Patent Publication Number: US-7725239-B2

Title: Plant control system

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
   This application is a National Stage entry of International Application No. PCT/JP2005/017499, filed Sep. 22, 2005, the entire specification claims and drawings of which are incorporated herewith by reference. 
   TECHNICAL FIELD 
   This invention relates to a plant control system. 
   BACKGROUND ART 
   It has been known, when a plant (controlled object) has nonlinear characteristics, to model the plant by linear elements and nonlinear elements, to correct inputs determined by a linear controller through a nonlinear compensator so as to determine the final control input, as taught, for example, by Patent Reference 1 mentioned below. By the use of such a nonlinear compensator, the technique described in Patent Reference 1 has an advantage that can control a plant having nonlinear characteristics with high accuracy. 
   Patent Reference 1: Japanese Laid-Open Patent Application Hei 9 (1997)-297240. 
   DISCLOSURE OF THE INVENTION 
   Problems to be Solved by the Invention 
   However, in the technique described in Patent Reference 1, if an error arises between the nonlinear characteristics supposed at the time when the nonlinear compensator was designed and the nonlinear characteristics of the actual plant, the nonlinear compensation can not be done accurately, thereby disadvantageously degrading the control ability. For that reason, in the control using a nonlinear compensator, a technique to adapt or match nonlinear compensation in the nonlinear compensator to actual nonlinear characteristics has long been waited for. 
   An object of this invention is therefore to solve the foregoing problem by providing a plant control system that can adapt or match nonlinear compensation of a nonlinear compensator to actual nonlinear characteristics. 
   Means for Solving the Problems 
   In order to achieve the object, as recited in claim  1 , this invention provides a system for controlling a plant ( 42 ,  44 ) having a linear element and a nonlinear element, comprising: a linear controller ( 110 ) that calculates a provisional input Usl to converge an output (Cain, Cr) of the plant to a desired value (Cain_cmd, Cr_cmd) in accordance with control algorithm based on the linear element; a nonlinear compensator ( 112 ) that is set to cancel the provisional input and characteristics of the nonlinear element of the plant using a nonlinear function that inputs the provisional input Usl and calculates a control input Ucair, Ucr; and a nonlinear characteristic adaptor ( 140 ) that corrects the nonlinear compensator based on an error e_nl between an output estimated value Cain_est Cr_est of the plant calculated by an estimation model ( 114   a ) solely comprising the linear element and the output Cain, Cr of the plant. 
   As recited in claim  2  mentioned below, this invention provides the system wherein the nonlinear characteristic adapter ( 114 ) corrects the nonlinear compensator in accordance with response-specifying control algorithm such that the error e_nl between the output estimated value Cain_est, Cr_est and the output Cain, Cr becomes zero. 
   As recited in claim  3  mentioned below, the invention provides the system further including: an adaptive disturbance observer ( 102 ) that calculates a disturbance estimated value c 1  applied to the plant; and the nonlinear characteristic adapter ( 114 ) calculates the output estimated value Cain_est, Cr_est based on a value Uest obtained by eliminating a term concerning the disturbance estimated value c 1  from the control input Ucain, Ucr. 
   As recited in claim  4  mentioned below, this invention provides the system further including: an adaptive disturbance observer ( 102 ) that calculates a disturbance estimated value c 1  applied to the plant; and the nonlinear characteristic adapter ( 114 ) calculates the output estimated value Cain_est, Cr_est based on a value Uest obtained by eliminating a term concerning the disturbance estimated value c 1  from the control input Ucain, Ucr. 
   As recited in claim  5  mentioned below, this invention provides the system wherein the plant is a variable phase mechanism that variably regulates a phase of an intake valve of an internal combustion engine. 
   As recited in claim  6  mentioned below, this invention provides the system wherein the plant is a variable compression ratio mechanism that regulates a compression ratio of an internal combustion engine. 
   EFFECTS OF THE INVENTION 
   In the plant control system recited in claim  1 , since in a system calculating control input Ucain, Ucr based on a linear controller that calculates a provisional input Usl to converge an output (Cain, Cr) of the plant to a desired value (Cain_cmd, Cr_cmd) in accordance with control algorithm based on the linear element, a nonlinear compensator ( 112 ) that is set to cancel the provisional input and characteristics of the nonlinear element of the plant using a nonlinear function that inputs the provisional input Usl and calculates a control input Ucair, Ucr; and; a nonlinear characteristic adaptor ( 140 ) is provided that corrects the nonlinear compensator based on an error e_nl between an output estimated value Cain_est, Cr_est of the plant calculated by an estimation model ( 114   a ) solely comprising the linear element and the output Cain, Cr of the plant, even when the nonlinear variance or aging degradation, it becomes possible to accurately compensate the nonlinear characteristics by the nonlinear compensator, and to control the plant output to its desired value with high accuracy and high response. 
   In the plane control system recited in claim  2 , since the nonlinear characteristic adapter ( 114 ) corrects the nonlinear compensator in accordance with response-specifying control algorithm such that the error e_nl between the output estimated value Cain_est, Cr_est and the output Cain, Cr becomes zero, in addition to the effects mentioned above, it becomes possible to improve the control ability, since it becomes possible to make the correction of the nonlinear compensator immediately without causing overshooting to occur. 
