Patent Publication Number: US-9416689-B2

Title: Method and apparatus for controlling a phase varying apparatus

Description:
FIELD OF THE INVENTION 
     The present invention relates to a control method and a control apparatus for controlling a phase varying apparatus for varying the opening and closing timing of a valve. 
     BACKGROUND OF THE INVENTION 
     A method of using a phase varying apparatus for varying the opening and closing timing of an engine valve is adopted as a method for optimizing performance of an automobile engine over its entire velocity range from a low velocity range to a high velocity range. In this specification, “engine performance” widely includes fuel economy performance, engine response, low emission performance, idling stability and the like. The phase varying apparatus can select the optimal valve opening and closing timing in accordance with engine operating conditions such as engine rpm by varying the phase relationship of a crankshaft and a camshaft, thereby immensely improving engine performance. 
     Patent Publication No. 1 discloses a phase varying apparatus for operating a ring gear and a planetary gear of a planetary gear train using two electromagnetic clutches and the main unit of this phase varying apparatus is directly connected to the camshaft. Since the phase varying apparatus is directly connected to the engine, the phase varying apparatus is installed in an environment easily affected by external disturbances such as engine temperature, ambient temperature, vibration and the like. Therefore, in an ECU (engine control unit) constituting controller, not only conventional PID control but also a sliding mode control of high robustness is employed to appropriately control the valve opening and closing timing. 
     PRIOR ART PUBLICATION 
     Patent Publication 
     Patent Publication No. 1 
     Japanese Patent Application Laid Open No. 2008-115867 
     SUMMARY OF THE INVENTION 
     Problems to be Solved by the Invention 
     The valve opening and closing timing is controlled by the ECU based on the crankshaft rpm but in the case where the engine rpm is low in the idling state or the like, since information input to the ECU decreases, the responsiveness of the phase varying apparatus becomes low and desired engine performance sometimes cannot be obtained. An object to be achieved by the present invention is therefore to provide a phase control method and a phase control apparatus for controlling a phase varying apparatus capable of enabling the phase varying apparatus to achieve adequately high responsiveness under a condition of low engine rpm. 
     Means for Solving the Problems 
     According to the present invention, the following technical means are provided for solving the above mentioned problem. More specifically, an invention defined in claim  1  is directed to a phase control method for controlling a phase varying apparatus  51  for varying a valve timing of an engine valve in an internal combustion engine  11  by varying a phase of rotation of a camshaft  53  with respect to a crankshaft  22 , the phase varying apparatus  51  comprising a driving rotor to which rotation is transmitted from the crankshaft, a driven rotor which is coaxial with the drive rotor and disposed on a side of the camshaft and a phase variation mechanism for varying a relative angle between the driving rotor and the driven rotor using an electromagnetic clutch  70  to control the phase varying apparatus  51 , wherein a relative angle between the crankshaft and the camshaft in the current step, which is calculated based on a rotational velocity value of the crankshaft  22  and the rotational velocity value of the camshaft  23 , and a command value to the electromagnetic clutch  70  in the current step are inputted into a phase varying apparatus estimator  51  and wherein an estimated relative angle value one step later is calculated by a Karman filter using the thus inputted values in the phase varying apparatus estimator  51  so as to input the thus calculated estimated relative angle value one step later to a sliding mode controller  103  as a feedback signal, and wherein a command value to the electromagnetic clutch  70  one step later is calculated using common parameters to those used in the phase varying apparatus estimator  51  based on the thus inputted value in the sliding mode controller  103  and the thus calculated command value is outputted to the phase varying apparatus  51 . 
     Further, an invention defined in claim  2  is directed to a phase control method in accordance with claim  1 , wherein the command value to the electromagnetic clutch  70  is calculated from an output value from the sliding mode controller  103  and an output value from a feed forward controller  111  for equalizing the relative angle to a target phase angle registered in advance. 
     Furthermore, an invention defined in claim  3  is directed to a phase control method in accordance with claim  1  or  2 , wherein when a sensor flag of a sensor for detecting a rotation angle of the crankshaft  22  or the camshaft  53  in the internal combustion engine  11  is not set, the Kalman filter calculates an estimated relative angle value one step later from only the command value to the electromagnetic clutch  70  in the current step, and when the sensor flag is set, the Kalman filter calculates an estimated relative angle value one step later based on the relative angle in the current step and the command value to the electromagnetic clutch  70  in the current step. 
     Moreover, an invention defined in claim  4  is directed to a phase control method in accordance with any one of claims  1  to  3 , wherein system identification of the phase varying apparatus  51  is effected by the Kalman filter using the relative angle in the current step and the command value to the electromagnetic clutch  70  in the current step to create a parametric model and the estimated relative angle value one step later is calculated using the parametric model. 
     Further, an invention defined in claim  5  is directed to a phase control apparatus for controlling a phase varying apparatus  51  for varying a valve timing of an engine valve in an internal combustion engine  11  by varying a phase of rotation of a camshaft  53  with respect to a crankshaft  22 , the phase varying apparatus comprising a driving rotor to which rotation is transmitted from the crankshaft, a driven rotor which is coaxial with the driving rotor and disposed on a side of the camshaft  53 , and a phase variation mechanism for varying a relative angle between the driving rotor and the driven rotor using an electromagnetic clutch  70  to control the phase varying apparatus  51 , the phase control apparatus comprising a phase variable apparatus estimator  107  for calculating an estimated relative angle value one step later by Kalman filter using a relative angle between the crankshaft  22  and the camshaft  53  in the current step calculated based on a rotational velocity value of the crankshaft  22  and a rotational velocity value of the camshaft  53 , and a command value to the electromagnetic clutch  70  in the current step, and a sliding mode controller  103  for receiving the estimated relative angle value one step later as a feedback signal and a command value to the electromagnetic clutch  70  one step later is calculated using parameters common to those used for the calculation in the phase varying apparatus estimator  107  based on the input value of the feedback signal, and outputting the thus calculated command value one step later. 
