Patent Publication Number: US-7593805-B2

Title: Control system for internal combustion engine

Description:
FIELD OF THE INVENTION 
   The present invention relates to a control system for internal combustion engines which is equipped with a variable valve lift mechanism which changes valve lift as the lift of intake valves, while restricting the valve lift such that it does not exceed a predetermined limit lift, and a variable intake air amount mechanism that changes the air intake amount. 
   BACKGROUND ART 
   Conventionally, as a control system for internal combustion engine of this kind, one disclosed in Patent Literature 1 is known. The variable valve lift mechanism of this internal combustion engine (hereinafter referred to as “the engine”) is provided for each cylinder, and continuously changes the valve lift between a predetermined minimum value and a predetermined maximum value, and comprises a drive shaft connected to a crankshaft, and a control shaft. The drive shaft is provided with a link arm and a swing cam for driving an intake valve, and the link arm and the swing cam are connected to a rocker arm provided on the control shaft. 
   The control shaft extends parallel with the drive shaft, and is supported by a bearing such that it is rotatable within a predetermined angle range. Further, the control shaft has a pin protruding in a radial direction, and is connected to a rotary drive mechanism, and the bearing is formed with a protrusion. When the rotary drive mechanism causes the control shaft to rotate, the relative angles of the rocker arm on the control shaft with respect to the swing cam and the link arm are changed, whereby the valve lift is changed. Further, when the control shaft rotates in a predetermined direction, the pin on the control shaft abuts against the protrusion of the bearing, whereby the rotation of the control shaft is blocked. Further, the intake pipe of the engine is provided with a throttle valve. 
   In the conventional control system, normally, the throttle valve is controlled to be fully open, and according to the operating condition of the engine, the valve lift is controlled via the variable valve lift mechanism, whereby the intake air amount is controlled. Further, when the engine is in a low load operating condition, the control shaft is caused to rotate until the pin abuts against the protrusion of the bearing, and is held in the state in which the pin is in abutment with the protrusion, whereby the valve lift is held at a predetermined minimum value. By controlling the opening degree of the throttle valve, the intake air amount is controlled. 
   In the above-described conventional control system, in controlling the valve lift, when the engine is in the low load operating condition, the control shaft is caused to rotate until the pin abuts against the protrusion of the bearing. Therefore, there is a fear that impact occurring upon the abutment deforms the pin or the protrusion. To avoid this, it is envisaged to reduce the rotational speed of the control shaft so as to reduce the impact, or provide a cushioning member on the pin or the protrusion so as to suppress the influence of the impact. However, in the former case, time taken to rotate the control shaft until the pin abuts against the protrusion, i.e. time taken to control the valve lift to the minimum value becomes longer, which results in a longer time period taken before the intake air amount converges to an appropriate value. During the time, the operating condition of the engine becomes unstable, which can degrade drivability. On the other hand, when the cushioning member is provided on the pin or the protrusion, the minimum value of the valve lift which should be obtained when the two are in contact with each other is prone to vary, which makes it impossible to carry out accurate control of the intake air amount. Further, the addition of the cushioning member increases the manufacturing costs accordingly, and the necessity of securing a space therefor degrades the degree of freedom of design. 
   The present invention has been made to provide a solution to the above-described problems, and an object thereof is to provide a control system for internal combustion engine, which is capable of reducing impact occurring when a movable part of a variable valve lift mechanism abuts against a restriction part, while maintaining excellent drivability. 
   [Patent Literature 1] Japanese Laid-Open Patent Publication (Kokai) No. 2003-254100 
   DISCLOSURE OF THE INVENTION 
   To attain the object, the invention as claimed in claim  1  provides a control system  1  for an internal combustion engine, comprising a variable valve lift mechanism  50  that changes a valve lift Liftin which is a lift of an intake valve  4  of the engine  3  by driving a movable part (short arm  65  in the embodiment (the same applies hereinafter in this section)) thereof, and includes a restriction part (minimum lift stopper  67   a ) for having the movable part abut thereagainst, for thereby restricting the valve lift Liftin such that the valve lift Liftin does not exceed a predetermined limit lift (minimum value Liftin_L), a variable intake air amount mechanism (throttle valve mechanism  11 ) that changes an intake air amount of the engine  3 , operating condition-detecting means (crank angle sensor  20 , engine coolant temperature sensor  21 , accelerator pedal opening sensor  27 , ECU  2 ) for detecting an operating condition of the engine  3 , abutment determination means (ECU  2 , steps  71  and  74  in  FIG. 16 ) for determining whether or not the movable part is in abutment with the restriction part, control means (ECU  2 , steps  31 ,  32 ,  37  to  40  in  FIG. 10 ,  FIGS. 11 to 13 , steps  80 ,  86  to  90  and  84  in  FIG. 21 ) for controlling the variable intake air amount mechanism based on the detected operating condition of the engine  3 , when the abutment determination means determines that the movable part is in abutment with the restriction part, valve lift-detecting means (pivot angle sensor  26 , ECU  2 ) for detecting the valve lift Liftin, target valve lift-determining means (ECU  2 , step  50  in  FIG. 14 ,  FIG. 15 ) for determining a target valve lift Liftin_cmd, and control input-calculating means (ECU  2 , step  54  in FIG.  14 ) for calculating a control input (lift control input Uliftin) for controlling the variable valve lift mechanism  50  with a predetermined control algorithm such that the detected valve lift Liftin follows up the determined target valve lift Liftin_cmd, wherein the predetermined control algorithm includes a disturbance suppression parameter (switching function-setting parameter POLE_lf) for suppressing influence of disturbance applied to the variable valve lift mechanism  50 , and wherein the control input calculating means includes disturbance suppression parameter-setting means (ECU  2 , step  73  in  FIG. 16 ) for setting the disturbance suppression parameter such that a degree of suppression of the influence of the disturbance by the disturbance suppression parameter is made smaller when a determination that the movable part is in abutment with the restriction part is made than before the determination is made. 
   According to this control system for an internal combustion engine, the target valve lift-determining means determines a target valve lift, and the control input-calculating means calculates a control input for controlling the variable valve lift mechanism with a predetermined control algorithm such that the valve lift follows up the target valve lift. Further, the movable part abuts against the restriction part, whereby the valve lift is restricted such that it does not exceed a predetermined limit lift. This restricts the valve lift such that it does not exceed the limit lift when the target valve lift exceeds the limit lift. Further, the abutment determination means determines whether or not the movable part is in abutment with the restriction part, and when it is determined that the movable part is in abutment with the restriction part, the variable intake air mechanism is controlled by the control means according to the detected operating condition of the engine. As described above, when the valve lift is equal to the limit lift due to the abutment of the movable part against the restriction part, the intake air amount is controlled by controlling the variable intake air mechanism according to the operating condition of the engine. 
   Further, the predetermined control algorithm includes a disturbance suppression parameter for suppressing the influence of disturbance applied to the variable valve lift mechanism, and when a determination that the movable part is in abutment with the restriction part is made, the disturbance suppression parameter is set by the disturbance suppression parameter-setting means such that the degree of suppression of the influence of the disturbance by the disturbance suppression parameter is made smaller than before the determination is made. 
   In calculating the control input with the predetermined control algorithm such that the valve lift follows up the target valve lift, when the control algorithm includes the disturbance suppression parameter, the control input is calculated according to the disturbance suppression parameter as follows: When the disturbance suppression parameter is set such that the degree of suppression of the influence of disturbance is increased, the control input is calculated such that the driving force applied to the movable part is increased so as to secure the follow-up characteristic of the valve lift to the target valve lift while more effectively suppressing the influence of the disturbance. On the other hand, when the disturbance suppression parameter is set such that the degree of suppression of the disturbance is reduced, the control input is calculated such that the driving force applied to the movable part for causing the valve lift to follow up the target valve lift is made smaller. 
   Therefore, as described above, when the movable part abuts against the restriction part, by setting the disturbance suppression parameter such that the degree of suppression of the disturbance thereby becomes smaller, the driving force applied to the movable part is reduced when the movable part has begun to abut against the restriction part, and hence it is possible to reduce impact occurring when the movable part abuts against the restriction part. This makes it possible to prevent the movable part and the restriction part from being deformed, and hence to prolong the service life for the variable valve lift mechanism. Further, the driving force applied to the movable part can be secured until the movable part abuts against the restriction part, it is possible to converge the intake air amount to a desired value quickly without lowering the moving speed of the movable part. As a result, the operating condition of the engine is made stable whereby it is possible to secure excellent drivability. Further, it is not required to additionally provide the cushioning member, which makes it possible to prevent the intake air amount from being varied due to variations in the valve lift at the limit lift, differently from the case of the cushion member being provided. Further, it is possible to prevent the addition of the cushioning member from increasing the manufacturing cost and reducing the degree of freedom of design. 
   The invention as claimed in claim  2  is a control system for internal combustion engine  1 , as claimed in claim  1 , wherein the control means starts control of the variable intake air amount mechanism immediately after it is determined that the movable part has abutted against the restriction part (steps  80 ,  86  to  90  and  84  in  FIG. 21 ). 
   With this configuration, immediately after it is determined that the movable part has abutted against the restriction part, the control of the variable intake air amount mechanism based on the operating condition of the engine is started. This causes the control of the intake air amount by the variable intake air amount mechanism to be started simultaneously when the valve lift reaches the limit lift, whereby it is possible to perform a smooth transition from the intake air amount control mainly based on the variable valve lift mechanism to the intake air amount control mainly based on the variable intake air mechanism, without interrupting the control of the intake air amount. 
   The invention as claimed in claim  3  is a control system for internal combustion engine  1 , as claimed in claim  1  or  2 , wherein the control means controls the variable intake air amount mechanism according to the detected valve lift Liftin, when it is determined that the movable part is not in abutment with the restriction part (steps  80  to  82 , and  84  in  FIG. 21 , and  FIG. 22 ). 
   With this configuration, when the movable part is in abutment with the restriction part, the variable intake air amount mechanism is controlled according to the operating condition of the engine, and in addition thereto, when the movable part is not in abutment with the restriction part, the control of the variable intake air amount mechanism based on the valve lift is carried out. With this configuration, at the time point of the valve lift reaching the limit lift, the operation amount of the variable intake air amount mechanism has already been controlled to a value suitable for the valve lift, and hence, when the control of the variable intake air amount mechanism based on the operating condition of the engine is started in accordance with the valve lift reaching the limit lift, the operation amount of the variable intake air amount mechanism can be quickly changed to a proper value without drastically changing the same. This makes it possible to smoothly change the intake air amount, and hence the torque and the rotational speed of the internal combustion engine can be smoothly changed without any step. 
   The invention as claimed in claim  4  is a control system for internal combustion engine  1  as claimed in any one of claims  1  to  3 , wherein the predetermined control algorithm includes a predetermined two-degree-of-freedom control algorithm (step  54  in  FIG. 14 ). 
   With this configuration, the control input is calculated with the control algorithm including a predetermined two-degree-of-freedom control algorithm. Therefore, e.g. in the case where the target value filter type two-degree-of-freedom control algorithm is employed as the two-degree-of-freedom control algorithm, the target value filter algorithm thereof enables the follow-up speed of the valve lift to the target valve lift to be properly set, and the feed control algorithm thereof enables the follow-up behavior of the valve lift to the target valve lift to be properly set. This makes it possible to cause the valve lift to accurately follow up the target valve lift while avoiding the occurrence of overshooting. As a result, the impact occurring when the movable part abuts against the restriction part can be positively reduced. 
   The invention as claimed in claim  5  is a control system for internal combustion engine  1 , as claimed in any one of claims  1  to  4 , further comprising hold determination means (ECU  2 , step  74  in  FIG. 16 ) for determining whether or not the valve lift Liftin is held at the predetermined limit lift after it is determined that the movable part has abutted against the restriction part, and wherein the disturbance suppression parameter-setting means sets the disturbance suppression parameter such that the degree of suppression of the influence of the disturbance by the disturbance suppression parameter is increased, when the hold determination means has determined that the valve lift Liftin is held at the predetermined limit lift (step  66  in  FIG. 16 ). 
   With this configuration, when the hold determination means determines that the valve lift is held at the limit lift after the movable part abuts against the restriction part, the disturbance suppression parameter is set such that the degree of suppression of the influence of the disturbance thereby is increased. This increases the driving force applied to the movable part for causing the aforementioned valve lift to follow up the target valve lift, i.e. the force for holding the valve lift at the limit lift, after the movable part has abutted against the restriction part. As a result, after abutting against the restriction part, the movable part can be positively held in the state in abutment with the restriction part without being moved away from the restriction part by the vibration of the engine or the like. Therefore, it is possible to accurately perform the control of the intake air amount by the variable intake air amount mechanism while preventing variation in the intake air amount from being caused by the separation of the movable part from the restriction part. 
   The invention as claimed in claim  6  is a control system for internal combustion engine  1 , as claimed in any one of claims  1  to  5 , wherein the disturbance suppression parameter-setting means sets the disturbance suppression parameter such that the degree of suppression of the influence of the disturbance by the disturbance suppression parameter is increased, when at least one of the target valve lift Liftin_cmd and the valve lift Liftin is within a predetermined range defined by the predetermined limit lift and at the same time becomes equal to a value other the predetermined limit lift, after it is determined that the movable part has abutted against the restriction part (steps  61  and  66  in  FIG. 16 ). 
   With this configuration, after the movable part abuts against the restriction part, and when the target valve lift and/or the valve lift are/is within the predetermined range, and at the same time becomes equal to a value other than the limit lift, the disturbance suppression parameter is set such that the degree of suppression of the influence of the disturbance thereby is increased. This causes, during execution of the control of the variable intake air amount mechanism responsive to the abutment of the movable part against the restriction part, when the control of the valve lift executed in parallel therewith causes the target valve lift and/or the valve lift to be equal to such a value mentioned above, that is, in controlling the valve lift in such a direction as will cause the movable part once having abutted against the restriction part to move away therefrom, and/or when the valve lift is actually controlled as such, it is possible to increase the driving force applied to the movable part for causing the valve lift to follow up the target valve lift, which makes it possible to improve the follow-up characteristic of the valve lift to the target valve lift. 
   Therefore, during a transition in which e.g. when the intake air amount is caused to be quickly changed in such a direction that the movable part is moved away from the restriction part, after the movable part has abutted against the restriction part and the valve lift has become equal to the limit lift, it is possible to cause the intake air amount to converge to a desired value quickly, which enables excellent drivability to be secured. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     [ FIG. 1 ] 
     A schematic diagram schematically showing the arrangement of an internal combustion engine to which is applied a control system according to the present invention. 
     [ FIG. 2 ] 
     A schematic block diagram of the control system. 
     [ FIG. 3 ] 
     A schematic cross-sectional view of a variable intake valve-actuating mechanism and an exhaust valve-actuating mechanism of the engine. 
     [ FIG. 4 ] 
     A schematic cross-sectional view of a variable valve lift mechanism of the variable intake valve-actuating mechanism. 
     [ FIG. 5 ] 
     ( a ) is a diagram showing a lift actuator in a state in which a short arm thereof is in contact with a maximum lift stopper, and ( b ) is a diagram showing the lift actuator in a state in which the short arm thereof is in contact with a minimum lift stopper. 
     [ FIG. 6 ] 
     ( a ) is a diagram showing an intake valve placed in an open state when a lower link of the variable valve lift mechanism is in a maximum lift position, and ( b ) is a diagram showing the intake valve placed in an open state when the lower link of the variable valve lift mechanism is in a minimum lift position. 
     [ FIG. 7 ] 
     A diagram showing a valve lift curve (solid line) obtained when the lower link of the variable valve lift mechanism is in the maximum lift position, and a valve lift curve (two-dot chain line) obtained when the lower link of the variable valve lift mechanism is in the minimum lift position. 
     [ FIG. 8 ] 
     A flowchart showing a process including an intake air amount control process, which is executed by an ECU of the control system. 
     [ FIG. 9 ] 
     A flowchart showing an overcurrent determination process in  FIG. 8 . 
     [ FIG. 10 ] 
     A flowchart showing an intake air amount control process in  FIG. 8 . 
     [ FIG. 11 ] 
     A diagram showing, by way of example, a table for use in calculating a start-time value Gcyl_cmd_crk of the target intake air amount, which is used in the  FIG. 10  process. 
     [ FIG. 12 ] 
     A diagram showing, by way of example, a map for use in calculating a catalyst warmup value Gcyl_cmd_ast of the target intake air amount, which is used in the  FIG. 10  process. 
     [ FIG. 13 ] 
     A diagram showing, by way of example, a map for use in calculating a normal operation value Gcyl_cmd_drv of the target intake air amount, which is used in the  FIG. 10  process. 
     [ FIG. 14 ] 
     A flowchart showing a valve lift control process in  FIG. 10 . 
     [ FIG. 15 ] 
     A diagram showing, by way of example, a map for use in calculating a target valve lift Liftin_cmd, which is used in the  FIG. 14  process. 
     [ FIG. 16 ] 
     A flowchart showing an abutment determination process in  FIG. 14 . 
     [ FIG. 17 ] 
     A block diagram of a determination parameter-calculating section. 
     [ FIG. 18 ] 
     A block diagram showing a gain characteristic and a phase characteristic of a first filter. 
     [ FIG. 19 ] 
     A schematic diagram of a power spectrum of a lift difference DL(k), a first filtered value DLf(m), and a determination parameter WVliftin(k). 
     [ FIG. 20 ] 
     A diagram illustrating an example of operation of the abutment determination process. 
     [ FIG. 21 ] 
     A flowchart showing a throttle control process in  FIG. 10 . 
     [ FIG. 22 ] 
     A diagram showing, by way of example, a map for use in calculating a normal-time value TH_cmd_op of a target throttle valve opening for use in the  FIG. 21  process. 
   