   In the plant control system recited in claim  3 , since the system further includes an adaptive disturbance observer ( 102 ) that calculates a disturbance estimated value c 1  applied to the plant; and the nonlinear characteristic adapter ( 114 ) correcting means calculates the output estimated value Cain_est, Cr_est based on a value Uest obtained by eliminating a term concerning the disturbance estimated value c 1  from the control input Ucain, Ucr, in addition to the effects mentioned above, it becomes possible to prevent the plant output from exhibiting overshooting relative to the desired value and to further improve the control ability, since the disturbance compensation by the disturbance estimated value c 1  and correction of nonlinear compensator do not interfere with each other. 
   In the plant control system recited in claim  4 , since the system further includes: an adaptive disturbance observer ( 102 ) that calculates a disturbance estimated value c 1  applied to the plant; and the nonlinear characteristic adapter ( 114 ) calculates the output estimated value Cain_est, Cr_est using the disturbance estimated value c 1 , in addition to the effects mentioned above, it becomes similarly possible to prevent the plant output from exhibiting overshooting relative to the desired value and to further improve the control ability, since the disturbance compensation by the disturbance estimated value c 1  and correction of the nonlinear compensator do not interference with each other. 
   In the plant control system recited in claim  5 , since the plant is a variable phase mechanism that variably regulates a phase of an intake valve of an internal combustion engine, in addition to the effects mentioned above, it becomes possible to control the phase of the intake valve (valve opening/closing timing) to a desired phase with high accuracy and high response, without causing overshooting to occur. 
   In the plant control system recited in claim  6 , since the plant is a variable compression ratio mechanism that regulates a compression ratio of an internal combustion engine, in addition to the effects mentioned above, at the time of switching increase/decrease of the compression ratio, it becomes possible to control to change the compression ratio, not abruptly, but smoothly. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a schematic diagram showing the overall structure of a plant control system according to a first embodiment of this invention; 
       FIG. 2  is a side view specifically showing an internal combustion engine shown in  FIG. 1  with focus on a valve operating system; 
       FIG. 3  is a side view showing a variable phase mechanism shown in  FIG. 1 ; 
       FIG. 4  is a front view showing the variable phase mechanism shown in FIG.  3 ; 
       FIG. 5  is a front view schematically showing the structure of an electromagnetic brake in the variable phase mechanism shown in  FIG. 3 ; 
       FIG. 6  is a flowchart showing the operation of an ECU shown in  FIG. 1 ; 
       FIG. 7  is a graph showing the characteristics of the braking force Fbrk and voltage inputted to the electromagnet of the electromagnetic brake in the variable phase mechanism (control input; phase command value) Ucain shown in  FIG. 3  to  FIG. 5 ; 
       FIG. 8  is a block diagram showing the configuration of a control system obtained by applying a two-degree-of-freedom response-specifying control to the prior art described in Patent Reference 1; 
       FIG. 9  is a graph showing the characteristics of scheduled model parameters used in the control system shown in  FIG. 8 ; 
       FIG. 10  is a graph showing the characteristics of correction factor of the scheduled model parameters used in the control system shown in  FIG. 8 ; 
       FIG. 11  is a time chart showing results (simulation results) of controlling the variable phase mechanism (VTC) by the control system shown in  FIG. 8 ; 
       FIG. 12  is a graph showing an offset due to temperature rise of the electromagnet or the like in the characteristics shown in  FIG. 7 ; 
       FIG. 13  is a graph showing table characteristics of nonlinear function Gnl to be used to improve the control system shown in  FIG. 8 ; 
       FIG. 14  is a graph showing table characteristics of value Fnl that compensates the characteristics of the nonlinear function shown in  FIG. 13  to linearize the same; 
       FIG. 15  is a block diagram showing the configuration of a control system obtained by improving the control system shown in  FIG. 8 ; 
       FIG. 16  is a time chart showing results (simulation results) of controlling the variable phase mechanism (VTC) by the control system shown in  FIG. 15 ; 
       FIG. 17  is a block diagram showing the configuration of a control system obtained by further improving the control system shown in  FIG. 15 ; 
       FIG. 18  is a time chart showing results (simulation results) of controlling the variable phase mechanism (VTC) by the control system shown in  FIG. 17 ; 
       FIG. 19  is a block diagram showing the configuration of a control system obtained by still further improving the control system shown in  FIG. 17 ; 
       FIG. 20  is a time chart showing results (simulation results) of controlling the variable phase mechanism (VTC) by the control system shown in  FIG. 19 ; 
       FIG. 21  is a subroutine flowchart showing the processing of variable mechanism control referred to in the flowchart of  FIG. 6 ; 
       FIG. 22  is a subroutine flowchart showing the processing of the phase controls, etc., referred to in the flowchart of  FIG. 21 ; 
       FIG. 23  is a subroutine flowchart showing the processing of ignition timing control referred to in the flowchart of  FIG. 6 ; 
       FIG. 24  is a schematic diagram showing the overall structure of a plant control system according to a second embodiment of this invention; 
       FIG. 25  is a schematic diagram similar to  FIG. 19  but showing the overall structure of a plant control system according to a third embodiment of this invention; 
       FIG. 26  is a graph showing the characteristics of force Fcr generated in response to control input Ucr of hydraulic mechanism of a variable compression ratio mechanism shown in  FIG. 2 ; and 
       FIG. 27  is a graph showing nonlinear table characteristics used in a nonlinear compensator in the control system shown in  FIG. 25 . 
   