     Furthermore, an invention defined in claim  6  is directed to a phase control apparatus in accordance with claim  5 , wherein the command value to the electromagnetic clutch  70  is calculated based on an output value from the sliding mode controller  103  and an output value from a feed forward controller  111  for equalizing the relative angle to a target phase angle registered in advance. 
     Moreover, an invention defined in claim  7  is directed to a phase control apparatus in accordance with claim  5  or  6 , which further comprises a phase varying apparatus estimator  107  and in which when a sensor flag of a sensor for detecting a rotation angle of the crankshaft  22  or the camshaft  53  in the internal combustion engine  11  is not set, the Kalman filter calculates the estimated relative angle value one step later from only the command value to the electromagnetic clutch  70  in the current step, and when the sensor flag is set, the Kalman filter calculates the estimated relative angle value one step later and the command value to the electromagnetic clutch in the current step and feeds back the estimated relative angle value one step later. 
     Further, an invention defined in claim  8  is directed to a phase control apparatus in accordance with any one of claims  5  to  7 , which further comprises a phase varying apparatus estimator  107  for effecting system identification of the phase varying apparatus  51  by the Kalman filter using the relative angle in the current step and the command value to the electromagnetic clutch  70  in the current step to create a parametric model and the estimated relative angle value one step later is calculated using the parametric model. 
     Technical Advantages of the Invention 
     According to the invention defined in claim  1  or the invention defined in claim  5 , an estimated relative angle value one step later is calculated in the phase varying apparatus estimator  107  based on a relative angle calculated from the rotational velocity of the crankshaft  22  and the rotational velocity of the camshaft  53  and a command value to the electromagnetic clutch  70  in the current step, so as to input the thus calculated estimated relative angle value to the sliding mode controller  103  as a feedback signal and a command value to the electromagnetic clutch  70  one step later in the sliding mode controller  103 . Therefore, even in the case where the rotational velocity of the crankshaft  22  is low, a necessary number of input signals for the sliding mode controller  103  can be obtained. Further, since the calculation of the estimated relative angle value in the phase varying apparatus estimator  107  and the calculation of the command value in the sliding mode controller  103  are effected using common parameters, it is possible to apply a model information estimated by the phase variable apparatus estimator  107  to the control of the sliding mode controller  103  and therefore, the phase varying apparatus can be controlled with high responsivity and control performance can be improved. 
     According to the invention defined in claim  2  or the invention defined in claim  6 , in addition to the technical effects of the invention defined in claim  1  or the invention defined in claim  5 , since the command value to the electromagnetic clutch one step later is calculated from the output value from the sliding mode controller and the output value from the feed forward controller for outputting the target phase angle registered in advance, the resistance to disturbance of the entire system can be improved. 
     According to the invention defined in claim  3  or the invention defined in claim  7 , in addition to the technical effects of the invention defined in claim  1  or  2  or the invention defined in claim  5  or  6 , when a sensor flag of the sensor for detecting a rotation angle of the associated shaft in the internal combustion engine  11  is not set, the Kalman filter calculates an estimated relative angle value one step later from only the command value to the electromagnetic clutch in the current step, and when the sensor flag is set, the Kalman filter calculates an estimated relative angle value one step later based on the relative angle in the current step and the command value to the electromagnetic clutch in the current step. Therefore, the estimated relative angle value can be calculated by acquiring an accurate value when the sensor responds, whereby an accurate command can be supplied to the electromagnetic clutch. 
     According to the invention defined in claim  4  or the invention defined in claim  8 , in addition to the technical effects of the invention defined in any one of claims  1  to  3  or those of the invention defined in any one of claims  5  to  7 , the system identification of the phase varying apparatus is effected by the Kalman filter to create a parametric model and the estimated relative angle value is calculated one step later using the parametric model. Therefore, it is possible to send a more accurate command to the electromagnetic clutch. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a configuration diagram of an internal combustion engine for a vehicle. 
         FIG. 2  is a longitudinal cross sectional view of a phase varying apparatus which is an apparatus to be controlled by a controlling method according to a preferred embodiment of the present invention. 
         FIG. 3  is a perspective view showing the internal structure of the phase varying apparatus shown in  FIG. 2 . 
         FIG. 4  shows a design model of a control system of the phase varying apparatus shown in  FIG. 2 . 
         FIG. 5  is a block diagram showing a control system of a phase varying apparatus which is a preferred embodiment of the present invention. 
         FIG. 6  is a block diagram showing an estimator of a phase varying apparatus which is a preferred embodiment of the present invention. 
         FIG. 7  is a diagram showing control results by a controlling method which is a preferred embodiment of the present invention. 
     