   BEST MODE FOR CARRYING OUT THE INVENTION 
   The present invention will now be described in detail with reference to the drawings showing a preferred embodiment thereof.  FIG. 1  schematically shows the arrangement of an internal combustion engine (hereinafter simply referred to as “the engine”)  3  to which is applied a control system  1  of the present invention. Referring to  FIGS. 1 and 3 , the engine  3  is an in-line four-cylinder DOHC gasoline engine having four cylinders  3   a  and pistons  3   b  (only one of which is shown), and installed on a vehicle (not shown). Further, the engine  3  includes an intake valve  4  and an exhaust valve  7  for opening and closing an intake port and an exhaust port of each cylinder  3   a , respectively, a variable intake valve-actuating mechanism  40  having an intake camshaft  5  and intake cams  6  for actuating the intake valves  4 , and an exhaust valve-actuating mechanism  30  having an exhaust camshaft  8  and exhaust cams  9  for actuating the exhaust valves  7 . 
   The intake valve  4  has a stem  4   a  thereof slidably fitted in a guide  4   b . The guide  4   b  is rigidly fixed to a cylinder head  3   c . The intake valve  4  includes upper and lower spring sheets  4   c  and  4   d , and a valve spring  4   e  disposed therebetween (see  FIG. 4 ), and is urged by the valve spring  4   e  in the valve-closing direction. 
   The intake camshaft  5  and the exhaust camshaft  8  are rotatably mounted through the cylinder head  3   c  via holders, not shown. Further, the intake camshaft  5  has an intake sprocket coaxially fitted on one end thereof. The intake sprocket is connected to a crankshaft  3   d  via the intake sprocket and a timing belt (neither of which is shown). With the above configuration, the intake camshaft  5  performs one rotation per two rotations of the crankshaft  3   d . The intake cam  6  is integrally formed on the intake camshaft  5  for each cylinder  3   a.    
   The variable intake valve-actuating mechanism  40  is provided for actuating the intake valve  4  of each cylinder  3   a  so as to open and close the same, in accordance with rotation of the intake cam  6 , and continuously changing the lift of the intake valve  4 , which will be described in detail hereinafter. It should be noted that in the present embodiment, the lift of the intake valve  4  (hereinafter referred to as “the valve lift”) Liftin represents the maximum stroke of the intake valve  4 . 
   The exhaust valve  7  has a stem  7   a  thereof slidably fitted in a guide  7   b . The guide  7   b  is rigidly fixed to the cylinder head  3   c . Further, the exhaust valve  7  is provided with upper and lower spring sheets  7   c  and  7   d , and a valve spring  7   e  disposed therebetween, and is urged by the valve spring  7   e  in the valve-closing direction. 
   The exhaust camshaft  8  has an exhaust sprocket (not shown) coaxially fixed to one end thereof, and is connected to the crankshaft  3   d  by the exhaust sprocket and the aforementioned timing belt, whereby the exhaust camshaft  8  performs one rotation per two rotations of the crankshaft  3   d . The exhaust cam  9  is integrally formed on the exhaust camshaft  8  for each cylinder  3   a.    
   The exhaust valve-actuating mechanism  30  includes rocker arms  31 . Each rocker arm  31  is pivotally moved in accordance with rotation of the associated exhaust cam  9  to thereby actuate the exhaust valve  7  for opening and closing the same against the urging force of the valve spring  7   e.    
   The engine  3  is provided with a crank angle sensor  20  (operating condition-detecting means) and an engine coolant temperature sensor  21  (operating condition-detecting means). The crank angle sensor  20  is comprised of a magnet rotor and an MRE (magnetic resistance element) pickup, and delivers a CRK signal and a TDC signal, which are both pulse signals, to the ECU  2  of the control system  1 , described hereinafter, in accordance with rotation of the crankshaft  3   d.    
   The CRK signal is delivered whenever the crankshaft  3   d  rotates through a predetermined angle (e.g. 10°). The ECU  2  calculates the rotational speed NE of the engine  3  (hereinafter referred to as “the engine speed NE”) based on the CRK signal. The TDC signal indicates that each piston  3   b  in the associated cylinder  3   a  is in a predetermined crank angle position slightly before the TDC position at the start of the intake stroke, and in the illustrated example of the four-cylinder type engine, the TDC signal is delivered whenever the crankshaft  3   d  rotates through a predetermined crank angle of 180°. 
   The engine coolant temperature sensor  21  is implemented e.g. by a thermistor, and detects an engine coolant temperature TW to deliver a signal indicative of the sensed engine coolant temperature TW to the ECU  2 . The engine coolant temperature TW represents the temperature of an engine coolant circulating through a cylinder block  3   e  of the engine  3 . 
   Furthermore, the engine  3  has an intake pipe  10  which is provided with an air flow sensor  22 , a throttle valve mechanism  11  (variable intake air amount mechanism), a throttle valve opening sensor  23 , an intake pipe absolute pressure sensor  24 , an intake air temperature sensor  25 , and a fuel injection valve  12 , from upstream to downstream in the mentioned order. 
   The air flow sensor  22  is formed by a hot-wire air flow meter, and detects the amount of intake air passing through the throttle valve mechanism  11  (hereinafter referred to as “the TH passing intake air amount”) Gth to deliver a signal indicative of the sensed TH passing intake air amount Gth to the ECU  2 . 
   The throttle valve mechanism  11  includes a throttle valve  11   a , and a TH actuator  11   b  for opening and closing the throttle valve  11   a . The throttle valve  11   a  is arranged in the intake pipe  10  in a manner capable of performing pivotal motion, for varying the amount of intake air by a change in the pivotal motion. The TH actuator  11   b  is a combination of a motor, and a gear mechanism, neither of which is shown, and is driven by a control signal commensurate with a throttle control input Uth, referred to thereinafter, which is input from the ECU  2 , whereby the opening of the throttle valve  11   a  (hereinafter referred to as “the throttle valve opening”) TH is controlled. The throttle valve opening sensor  23  detects the throttle valve opening TH, and delivers a detection signal indicative of the detected throttle valve opening TH to the ECU  2 . 
   Further, the throttle valve mechanism  11  is provided with a lock mechanism (not shown) which locks the operation of the throttle valve mechanism  11 , when the throttle valve control input Uth is set to a failure-time value Uth_fs, or is not input to the throttle actuator  11   b  due to a disconnection. That is, the throttle valve opening TH is prevented from being changed by the throttle valve mechanism  11 , but is held at the minimum value TH_L. It should be noted that the minimum value TH_L is set to set such that a predetermined failure-time intake air amount is secured when the valve lift Liftin is held at a minimum value Liftin_L (predetermined limit lift), referred to hereinafter. The failure-time intake air amount is set such that it enables the idling or starting of the engine to be properly performed during stoppage of the vehicle, and a low-speed traveling state to be maintained during travel of the vehicle. 
   A portion of the intake pipe  10  downstream of the throttle valve  11   a  forms a surge tank  10   a , and the intake pipe absolute pressure sensor  24  and the intake air temperature sensor  25  are disposed in the surge tank  10   a . The intake pipe absolute pressure sensor  24  is formed e.g. by a semiconductor pressure sensor, for detecting the absolute pressure within the intake pipe  10  (hereinafter referred to as “the intake pipe absolute pressure”) PBA to deliver a detection signal indicative of the detected intake pipe absolute pressure PBA to the ECU  2 . The intake air temperature sensor  25  is formed by a thermistor, for detecting the temperature of air within the intake pipe  10  (hereinafter referred to as “the intake air temperature”) TA to deliver a detection signal indicative of the detected intake air temperature TA to the ECU  2 . 
   The fuel injections valve  12  is for injecting fuel into the intake pipe  10 , and the injection timing and injection amount of fuel are controlled by a drive signal from the ECU  2 . 
   Further, the cylinder head  3   c  of the engine has spark plugs  13  mounted therein, and the ignition timing of each spark plug is also controlled by the ECU  2  (see  FIG. 2 .) 
   Next, referring to  FIGS. 4 to 7 , a description will be given of the aforementioned variable intake valve-actuating mechanism  40 . The variable intake valve-actuating mechanism  40  is comprised of the intake camshaft  5 , the intake cams  6 , and a variable valve lift mechanism  50 . 
   The variable valve lift mechanism  50  is provided for actuating the intake valves  4  to open and close the same, in accordance with rotation of the intake cams  6 , and continuously changing the valve lift Liftin between a predetermined maximum value Liftin_H and the minimum value Liftin_L. The variable valve lift mechanism  50  is comprised of rocker arm mechanisms  51  of a four joint link type, provided for the respective cylinders  3   a , and a lift actuator  60  simultaneously actuating these rocker arm mechanisms  51 . 
   Each rocker arm mechanism  51  is comprised of a rocker arm  52 , and upper and lower links  53  and  54 . The upper link  53  has one end pivotally mounted to a rocker arm shaft  56  fixed to the cylinder head  3   c , and the other end pivotally mounted to an upper end of the rocker arm  52  by an upper pin  55 . 
   Further, a roller  57  is pivotally disposed on the upper pin  55  of the rocker arm  52 . The roller  57  is in contact with a cam surface of the intake cam  6 . As the intake cam  6  rotates, the roller  57  rolls on the intake cam  6  while being guided by the cam surface of the intake cam  6 . As a result, the rocker arm  52  is vertically driven, and the upper link  53  is pivotally moved about the rocker arm shaft  56 . 
   Furthermore, an adjusting bolt  52   a  is mounted to an end of the rocker arm  52  toward the intake valve  4 . The adjusting bolt  52   a  is in contact with a stem  4   e  of the intake valve  4  and when the rocker arm  52  is vertically moved in accordance with rotation of the intake cam  6 , the adjusting bolt  52   a  vertically drives the stem  4   a  to open and close the intake valve  4 , against the urging force of the valve spring  4   e.    
   Further, the lower link  54  has one end pivotally mounted to a lower end of the rocker arm  52  by a lower pin  58 , and the other end of the lower link  54  has a connection shaft  59  pivotally mounted thereto. The lower link  54  is connected to a short arm  65  (movable part), described hereinafter, of the lift actuator  60  by the connection shaft  59 . 
