cam phase #CAINL0, namely, if the control amount from the most-retarded position is an extremely small target cam phase (e.g., during low-load operation immediately after an idling-released state), a very large difference cannot be produced in the operational state, as compared with the case where a driving force is applied to the second hydraulic pressure control valve  64  and the second valve operating characteristic changing mechanism V 2 , and there is little difference between when the cam phase has been changed and when the cam phase has not been changed. Therefore, the processing is advanced to Steps S 13  to S 15  to prohibit the operation of the second valve operating characteristic changing mechanism V 2 . 
     When the current value CAINCMD(n) of the target cam phase is equal to or larger than the control-executed cam phase #CAINL0 at Step S 31 , there is a pause at Step S 32  for the counting of the second valve operating characteristic changing mechanism operating delay timer TMCADLY to be completed to prevent hunting upon switching between the starting mode and the basic mode, and thereafter, the second valve operating characteristic changing mechanism control permitting flag F_VTC is set at “1” at Step S 33  to permit the operation of the second valve operating characteristic changing mechanism V 2 . 
     The flow chart shown in FIGS. 11 and 12 shows a routine of feedback-control of the cam phase by the second valve operating characteristic changing mechanism V 2 . This routine is carried out at every predetermined time interval. First, when the second valve operating characteristic chancing mechanism failure flag F_VTCNG has been set at “0” at Step S 41  to indicate that the second valve operating characteristic changing mechanism V 2  is normal, and the second valve operating characteristic changing mechanism control permitting flag F VTC has been set at “1” at Step S 42  to indicate that the second valve operating characteristic changing mechanism V 2  is in operation, a deviation DCAINCMD between the target cam phase CAINCMD calculated in the routine shown in FIGS. 9 and 10 and an actual cam phase CAIN calculated from the outputs from the cam shaft sensor S 1  and the crankshaft sensor S 3  is calculated at Step S 43 , and a deviation DCANIN between the last value CAIN(n−1) and the current value CAIN(n) of the actual cam phase is calculated at Step S 44 . 
     If the second valve operating characteristic changing mechanism control permitting flag F_VTC has been changed from “0” to “1” at Step S 45 , i.e., if the operation of the second valve operating characteristic changing mechanism V 2  has been changed from the prohibition to the permission in a current loop, the processing is advanced to Step S 46 , at which the deviation DCAINCMD is compared with a first feed-forward control determining value #DCAINFFO (e.g., 10° in terms of the crank angle). As a result, if the deviation DCAINCMD is larger than the first feed-forward control determining value #DCAINFFO, a second valve operating characteristic changing mechanism feed-forward control flag c is set at “1” at Step S 47 , at which the second valve operating characteristic changing mechanism V 2  to be intrinsically feedback controlled is feed-forward controlled. 
     Namely, a current value DVIIN(n) of an I term for controlling the second valve operating characteristic changing mechanism V 2  in a PID feedback manner is set at “0” at Step S 48 , and a current value DVIN of an operational amount of the second valve operating characteristic changing control is set at a highest limit value #DVLMTHO at Step S 49 . Thereafter, a duty ratio DOUTTVT of the second hydraulic pressure control valve  64  of the second valve operating characteristic changing mechanism V 2  is determined as a current value DVIN(n) of the operational amount at Step S 67 . In a subsequent loop, the answer at Step S 45  and the answer at Step S 50  are YES and hence, the magnitude of the deviation DCAINCMD is compared again with the first feed-forward control determining value #DCAINFFO at Step S 46 . When the deviation DCAINCMD is larger, the processing is advanced via Steps S 47  to S 49  to Step S 67 . 
     Therefore, if the deviation DCAINCMD between the target cam phase CAINCMD and the actual cam phase CAIN is large when the control of the second valve operating characteristic changing mechanism V 2  has been started, the second valve operating characteristic changing mechanism V 2  is controlled substantially in the feed-forward manner by setting the current value DVIN of the control amount of the second valve operating characteristic changing control at the highest limit value #DVLMTHO which is a constant, while the above-described state is continued. 