    
    
     PREFERRED EMBODIMENTS OF THE INVENTION 
     Preferred embodiments of the present invention will be described below in detail based on the above technical idea with reference to accompanying drawings. 
     A preferred embodiment of the present invention will be described below with reference to accompanying drawings. 
       FIG. 1  is a configuration diagram showing a phase varying apparatus according to the preferred embodiment and an internal combustion engine for a vehicle on which the phase varying apparatus and a controller for controlling it are mounted. An electronically controlled throttle valve  14  is provided in an intake passage  12  of the internal combustion engine  10  and air is inspired through the electronically controlled throttle valve  14  and an intake valve  15  into a combustion chamber  16 . 
     Exhausted gas is discharged from the combustion chamber  16  through an exhaust valve  17 , and after being cleaned, is ejected into the atmosphere. The intake valve  15  and the exhaust valve  17  are driven to be opened and closed by cams mounted on an exhaust-side camshaft  21  and an intake side camshaft  20 , respectively. A phase varying apparatus  51  is provided on the intake-side camshaft  20  that varies valve timing by varying the phase of the camshaft with respect to a crankshaft  22 , namely, a relative angle. 
     Although the phase varying apparatus  51  is provided on only the intake side in this preferred embodiment, instead of the phase varying apparatus  51  on the intake side or in addition to the phase varying apparatus  51  on the intake side, a phase varying apparatus  51  may be provided on the side of the exhaust valve  17 . 
     An electromagnetic fuel injection valve  18  is provided at an intake port  13  at an upstream portion of the intake valve  15  of each of cylinders and the fuel injection valve  18  is configured so that when it is driven to be opened by an injection pulse signal from an engine control unit (ECU)  151 , it injects fuel adjusted to a predetermined pressure toward the intake valve  15 . 
     Detected signals are input to the ECU  151 , which has a built-in microcomputer, from various sensors, and the ECU  151  performs arithmetic processing based on the inputted detected signals to control the electronically controlled throttle valve  14 , the phase varying apparatus  51 , the fuel injection valve  18  and the like. A phase control apparatus  102 , according to the present invention, of the phase varying apparatus  51  is incorporated into the ECU  151 . 
     As sensors, there are provided an accelerator position sensor  19  for detecting the position of the accelerator, a crank angle sensor  23  for detecting a rotation signal from the crankshaft  22 , a cam angle sensor  24  for detecting a rotation signal from the intake-side camshaft  20  and the like. 
     One embodiment of the phase varying apparatus  51  which is an apparatus to be controlled by the phase control apparatus  102  according to the present invention will be described below with reference to the accompanying drawings.  FIG. 2  shows a longitudinal view of the phase varying apparatus  51  and  FIG. 3  is a perspective view showing the internal structure of the phase varying apparatus  51  shown in  FIG. 2 . 
     The phase varying apparatus  51  shown in  FIGS. 2 and 3  is used in a state integrally built into an internal combustion engine  11  of an automobile and constituted so that it transmits the rotation of the crankshaft  22  to the camshaft  53  so as to open and close the intake valve  15  and the exhaust valve  17  in synchronism with the rotation of the crankshaft  22  and controls the opening and closing timings of the intake valve  15  and the exhaust valve  17  of the internal combustion engine  11  depending upon driving conditions such as load applied on the internal combustion engine, engine rpm and the like. 
     The phase varying apparatus  51  includes an annular-shaped external cylinder portion  52  which is a sprocket to which a drive force of the crankshaft  22  of the internal combustion engine  11  is transmitted, an annular-shaped internal cylinder portion  54  disposed coaxially with the external cylinder portion  52  on the driven side, and which can be relatively rotated in relation to the external cylinder portion  52  and constitutes a part of the camshaft  53 , an intermediate movement member  55  which helical-spline-engages with the external cylinder portion  52  and the internal cylinder portion  54  to be disposed therebetween and moves in the axial direction to vary the phase of the internal cylinder portion  54  with respect to the external cylinder portion  52 , and an electromagnetic braking means  56  for operating the intermediate movement member  55  which is provided on the side of the internal cylinder portion  54  on which the camshaft  53  is not provided and is mounted on the cover (an engine case)  57 . The intermediate movement member  55  and the electromagnetic braking means  56  constitute a phase variation mechanism. In this preferred embodiment, the external cylinder portion  52  corresponds to the driving rotor and the internal cylinder portion  54  corresponds to the driven rotor. Although the phase variation mechanism is driven by the electromagnetic braking means  56  in this embodiment, in some cases the electromagnetic braking means is driven by an electric motor and the phase variation mechanism is hydraulically driven. 
     The external cylinder portion  52  includes a sprocket body  59  formed with a ring-like concave portion  58  at an inner circumference edge, an inner flange plate  60  which is in close contact with the side surface of the sprocket body  59  and forms a flange engagement groove  58 A in cooperation with the concave portion  58 , and a spline case  61  which co-fasten the inner flange plate  60  to the sprocket body  59  and is formed on the inner circumference thereof with a spline-engagement portion for engagement with the intermediate movement member  55 . 
     A step portion  58   c  is provided to face the outer circumference edge of a flange  62  described later on the side of the internal cylinder portion  54  between a large diameter concave portion  58   a  of the concave portion  58  on the opening side thereof and the small diameter concave portion  58   b  of the concave portion  58  on the back side thereof. 
     The rotation of the crankshaft  22  of the internal combustion engine  11  is transmitted via a chain C to the external cylinder portion  52  serving as a sprocket (the sprocket body  59 ). The reference numeral  63  designates a fastening screw for integrating the sprocket body  59 , the inner flange plate  60  and the spline case  61 . Since the sprocket body  59 , the inner flange plate  60  and the spline case  61  constitute the sprocket (the external cylinder portion  52 ), it is easily to form a flange engagement groove  58 A and form a spline engagement portion  64  in the external cylinder portion  52  (the spline case  61 ). 