   As shown in  FIG. 5 , the lift actuator  60 , which is driven by the ECU  2 , is comprised of a motor  61 , a nut  62 , a link  63 , a long arm  64 , and the short arm  65 . The motor  61  is connected to the ECU  2 , and disposed outside a head cover  3   f  of the engine  3 . The rotational shaft of the motor  61  is a screw shaft  61   a  formed with a male screw and the nut  62  is screwed onto the screw shaft  61   a . The link  63  has one end pivotally mounted to the nut  62  by a pin  63   a , and the other end pivotally mounted to one end of the long arm  64  by a pin  63   b . Further, the other end of the long arm  64  is attached to one end of the short arm  65  by a pivot shaft  66 . The pivot shaft  66  is circular in cross section, and is pivotally supported by the head cover  3   f  of the engine  3 . The long arm  64  and the short arm  65  are pivotally moved about the pivot shaft  66  in unison with the pivot shaft  66 . 
   Furthermore, the aforementioned connection shaft  59  pivotally extends through an end of the short arm  65  on a side opposite to the pivot shaft  66 , whereby the short arm  65  is connected to the lower link  54  by the connection shaft  59 . Further, in the vicinity of the short arum  65 , a minimum lift stopper  67   a  (restriction part) and a maximum lift stopper  67   b  are arranged in a manner spaced from each other. These two stoppers  67   a  and  67   b  restrict the pivotal motion range of the short arm  65   b  as described hereinbelow. 
   Next, a description will be given of the operation of the variable valve lift mechanism  50  configured as above. In the variable valve lift mechanism  50 , when a lift control input Uliftin (control input), described hereinafter, is input from the ECU  2  to the lift actuator  60 , the screw shaft  61   a  of the motor  61  rotates, and the nut  62  is moved in accordance with the rotation of the screw shaft  61   a , whereby the long arm  64  and the short arm  65  are pivotally moved about the pivot shaft  66 , and in accordance with the motion of the connecting shaft  59  caused by the pivotal motion of the short arm  65 , the lower link  54  of the rocker arm mechanism  51  is pivotally moved about the lower pin  58 . That is, the lower link  54  is driven by the lift actuator  60 . 
   As shown in  FIG. 5(   a ), when the short arm  65  is pivotally moved counterclockwise as viewed in the figure, the short arm  65  is brought into abutment with the maximum lift stopper  67   b  and stopped thereat, whereby the lower link  54  is also stopped at the maximum lift position shown by a solid line in  FIG. 4 . On the other hand, as shown in  FIG. 5(   b ), when the short arm  65  is pivotally moved clockwise, the short arm  65  is brought into abutment with the minimum lift stopper  67   a  and stopped thereat, whereby the lower link  54  is also stopped at the minimum lift position shown by a two-dot chain line in  FIG. 4 . 
   As described above, under the control of the ECU  2 , the range of pivotal motion of the short arm  65  is restricted by the two stoppers  67   a  and  67   b  between the maximum lift position shown in  FIG. 5(   a ) and the minimum lift position shown in  FIG. 5(   b ), whereby the range of pivotal motion of the lower link  54  is also restricted between the maximum lift position indicated by the solid line in  FIG. 4  and the minimum lift position indicated by the two-dot chain line. 
   The rocker arm mechanism  51  is configured such that when the lower link  54  is in the maximum lift position, the distance between the center of the upper pin  55  and the center of the lower pin  58  becomes longer than the distance between the center of the rocker arm shaft  56  and the center of the connection shaft  59 , whereby as shown in  FIG. 6(   a ), when the intake cam  6  rotates, the amount of movement of the adjusting bolt  52   a  becomes larger than the amount of movement of a contact point where the intake cam  6  and the roller  57  are in contact with each other. 
   On the other hand, the rocker arm mechanism  51  is configured such that when the lower link  54  is in the minimum lift position, the distance between the center of the upper pin  55  and the center of the lower pin  58  becomes shorter than the distance between the center of the rocker arm shaft  56  and the center of the connection shaft  59 , whereby as shown in  FIG. 6(   b ), when the intake cam  6  rotates, the amount of movement of the adjusting bolt  52   a  becomes smaller than the amount of movement of the contact point where the intake cam  6  and the roller  57  are in contact with each other. 
   For the above reason, when the lower link  54  is in the maximum lift position, the intake valve  4  is opened with a larger valve lift Liftin than when the lower link  54  is in the minimum lift position. More specifically, during rotation of the intake cam  6 , when the lower link  54  is in the maximum lift position, the intake valve  4  is opened according to a valve lift curve indicated by a solid line in  FIG. 7 , and the valve lift Liftin assumes its maximum value Liftin_H. On the other hand, when the lower link  54  is in the minimum lift position, the intake valve  4  is opened according to a valve lift curve indicated by a two-dot chain line in  FIG. 7 , and the valve lift Liftin assumes its minimum value Liftin_L. 
   As described above, in the variable valve lift mechanism  50 , the lower link  54  is pivotally moved by the lift actuator  60  between the maximum lift position and the minimum lift position, whereby it is possible to steplessly change the valve lift Liftin between the maximum value Liftin_H and the minimum value Liftin_L. 
   Further, the variable valve lift mechanism  50  is provided with a lock mechanism (not shown) which locks the operation of the variable valve lift mechanism  50  when the lift control input Uliftin is set to a failure-time value Uliftin_fs, referred to hereinafter, or when the lift control input Uliftin is not input due to a disconnection. More specifically, the variable valve lift mechanism  50  is inhibited from changing the valve lift Liftin, whereby the valve lift Liftin is held at the minimum value Liftin_L. It should be noted that when the throttle valve opening TH is held at the aforementioned minimum value TH_L, the minimum value Liftin_L is set to such a value as will ensure the aforementioned failure-time intake air amount. 
   The engine  3  is provided with a pivot angle sensor  26  (valve lift detecting means) (see  FIG. 2 ). The pivot angle sensor  26  detects a pivot angle θ lift of the short arm  65  and delivers a signal indicative of the detected pivot angle of the short arm  65  to the ECU  2 . The pivot angle θ lift of the short arm  65  indicates a position of the short arm  65  between the maximum lift and the minimum lift. The ECU  2  calculates the valve lift Liftin based on the pivot angle θ lift. 
   Further, as shown in  FIG. 2 , an accelerator pedal opening sensor  27  (operating condition-detecting means) delivers a signal indicative of a stepped-on amount of an accelerator pedal, not shown, of the vehicle (hereinafter referred to as “the accelerator pedal opening”) AP to the ECU  2 , and an electric current sensor  28  delivers a detection signal indicative of the value of electric current actually flowing through the motor  61  of the lift actuator  60  (hereinafter referred to as “the current value”) Imot to the ECU  2 . 
   Next, as shown in  FIG. 2 , the vehicle is provided with an ignition switch (hereinafter referred to as “the IG•SW”)  29 . The IG•SW  29  is turned on or off by the operation of an ignition key, not shown, and delivers a signal indicative of the ON/OFF state thereof to the ECU  2 . 
   The ECU  2  is implemented by a microcomputer including a CPU, a RAM b, a ROM, and an I/O interface circuit (neither of which is shown), and the RAM maintains data stored therein by a backup power supply even after the IG•SW  29  is turned off. The ECU  2  determines operating conditions of the engine  3 , based on the detection signals delivered from the above-mentioned sensors and switch  20  to  29 , and the like, and controls the valve lift Liftin and the throttle valve opening TH to thereby control the intake air amount. It should be noted that in the present embodiment, the ECU  2  forms the operating condition-detecting means, abutment determination means, control means, valve lift-detecting means, target valve lift-determining means, control input-calculating means, disturbance suppression parameter-setting means, and hold determination means. 
   It should be noted that the control of the above intake air amount is executed mainly by the valve lift Liftin when the engine  3  is in a low-to-high load operating condition. Further, during a very low-to-low load operating condition, the intake air amount is inherently small, and hence it is required to control the intake air amount in a fine-grained manner. Therefore, the control of the intake air amount is executed by controlling the throttle valve opening TH in a state where the valve lift Liftin is held at the minimum value Liftin_L. 
   Next, referring to  FIG. 8 , a description will be given of a process including the above-mentioned control of the intake air amount, which is executed by the ECU  2 . The present process is executed whenever a predetermined control period ΔT (e.g. 5 msec) elapses. First, in a step  1 , an overcurrent determination process is executed. This process determines whether the motor  61  of the lift actuator motor  60  is in an overcurrent state, i.e. in a excessively loaded state, due to undesired fixture or failure of a movable part of the variable valve lift mechanism  50 . Then, depending on the result of the overcurrent determination process, an intake air amount control process is executed (step  2 ), followed by terminating the present process. 
   Next, a description will be given of the aforementioned overcurrent determination process, with reference to  FIG. 9 . First, in a step  10 , it is determined whether or not the second overcurrent determination flag F_Imot_emg 2  is equal to 1. If the answer to this question is negative (NO), it is determined whether or not the current value Imot is not less than an upper limit value Imot_max (step  11 ). 
   If the answer to this question is negative (NO), i.e. if Imot&lt;Imot_max holds, it is judged that the lift actuator  60  is not in the overcurrent/overloaded state, a cumulative value Simot is set to a value of 0 (step  12 ), followed by terminating the present process. 
   On the other hand, if the answer to the question of the step S 11  is affirmative (YES), i.e. Imot≧Imot_max holds, the cumulative value Simot is calculated by the following equation (1) (step  13 ), and is stored in the RAM. 
   