     The purpose of employing the above-described control is as follows: Even if the second valve operating characteristic changing mechanism V 2  is controlled in the feedback manner from the beginning, the responsiveness can be ensured. However, after the cam phase has reached the target value, there is a high possibility that an overshoot is not avoided, and it is difficult to ensure a high-accuracy convergence. Therefore, the feed-forward control is employed at the beginning of the start of the control and continued for a period while the convergence is feared because of a large deviation DCAINCMD, whereby the responsiveness and the convergence can be reconciled. 
     If the deviation DCAINCMD is equal to or smaller than the first feed-forward control determining value #DCAINFFO from the beginning of the start of the control at Step S 46 , or if the deviation DCAINCMD becomes equal to or smaller than the first feed-forward control determining value #DCAINFFO during the feed-forward control at Step S 46 , the second valve operating characteristic changing mechanism feed-forward control flag F_VTCFF is set at “0” at Step S 51 , progressing to Step S 52 . If the last value DVIIN(n−1) of the I term of the PID feedback control is 0 at Step S 52 , the last value DVIIN(n−1) of the I term is determined at an I-term initial value #DVISEN at Step S 53 . 
     At subsequent Step S 54 , the deviation DCAINCMD (a positive value; when the target cam phase is larger than the actual cam phase) is compared with the second feed-forward control determining value #DCAINFFR which is smaller than the first feed-forward control determining value #DCAINFFO. As a result, if there is a large difference between both of them, the current value DVIN(n) of the operational amount is set at the highest limit value #DVLMTH2 at Step S 56 , and then, the duty ratio DOUTVT of the second hydraulic pressure control valve  64  of the second valve operating characteristic changing mechanism V 2  is determined as the current value DVIN(n) of the operational amount at Step S 67 . 
     Likewise, the deviation DCAINCMD (a negative value; when the actual cam phase is larger than the target cam phase) is compared, at Step S 55 , with a third feed-forward control determining value #DCAINFFA whose absolute value is smaller than the first feed-forward control determining value #DCAINFFO. As a result, if there is a large difference between them, the current value DVIN(n) of the operational amount is set at a lowest limit value #DVLMTL1 at Step S 57  and then, the duty ratio DOUTVT of the second hydraulic pressure control valve  64  of the second valve operating characteristic changing mechanism V 2  is determined as the current value DVIN(n) of the operational amount at Step S 67 . 
     Before the deviation DCAINCMD becomes equal to or smaller than the second and third feed-forward control determining values #DCAINFFR and #DCAINFFA at Steps S 54  and S 55  even after the deviation DCAINCMD becomes equal to or smaller than the first feed-forward control determining value #DCAINFFO at Step S 46 , the current value DVIN(n) of the operational amount is changed from the highest limit value #DVLMTHO to the highest limit value #DVLMTH2 or the lowest limit value #DVLMTL1 to continue the feed-forward control, whereby the responsiveness and convergence can be reconciled. 
     The lowest limit value #DVLMTL1 (see Step S 57 ) is a fixed value, while the highest limit value #DVLMTH2 (see Step S 56 ) is a variable value to increase the convergence of the feed-forward control, and is searched from a map shown in FIG. 14 based upon the cooling-water temperature detected by the cooling-water temperature sensor S 2  being used as a parameter or with the deviation DCAINCMD being used as a parameter. 
     The highest limit value #DVLMTH2 is increased in accordance with the rising of the cooling-water temperature TW for the purpose of compensating for the oil temperature rising with the rising of the cooling-water temperature TW, resulting in a decrease in hydraulic pressure, and that the coil temperature of the duty solenoid  67  is raised, resulting an increase in electric resistance, by increasing the highest limit value #DVLMTH2 determining the operational amount DVIN. The highest limit value #DVLMTH2 is increased in accordance with an increase in the deviation DCAINCMD for the purpose of increasing the operational amount DVIN to immediately converge the actual cam phase CAIN into the target cam phase CAINCMD, when the deviation DCAINCMD is large. 