     A part of the inner and outer circumferential surface of the intermediate movement member  55  is formed with a male helical spline  65  and a female helical spline  66  and the outer circumferential surface of the internal cylinder portion  54  is formed with a male helical spine  67 . The inner circumferential surface of the spline case  61  is formed with a female helical spine  68 . Here, since the directions of the spline  65  formed on the inner circumferential surface of the intermediate movement member  55  and the spline  66  formed on the outer circumferential surface thereof are reverse, the phase of the internal cylinder portion  54  with respect to the phase of the external cylinder portion  52  can be greatly varied by slightly movement of the intermediate movement member  55  in an axial direction. The outer circumferential surface of the intermediate movement member  55  is formed with a male square screw thread portion  69 . 
     The electromagnetic braking means  56  includes a an electromagnetic clutch  70  supported by the cover (engine case)  57 , a rotatable drum  72  which is rotatably supported by a bearing  71  in the internal cylinder portion  54 , with which the male square screw thread portion  69  of the intermediate movement member  55  engages and to which the braking force is transmitted from the electromagnetic clutch  70 , and a torsion coil spring  73  in the axial direction between the rotatable drum  72  and the external cylinder portion  52 . 
     The electromagnetic clutch  70  is mounted on the outer side of a boss portion  57   a  of the cover  57 . The inner surface of the rotatable drum  72  is formed with a female square screw thread portion  74  and the rotatable drum  72  and the intermediate movement member  55  can be relatively rotated in the circumferential direction along the square screw thread portions  74 ,  69 . Specifically, the intermediate movement member  55  can be moved in the axial direction while being rotated along the square screw thread portions  74 ,  69 . 
     Further, the rotatable drum  72  and the external cylinder portion  52  are connected with each other by the wound-up torsion coil spring  73  and when no braking force is applied to the rotatable drum  72 , the external cylinder portion  52 , the internal cylinder portion  54 , the intermediate movement member  55  and the rotatable drum  72  are integrally rotated. Moreover, since the torsion coil spring  73  disposed between the rotatable drum  72  and the external cylinder portion  52  (the spline case  61 ) is disposed in the axial direction, the entirety of the phase varying apparatus can extend in the axial direction by a distance equal to the extendable length of the torsion coil spring  73 , while the phase varying apparatus is compact in the radial direction. 
     The intermediate movement member  55  is moved along the square screw thread portions  74 ,  69  in the axial direction, while being rotated by controlling ON and OFF of the electromagnetic clutch  70  and current supplied to the electromagnetic clutch  70 , whereby the phases of the external cylinder portion  52  and the internal cylinder portion  54  are varied so that the valve opening and closing timing is adjusted by a cam  53   a  of the camshaft  53 . 
     More specifically, when the electromagnetic clutch  70  is not yet turned ON (no current is supplied), the electromagnetic clutch  70  is located at a position indicated by the chain double-dashed line in  FIG. 2  so that a gap is formed between the rotatable drum  72  and the electromagnetic clutch  70  and the external cylinder portion  52  and the internal cylinder portion  54  are integrally rotated without phase difference therebetween. When the electromagnetic clutch  70  is turned ON (current is supplied), the electromagnetic clutch  70  slides to the right in  FIG. 2  to attract the rotatable drum  72 , whereby a braking force transmitted from the electromagnetic clutch  70  is applied to the rotatable drum  72 . 
     As a result, delay of rotation is generated in the rotatable drum  72  with respect to the external cylinder portion  52 . More specifically, the intermediate movement member  55  is advanced (moved to the right in  FIG. 2 ) by the square screw thread portions  69 ,  74  and the internal cylinder portion  54  (the camshaft  53 ) is rotated with respect to the external cylinder portion  52  (the sprocket body  59 ) by the male and female helical splines  65 ,  66  of the intermediate movement member  55  so that the phase of the internal cylinder portion  54  becomes different from that of the external cylinder portion  52 . Thus, the rotatable drum  72  is kept at a position where the thus transmitted braking force and a spring force of the torsion coil spring  73  are balanced (a position where the difference in phases of the internal cylinder portion  54  and the external cylinder portion  52  becomes a predetermined value). 
     On the other hand, when the electromagnetic clutch  70  is turned OFF, since no braking force is transmitted from the electromagnetic clutch  70  to the rotatable drum  72 , only the spring force of the torsion coil spring  73  is applied to the intermediate movement member  55  and the intermediate movement member  55  is retracted (moved to the left in  FIG. 2 ) by the square screw thread portions  69 ,  74  to be returned to its original position and the internal cylinder portion  54  (the camshaft  53 ) is rotated in a forward direction or a reverse direction with respect to the external cylinder portion  52  (the sprocket body  59 ), whereby the difference in phases between the internal cylinder portion  54  and the external cylinder portion  52  is eliminated. 
     In this embodiment, explanation was made as to the case where the phase variation mechanism was operated by the balance between the spring force of the torsion spring  73  and the braking force but the phase variation mechanism may be operated using two electric means, for example. 
     Further, the outer circumferential surface of the internal cylinder portion  54  (the journal surface between the internal cylinder portion  54  and the sprocket body  59 ) is formed with the flange  62  and on the other hand, the inner circumferential surface of the external cylinder portion (the sprocket body  59 ) is formed with the flange engagement groove  58 A. Further, friction torque application members  75 ,  76  are disposed between the side surface of the flange  62  and the side surface of the flange engagement groove  58 A. As a result, a friction torque of a sliding portion where the external cylinder portion  52  and the internal cylinder portion  54  slide on each other increases, thereby preventing tapping sound from being generated by collision of teeth of the helical spline engagement portions  67 ,  65 ,  66 ,  64  and the square screw thread portions  69 ,  74  among the intermediate movement member  55 , the external cylinder portion  52  and the internal cylinder portion  54 . 
       FIG. 4  shows a design model of a control system of the phase varying apparatus  51  which is an apparatus to be controlled by a controlling method according to a preferred embodiment of the present invention. In this design model of the control system, the clutch torque of the electromagnetic clutch  70  is applied so as to counteract the spring torque of the torsion coil spring  73  applied with an initial torque in a spring torque direction and a relative angle of the internal cylinder portion  54  with respect to the external cylinder portion  52  is generated in a phase transform direction. The equation of state is shown in a mathematical formula 1. 
     