   BEST MODES OF CARRYING OUT THE INVENTION 
   Preferred embodiments for carrying out a plant control system according to the present invention will now be explained with reference to the attached drawings. 
   First Embodiment 
     FIG. 1  is a schematic diagram showing the overall structure of a plant control system according to the first embodiment of the invention. 
   It should be noted that a control system of an internal combustion engine, more specifically a system that variably controls the phase of intake valves (and exhaust valves), i.e., valve opening/closing timing of the engine, is taken as an example of a plant control system. 
   Explaining this, the symbol  10  designates an internal combustion engine (hereinafter called “engine”) comprising a four-cycle, four-cylinder, DOHC (double overhead cam), gasoline engine. The engine  10  is equipped with an air intake pipe  12 . Air sucked into the air intake pipe  12  through an air cleaner (not shown) flows through an intake manifold (not shown). A fuel injector  16  is installed near the intake ports of each of the four cylinders  14  (only one shown). When energized, the injectors  16  inject fuel (gasoline) into the intake air. 
   When the two intake valves (only one shown)  20  open, the produced air-fuel mixture flows into a combustion chamber  22  to be ignited by a spark plug  24 . The resulting explosive combustion drives a piston  26  downward as viewed in the drawing to rotate a crankshaft  30 . When the two exhaust valves (only one shown)  32  open, the exhaust gas produced by the combustion passes through an exhaust manifold and an exhaust system  34  connected thereto to be discharged to the exterior of the engine  10  after being purified by a catalytic converter  36 . 
   The engine  10  is equipped with a variable lift mechanism  40  for variably regulating the lift or valve opening height of the intake valves  20 , a variable phase mechanism  42  for variably regulating the phase of an intake camshaft and an exhaust camshaft that drive the intake valves  20  and the exhaust valves  32  (thereby regulating the timing of valve opening and closing), and a variable compression ratio mechanism  44  for variably regulating the compression ratio by changing the top dead center (and bottom dead center) of the pistons  26 . 
   The variable lift mechanism  40  will be explained first. 
     FIG. 2  is a side view showing the engine  10  of  FIG. 1  more concretely with focus on the valve operating system of the engine  10 . As illustrated, an intake camshaft  50  and an exhaust camshaft  52  are installed in parallel above the intake valves  20  and exhaust valves  32 . They are connected to the crankshaft  30  through timing belts or the like (not shown) so that each is rotated at one-half the rotational speed of the crankshaft  30 . 
   Intake cams  50   a  are attached to the intake camshaft  50 . A rocker arm  40   a  is provided near each intake cam  50   a  with its one end in contact with the intake cam  50   a  and its other end in contact with the tip of the stem of the associated intake valve  20 . An upper link arm  40   b  is connected to the rocker arm  40   a  by a link pin  40   b   1  and a lower link arm  40   c  is connected thereto by a link pin  40   c   1 . The upper link arm  40   b  is fastened to the cylinder block (engine main body)  14   a  by another link pin  40   b   2 . 
   Another link pin  40   c   2  of the lower link arm  40   c  is connected to a movable shaft (control shaft; not shown) lying parallel to the crankshaft  30 . The movable shaft is connected to an electric motor  40   d  through reduction gearing (not shown). Rotation of the movable shaft by the motor  40   d  via the reduction gearing moves the center of rotation where the line connecting link pins  40   b   1 ,  40   b   2  of the upper link arm  40   b  and the line connecting the link pins  40   c   1 ,  40   c   2  of the lower link arm  40   c  intersect, thereby changing the distance between the intake cam  50   a  and rocker arm  40   a  to change or regulate the amount of lift of the intake valve  20 . 
   The variable phase mechanism  42  will be explained next. The variable phase mechanism  42  is connected to the intake camshaft  50 . 
     FIG. 3  is a side view schematically showing the variable phase mechanism  42 ,  FIG. 4  is a front view thereof and  FIG. 5  is a front view schematically showing the structure of an electromagnetic brake therein. 
   The explanation will be made in reference with  FIGS. 3 to 5 . The variable phase mechanism  42  is equipped with a planetary gear mechanism  42   a  and an electromagnetic brake  42   b  fastened to the cylinder block  14   a . A ring gear  42   a   1  of the planetary gear mechanism  42   a  is fastened to the intake camshaft  50 . Three planetary gears  42   a   2  mesh with the ring gear  42   a   1  at intervals of 120 degrees. 
   As best shown in  FIG. 4 , the three planetary gears  42   a   2  are interconnected by a carrier  42   a   3  having the shape of an equilateral regular triangle in plan view and, as shown in  FIG. 3 , are connected through the carrier  42   a   3  to a sprocket  56  that is driven by the crankshaft  30 . The carrier  42   a   3  is connected through a connector  42   b   1  of the electromagnetic brake  42   b  shown in  FIG. 5  to one end of a return spring (compression spring)  42   b   2 . 
   A sun gear  42   a   4  meshes with the three planetary gears  42   a   2 . The sun gear  42   a   4  is similarly fastened to a connector  42   b   3  of the electromagnetic brake  42   b  shown in  FIG. 5  and connected through the connector  42   b   3  to the other end of the return spring  42   b   2 . 
   As shown in  FIG. 5 , the electromagnetic brake  42   b  includes an annular permanent magnet  42   b   4  located on the outer periphery of the annular connector  42   b   3  to which the sun gear  42   a   4  is connected and an annular electromagnet  42   b   5  located on the outer periphery of the permanent magnet  42   b   4 . The permanent magnet  42   b   4  has a bipolar structure composed of four magnetic pole pieces arranged with alternating north-south polarities. 
   The electromagnet  42   b   5  is composed of four conductors, i.e., laminated steel plates arranged in one-to-one correspondence with the four magnetic pole pieces. The conductors are wound with coils (not shown) that are applied with energizing current by an energizing circuit (not shown) to be magnetized in the north pole or south pole depending on the energization direction. Thus the electromagnetic brake  42   b  resembles a DC motor in structure. 
   The return spring  42   b   2  operates through the connectors  42   b   1 ,  42   b   3  to bias the sun gear  42   a   4  clockwise relative to the carrier  42   a   3  as viewed in  FIG. 5 . That is, the sun gear  42   a   4  is biased in the retarded direction, specifically in the direction of retarding the opening (and closing) of the intake valves  20  relative to the rotation of the crankshaft  30 . 
   In the variable phase mechanism  42  of the illustrated structure, the sprocket  56  is rotated one-half turn in the direction of the arrow a in  FIG. 4  with rotation of the crankshaft  30 . The rotation of the sprocket  56  is transmitted through the carrier  42   a   3  to the planetary gears  42   a   2  to rotate them in the direction of the arrow b in  FIG. 4 . As a result, the ring gear  42   a   1  and the intake camshaft  50  connected thereto are rotated in the same direction as the direction of rotation of the sprocket  56  (direction of arrow a) and the sun gear  42   a   4  is rotated in the direction indicated by the arrow c in  FIG. 4 . 
   If at this time the electromagnet  42   b   5  is energized to brake the rotation of the permanent magnet  42   b   4  connected to the sun gear  42   a   4  through the connector  42   b   3 , the intake camshaft  50  will be moved relative to the sprocket  56  in the advanced direction indicated by the arrow d in  FIG. 5  by an amount proportional to the braking force, thereby moving ahead or angularly advancing the contact point between the intake cam  50   a  and rocker arm  40   a  relative to the crank angle. 