     
       
         
           
             
               
                 
                   SImot 
                   ⁡ 
                   
                     ( 
                     k 
                     ) 
                   
                 
                 = 
                 
                   
                     SImot 
                     ⁡ 
                     
                       ( 
                       
                         K 
                         - 
                         1 
                       
                       ) 
                     
                   
                   + 
                   
                     
                       Imot 
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     · 
                     Stime 
                   
                 
               
             
             
               
                 ( 
                 1 
                 ) 
               
             
           
         
       
     
   
   In the equation (1), Stime represents a sampling period, which in the present case is equal to the control period ΔT. Each discrete data with a symbol (k) represents data sampled (or calculated) in synchronism with the control period ΔT. The symbol k represents a position in the sequence of sampling cycles of discrete data. For example, the symbol k indicates that discrete data therewith is a value sampled in the current control timing, and a symbol k−1 indicates that discrete data therewith is a value sampled in the immediately preceding control timing. This also applies to the following discrete data. It should be noted that in the following description, the symbol k and the like provided for the discrete data are omitted as deemed appropriate. 
   As shown in the equation (1), the cumulative value SImot is calculated by cumulative calculation of the product of the current value Imot and the sampling period Stime. In this case, the current value Imot is in proportional relationship with the torque of the motor  61  of the lift actuator  60 , i.e. load thereon, and hence the cumulative value Simot represents the magnitude of load on the lift actuator  60  and its duration. 
   Next, it is determined whether or not the cumulative value SImot is not less than a first predetermined reference value Simot_J 1  (step  14 ). The first predetermined reference value Simot_J 1  is a threshold value with reference to which it is determined whether or not the lift actuator  60  is in a condition close to the overcurrent/overloaded state. If the answer to this question is negative (NO), the present process is immediately terminated, whereas if the answer to the question of the step  14  is affirmative (YES), i.e. if Simot≧Simot_J 1  holds, it is judged that the lift actuator  60  is in a condition close to the overcurrent/overloaded state, to indicate the above condition of the lift actuator  60 , the first overcurrent determination flag F_Imot_emg 1  is set to 1 (step  15 ), and is stored in the RAM. 
   Next, it is determined whether or not the cumulative value Simot is not less than a second predetermined reference value Simot_J 2  (step  16 ). The second predetermined reference value Simot_J 2  is a threshold value with reference to which it is determined whether or not the lift actuator  60  is in the overcurrent/overloaded state, i.e. whether or not the variable valve lift mechanism  50  is faulty, and is set to a value more than the first predetermined reference value Simot_J 1 . 
   If the answer to the question of the step  16  is negative (NO), the present process is immediately terminated, whereas if the answer to the question of the step  16  is affirmative (YES), i.e. if Simot≧Simot_J 2  holds, it is judged that the lift actuator  60  is in the overcurrent/overloaded state, and the variable valve lift  50  is faulty, to indicate the fact, the second overcurrent determination flag F_Imot_emg 2  is set to a value of 1 and is stored in the RAM (step  17 ), followed by terminating the present process. 
   When the second overcurrent determination flag F_Imot_emg 2  is set to 1, as described above, the answer to the question of the step  10  becomes affirmative (YES), and hence it is determined whether or not a reset flag F_RESET is equal to 1 (step  18 ). The reset flag F_RESET is set to 1 in a predetermined determination process when a predetermined reset condition is satisfied. More specifically, when a reset operation is executed by an external diagnosis apparatus or a battery canceling operation is executed, during maintenance, it is determined the predetermined reset condition is satisfied, so that the reset flag F_RESET is set to 1. 
   If the answer to the question of the step  18  is negative (NO), the present process is immediately terminated, whereas if the answer to the question of the step  18  is affirmative (YES), the cumulative value Simot is set to a value of 0, and the two flags F_Imot_emg 1  and F_Imot_emg 2  are both reset to 0 (step  19 ), followed by executing the step  11  et seq. 
   Next, the intake air amount control process in the step  2  in  FIG. 8  will be described with reference to  FIG. 10 . The present process is executed for calculating the lift control input Uliftin and the throttle control input Uth so as to control the intake air amount. First, it is determined whether or not an engine start flag F_ENGSTART is equal to 1. The engine start flag F_ENGSTART is set to 1 when it is determined in a determination process, according to the engine speed NE and the output of the IG•SW  29 , that the engine is being started, i.e. being cranked. 
   If the answer to the question of the step  30  is affirmative (YES), i.e. if the engine starting control is being executed, a start-time value Gcyl_cmd_crk of the target intake air amount is calculated by searching a table shown in  FIG. 11  according to the engine coolant temperature TW (step  31 ). As shown in the figure, in this table, the start-time value Gcyl_cmd_crk of the target intake air amount is set to a larger value as the engine coolant temperature TW is lower. This is because as the engine coolant temperature TW is lower, the friction of the engine is larger, and the engine  3  is more difficult to start, and hence it is required to increase the intake air amount. 
   Subsequently, the target intake air amount Gcyl_cmd is set to the start-time value Gcyl_cmd_crk (step  32 ). Next, as described hereinafter, a valve lift control process is executed (step  33 ), and a throttle control process is executed (step  34 ), followed by terminating the present process. 
   On the other hand, if the answer to the question of the step  30  is negative (NO), i.e. if the engine starting control is not being executed, it is determined whether or not the accelerator opening AP is smaller than a predetermined value APREF (step  35 ). If the answer to the question is affirmative (YES), i.e. if the accelerator pedal is not stepped on, it is determined whether or not a timer value Tcat of a catalyst warmup timer is smaller than a predetermined value Tcatlmt (step  36 ). This catalyst warmup timer counts time over which the catalyst warmup control is being executed, and is formed by an upcount timer. It should be noted that the catalyst warmup control process is executed for activating a catalyst, not shown, disposed in an exhaust pipe, not shown, for reducing emissions from the engine  3 . 
   If the answer to the question of the step  36  is affirmative (YES), if Tcat&lt;Tcatlmt holds, i.e. during execution of the catalyst warmup control, by searching a map shown in  FIG. 12  according to the timer value Tcat of the catalyst warmup timer and the engine coolant temperature TW, a catalyst warmup control value Gcyl_cmd_ast of the target intake air amount is calculated (step  37 ). In the figure, TW 1  to TW 3  represent predetermined values of the engine coolant temperature TW set such that the relationship of TW 1 &lt;TW 2 &lt;TW 3  holds. It should be noted that the catalyst warmup control value Gcyl_cmd_ast of the target intake air amount is calculated by interpolation, when the engine coolant temperature TW is equal to a value other than the first to third predetermined values TW 1  to TW 3 . 
   Further, the catalyst warmup value Gcyl_cmd_ast of the target intake air amount is set to a larger value as the engine coolant temperature TW is lower. This is because as the engine coolant temperature TW is lower, it inherently takes a longer time period to activate the catalyst, and hence the volume of exhaust gasses is increased to shorten the time period required for activating the catalyst. Furthermore, in the above map, in a region where the timer value Tcat of the catalyst warmup timer is small, the catalyst warmup value Gcyl_cmd_ast of the target intake air amount is set to a larger value as the timer value Tcat is larger, and in a region where the timer value Tcat is large, the catalyst warmup value Gcyl_cmd_ast is set to a smaller value as the timer value Tcat is larger. This is because as the time over which the catalyst warmup control is executed becomes longer, the warming up of the engine  3  proceeds to reduce the friction, so that in such a case, unless the target intake air amount Gcyl_cmd is reduced, the ignition timing is excessively retarded so as to hold the engine speed NE at a target value, which makes unstable the combustion state of the engine. 
   Then, the target intake air amount Gcyl_cmd is set to the above catalyst warmup value Gcyl_cmd_ast (step  38 ), and then, the aforementioned step  33  et seq. are carried out. 
   On the other hand, if the answer to the question of the step  35  or the step  36  is negative (NO), i.e. if the accelerator pedal is stepped on or if Tcat≧Tcatlmt holds, a normal operation value Gcyl_cmd_drv of the target intake air amount is calculated by searching a map shown in  FIG. 13  according to the engine speed NE and the accelerator pedal opening AP (step  39 ). In  FIG. 13 , AP 1  to AP 3  represent first to third predetermined values (AP 1 &gt;AP 2 &gt;AP 3 ) of the accelerator pedal opening AP. It should be noted that the normal operation value Gcyl_cmd_drv of the target intake air amount is calculated by interpolation, when the accelerator pedal opening AP is equal to a value other than the first to third predetermined values AP 1  to AP 3 . 
   In this map, the normal operation value Gcyl_cmd_drv of the target intake air amount is set to a larger value as the engine speed NE is higher or as the accelerator pedal opening AP is larger. This is because as the engine speed NE is higher or as the accelerator pedal opening AP is larger, the load on the engine  3  is higher, and hence a larger intake air amount is required. 
   Subsequently, the target intake air amount Gcyl_cmd is set to the normal operation value Gcyl_cmd_drv (step  40 ) and thereafter, the aforementioned step  33  et seq. are executed. 
   Next, the valve lift control process in the step  33  in  FIG. 10  will be described with reference to  FIG. 14 . This process is for calculating the aforementioned lift control input Uliftin for controlling the variable valve lift mechanism  50 . First, in a step  50 , a target valve lift Liftin_cmd as a target value of the valve lift Liftin is calculated by searing a map shown in  FIG. 15  according to the engine speed NE, and the target intake air amount Gcyl_cmd set in the step  32 ,  38  or  40 . In this map, Gcyl_cmd 1  to Gcyl_cmd 3  represent first to third predetermined values (Gcyl_cmd 1 &lt;Gcyl_cmd 2 &lt;Gcyl_cmd 3 ) of the target intake air amount Gcyl_cmd. It should be noted that the target valve lift Liftin_cmd is determined by interpolation when the target intake air amount Gcyl_cmd is equal to a value other than the first to third predetermined values Gcyl_cmd 1  to Gcyl_cmd 3 . 
   Further, in this map, the target valve lift Liftin_cmd is set to a larger value as the engine speed NE is higher, or as the target intake air amount Gcyl_cmd is larger. This is because as the engine speed NE is higher, or as the target intake air amount Gcyl_cmd is larger, the output required of the engine  3  is larger, and hence a larger intake air amount is required. Further, when the target intake air amount Gcyl_cmd is equal to the first predetermined value Gcyl_cmd 1 , and at the same time, the engine speed NE is equal to a predetermined value NEREF (e.g. 1100 rpm), the target valve lift Liftin_cmd is set to a predetermined value Liftin_stb slightly larger than the aforementioned minimum value Liftin_L of the valve lift Liftin. Further, when Gcyl_cmd=Gcyl_cmd 1  and NE&lt;NEREF holds, that is, when the engine  3  is in the very low-to-low load operating condition, the target valve lift Liftin_cmd is set to a value slightly smaller than the minimum value Liftin_L. This is to cause the short arm  65  to be positively brought into the minimum lift stopper  67   a  to thereby positively hold the valve lift Liftin at the minimum value Liftin_L when the engine  3  is in the very low-to-low load operating condition, irrespective of the differences between individual products of the short arm  65  and the minimum lift stoppers  67   a  manufactured by mass production or aging of the same. 
   Then, it is determined whether or not the aforementioned second overcurrent flag F_Imot_emg 2  is equal to 1 (step  51 ). If the answer to the question of the step  51  is affirmative (YES), i.e. if the variable valve lift mechanism  50  is faulty, the lift control input U_Liftin is set to the predetermined failure-time value U_Liftin_fs (step  52 ), followed by terminating the present process. As a result, as described above, the valve lift Liftin is held at the minimum value Liftin_L, whereby it is possible to suitably carry out idling or starting of the engine  3  during stoppage of the vehicle, and at the same time maintain the low-speed traveling state during travel of the vehicle. 
   On the other hand, if the answer to the question of the step  51  is negative (NO), i.e. if F_Imot_emg 2 =0 holds, in other words, if the variable valve lift mechanism is normal, an abutment determination process, described hereinafter, is executed (step  53 ), and the lift control input Uliftin is calculated (step  54 ), followed by terminating the present process. 
   The calculation of the lift control input Uliftin is executed based on the valve lift Liftin and the target valve lift Liftin_cmd calculated in the step  50  with a target value filter-type two-degree-of-freedom sliding mode control algorithm represented by the following equations (2) to (8). That is, the lift control input Uliftin is calculated as a value for causing the valve lift Liftin to follow up and converge to the target valve lift Liftin_cmd. 
   