       
         
           
             
               
                 
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     In the mathematical formula 1, X (t) is a state variable showing the inner state of the phase varying apparatus  51  which is an apparatus to be controlled, d (t) is an input variable input to the phase varying apparatus  51 , y (t) is an output variable from the phase varying apparatus  51  and A, B, C and D are coefficients which can be obtained from constituent elements of the phase varying apparatus  51 . 
       FIG. 5  is a block diagram showing a control system of a controlling apparatus which is a preferred embodiment of the present invention. The phase varying apparatus according to the present invention is constituted by a sliding mode controller  103 , a velocity difference calculator  105  for receiving positional information from the crank angle sensor  23  and the cam angle sensor  24  and calculating the difference in velocity of the cams, an integrator  106  for integrating velocity values from the velocity difference calculator  105 , a phase varying apparatus estimator  107  for calculating an estimated relative velocity value from the output of the integrator  106 , a feed forward controller  111  for calculating an output value for equalizing a phase angle to a target phase angle registered in advance, a subtractor  108 , a differentiator  109 , an adder  110  and a PWM (pulse-width modulation) drive circuit  104  for receiving an output signal from the adder  110  and controlling the electromagnetic clutch  70 . The electromagnetic clutch  70  of the phase varying apparatus  51  is controlled by electrical current from the PWM drive circuit  104 . 
     In this embodiment, since a command value to be supplied to the electromagnetic clutch  70  is calculated based on an output value from the sliding mode controller  103  and an output value from the feed forward controller  111  for outputting the target phase angle registered in advance, the entire system can be made to have high resistance to disturbance. 
     The state equations of each controller and the like will be described below. An equation of state of the target orbit of a relative angle for effecting feed forward control is expressed by a mathematical formula 2. In the mathematical formula 2, r (t) is a target phase angle, Xr (t) is an internal state of the feed forward control system, Ar is a matrix of the feed forward control system and Br is an input matrix of the feed forward control. At this time, an input target value is a step input. A mathematical formula 3 that is a state equation can be obtained from the mathematical formula 1 and mathematical formula 2.
 