   Therefore, when the sun gear  42   a   4  has rotated relatively by a certain angle to bring the braking force and the return spring force into equilibrium, the planetary gears  42   a   2  stop operating, so that the sprocket  56  and intake camshaft  50  rotate unitarily while maintaining the certain angle therebetween. In other words, the cam phase is controlled in the advanced and retarded directions by increasing and decreasing the braking force. Although the detailed description is omitted, the phase, i.e., timing of valve opening and closing of the exhaust valves  32  is variably regulated (controlled) by a similar variable phase mechanism  42  connected to the exhaust camshaft  52 . 
   The variable compression ratio mechanism  44  will now be explained. As shown in  FIG. 2 , a first link  44   b  of substantially triangular shape in plan view is connected to a connecting rod  26   a  of the piston  26  by a link pin  44   a.    
   The first link  44   b  is formed at a location eccentric or radially offset from the link pin  44   a  with a hole  44   b   1  for rotatably accommodating the crankshaft  30  and one end thereof is connected to a second link  44   c  by a link pin  44   b   2 . A smaller-diameter link pin  44   c   1  provided at the tip of the second link  44   c  is eccentrically connected to a larger-diameter movable shaft (control shaft)  44   c   2  formed at the tip of a third link  44   d  fastened to the cylinder block  14   a.    
   The movable shaft  44   c   2  is rotated by a hydraulic mechanism  44   e , thereby at the four-joint linkage composed of the first link  44   b , second link  44   c  and third link  44   d , changing the TDC (top dead center; and BDC (bottom dead center)) of the pistons  26  to variably regulate or control the compression ratio of the combustion chambers  22 . 
   The explanation of  FIG. 1  will be resumed. A crankshaft sensor  60  installed near the crankshaft  30  outputs a cylinder discrimination signal for specifying the crank angle positions at the four cylinders  14 , a TDC signal indicative of a position related to the TDC of the four pistons  26 , and a signal indicative of unit crank angles, for example, crank angle signals (CRK signals) produced at every one degree. 
   A camshaft sensor  62  installed near the intake camshaft  50  (shown in  FIG. 2 ) produces an output or signal at every predetermined angle of rotation, e.g., every one degree of rotation, of the intake camshaft  50 . A lift sensor  64  constituted as rotary encoder or the like and installed near the reduction gearing of the motor  40   d  in the variable lift mechanism  40  produces an output or signal corresponding to the amount of lift or amount of valve opening Liftin of the intake valves  20  owing to the geared-down rotation of the motor  40   d . A compression ratio sensor  66  installed near the hydraulic mechanism  44   e  in the variable compression ratio mechanism  44  uses the detected stroke or amount of rotation of the hydraulic mechanism  44   e  to produce an output corresponding to the actual compression ratio Cr of the combustion chambers  22 . 
   An airflow meter (AFM)  68  installed near the end of the air intake pipe  12  produces an output or signal corresponding to the intake air quantity Q. A water temperature sensor  70  installed near a coolant channel (not shown) of the cylinder  14  produces an output or signal indicative of the coolant temperature TW of the engine  10 . 
   An accelerator position sensor  74  is installed near the accelerator pedal (not shown) provided on the floor near the driver&#39;s seat of the vehicle (not shown) in which the engine  10  is mounted and produces an output or signal corresponding to the accelerator opening or depression amount AP produced by the driver&#39;s depression of the accelerator pedal. 
   The outputs of the forgoing sensors are sent to an ECU (Electronic Control Unit)  80 . As shown in the drawing, the ECU  80  is composed of a microcomputer comprising a CPU  80   a , memory  80   b , input interface  80   c  and output interface  80   d , and also including an A/D converter circuit, waveforming circuit, counter and other components that are not shown in the drawing. 
   The outputs of some sensors, including the crankshaft sensor  60 , are wave-formed by the wave-forming circuit, while the outputs of others, including the airflow meter (AFM)  68 , are converted to digital values by the A/D converter circuit. The ECU  80  detects the engine speed NE by using the counter to count the CRK signals outputted by the crankshaft sensor  60 . In addition, it detects the cam phase Cain (timing of the opening and closing of the intake valves  20 ) based on the CRK signals and the output of the camshaft sensor  62 . 
   The ECU  80  controls variable mechanisms including the variable phase mechanism  42 , fuel injection quantity and ignition timing of the engine  10  based on the foregoing values and other sensor outputs, as explained later. 
     FIG. 6  is a flowchart showing the processing of the operation of the ECU  80 . 
   Explaining this, in S 10 , the variable mechanisms are controlled. Specifically, based on the operating state of the engine  10  detected from the sensor outputs, the variable lift mechanism  40 , variable phase mechanism  42  and variable compression ratio mechanism  44  are controlled such that the intake air quantity of the engine  10  is optimized under the detected operating state. The processing of S 10  starts at starting of the engine  10  and executed at every predetermined interval, e.g., every 10 milliseconds. 
   Next in S 12 , fuel control to calculate the fuel injection quantity based on the intake air quantity is conducted, and in S 14 , the ignition timing is controlled also based on the intake air quantity. The processing of S 12  and S 14  starts at starting of the engine  10  and executed synchronously with the TDC or crank angle thereabout. 
   Before making the detailed explanation of the operation of the flowchart in  FIG. 7 , a problem to be solved by this invention will be explained. 
   As mentioned above, in the technique described in Patent Reference 1, if an error arises between the nonlinear characteristics supposed at the time when the nonlinear compensator was designed and the nonlinear characteristics of the actual plant, the nonlinear compensation can not be done accurately, thereby disadvantageously degrading the control ability. Therefore, since the technique to adapt or match nonlinear compensation in the nonlinear compensator to actual nonlinear characteristics has long been waited for in the control using a nonlinear compensator, the object of this invention is to provide a plant control system that can adapt or match nonlinear compensation of a nonlinear compensator to actual nonlinear characteristics. 
   In the variable phase mechanism  42  shown in  FIG. 3  to  FIG. 5 , the relationship between the braking force Fbrk and voltage inputted to the electromagnet  42   b   5  (control input; phase command value) Ucain of the electromagnetic brake  42   b  has nonlinearity like that shown in  FIG. 7 . Specifically, when the input voltage Ucain is made smaller than a certain value, the braking force Fbrk exhibits sharp decrease relative to the input. On the other hand, when the input voltage is made larger than a certain extent, the braking force shows sharp increase relative to the input. 
   This is because the amount of electromagnetic force to be generated has linear characteristics relative to the current, i.e., the voltage applied to the electromagnet  42   b   5 , but the electromagnetic force is inversely proportional to the square of distance. Note that although the characteristics should, in fact, be indicated by a continues curve, they are shown by a broken line in  FIG. 7 . 
   Here, the controlled object, specifically the plant, i.e., the variable phase mechanism (VTC)  42  is expressed using a linear model mentioned below. 
   [Numeral 1]
 