     Only when the target cam phase CAINCMD is larger than the actual cam phase CAIN, namely, only when the second valve operating characteristic changing mechanism V 2  is operated in the advancing direction, the highest limit value #DVLMTH2 which is the variable value, is employed, because the reaction force received from the intake valves  10 ,  10  by the intake cam shaft  5  acts to change the cam phase in the retarding direction and for this reason, it is necessary to reliably advance the cam phase against such reaction force. Not only the highest limit value #DVLMTH2 but also the lowest limit value #DVLMTL1 can be changed with the cooling-water temperature TW and the deviation DCAINCMD used as parameters. If so, it is a matter of course that further accurate control is feasible. 
     Now, when the deviation DCAINCMD is brought to a sufficiently small value by the above-described feed-forward control, whereby both of Steps S 54  and S 55  are not established, a P-term gain KVP, an I-term gain KVI and a D-term gain KVD are calculated at Step S 58  and then, a P term DVPIN, an I term DVIIN and a D term DVDIN are calculated at Step S 59  according to 
     
       
         DVPIN←KVP*DCAINCMD  
       
     
     
       
         DVIIN(n)←KVI*DCAINCMD+DCAINCMD(n−1)  
       
     
     
       
         DVDIN←KVD*DCANIN  
       
     
     in order to carry out the PID feedback control. 
     At subsequent Steps S 60  to S 63 , the over-growth of the I term DVIIN is inhibited to reduce the convergence by carrying out the limit control of the I term DVIIN. More specifically, if the current value DVIIN(n) of the I term exceeds the highest limit value #DVLMTH1 at Step S 60 , the highest limit value #DVLMTH1 is determined as the current value DVIIN(n) of the I term at Step S 62 . If the current value DVIIN(n) of the I term is smaller than the lowest limit value #DVLMTL at Step S 61 , the lowest limit value #DVLMTL1 is determined as the current value DVIIN(n) of the I term at Step S 63 . 
     If the current value DVIIN(n) of the I term is between the highest limit value #DVLMTH1 and the lowest limit value #DVLMTL at Steps S 60  and S 61 , the current value DVIN(n) of the operational amount of the PID feedback control is calculated as a sum of the P term DVPIN, the I term DVIIN and the D term DVDIN at Step S 64 . 
     Then, at Steps S 65 , S 66 , S 56  and S 57 , the limit processing of the current value DVIN of the operational amount is carried out. More specifically, if the current value DVIN(n) of the operational amount exceeds the highest limit value #DVLMTH at Step S 65 , the highest limit value #DVLMTH is determined as the current value DVIN(n) of the operational amount at Step S 56 . If the current value DVIN(n) of the operational amount is smaller than the lowest limit value #DVLMTL at Step S 66 , the lowest limit value #DVLMTL1 is determined as the current value DVIN(n) of the operational amount at Step S 57 . The operational amount DVIN is brought to the duty ratio DOUTVT of the second hydraulic pressure control valve  64  at Step S 67 , whereby the second valve operating characteristic changing mechanism V 2  is feedback-controlled to converge the deviation DCAINCMD between the target cam phase CAINCMD and the actual cam phase CAIN to 0. 
     When the second valve operating characteristic changing mechanism V 2  is in failure, whereby the second valve operating characteristic changing mechanism failure flag F_VTCNG has been set at “1” at Step S 41 , the current value DVIN(n) is set at a failure-restoring preset value #DVLMTM corresponding to the duty ratio of the duty solenoid  67 , for example, equal to 50% at Step S 69  via Step S 68 , and a failure-restoring timer TMVTCNG (e.g., 3 sec) is set at subsequent Step S 70 . From the next loop, the answer at Step S 68  is NO for the period until the counting of the failure-restoring timer TMVTCNG is completed. Therefore, the current value DVIN(n) is set at “0” at Step S 71 . 