     
       
         
           
             
               
                 
                     
                 
                 ⁢ 
                 
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                           i 
                           = 
                           0 
                         
                         k 
                       
                       ⁢ 
                       
                         σ_lf 
                         ⁢ 
                         
                           ( 
                           i 
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 ( 
                 8 
                 ) 
               
             
           
         
       
     
   
   In the control algorithm, first, a filtered value Liftin_cmd_f of the target valve lift is calculated with a target value filter algorithm, i.e. a first-order lag filter algorithm expressed by the equation (2). In the equation (2), POLE_f_lf represents a target value filter-setting parameter which is set, in the abutment determination process in the step  53 , to a value which satisfies the relationship of −1&lt;POLE_f_lf&lt;0. 
   Next, the Lift control input Uliftin is calculated with a sliding mode control algorithm expressed by the equations (3) to (8). That is, as shown in the equation (3), the Lift control input Uliftin is calculated as the sum of an equivalent control input Ueq_lf, a reaching law input Urch_lf, and an adaptive law input Uadp_lf. 
   The equivalent control input Ueq_lf is calculated by the equation (4). In the equation (4), a1_lf, a2_lf, b1_lf, and b2_lf represent model parameters of a plant model expressed by an equation (9), referred to hereinafter, which are set to respective predetermined values. Further, POLE_lf is a switching function-setting parameter (disturbance suppression parameter), and is set, in the abutment determination process, to a value satisfying the relationship of −1&lt;POLE_lf&lt;0. 
   Further, the reaching law input Urch_lf is calculated by the equation (5). In the equation (5), Krch_lf represents a predetermined reaching law gain. The symbol σ_lf represents a switching function defined as in the equation (6). E_lf in the equation (6) is a follow-up error calculated by the equation (7). Further, the adaptive law input Uadp_lf is calculated by the equation (8). In the equation (8), Kadp_lf represents a predetermined reaching law gain. 
   The above equations (2) to (8) are derived as follows: A plant is defined as a system to which is inputted the lift control input Uliftin and from which is outputted the valve lift Liftin as the controlled variable, and is a modeled into a discrete-time system model, whereby the following equation (9) is obtained. 
   When the target value filter-type two-degree-of-freedom sliding mode control theory is applied to the model defined by the equation (9) such that the valve lift Liftin follows up and converges to the target valve lift Liftin_cmd, the aforementioned equations (2) to (8) are derived. 
   
     
       
         
           
             
               
                 [ 
                 
                   Math 
                   . 
                   
                       
                   
                   ⁢ 
                   2 
                 
                 ] 
               
             
             
               
                   
               
             
           
           
             
               
                 
                   Liftin 
                   ⁡ 
                   
                     ( 
                     
                       k 
                       + 
                       1 
                     
                     ) 
                   
                 
                 = 
                 
                   
                     a 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                     ⁢ 
                     
                       _lf 
                       · 
                       
                         Liftin 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                     
                   
                   + 
                   
                     a 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                     ⁢ 
                     
                       _lf 
                       · 
                       
                         Liftin 
                         ⁡ 
                         
                           ( 
                           
                             k 
                             - 
                             1 
                           
                           ) 
                         
                       
                     
                   
                   + 
                   
                     b 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                     ⁢ 
                     
                       _lf 
                       · 
                       
                         Uliftin 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                     
                   
                   + 
                   
                     b 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                     ⁢ 
                     
                       _lf 
                       · 
                       
                         Uliftin 
                         ⁡ 
                         
                           ( 
                           
                             k 
                             - 
                             1 
                           
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 ( 
                 9 
                 ) 
               
             
           
         
       
     
   
   In the aforementioned target value filter-type two-degree-of-freedom sliding mode control algorithm has the following characteristics: By changing the target filter-setting parameter POLE_f_lf within a range of −1&lt;POLE_f_lf&lt;0, the follow-up speed of the filtered value Liftin_cmd_f of the target valve lift to the target valve lift Liftin_cmd, i.e. the follow-up seeped of the valve lift Liftin to the target valve lift Liftin_cmd is changed. More specifically, the follow-up speed becomes lower as the target value filter-setting parameter POLE_f_lf is closer to a value of −1. Therefore, by setting the target value filter-setting parameter POLE_f_lf to a value closer to a value of −1, the lift control input Uliftin for causing the valve lift Liftin to follow up the target valve lift Liftin_cmd becomes smaller, so that the current value Imot becomes smaller, and the driving force applied to the short arm  65  for causing the valve lift Liftin to the target valve lift Liftin_cmd becomes smaller. 
   Further, by changing the switching function-setting parameter POLE_lf within the range of −1&lt;POLE_lf&lt;0, the follow-up speed and the follow-up behavior of the follow-up error E_lf to a value of 0, i.e. the follow-up speed and the follow-up behavior of the valve lift Liftin to the target valve lift Liftin_cmd is changed. In other words, the degree of suppression of influence of disturbance applied to the lift actuator  60  (hereinafter simply referred to as “the disturbance suppression degree”) is changed. More specifically, as the switching function-setting parameter POLE_lf is closer to a value of −1, the occurrence of a larger follow-up error E_lf is permitted, which causes reduction of the disturbance suppression degree. Therefore, by setting the switching function-setting parameter POLE_lf to a value closer to a value of −1, the lift control input Uliftin calculated when the follow-up error E_lf has occurred becomes smaller. As a result, the current value Imot becomes smaller, and the driving force applied to the short arm  65  for causing the valve lift Liftin to follow up the target valve lift Liftin_cmd becomes smaller. 
   Next, the abutment determination process in the step  53  in  FIG. 14  will be described with reference to  FIG. 16 . The present process determines whether or not the short arm  65  of the variable valve lift mechanism  50  is in abutment with the minimum lift stopper  67   a , and sets, according to the result of the determination, the switching function-setting parameter POLE_lf and the target value filter-setting parameter POLE_f_lf. 
   First, in a step  60 , a determination parameter WVliftin is calculated. The determination parameter WVliftin is used for determining whether or not the short arm  65  is in abutment with the minimum lift stopper  67   a , and is calculated based on a lift difference DL(k) by a determination parameter-calculating section  70  shown in  FIG. 17 . The lift difference DL(k) represents the difference (=Liftin(k)−Liftin(k−1)) between the present value Liftin(k) and the immediately preceding value Liftin(k−1) of the valve lift. It should be noted that the determination parameter-calculating section  70  is formed by the ECU  2 . 
   The determination parameter-calculating section  70  includes a first filter  71 , a first downsampler  72 , a second filter  73 , and a second downsampler  74 . 
   The first filter  71  is a low-pass filter which has a gain characteristic and a phase characteristic as shown in  FIG. 18 , and samples and filters the lift difference DL(k) whenever the aforementioned control period ΔT elapses, thereby generating a first filtered value DLf(k) to deliver the same to the first downsampler  72 . More specifically, out of the lift difference DL(k), components in a frequency region not lower than a predetermined first frequency ω corresponding to ½ of the sampling frequency of the lift difference DL(k) are removed. Further, a gain for components of the lift difference DL(k) in a low frequency region LωA not higher than a predetermined frequency ω ref lower than the first frequency ω is set to a predetermined value GREF larger than a value of 1, whereby the components in the low frequency region LωA are amplified. It should be noted that the first filter value DLf(k) is calculated (generated) by the following equation (10):
 