Cain( k+ 1)= a 1 sc  Cain( k )+ a 2 sc  Cain( k− 1)+ b 1 sc U cain( k )+ b 2 sc U cain( k− 1)  (1-1)
 
   In the above, a 1   sc , a 2   sc , b 1   sc , b 2   sc  are model parameters scheduled in response to NE and Cain. 
   An expanded controlled object including a disturbance estimation value c 1  is defined as follows. 
   [Numeral 2]
 
Cain( k+ 1)= a 1 sc  Cain( k )+ a 2 sc  Cain( k− 1)+ b 1 sc U cain( k )+ b 2 sc U cain( k− 1)+ c 1  (1-2)
 
   The response-specifying control, specifically sliding mode control, more specifically two-degree-of-freedom response-specifying control, that can respectively specify convergence time and convergence behavior of desired value response and disturbance suppressing response, is realized by the control system shown in  FIG. 8  and Eq. 1-3 to Eq. 1-16. The control system shown there is that obtained by applying a two-degree-of-freedom response-specifying control to the prior art described in Patent Reference 1. 
   As shown in  FIG. 8 , the two-degree-of-freedom response-specifying control system comprises SMC (Sliding Mode Controller)  100 , an adaptive disturbance observer  102  and a model parameter scheduler  104 . 
   The SMC  100  is defined as follows: 
   [Numeral 3]
 
 U cain( k )= U eq( k )+ U rch( k )  (1-3)
 
Equivalent Control Input
 
                   Ueq   ⁡     (   k   )       =       1     b   ⁢           ⁢   1   ⁢     sc   ⁡     (   k   )           ⁢     {         (     1   -     a   ⁢           ⁢   1   ⁢           ⁢     sc   ⁡     (   k   )         -   POLE     )     ⁢           ⁢     CAIN   ⁡     (   k   )         +       (     POLE   -     a   ⁢           ⁢   2   ⁢     sc   ⁡     (   k   )           )     ⁢           ⁢     CAIN   ⁡     (     k   -   1     )         -     b   ⁢           ⁢   2   ⁢     sc   ⁡     (   k   )       ⁢           ⁢     Ucain   ⁡     (     k   -   1     )         -     c   ⁢           ⁢   1   ⁢     (   k   )       +     CAIN_cmd   ⁢   _f   ⁢     (   k   )       +       (     POLE   -   1     )     ⁢           ⁢   CAIN_cmd   ⁢   _f   ⁢     (     k   -   1     )       -     POLE   ⁢           ⁢   CAIN_cmd   ⁢   _f   ⁢     (     k   -   2     )         }               (     1   ⁢     -     ⁢   4     )               
Reaching Law Input
 
                   Urch   ⁡     (   k   )       =       -     Krch     b   ⁢           ⁢   1   ⁢     sc   ⁡     (   k   )             ⁢     σ   ⁡     (   k   )                 (     1   ⁢     -     ⁢   5     )               
Switching Function
 σ( k )= E cain( k )+POLE  E cain( k− 1)  (1-6)   E cain( k )=CAIN( k )−CAIN_cmd —   f ( k− 1)  (1-7) Desired Value Filter CAIN_cmd —   f ( k )=−POLE —   f  CAIN_cmd —   f ( k− 1)+(1+POLE —   f )CAIN_cmd( k )  (1-8)     Krch: Feedback gain   POLE: Switching-function-setting parameter   POLE_f: Desired-value-filter coefficient; Here, −1&lt;POLE_f&lt;POLE&lt;0   
   The adaptive disturbance observer  102  is defined as follows: 
   [Numeral 4] 
                   c   ⁢           ⁢   1   ⁢     (   k   )       =       c   ⁢           ⁢   1   ⁢     (     k   -   1     )       +       Pdov     1   +   Pdov       ⁢   e_dov   ⁢     (   k   )                 (     1   ⁢     -     ⁢   9     )                 e _dov( k )=CAIN( k )−CAIN_hat( k )  (1-10) CAIN_hat( k )=θ T ( k )ζ( k )  (1-11) θ T ( k )=[ a 1 sc ( k ) a 2 sc ( k ) b 1 sc ( k ) b 2 sc ( k ) c 1( k− 1)] ζ T ( k )=[CAIN( k− 1)CAIN( k− 2) U cain( k− 1) U cain( k− 2)1]  (1-12)     Pdov: Identifying gain   a 1   sc , a 2   sc , b 1   sc , b 2   sc : Scheduled model parameters calculated (MAP-retrieved) in response to NE or Cain   
   The model parameter scheduler  104  is defined as follows: 
   [Numeral 5]
 
a1sc(k)←a1sc_map(k)  (1-13)
 
a2sc(k)←a2sc_map(k)  (1-14)
 
b1sc(k)←b1sc_map(k)×Kbsc(k)  (1-15)
 
b2sc(k)←b2sc_map(k)×Kbsc(k)  (1-16)
 
   In the equations mentioned above and below, a 1   sc _map, a 2   sc _map, b 1   sc _map and b 2   sc _map are (scheduled) model parameters obtained by retrieving characteristics shown in  FIG. 9  by an detected engine speed NE. Kbsc is a correction factor of the (scheduled) model parameters obtained by retrieving characteristics shown in  FIG. 10  by a detected phase Cain. The suffix k is a discrete system sample time and more specifically, the time at which the flowchart of  FIG. 6  is executed. 
     FIG. 11  is a time chart that shows results (simulation results) of controlling the variable phase mechanism (VTC)  42  having the nonlinear characteristics by the linear control system shown in  FIG. 8 . In  FIG. 11 , a disturbance (external force) dout is applied at time t 2 . At time t 1  preceding thereto, the nonlinear characteristics cause offset to happen due to temperature rise of the electromagnet  42   b   5  or the like, as shown in  FIG. 12 . 
   In the result of control in  FIG. 11 , since the adaptive disturbance observer  102  can not absorb the modeling error, instantaneously, caused by the controlled object&#39;s nonlinearity, overshooting markedly occurs in the follow-up to the desired value markedly. It can be seen from the result that less overshooting that characterizes the two-degree-of-freedom response-specifying control is lost. However, even in this configuration, because the influences by doft, dout can be absorbed by the adaptive disturbance observer  102 , there is no steady-state error between the phase Cain and desired value Cain-cmd. 
   Therefore, in order to design a control system that takes the controlled object&#39;s nonlinearity into account, the controlled object is modeled by nonlinear elements and linear elements (lag elements) as follows: 
   [Numeral 6]
 
Cain( k+ 1)= a 1 sc  Cain( k )+ a 2 sc  Cain( k− 1)+ b 1 sc Unl ( k )+ b 2 sc Unl ( k− 1)  (1-17)
 
 Unl ( k )= dUnl ( k )+ Cn 1  (1-18)
 
 dUnl ( k )= Gnl ( dU cain′( k ))  (1-19)
 
 dU cain′( k )= U cain( k )− Cn 1  (1-20)
 
   Gnl shown in Eq. 1-19 is a nonlinear function and is set as table values as shown in  FIG. 13 . This will be the same in equations mentioned below. 
   Next, the value Fnl that compensates and linearizes the characteristics of nonlinear function shown in  FIG. 13  is defined as table values as shown in  FIG. 14 , and renaming the control input Ucain shown in  FIG. 8  as Usl and based on Usl, the control input Ucain is newly calculated as follows: 
   [Numeral 7]
 