 {dot over (X)}   r ( T )= A   r   ×X   r ( t )+ B   r   r ( t )  [Mathematical Formula 2]
 
{dot over ( X )}( t )− {dot over (X)}   r ( t )= A{X ( t )− X   r ( t )}+( A−A   r ) X   r ( t )+ Bd ( t )− B   r   r ( t )+ D   [Mathematical Formula 3]
 
     A mathematical formula 4 can be obtained by dividing d (t) into d 1  (t) by feedback control and feed forward input d 2  (t) and a feed forward input is given from a mathematical formula 5. At this time, E is a deviation between a target phase angle and a current transform angle. 
     
       
         
           
             
               
                 
                   
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                   ] 
                 
               
             
           
         
       
     
     In order to design the sliding mode controller  103 , it is necessary to effect switching hypersurface (equivalent control input) design as a first stage, effect a reaching rule (non-linear switching input) design as a second stage and effect chattering prevention design. Since the switching hypersurface design for constraining the state as the first stage basically corresponds to design of a linear control, the design is made by an optimal control theory which is a linear control theory. Concretely, a mathematical formula 6 is obtained by adding the integrator to the mathematical formula 4 to generate an augmentation system and an evaluation function expressed by a mathematical formula 8 is used. Here, Q is a sliding mode weighting function. A solution for minimizing the evaluation function J is represented by a positive definite symmetrical unique solution P E  of the Riccati equation of a mathematical formula 9 and the switching hypersurface can be represented by a mathematical formula 10. In the sliding mode, conditions of a mathematical formula 11 are applied and the equivalent control input d leq  expressed by a mathematical formula 13 can be obtained from a mathematical formula 12. At this time, σ is a sliding mode switching function. 
                       ⅆ     ⅆ   t       ⁡     [           E   1               E   2           ]       =         [           A   11           A   12               A   21           A   22           ]     ⁡     [           E   1               E   2           ]       +       [           B   1               B   2           ]     ⁢         d   1     ⁡     (   t   )       .                 [     Mathematical   ⁢           ⁢   Formula   ⁢           ⁢   6     ]                       ⁢       E   ⁡     (   t   )       =       AE   ⁡     (   t   )       +       Bd   1     ⁡     (   t   )                   [     Mathematical   ⁢           ⁢   Formula   ⁢           ⁢   7     ]               {           J   =     ∫       E   T     ⁢     Q   E     ⁢   E   ⁢           ⁢     ⅆ   t                         Q   E     =     [           Q     E   ⁢           ⁢   11             Q     E   ⁢           ⁢   12                 Q     E   ⁢           ⁢   21             Q     E   ⁢           ⁢   22             ]       ,       Q     E   ⁢           ⁢   21     T     =     Q     E   ⁢           ⁢   12         ,       Q   E     &gt;   0                     [     Mathematical   ⁢           ⁢   Formula   ⁢           ⁢   8     ]                       ⁢     {               P   E     ⁢     A   11   *       +       A   11     *   T       ⁢     P   E       +                     P   E     ⁢     A   12     ⁢     Q     E   ⁢           ⁢   22       -   1       ⁢     A   12   T     ⁢     P   E       +     Q   11   *       =   0                 A   11   *     =       A   11     -       A   12     ⁢     Q     E   ⁢           ⁢   22       -   1       ⁢     Q     E   ⁢           ⁢   12     T                       Q     E   ⁢           ⁢   11     *     =       Q     E   ⁢           ⁢   11       -       Q     E   ⁢           ⁢   12       ⁢     Q     E   ⁢           ⁢   22       -   1       ⁢     Q     E   ⁢           ⁢   12     T                           [     Mathematical   ⁢           ⁢   Formula   ⁢           ⁢   9     ]                       ⁢       S   =     [           A   12   T     ⁢     P   E       +     Q     E   ⁢           ⁢   12     T       ,     Q     E   ⁢           ⁢   22         ]       ,             [     Mathematical   ⁢           ⁢   Formula   ⁢           ⁢   10     ]                       ⁢       σ   .     =       S   ⁢     E   .       =   0               [     Mathematical   ⁢           ⁢   Formula   ⁢           ⁢   11     ]                       ⁢       S   ⁡     (     AE   +       Bd     1   ⁢   eq       ⁡     (   t   )         )       =   0             [     Mathematical   ⁢           ⁢   Formula   ⁢           ⁢   12     ]                       ⁢         d     1   ⁢   eq       ⁡     (   t   )       =       -       (   SB   )       -   1         ⁢   SAE               [     Mathematical   ⁢           ⁢   Formula   ⁢           ⁢   13     ]                 P   E   A   11   *+A   11   *T   P   E   +P   E   A   12   Q   E22   −1   A   12   T   P   E   +Q   E11 *=0   A   11   *=A   11   −A   12   Q   E22   −1   Q   E12   T      Q   E11   *=Q   E11   −Q   E12   Q   E22   −1   Q   E12   T   [Mathematical Formula 9]
 