 DLf ( k )=α· DL ( k )+α· DL ( k− 1)  (10)
 
   wherein α represents a predetermined value (e.g. 0.7071). 
   The first downsampler  72  thins out the first filtered value DLf(k) input thereto at the control period ΔT by sampling every second value thereof, and delivers the sampled first filtered value DLf(m) to the second filter  73 . 
   The second filter  73  is configured substantially in the same manner as the first filter  70 , and generates a second filtered value DLf′(m) by filtering the first filtered value DLf(m) input thereto to deliver the same to the second downsampler  74 . More specifically, the second filter  73  removes from the first filtered value DLf(m) components thereof in a frequency region not lower than half the frequency corresponding to the repetition period of input of the first filtered value DLf(m), i.e. a predetermined second frequency ω/2 which is equal to half the first frequency ω. Further, a gain for components of the first filtered value DLf(m) in a low frequency region not higher than a predetermined frequency lower than the second frequency ω/2 is set to a predetermined value larger than a value of 1, whereby the components in this low frequency region are amplified. It should be noted that the second filtered value DLf′(m) is calculated (generated) by the following equation (11):
 
 DLf′ ( m )=α· DLf ( m )+α· DLf ( m− 1)  (11)
 
   The second downsampler  74  thins out the second filtered value DLf′(m) input thereto by sampling every second value thereof, and outputs the thinned value as a determination parameter WVliftin(k). 
   As described above, the determination parameter WVliftin is calculated (generated) by repeatedly carrying out the above-described filtering and thinning processes on the lift difference DL. With this configuration, the determination parameter WVliftin is calculated such that noise contained in components in the high frequency region is removed, and components in the lower frequency region of the lift difference DL are amplified, whereby it is obtained as a value improved in the SN ratio of the lift difference DL. Further, the aforementioned filtering process has a differentiation-like function, and hence the determination parameter WVliftin calculated as described above represents a differential value of the rate of change of the valve lift Liftin, i.e. an acceleration of the short arm  65  performing the pivotal motion. 
   Referring to  FIG. 16 , in a step  61  following the step  60 , it is determined whether or not the valve lift Liftin, and the target valve lift Liftin_cmd calculated in the step  50  in  FIG. 14  are both not higher than the aforementioned predetermined value Liftin_stb. 
   If the answer to this question is negative (NO), in steps  62 ,  63 , and  64 , a low lift flag F_lowlift, a hold flag F_pressmod, and an abutment start flag F_contmod are reset to 0. Then, it is determined whether or not the first overcurrent determination flag F_Imot_emg 1  set in the step  15  in  FIG. 9  is equal to 1 (step  65 ). 
   If the answer to this question is negative (NO), the switching function-setting parameter POLE_lf and the target filter-setting parameter POLE_f_lf are set to predetermined normal-time values POLE_base and POLE_f_base (e.g. −0.4 and −0.9, respectively) (step  66 ), followed by terminating the present process. 
   On the other hand, if the answer to the question of the step  65  is affirmative (YES), which means F_Imot_emg 1 =1 holds, i.e. if the lift actuator  60  is in a state close to the overcurrent and overload condition, the switching function-setting parameter POLE_lf and the target filter-setting parameter POLE_f_lf are set to predetermined overcurrent-time values POLE_imot and POLE_f_imot (step  67 ), followed by terminating the present process. 
   The overcurrent-time value POLE_imot is set to a value closer to a value of −1 than the normal-time value POLE_base (−1&lt;POLE_imot&lt;POLE_base), and is equal to e.g. −0.8. Further, the overcurrent-time value POLE_f_imot of the target value filter-setting parameter is set to a value closer to a value of −1 than the normal-time value POLE_f_base (−1&lt;POLE_f_imot&lt;POLE_f_base), and is equal to e.g. −0.95. The overcurrent-time value POLE_f_imot is thus set because as the switching function-setting parameter POLE_lf and the target filter-setting parameter POLE_f_lf are closer to a value of −1, the current value Imot becomes smaller, and therefor to make use of this to thereby prevent the lift actuator  60  from entering the overcurrent/overloaded state. 
   On the other hand, if the answer to the question of the step  61  is affirmative (YES), i.e. if the valve lift Liftin and the target valve lift Liftin_cmd are both not higher than the predetermined value Liftin_stb, which means they are very small, in the following step  68  et seq., it is determined whether or not the short arm  65  is abutment with the minimum lift stopper  67   a . First, in the step  68 , assuming that the valve lift Liftin is set toward the low lift side, to indicate this, the low lift flag F_lowlift is set to 1. 
   Next, in steps  69  and  70 , it is determined whether or not the hold flag F_pressmod and the abutment start flag F_contmod are equal to 1, respectively. If both of the answers to these questions are negative (NO), it is determined whether or not the determination parameter WVliftin calculated in the step  60  is not higher than a predetermined first reference value WVcol 1  (e.g. −3) (step  71 ). 
   If the answer to this question is negative (NO), the step  63  et seq. are executed. On the other hand, if the answer to the question of the step  71  is affirmative (YES), i.e. if the determination parameter WVliftin becomes not larger than the first reference value WVcol 1 , it is determined that the short arm  66  has begun to abut against the minimum lift stopper  67   a . The determination is thus made because since the determination parameter WVliftin represents the acceleration of the short arm  65  performing pivotal motion, and hence satisfaction of the relationship of WVliftin≦WVcol 1  makes it possible to presume that the short arm  65  has begun to abut against the minimum lift stopper  67   a , which has caused reduction of the acceleration of the short arm  65 . Next, to indicate that the short arm  65  has begun to abut against the minimum lift stopper  67   a , the abutment start flag F_contmod is set to 1 (step  72 ). Next, in response to the determination, the switching function-setting parameter POLE_lf and the target value filter-setting parameter POLE_f_lf are set to respective predetermined abutment start-time values POLE_low and POLE_f_low (step  73 ), followed by terminating the present process. 
   The abutment start-time value POLE_low is set to a value close to a value of −1 than the aforementioned overcurrent-time value POLE_imot (−1&lt;POLE_low&lt;POLE_imot&lt;POLE_base), and is equal to e.g. −0.99. Further, the abutment start-time value POLE_f_low of the target value filter-setting parameter is set to a value closer to a value of −1 than the aforementioned overcurrent-time value POLE_f_imot (−1&lt;POLE_f_low&lt;POLE_f_imot&lt;POLE_f_base), and is equal to e.g. −0.97. 
   When the abutment start flag F_contmod is set to 1 in the step  72 , the answer to the question of the step  70  becomes affirmative (YES), and in this case, it is determined whether or not the determination parameter WVliftin is not lower than a second reference value WVcol 2  (e.g. −3) (step  74 ). 
   If the answer to this question is negative (NO), the step  72  et seq. are executed. On the other hand, if the answer to this question is affirmative (YES), which means that the determination parameter WVliftin becomes not lower than the second reference value WVcol 2 , i.e. the determination parameter having become not higher than the first reference value WVcol 1  becomes not lower than the second reference value WVcol 2 , it is determined that the acceleration of the short arm  65  has passed its peak and the abutting motion of the short arm  65  against the minimum lift stopper  67   a  is terminated whereby the valve lift Liftin is held at the minimum value Liftin_L. Then, to indicate this, the hold flag F_pressmod is set to 1 (step  75 ). Next, the step  64  et seq. are executed. Further, when the hold flag F_pressmod is set to 1 in the step  75 , the answer to the question of the step  69  becomes affirmative (YES), and in this case, the step  64  et seq. are executed. 
     FIG. 20  shows an example of the operation of the system during the execution of the aforementioned abutment determination process. This example shows an operation of the system in the case the where the first and second reference values WVcol 1  and WVclo 2  are set to the same value, and the valve lift Liftin is controlled such that it is changed from the state converged to the target valve lift Liftin_cmd to the minimum value Liftin_L in accordance with reduction of the target valve lift Liftin_cmd. 
   As shown in  FIG. 20 , when the target valve lift Liftin_cmd begins to be reduced (time point t 1 ), the valve lift Liftin is reduced such that it converges to the target valve lift Liftin_cmd. Then, when the valve lift Liftin becomes close to the minimum value Liftin_L, the determination parameter WVliftin begins to drop suddenly. Further, when the valve lift Liftin is reduced to the minimum value Liftin_L and the short arm  65  has begun to abut against the minimum lift stopper  67   a , the determination parameter WVliftin becomes lower than the first reference value WVcol 1  (time point t 2 ). Therefore, when WVliftin≦WVcol 1  holds (Yes to the step  71 ), it can be determined that the short arm  65  has begun to abut against the minimum lift stopper  67   a . Further, in accordance therewith, the switching function-setting parameter POLE_lf having been set to the normal-time value POLE_base is set to the abutment start-time value POLE_low closer to a value of −1 (step  73 ). 
   Further, when the abutting motion of the short arm  65  against the minimum lift stopper  67   a  is terminated, whereby the valve lift Liftin is held at the minimum value Liftin_L, the determination parameter WVliftin increases from the reduced state to become larger than the second reference value WVcol 2  (time point t 3 ). Therefore, when the determination parameter WVliftin becomes not larger than the first reference value WVcol 1  and then becomes not smaller than the second reference value WVcol  2  (Yet to the step  74 ), it can be determined that the valve lift Liftin is held at the minimum lift value Liftin_L. Further, in accordance therewith, the switching function-setting parameter POLE_lf having been set to the abutment start-time value POLE_low is set to the normal-time value POLE_base (step  66 ). 
   As described hereinabove, according to the abutment determination process, when the valve lift Liftin is larger than the predetermined value Liftin_stb (NO to the step  61 ), i.e. when the intake air amount is to be controlled mainly by the valve lift Liftin without holding the valve lift Liftin at the minimum value Liftin_L, the switching function-setting parameter POLE_lf and the target value filter-setting parameter POLE_f_lf are set to the respective normal-time values POLE_base and POLE_f_base which are close to a value of 0 (step  66 ), whereby an excellent follow-up characteristic of the valve lift Liftin to the target valve lift Liftin_cmd is ensured. 
   Further, when it is determined that the short arm  65  has begun to abut against the minimum lift stopper  67   a  (YES to the step  71 ), the switching function-setting parameter POLE_lf and the target value filter-setting parameter POLE_f_lf are set to the respective start-time values POLE_low and POLE_f_low (step  73 ). 
   As described hereinabove, the start-time values POLE_low and POLE_f_low are set to respective values closer to a value of −1 than the normal-time values POLE_base and POLE_f_base. From this, when the short arm  65  has begun to abut against the minimum lift stopper  67   a , as is apparent from the characteristic of the aforementioned target filter-type two-degree-of-freedom sliding mode control algorithm, the driving force applied to the short arm  65  for causing the valve lift Liftin to follow up the target valve lift Liftin_cmd can be reduced. As a result, it is possible to reduce impact occurring when the short arm  65  abuts against the minimum lift stopper  67   a , and therefore prevent the short arm  65  and the minimum lift stopper  67   a  from being deformed, and hence to prolong the service life of the variable valve lift mechanism  50 . 
   Further, the driving force applied to the short arm  65  can be secured until the short arm  65  abuts against the minimum lift stopper  67   a , it is possible to control the intake air amount to a proper value quickly without lowering the follow-up speed of the valve lift Liftin to the target valve lift Liftin_cmd. As a result, it is possible to secure a stable operating condition of the engine  3 , to thereby secure excellent drivability. Further, it is not required to additionally provide the short arm  65  and the minimum lift stopper  67   a  with cushioning members, which makes it possible to prevent the intake air amount from being varied due to variations in the valve lift Liftin at the minimum value Liftin_L, differently from the case of the cushion members being provided, and prevent the addition of the cushioning members from increasing the manufacturing cost or reducing the degree of freedom of design. 
   Further, after it is determined that the short arm  65  has abutted against the minimum lift stopper  67   a , when it is determined that the valve lift Liftin is held at the minimum value Liftin_L (YES to the step  74 ), the switching function-setting parameter POLE_lf and the target filter-setting parameter POLE_f_lf are set to the respective normal-time values POLE_base and POLE_f_base (step  66 ). This causes an increase in the driving force applied to the short arm  65  for causing the valve lift Liftin to follow up the target valve lift Liftin_cmd, i.e. the force for holding the valve lift Liftin at the minimum value Liftin_L. As a result, after abutting against the minimum lift stopper  67   a , the short arm  65  can be positively held in the state in abutment with the minimum lift stopper  67   a  without being moved away from the minimum lift stopper  67   a  by the vibration of the engine  3  or the like. 
   Further, during a time period from the start of abutment of the short arm  65  against the minimum lift stopper  67   a  to the end thereof, the target valve lift Liftin_cmd is set to a larger value than the predetermined value Liftin_stb, and when the valve lift Liftin is caused to increase, the answer to the question of the step  61  becomes negative (NO), so that the step  66  is executed. As a result, when the switching function-setting parameter POLE_lf and the target value filter-setting parameter POLE_f_lf are set to the respective normal-time values POLE_base and POLE_f_base. 
   This makes it possible, as described hereinabove, to instantly increase the driving force applied to the short arm  65  from the state reduced hitherto, when the valve lift Liftin is increased e.g. by a driver&#39;s demand of acceleration immediately after the short arm  65  has begun to abut against the minimum lift stopper  67   a . As a result, it is possible to improve the follow-up characteristic of the valve lift Liftin to the target valve lift Liftin_cmd, and hence increase the intake air amount to a suitable value quickly. Therefore, it is possible to secure excellent drivability. 
   Further, since the abutment determination is performed using the determination parameter WVliftin representative of the acceleration of the short arm  65  which varies according to the actual abutment state of the short arm  65  against the minimum lift stopper  67   a , the determination can be performed with accuracy without being influenced by differences between individual products of the short arm  65  and the minimum lift stopper  67   a  and wear caused by aging thereof, differently from the case where the determination is carried out based on the position of the short arm  65  directly detected by a sensor or the like. Further, as described hereinabove, since the determination parameter WVliftin is obtained as a value improved in the SN ratio of the lift difference DL, it is possible to carry out the abutment determination even more accurately while suppressing influence of nose contained in the lift difference DL. 
   Next, the throttle control process in the step  34  in  FIG. 10  will be described with reference to  FIG. 21 . First, in a step  80 , it is determined whether or not any of the abutment start flag F_contmod, the hold flag F_pressmod, and the second overcurrent determination flag F_Imot_emg 2 , mentioned above, is equal to 1. 
   If the answer to this question is negative (NO), i.e. if all of the abutment start flag F_contmod, the hold flag F_pressmod, and the second overcurrent determination flag F_Imot_emg 2  are equal to 0, i.e. the short arm  65  is not in contact with the minimum lift stopper  67   a  but the intake air amount control mainly based on the valve lift Liftin is being executed, a normal-time value TH_cmd_op of the target throttle valve opening is calculated by searching a map shown in  FIG. 22  according to the valve lift Liftin and the engine speed NE (step  81 ). In  FIG. 22 , NE 1  to NE 3  represent first to third predetermined values (NE 1 &gt;NE 2 &gt;NE 3 ) of the engine speed NE. It should be noted that the normal-time value TH_cmd_op is calculated by interpolation when the engine speed NE is equal to a value other than the first to third predetermined values NE 1  to NE 3 . 
   Further, in the above map, as the valve lift Liftin is larger or the engine speed NE is higher, the normal-time value TH_cmd_op is set to a larger value. This is because load on the engine  3  is higher as the valve lift Liftin is larger or the engine speed NE is higher, and hence the larger intake air amount is demanded. 
   Next, the target throttle valve opening TH_cmd is set to the normal-time value TH_cmd_op (step  82 ). Next, it is determined whether or not a throttle failure flag F_THNG is equal to 1 (step  83 ). The throttle failure flag F_THNG set to 1 in a failure determination process (not shown), when it is determined that the throttle valve mechanism  11  is faulty. 
   If the answer to the question of the step  83  is negative (NO), i.e. if the throttle valve mechanism  11  is normal, the throttle control input Uth is calculated with the target value filter-type two-degree-of-freedom sliding mode control algorithm expressed by the following equations (12) to (15), such that the throttle valve opening TH follows up and converges to the target throttle valve opening TH_cmd (step  84 ), followed by terminating the present process. 
   