 U cain( k )= dU cain( k )+ Cn 1  (1-21)
 
 dU cain( k )= Fnl ( dUsl ( k ))  (1-22)
 
 dUsl ( k )= Usl ( k )− Cn 1  (1-23)
 
   With this, the relationship between Usl and Unl becomes linear (proportional or equal), and the dynamic characteristics from Usl to Cain can be linearized.  FIG. 15  shows a block diagram that illustrates the configuration of the obtained control system. 
   Accordingly, it suffices if a linear controller  110  (comprising the SMC  100 , adaptive disturbance observer  102  and model parameter scheduler  104  in  FIG. 8 ) for calculating the provisional input recognizes the linearized controlled object as shown in the following equation. 
   [Numeral 8]
 
Cain( k+ 1)= a 1 sc  Cain( k )+ a 2 sc  Cain( k− 1)+ b 1 sc Usl ( k )+ b 2 sc Usl ( k− 1)  (1-24)
 
   Putting equations in order, in the control system shown in  FIG. 15 , equations for the nonlinear compensator  112  are as follows: 
   [Numeral 9]
 
 U cain( k )= dU cain( k )+ Cn 1  (1-25)
 
 dU cain( k )= Fnl ( dUsl ( k ))  (1-26)
 
 dUsl ( k )= Usl ( k )− Cn 1  (1-27)
 
   Equations for the linear controller (two-degree-of-freedom response-specifying controller)  110  are as follows: 
   [Numeral 10]
 
 Usl ( k )= U eq( k )+ U rch( k )  (1-28)
 
Equivalent Control Input
 
                   Ueq   ⁡     (   k   )       =       1     b   ⁢           ⁢   1   ⁢     sc   ⁡     (   k   )           ⁢     {         (     1   -     a   ⁢           ⁢   1   ⁢     sc   ⁡     (   k   )         -   POLE     )     ⁢           ⁢     CAIN   ⁡     (   k   )         +       (     POLE   -     a   ⁢           ⁢   2   ⁢     sc   ⁡     (   k   )           )     ⁢           ⁢     CAIN   ⁡     (     k   -   1     )         -     b   ⁢           ⁢   2   ⁢     sc   ⁡     (   k   )       ⁢           ⁢   Us   ⁢           ⁢   1   ⁢           ⁢     (     k   -   1     )       -     c   ⁢           ⁢   1   ⁢     (   k   )       +     CAIN_cmd   ⁢   _f   ⁢     (   k   )       +       (     POLE   -   1     )     ⁢   CAIN_cmd   ⁢   _f   ⁢     (     k   -   1     )       -     POLE   ⁢           ⁢   CAIN_cmd   ⁢   _f   ⁢     (     k   -   2     )         }               (     1   ⁢     -     ⁢   29     )               
Reaching Law Input
 
                   Urch   ⁡     (   k   )       =       -     Krch     b   ⁢           ⁢   1   ⁢     sc   ⁡     (   k   )             ⁢     σ   ⁡     (   k   )                 (     1   ⁢     -     ⁢   30     )               
Switching Function
 σ( k )= E cain( k )+POLE  E cain( k− 1)  (1-31)   E cain( k )=CAIN( k )−CAIN_cmd —   f ( k− 1)  (1-32) Desired Value Filter CAIN_cmd —   f ( k )=−POLE —   f  CAIN_cmd —   f ( k− 1)+(1+POLE —   f )CAIN_cmd( k )  (1-33)     Krch: Feedback gain   POLE: Switching-function-setting parameter   POLE_f: Desired-value-filter coefficient; Here, −1&lt;POLE_f&lt;POLE&lt;0   
   Equations for the adaptive disturbance observer  102  ( FIG. 8 ) that constitutes the linear controller  110  are as follows: 
   [Numeral 11] 
                   c   ⁢           ⁢   1   ⁢     (   k   )       =       c   ⁢           ⁢   1   ⁢     (     k   -   1     )       +       Pdov     1   +   Pdov       ⁢   e_dov   ⁢     (   k   )                 (     1   ⁢     -     ⁢   34     )                 e _dov( k )=CAIN( k )−CAIN_hat( k )  (1-35) CAIN_hat( k )=θ T ( k )ζ( k )  (1-36) θ T ( k )=[ a 1 sc ( k ) a 2 sc ( k ) b 1 sc ( k ) b 2 sc ( k ) c 1( k− 1)] ζ T ( k )=[CAIN( k− 1)CAIN( k− 2) Usl ( k− 1) Usl ( k− 2)1]  (1-37) 
Pdov: Identifying gain
 
   Similarly, equations for the model parameter scheduler  104  ( FIG. 8 ) that constitutes the linear controller  110  are as follows: 
   [Numeral 12]
 
a1sc(k)←a1sc_map(k)  (1-38)
 
a2sc(k)←a2sc_map(k)  (1-39)
 
b1sc(k)←b1sc_map(k)×Kbsc(k)  (1-40)
 
b2sc(k)←b2sc_map(k)×Kbsc(k)  (1-41)
 
     FIG. 16  shows the result of control using the nonlinear compensator  112  illustrated in  FIG. 15 . As seen from the figure, by inserting the nonlinear compensator  112 , the follow-up to the desired value is greatly improved and less overshooting that characterizes the two-degree-of-freedom response-specifying control returns. Rather, as regards suppression of doft, dout that indicates deviations or changes in the nonlinear characteristics, the convergence time periods are elongated. 
   In view of the above, it has been waited for a technique that can enhance the ability of suppression of doft, dout by improving the technique using the nonlinear compensator  112 . The present invention aims to provide a plant control system that solves this problem. 
   Explaining this, the configuration of the control system shown in  FIG. 15  has the function to compensate the nonlinear characteristics of the controlled object, but has no function to compensate change of the nonlinear characteristics of the controlled object (shown in  FIG. 12 ). Accordingly, in the plant control system according to this invention, the configuration shown in  FIG. 15  is added with the function to adapt to the change of the nonlinear characteristics of the controlled object. 
   In the control system shown in  FIG. 15 , if cancellation of the nonlinear characteristics by the nonlinear compensator  112  is done correctly, the output Cain of the controlled object in response to the control input Ucain and the output Cain-est of a controlled object model expressed by the following equation 2-1 will be equal to each other. 
   [Numeral 13]
 