     After effecting the switching hypersurface design, in order to constrain the state of the switching hypersurface design, the reaching rule design is effected as the second stage. The reaching rule design is effected by the eventual sliding mode control. A non-linear switching input is defined in a mathematical formula 14 by the eventual sliding mode control. In order to avoiding a chattering phenomenon, a smooth function is used and when an acceleration rate reaching rule function is used, the non-linear switching input can be obtained as expressed in mathematical formula 15. At this time, γ is a sliding mode relay input gain. 
     
       
         
           
             
               
                 
                   
                     
                       d 
                       
                         1 
                         ⁢ 
                         RLi 
                       
                     
                     ⁡ 
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       - 
                       γ 
                     
                     ⁢ 
                     
                       
                         σ 
                         
                            
                           σ 
                            
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Mathematical 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     14 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     
                       d 
                       
                         1 
                         ⁢ 
                         RL 
                       
                     
                     ⁡ 
                     
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                     ⁢ 
                     
                       
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                            
                         
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                         δ 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Mathematical 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     15 
                   
                   ] 
                 
               
             
           
         
       
     
     Therefore, the sliding mode controller  103  can be expressed by a mathematical formula 16. In the preferred embodiment of the present invention where the feed forward controller is used, the sliding mode controller  103  can be expressed by a mathematical formula 17. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                             
                         
                         ⁢ 
                         
                           
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                   [ 
                   
                     Mathematical 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     16 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     
                       
                         
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                         = 
                           
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                               2 
                             
                           
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                             { 
                             
                               
                                 
                                   ( 
                                   
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                                 ⁢ 
                                 
                                   
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                                     r 
                                   
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                             } 
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Mathematical 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     17 
                   
                   ] 
                 
               
             
           
         
       
     
     A Kalman filter constituting the phase varying apparatus estimator  107  will be described below referring to  FIG. 5 . When the mathematical formula 1 is discretized using the control period, a mathematical formula 18 can be obtained. A subscript d added to a right side of each of characters expresses discretization. One estimated relative angle value is output to the phase varying apparatus estimator  107  by a plurality of inputs. From rotational velocity value detected by the crank angle sensor  23  for detecting the rotation of the crankshaft  22  and a rotational velocity value detected by the cam angle sensor  24  for detecting the rotation of the intake-side camshaft  20 , the velocity difference calculator  105  calculates the difference in these rotational velocity values. Then, the integrator  106  calculates a relative angle between the crankshaft  22  and the camshaft  20  in the current step (hereinafter referred to “the relative angle in the current step”) and inputs the relative angle in the current step to the phase varying apparatus estimator  107 . Further, a command value in the current step to the electromagnetic clutch  70  is input to the phase varying apparatus estimator  107 . Based on these input values, an estimated relative angle value one step later is calculated by the Kalman filter constituting the phase varying apparatus estimator  107  and this value is input to the sliding mode controller  103  as a feedback signal.
 
 {dot over (X)}d[k+ 1]= A   d   X   d   [k]+B   d   d   d   [k]+D   d  
 
γ d   [k]=CX   d   [k][   Mathematical Formula 18]
 
     In this embodiment, the estimated relative angle value in the current step is calculated by the Kalman filter using the relative angle calculated from the rotational velocity values of the crankshaft  22  and the camshaft  53  and the command value input to the electromagnetic clutch  70  in the current step and the thus calculated estimated relative angle value is input to the sliding mode controller  103  as the feedback signal. Therefore, even when the rpm of the crankshaft  22  is low, a necessary number of input signals to be input into the controller can be obtained. Thus, the control system can be made so as to have high responsivity and stability. 
     The phase varying apparatus estimator  107  will be described below in detail referring to the block diagram shown in  FIG. 6 . The right side of the phase varying apparatus estimator  107  shown in  FIG. 6  shows an input and the left side thereof shows an output so as to coincide with  FIG. 5 . The phase varying apparatus estimator  107  according to the first embodiment of the present invention includes the Kalman filter  121  (a first formula of the mathematical formula 19 and a first formula of the mathematical formula 20),  115  (a third formula of the mathematical formula 20),  117  (a fifth formula of the mathematical formula 20) and  118  (a second formula of the mathematical formula 20) expressed in the mathematical formula 19 and the mathematical formula 20, a plurality of changing-over-switches  113 ,  115  whose input is switched by sensor flags and the like. Here, P d  is a covariance matrix of discretized error, Q d  is a weighting function of the Kalman filter, K d  is a discretized Kalman gain and a symbol “^” placed above X indicates that the value marked with the symbol is an estimated value. The sensor flag is that of a cam angle sensor  24  which is a proximity sensor for calculating the rpm of the camshaft  53 . When the cam angle sensor  24  is ON, the sensor flag is set and when the cam angle sensor  24  is OFF, the sensor flag is not set. Depending on the kind of the sensor, the relationship between ON and OFF of the cam angle sensor  24  may be reverse and instead of the sensor for the camshaft  53 , the sensor may be that for the crankshaft  22 . 
     