     
       
         
           
             
               
                 
                     
                 
                 ⁢ 
                 
                   [ 
                   
                     Math 
                     . 
                     
                         
                     
                     ⁢ 
                     3 
                   
                   ] 
                 
               
             
             
               
                   
               
             
           
           
             
               
                 
                     
                 
                 ⁢ 
                 
                   
                     Uth 
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         - 
                         K 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         rch_th 
                         · 
                         σ_th 
                       
                       ⁢ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     - 
                     
                       Kadp_th 
                       · 
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             0 
                           
                           k 
                         
                         ⁢ 
                         
                           σ_th 
                           ⁢ 
                           
                             ( 
                             i 
                             ) 
                           
                         
                       
                     
                   
                 
               
             
             
               
                 ( 
                 12 
                 ) 
               
             
           
           
             
               
                 
                     
                 
                 ⁢ 
                 
                   
                     σ_th 
                     ⁢ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       E_th 
                       ⁢ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     + 
                     
                       
                         pole_th 
                         · 
                         E_th 
                       
                       ⁢ 
                       
                         ( 
                         
                           k 
                           - 
                           1 
                         
                         ) 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 13 
                 ) 
               
             
           
           
             
               
                 
                     
                 
                 ⁢ 
                 
                   
                     E_th 
                     ⁢ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       TH 
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     - 
                     
                       TH_cmd 
                       ⁢ 
                       _f 
                       ⁢ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 14 
                 ) 
               
             
           
           
             
               
                 
                   TH_cmd 
                   ⁢ 
                   _f 
                   ⁢ 
                   
                     ( 
                     k 
                     ) 
                   
                 
                 = 
                 
                   
                     
                       - 
                       pole_f 
                     
                     ⁢ 
                     
                       _th 
                       · 
                       TH_cmd 
                     
                     ⁢ 
                     _f 
                     ⁢ 
                     
                       ( 
                       
                         k 
                         - 
                         1 
                       
                       ) 
                     
                   
                   + 
                   
                     
                       
                         ( 
                         
                           1 
                           + 
                           
                             pole_f 
                             ⁢ 
                             _th 
                           
                         
                         ) 
                       
                       · 
                       TH_cmd 
                     
                     ⁢ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                 
               
             
             
               
                 ( 
                 15 
                 ) 
               
             
           
         
       
     
   
   In the equation (12), Krch_th represents a predetermined reaching law gain, and Kadp_th represents a predetermined adaptive law gain, while σ_th is a switching function defined as in the equation (13). Further, in the equation (13), E_th is a follow-up error calculated by the equation (14). Further, in the equation (14), TH_cmd_f is a filtered vale of the target throttle vale opening TH_cmd, and is calculate with a target value filter algorithm (first-order lag filter algorithm) expressed by the equation (15). 
   On the other hand, if the answer to the question of the step  83  is affirmative (YES), which means F_THNG=1 holds, i.e. if the throttle valve opening mechanism  11  is faulty, the throttle control input Uth is set to the aforementioned failure-time value Uth_fs (step  85 ), followed by terminating the present process. This causes the throttle valve opening TH to be held at the minimum value TH_L, as described above, whereby the idling operation or the starting of the engine can be properly carried out during stoppage of the vehicle, and during travel of the vehicle, it is possible to maintain the low-speed traveling state. 
   On the other hand, if the answer to the question of the step  80  is affirmative (YES), which means the any of the of the abutment start flag F_contmod, the hold flag F_pressmod, and the second overcurrent determination flag F_Imot_emg 2  are equal to 1, i.e. the short arm  65  has begun to abut against the minimum lift stopper  67   a  or the valve lift Liftin has been held at the minimum value Liftin_L, it is determined whether or not the accelerator opening AP and the engine speed NE are smaller than respective predetermined value AP_IDLE and NE_IDLE for determination of idling (step  86 ). 
   If the answer to this question is negative (NO), i.e. the engine  3  is in an operating condition other idling, a lift hold-time value TH_cmd_gc of the target throttle valve opening is calculated with a target value filter-type two-degree-of-freedom sliding mode control algorithm expressed by the following equations (16) to (19), such that the actual intake air amount Gcyl converges to the target intake air amount Gcyl_cmd set in the step  32 ,  38  or  40  in  FIG. 10  (step  87 ). Then, the target throttle valve opening TH_cmd is set to the lift hold-time value TH_cmd_gc (step  88 ), and then the step  83  et seq. are executed. It should be noted that the actual intake air amount Gcyl is calculated using the TH passing intake air amount Gth, the intake pipe absolute pressure PBA, and the intake air temperature TA by the following equation (20): 
   
     
       
         
           
             
               
                 
                     
                 
                 ⁢ 
                 
                   [ 
                   
                     Math 
                     . 
                     