Cain_est( k )= a 1 sc  Cain( k− 1)+ a 2 sc  Cain( k− 2)+ b 1 sc Usl ( k− 1)+ b 2 sc Usl ( k− 2)  (2-1)
 
   On the contrary, if the cancellation of the nonlinear characteristics is not done correctly, since an error is present between the model expressed by the above equation and the static characteristics of the linearized controlled object shown in  FIG. 15 , an error e_nl is present between Cain and Cain_est represented by the following equation. 
   [Numeral 14]
 
 e   —   nl ( k )=Cain_est( k )−Cain( k )  (2-2)
 
   Paying an attention to it, the plant control system according to the present invention is configured such that the nonlinear compensator  112  is modified as follows to improve Cnl_adp used therein so as to make e_nl to zero, such that the cancellation of the nonlinear characteristics by the nonlinear compensator  112  is carried out correctly. 
   The improved nonlinear compensator is represented by the following equations. 
   [Numeral 15]
 
 U cain( k )= dU cain( k )+ Cnl   —   adp ( k )  (2-3)
 
 dU cain( k )= Fnl ( dUsl ( k ))  (2-4)
 
 dUsl ( k )= Usl ( k )− Cnl   —   adp ( k )  (2-5)
 
   In the above (and in the below), Cnl_adp is a nonlinear characteristic correction value. 
   The nonlinear characteristic correction value in the above equations is calculated by the following equations that use a simplified sliding mode algorithm. 
   [Numeral 16]
 
 Cnl   —   adp ( k )= Cnl _base+ Dcnl ( k )  (2-6)
 
 Dcnl ( k )= Krch   —   cnl σcnl ( k )+ Kadp   —   cnl  sum —   σcnl ( k )  (2-7)
 
σ cnl ( k )= e   —   nl ( k )+POLE —   cnl e   —   nl ( k− 1)  (2-8)
 
   In the above, Cnl_base is a basic value of the nonlinear characteristic correction value and is set to Cnl in Eq. 1-25, but may be scheduled by the engine speed NE or some similar parameter. 
   To be more specific, as shown in  FIG. 17 , the plant control system according to the present invention is configured to have a nonlinear characteristic adapter  114  such that Cnl_adp is determined in such a manner that e_nl is made zero and the cancellation of the nonlinear characteristics by the nonlinear compensator  112  is carried out correctly. 
     FIG. 18  shows results (simulation results) of the control system shown in  FIG. 17 . In the results shown in  FIG. 18 , the time period during which absolute values of the errors produced by doft and dout is decreased, is shortened. However, since overshooting behaviors are still present, further improvement of the control ability is expected. 
   The reason why overshooting behaviors are present is that the adaptive disturbance observer  102  for compensating the disturbance of the linear controller  110  and the nonlinear characteristic adapter  114  interfere with each other. Specifically, this is because the nonlinear characteristic adapter  114  recognizes e_nl (that is produced by the disturbance dout) as a discrepancy of the nonlinear characteristics and acts to correct Cnl_adp, whereas if an error is present due to the nonlinear characteristic offset doft, the adaptive disturbance observer  102  acts to correct it. 
   In order to avoid this interference, inputs to the controlled object model  114   a  used by the nonlinear characteristic adapter  114  are modified as follows: 
   [Numeral 17]
 
 U est( k )= U eq_est( k )+ U rch( k )  (2-9)
 
   
     
       
         
           
             
               
                 
                   Ueq_est 
                   ⁢ 
                   
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                         ⁡ 
                         
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                           CAIN 
                           ⁡ 
                           
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                         ⁢ 
                         
                             
                         
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                 ( 
                 
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   Compared to Usl, the term of disturbance estimation value c 1  estimated by the adaptive disturbance observer  102  is removed from the input Uest. Explaining this, in the output Cain of the actual controlled object, since the influence of the disturbance dout is canceled by the disturbance estimation value c 1 , the influence is not present in the output Cain. However, since the disturbance dout to be canceled is not present in the controlled object model  114   a , the influence of input increase due to the disturbance estimation value c 1  can be erroneously present in the model output Cain_est and hence, the error e_nl can be present erroneously. 
   Accordingly, using Uest, the controlled object model  114   a  is improved as follows: 
   [Numeral 18]
 
Cain_est( k )= a 1 sc  Cain( k− 1)+ a 2 sc  Cain( k− 2)+ b 1 sc U est( k− 1)+ b 2 sc U est( k− 2)  (2-11)
 
   Explaining the equations of the improved control system, those for the nonlinear compensator  112  are as follows: 
   [Numeral 19]
 
 U cain( k )= dU cain( k )+ Cnl   —   adp ( k )  (2-12)
 
 dU cain( k )= Fnl ( dUsl ( k ))  (2-13)
 
 dUsl ( k )= Usl ( k )− Cnl   —   adp ( k )  (2-14)
 
   The equations for nonlinear characteristic adapter  114  are as follows: 
   [Numeral 20]
 
 Cnl   —   adp ( k )= Cnl _base+ Dcnl ( k )  (2-15)
 
 Dcnl ( k )= Krch   —   cnl σcnl ( k )+ Kadp   —   cnl  sum —   σcnl ( k )  (2-16)
 
σ cnl ( k )= e   —   nl ( k )+POLE —   cnl e   —   nl ( k− 1)  (2-17)
 
 e   —   nl ( k )=Cain_est( k )−Cain( k )  (2-18)
 
Cain_est( k )= a 1 sc  Cain( k− 1)+ a 2 sc  Cain( k− 2)+ b 1 sc U est( k− 1)+ b 2 sc U est( k− 2)  (2-19)
 
 U est(k)= U eq_est( k )+ U rch( k )  (2-20)
 
   
     
       
         
           
             
               
                 
                   Ueq_est 
                   ⁢ 
                   
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                     k 
                     ) 
                   
                 
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                         ⁡ 
                         
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   The equations for the linear controller (two-degree-of-freedom response-specifying controller)  110  are as follows: 
   [Numeral 21]
 
 Usl ( k )= U eq( k )+ U rch( k )  (2-22)
 