       
         
           
             
               
                 
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                   [ 
                   
                     Mathematical 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     19 
                   
                   ] 
                 
               
             
             
               
                 
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                   [ 
                   
                     Mathematical 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     20 
                   
                   ] 
                 
               
             
           
         
       
     
     When the sensor flag is not set, a 0 value of  119  is selected by the changing-over-switch  113 ,  116 , whereby the output from the first changing-over-switch  113  definitely becomes zero and the Kalman filter  120  expressed by the first formula of the mathematical formula 19 calculates an estimated relative angle value one step later from only the command value to the electromagnetic clutch  70  in the current step. Open-loop estimation is used to estimate this state. 
     When the sensor flag is set, the changing-over-switches  113 ,  116  select other than 0 value of  119 . The estimated relative angle value is calculated by the Kalman filter  115 ,  117 ,  118  or  120  based on the relative angle in the current step and the command value to the electromagnetic clutch  70  in the current step. Closed-loop estimation is used to estimate this state. Each of these Kalman filters is an unscented Kalman filter used for a non-linear system. 
     When the flag of the sensor for detecting the rotation angle of the associated shaft is not set, the Kalman filter calculates an estimated relative angle value one step later based on only the command value to the electromagnetic clutch  70  in the current step. On the other hand, when the sensor flag is set, the Kalman filter calculates an estimated relative angle value one step later based on the relative angle in the current step and the command value to the electromagnetic clutch  70  in the current step. Therefore, an estimated relative angle value can be calculated by taking an accurate value in when the sensor responds, whereby an accurate command can be supplied to the electromagnetic clutch  70 . 
     Results when the internal combustion engine  11  is controlled by the phase control method according to the first preferred embodiment of the present invention are shown in  FIG. 7  wherein  FIG. 7 ( a )  shows the results when the phase varying apparatus estimator  107  was not used and  FIG. 7 ( b )  shows the results when the state was estimated by the phase varying apparatus estimator  107  according to the first embodiment of the present invention. In the graph of  FIG. 7 , X axis shows time and Y axis shows phase, namely, relative angle between the external cylinder portion  52  and the internal cylinder portion  54  in the phase varying apparatus  51 . The engine rotational velocity was 1000 rpm and a dot-and-dash line graph shows the command values of the phase while a solid line graph shows actual measured values of the phase. Particularly, overshoot and undershoot can be checked immediately after the phase change (portions enclosed by a circle) and good responsivity can be obtained. 
     A phase varying apparatus estimator  107  according to a second preferred embodiment of the present invention is constituted so as to effect system identification of the phase varying apparatus  51  and calculate an estimated relative angle value. More specifically, the system identification of the phase varying apparatus  51  is effected by the Kalman filter in the phase varying apparatus estimator  107  based on the relative angle in the current step and the command value to the electromagnetic clutch  70  in the current step, thereby creating a parametric model in which states of respective elements in the phase varying apparatus  51  are identified. For example, a model in which a spring coefficient, viscosity and the like when the temperature environment in the phase varying apparatus  51  is changed can be created. Based on the thus created parametric model obtained by the system identification, an estimated relative angle value can be calculated. 
     The accuracy of a control model can be improved by effecting the system identification of the phase varying apparatus  51  using the Kalman filter and calculating an estimated relative angle value one step later using the parametric model created by the system identification. Thus, it is possible to supply a more accurate command to the electromagnetic clutch  70 . 
     The explanation was made as to the control method and the control apparatus using the phase varying apparatus estimator  107 , such as the Kalman filter, applied to the system using the sliding mode controller  103 . However, the control method and the control apparatus according to the present invention can be applied to a general feedback controller other than the sliding mode controller  107 , such as a PID controller. 
     DESCRIPTION OF REFERENCE NUMERALS 
     
         
           11  an internal combustion engine 
           12  an intake valve 
           13  an exhaust valve 
           22  a crankshaft 
           23  a crank angle sensor 
           24  a cam angle sensor 
           51  a phase varying apparatus 
           52  an external cylinder portion 
           53  a camshaft 
           54  an internal cylinder portion 
           55  an intermediate movement member 
           70  an electromagnetic clutch 
           101  an engine control unit (ECU) 
           102  a phase control apparatus 
           103  a sliding mode controller 
           107  a phase varying apparatus estimator 
           111  a feed forward controller