     The above-described control ensures that when the second valve operating characteristic changing mechanism V 2  fails, the second hydraulic pressure control valve  64  can be brought into a most-retarded state and moreover, operated instantaneously into the advancing direction at a predetermined time interval. As a result, when a failure is generated due to dust, or when a failure is determined instantaneously by pulsation of the hydraulic pressure circuit or the like, the second valve operating characteristic changing mechanism V 2  or the second hydraulic pressure control valve  64  can be restored automatically to a normal state. 
     When the second valve operating characteristic changing mechanism control permitting flag F_VTC has been set at “0” at Step S 42  to prohibit the operation of the second valve operating characteristic changing mechanism V 2 , the second valve operating characteristic changing mechanism feed-forward control flag F_VTCFF is set at “0” at Step S 72 , and the current value DVIIN(n) of the I term is set at “0” at Step S 73 , progressing to Step S 74 . 
     If the first valve operating characteristic changing mechanism control permitting flag F_VTEC is at “0” (the low-speed valve timing) at Step S 74 , the current value DVIN(n) of the operational amount is fixed at a preset value #DVLMTLOL (corresponding to the duty ratio of 10%) suitable for the low-speed valve timing at Step S 75 . On the other hand, if the first valve operating characteristic changing mechanism control permitting flag F_VTEC is at “1” (the high-speed valve timing) at Step S 74 , the current value DVIN(n) of the operational amount is fixed at a preset value #DVLMTLOH (corresponding to the duty ratio of 50%) suitable for the high-speed valve timing at Step S 76 . 
     The preset value #DVLMTLOL (corresponding to the duty ratio of 10%) suitable for the low-speed valve timing corresponds to a value immediately before the locking pin  47  of the second valve operating characteristic changing mechanism V 2  is moved out of the locking bore  7   3 . The preset value #DVLMTLOH (corresponding to the duty ratio of 50%) suitable for the high-speed valve timing corresponds to a value at which the spool  66  of the second hydraulic pressure control valve  64  is maintained in the neutral position. 
     In this way, when the operation of the second valve operating characteristic changing mechanism V 2  is prohibited to fix the cam phase in the most-retarded state, the duty ratio of the second hydraulic pressure  64  is set at a value (e.g., 50%) suitable for the high-speed valve timing, whereby the spool  66  of the second hydraulic pressure control valve  64  is maintained in the neutral position, only when the high-speed valve timing has been selected by the first valve operating characteristic changing mechanism V 1 . Thus, it is possible to prevent the leakage of hydraulic pressure in the second valve operating characteristic changing mechanism V 2  and to ensure the establishment of the high-speed timing by the first valve operating characteristic changing mechanism V 1 . 
     The valve operating characteristic changing mechanism according to the present invention is not limited to the second valve operating characteristic changing mechanism V 2  used in the embodiment, and may be a valve operating characteristic changing mechanism adapted to change the cam phase by an electric actuator. The cooling-water temperature TW has been employed as an engine temperature in the embodiment, but another temperature such as an oil temperature may be employed. 
     As discussed above, by controlling the valve operating characteristic changing mechanism in the feed-forward manner with the basic operational amount, when the deviation exceeds the feed-forward determining threshold value, it is possible to prevent a reduction in convergence due to the occurrence of overshooting when the feedback control is carried out. In addition, by controlling the valve operating characteristic changing mechanism in the feedback manner, when the deviation becomes equal to or smaller than the feed-forward determining threshold value to eliminate the occurrence of the overshooting, the actual cam phase can be converged into the target cam phase with high responsiveness and high convergence. Moreover, in carrying out the feed-forward control, as the engine temperature is higher, or as the deviation is larger, the basic operational amount is increased. Therefore, it is possible to further enhance the convergence in the feed-forward control. 
     Although the embodiment of the present invention has been described, it will be understood that the present invention is not limited to the above-described embodiment, and various modifications may be made without departing from the subject matter of the present invention.