                         
                     
                     ⁢ 
                     4 
                   
                   ] 
                 
               
             
             
               
                   
               
             
           
           
             
               
                 
                   TH_cmd 
                   ⁢ 
                   _gc 
                   ⁢ 
                   
                     ( 
                     k 
                     ) 
                   
                 
                 = 
                 
                   
                     
                       
                         - 
                         Krch_gc 
                       
                       · 
                       σ_gc 
                     
                     ⁢ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   - 
                   
                     Kadp_gc 
                     · 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           0 
                         
                         k 
                       
                       ⁢ 
                       
                         σ_gc 
                         ⁢ 
                         
                           ( 
                           i 
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 ( 
                 16 
                 ) 
               
             
           
           
             
               
                 
                     
                 
                 ⁢ 
                 
                   
                     σ_gc 
                     ⁢ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       E_gc 
                       ⁢ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     + 
                     
                       
                         pole_gc 
                         · 
                         E_gc 
                       
                       ⁢ 
                       
                         ( 
                         
                           k 
                           - 
                           1 
                         
                         ) 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 17 
                 ) 
               
             
           
           
             
               
                 
                     
                 
                 ⁢ 
                 
                   
                     E_gc 
                     ⁢ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       Gcyl 
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     - 
                     
                       Gcyl_cmd 
                       ⁢ 
                       _f 
                       ⁢ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 18 
                 ) 
               
             
           
           
             
               
                 
                   Gcyl_cmd 
                   ⁢ 
                   _f 
                   ⁢ 
                   
                     ( 
                     k 
                     ) 
                   
                 
                 = 
                 
                   
                     
                       - 
                       pole_f 
                     
                     ⁢ 
                     
                       _gc 
                       · 
                       Gcyl_cmd 
                     
                     ⁢ 
                     _f 
                     ⁢ 
                     
                       ( 
                       
                         k 
                         - 
                         1 
                       
                       ) 
                     
                   
                   + 
                   
                     
                       
                         ( 
                         
                           1 
                           + 
                           
                             pole_f 
                             ⁢ 
                             _gc 
                           
                         
                         ) 
                       
                       · 
                       Gcyl_cmd 
                     
                     ⁢ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                 
               
             
             
               
                 ( 
                 19 
                 ) 
               
             
           
           
             
               
                 
                     
                 
                 ⁢ 
                 
                   [ 
                   
                     Math 
                     . 
                     
                         
                     
                     ⁢ 
                     5 
                   
                   ] 
                 
               
             
             
               
                   
               
             
           
           
             
               
                 
                     
                 
                 ⁢ 
                 
                   
                     Gcyl 
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       Gth 
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     - 
                     
                       
                         VB 
                         · 
                         
                           [ 
                           
                             
                               P 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               B 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 A 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                             - 
                             
                               P 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               B 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 A 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     k 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           ] 
                         
                       
                       
                         R 
                         · 
                         TA 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 20 
                 ) 
               
             
           
         
       
     
   
   In this equation (20), VB represents an intake pipe internal volume, and R represents a predetermined gas constant. Further, in the above equation (16), Krch_gc represents a predetermined reaching law gain, and Kadp_gc represents a predetermined adaptive law gain, while σ_gc is a switching function defined as in the equation (17). Further, in the equation (17), E_gc is a follow-up error calculated by the equation (18). Further, in the equation (18), Gcyl_cmd_f represent a filtered value of the target intake air amount Gycl_cmd, and is calculated with a target filter algorithm (first-order lag filter algorithm) expressed by the equation (19). 
   On the other hand, if the answer to the question of the step  86  is affirmative (YES), i.e. if the engine  3  is idling, an idle-time value TH_cmd_ne of the target throttle valve opening is calculated with a target value filter-type two-degree-of-freedom sliding mode control algorithm expressed by the following equations (21) to (24) such that the engine speed NE follows up and converges to a predetermined target engine speed NE_cmd (e.g. 650 rpm) (step  89 ). Next, the target throttle valve opening TH_cmd is set to the idle-time value TH_cmd_ne (step  90 ), and then the step  83  et seq. are executed. 
   
     
       
         
           
             
               
                 
                     
                 
                 ⁢ 
                 
                   [ 
                   
                     Math 
                     . 
                     
                         
                     
                     ⁢ 
                     6 
                   
                   ] 
                 
               
             
             
               
                   
               
             
           
           
             
               
                 
                   TH_cmd 
                   ⁢ 
                   _ne 
                   ⁢ 
                   
                     ( 
                     k 
                     ) 
                   
                 
                 = 
                 
                   
                     
                       
                         - 
                         Krch_ne 
                       
                       · 
                       σ_ne 
                     
                     ⁢ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   - 
                   
                     Kadp_ne 
                     · 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           0 
                         
                         k 
                       
                       ⁢ 
                       
                         σ_ne 
                         ⁢ 
                         
                           ( 
                           i 
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 ( 
                 21 
                 ) 
               
             
           
           
             
               
                 
                     
                 
                 ⁢ 
                 
                   
                     σ_ne 
                     ⁢ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       E_ne 
                       ⁢ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     + 
                     
                       
                         pole_ne 
                         · 
                         E_ne 
                       
                       ⁢ 
                       
                         ( 
                         
                           k 
                           - 
                           1 
                         
                         ) 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 22 
                 ) 
               
             
           
           
             
               
                 
                     
                 
                 ⁢ 
                 
                   
                     E_ne 
                     ⁢ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       NE 
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     - 
                     
                       NE_cmd 
                       ⁢ 
                       _f 
                       ⁢ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 23 
                 ) 
               
             
           
           
             
               
                 
                   NE_cmd 
                   ⁢ 
                   _f 
                   ⁢ 
                   
                     ( 
                     k 
                     ) 
                   
                 
                 = 
                 
                   
                     
                       - 
                       pole_f 
                     
                     ⁢ 
                     
                       _ne 
                       · 
                       NE_cmd 
                     
                     ⁢ 
                     _f 
                     ⁢ 
                     
                       ( 
                       
                         k 
                         - 
                         1 
                       
                       ) 
                     
                   
                   + 
                   
                     
                       
                         ( 
                         
                           1 
                           + 
                           
                             pole_f 
                             ⁢ 
                             _ne 
                           
                         
                         ) 
                       
                       · 
                       NE_cmd 
                     
                     ⁢ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                 
               
             
             
               
                 ( 
                 24 
                 ) 
               
             
           
         
       
     
   
   In this equation (21), Krch_ne represents a predetermined reaching law gain, and Kadp_ne represents a predetermined adaptive law gain, while σ_ne is a switching function defined as in the equation (22). Further, in the equation (22), E_ne is a follow-up error calculated by the equation (23). Further, in the equation (23), NE_cmd_f represent a filtered value of the target engine speed NE_cmd, and is calculated with a target value filter algorithm (first-order lag filter algorithm) expressed by the equation (24). 
   As described above, when the valve lift Liftin is equal to the minimum value Liftin_L (YES to the step  80 ), the throttle valve opening TH is controlled according to the target intake air amount Gcyl_cmd calculated based on the operating condition of the engine represented by the engine speed NE and the accelerator opening AP (steps  87 ,  88 , and  84 ), whereby the intake air amount control mainly based on the throttle valve opening TH is carried out. Further, the control of the intake air amount is started immediately after it is determined that the short arm  65  has begun to abut against the minimum lift stopper  67   a  (YES to the step  80 ). This makes it possible to perform a smooth transition from the intake air amount control mainly based on the valve lift Liftin to the intake air amount control mainly based on the throttle valve opening TH, without interrupting the control. 
   Further, during execution of the intake air amount control mainly based on the valve lift Liftin (NO to the step  80 ), in parallel therewith, the throttle valve opening TH is controlled according to the valve lift Liftin (steps  81 ,  82  and  84 ). Thus, at a time point the intake air mount control mainly based on the throttle valve opening TH is started, the throttle valve opening TH has already been controlled to a value suitable for the valve lift Liftin, and hence, at this start, the throttle valve opening TH can be quickly changed to a proper value without drastically changing the same. This makes it possible to smoothly change the intake air amount, and hence the engine speed NE and the torque of the engine  3  can be smoothly changed without any step. 
   As described heretofore, according to the present embodiment, the lift control input Uliftin is calculated with the target value filter-type two-degree-of-freedom sliding mode control algorithm, and hence the target filter algorithm thereof enables the follow-up speed of the valve lift Liftin to the target valve lift Liftin_cmd to be properly set, and the feedback control algorithm thereof enables the follow-up behavior of the valve lift Liftin to the target valve lift Liftin_cmd to be properly set. This makes it possible to cause the valve lift Liftin to accurately follow up the target valve lift Liftin_cmd while avoiding the occurrence of overshooting. As a result, the impact occurring when the short arm  65  abuts against the minimum lift stopper  67   a  can be positively reduced. 
   It should be noted that the present invention is not limited to the above-described embodiment, but it can be practiced in various forms. For example, although in the present embodiment, the present invention is applied to the minimum lift stopper  67   a , by way of example, it may be applied to the maximum lift stopper  67   b . Further, the present invention may be applied to a variable valve lift mechanism including one restriction part or three or more restriction parts on the maximum side or the minimum side. For example, the present invention may be applied to one in which a retractable stopper is disposed at an intermediate location between the minimum lift stopper  67   a  and the maximum lift stopper  67   b  within the movable range of the short arm  65 . 
   Further, in the present embodiment, as the variable intake air mechanism, there is used the throttle valve mechanism  11 , this is not limitative, but the use of any other suitable mechanism is also within the scope of the resent invention insofar as it is capable of changing the intake air amount. Further, in the present embodiment, the target value filter-type two-degree-of-freedom sliding mode control algorithm is used as the predetermined control algorithm for calculating the lift control input Uliftin such that the valve lift Liftin follows up the target valve lift Liftin_cmd, by way of example, this is not limitative, but the predetermined control algorithm may be any algorithm insofar as it is capable of calculating the lift control input Uliftin such that the valve lift Liftin follows up the target valve lift Liftin_cmd. For example, a general feedback control algorithm, such as a PID control algorithm, may be employed. 
   Further, in the present embodiment, the target value filter-type two-degree-of-freedom sliding mode control algorithm is employed as the two-degree-of-freedom control algorithm, it is to be understood that the two-degree-of-freedom control algorithm is not limited to this. For example, as the two-degree-of-freedom control algorithm, there may be employed a target value filter algorithm, such as a first-order lag filter algorithm, combined with a feedback control algorithm, such as a PID control algorithm. 
   Further, although in the present embodiment, the switching function-setting parameter POLE_lf is set to the normal-time value POLE_base in both of the case where it is determined that the valve lift Liftin is held at the minimum value Liftin_L and the case where the valve lift Liftin or the target valve lift Liftin_cmd is larger than the predetermined value Liftin_stb, this is not limitative, but it may be set to different values in the respective cases. For example, in the former case, since the driving force for holding the valve lift Liftin at the minimum value Liftin_L is not so necessary, and the switching function-setting parameter POLE_lf may be set such that the disturbance suppression degree is made smaller, than in the latter case. 
   Further, although in the present embodiment, after it is determined that the short arm  65  has abutted against the minimum lift stopper  67   a , to set the switching function-setting parameter POLE_lf such that the disturbance suppression degree is increased, the predetermined value Liftin_stb is used as the reference value for being compared with the valve lift Liftin or the target valve lift Liftin_cmd, this is not limitative, but the minimum lift value Liftin_L may be used. Besides, details of the configuration of the present embodiment may be changed or modified without departing from the spirit and scope of the present invention. 
   INDUSTRIAL APPLICABILITY 
   The control system according to the invention is very useful for an internal combustion engine, in reducing impact occurring when a movable part of a variable valve lift mechanism of the engine abuts against a restriction part of the same, while ensuring excellent drivability.