Equivalent Control Input
 
                   Ueq   ⁡     (   k   )       =       1     b   ⁢           ⁢   1   ⁢     sc   ⁡     (   k   )           ⁢     {         (     1   -     a   ⁢           ⁢   1   ⁢     sc   ⁡     (   k   )         -   POLE     )     ⁢           ⁢     CAIN   ⁡     (   k   )         +       (     POLE   -     a   ⁢           ⁢   2   ⁢     sc   ⁡     (   k   )           )     ⁢           ⁢     CAIN   ⁡     (     k   -   1     )         -     b   ⁢           ⁢   2   ⁢     sc   ⁡     (   k   )       ⁢     Usl   ⁡     (     k   -   1     )         -     c   ⁢           ⁢   1   ⁢     (   k   )       +     CAIN_cmd   ⁢   _f   ⁢     (   k   )       +       (     POLE   -   1     )     ⁢           ⁢   CAIN_cmd   ⁢   _f   ⁢     (     k   -   1     )       -     POLE   ⁢           ⁢   CAIN_cmd   ⁢   _f   ⁢     (     k   -   2     )         }               (     2   ⁢     -     ⁢   23     )               
Reaching Law Input
 
                   Urch   ⁡     (   k   )       =       -     Krch     b   ⁢           ⁢   1   ⁢     sc   ⁡     (   k   )             ⁢     σ   ⁡     (   k   )                 (     2   ⁢     -     ⁢   24     )               
Switching Function
 σ( k )= E cain( k )+POLE  E cain( k− 1)  (2-25)   E cain( k )=CAIN( k )−CAIN_cmd —   f ( k− 1)  (2-26) Desired Value Filter CAIN_cmd —   f ( k )=POLE —   f  CAIN_cmd —   f ( k− 1)+(1+POLE —   f )CAIN_cmd( k )  (2-27)     Krch: Feedback gain   POLE: Switching-function-setting parameter   POLE_f: Desired-value-filter coefficient; here, −1&lt;POLE_f&lt;POLE&lt;0   
   The equations for the adaptive disturbance observer  102  are as follows: 
   [Numeral 22] 
                   c   ⁢           ⁢   1   ⁢     (   k   )       =       c   ⁢           ⁢   1   ⁢     (     k   -   1     )       +       Pdov     1   +   Pdov       ⁢   e_dov   ⁢     (   k   )                 (     2   ⁢     -     ⁢   28     )                 e _dov( k )=CAIN( k )−CAIN_hat( k )  (2-29) CAIN_hat( k )=θ T ( k )ζ( k )  (2-30) θ T ( k )=[ a 1 sc ( k ) a 2 sc ( k ) b 1 sc ( k ) b 2 sc ( k ) c 1( k− 1)] ζ T ( k )=[CAIN( k− 1)CAIN( k− 2) Usl ( k− 1) Usl ( k− 2)1]  (2-31) 
   The equations for the model parameter scheduler  104  are as follows: 
   [Numeral 23]
 
a1sc(k)←a1sc_map(k)  (2-32)
 
a2sc(k)←a2sc_map(k)  (2-33)
 
b1sc(k)←b1sc_map(k)×Kbsc(k)  (2-34)
 
b2sc(k)←b2sc_map(k)×Kbsc(k)  (2-35)
 
     FIG. 19  is a block diagram showing the configuration of the control system using the improved nonlinear characteristic adapter  114 .  FIG. 20  shows the results of control (simulation results) when the control system shown in  FIG. 19  is used. As can be understood from  FIG. 20 , in the control system shown in  FIG. 19 , the interference between the nonlinear characteristic adapter  114  and adaptive disturbance observer  102  has been solved (decreased). The system can immediately decrease errors caused by doft or dout, without inviting overshooting. As a matter of course, the less overshooting that is a characterizing feature of the two-degrees-of-freedom response-specifying control is maintained. 
   On the assumption mentioned above, turning to the explanation of the flowchart of  FIG. 6 , in S 10 , as explained, the variable lift mechanism  40 , variable phase mechanism  42  and variable compression ratio mechanism  44  are controlled based on the operating state of the engine  10  detected from the sensor outputs, and the intake air quantity of the engine  10  is controlled from the detected operating state. 
     FIG. 21  is a subroutine flowchart showing the processing for the control. 
   Explaining this, in S 100 , it is determined whether any of three mechanisms comprising the variable lift mechanism  40 , variable phase mechanism  42  and variable compression ratio mechanism  44 , is faulty. When the result is affirmative, the program proceeds to S 102 , in which the command value U_Cr to be supplied to the variable compression ratio mechanism  44  is set at a fail command value U_Cr_fs for establishing the final compression ratio, the command value U_Liftin to be supplied to the variable lift mechanism  40  is set to a fail command value U_Liftin_fs of a level enabling vehicle creep, and the command value U_Cain to be supplied to the variable phase mechanism  42  is set at a fail command value U_Cain_fs that puts the phase on the retarded direction (specifically 0 (supply current zero)). 
   When the result in S 100  is negative, the program proceeds to S 104 , in which it is determined whether the engine  10  is being started. This is determined by checking whether the detected engine speed NE is below the full-firing engine speed. 
   When the result in S 104  is affirmative, the program proceeds to S 106 , in which the lift desired value Lift_cmd is calculated by retrieving the characteristics shown using the detected coolant temperature TW such that it increases with increasing friction, to S 108 , in which the phase desired value Cain_cmd is calculated by retrieving the characteristics shown using the detected coolant temperature TW such that the combustion becomes stable. The program then proceeds to S 110 , in which the compression ratio desired value Cr_cmd is set to a fixed value Cr_cmd_crk defined such that the engine speed NE at cranking is increased and the unburned HC component is reduced. 
   When the result in S 104  is negative, the program proceeds to S 112 , in which it is determined whether the detected accelerator opening AP is zero, i.e., whether the accelerator pedal is released. When the result in S 112  is negative, which can be taken to mean that the operator wants driving power, the program proceeds to S 114 , in which the lift desired value Lift_cmd is calculated by retrieving the characteristics shown using the detected engine speed NE and accelerator opening AP, to S 116 , in which the phase desired value Cain_cmd is calculated by retrieving the characteristics shown using the detected engine speed NE and accelerator opening AP. The program then proceeds to S 118 , in which the compression ratio desired value Cr_cmd is calculated by retrieving the characteristics shown using the detected engine speed NE and accelerator opening AP. 
   When the result in S 112  is affirmative, which can be taken to mean that the engine  10  is idling, the program proceeds to S 120 , in which it is determined whether the warm-up time period of the catalytic converter  36  has elapsed. When the result in S 120  is affirmative, the program proceeds to S 114  and on. When the result in S 120  is negative, the program proceeds to S 122 , in which, in order to warm up the catalytic converter  36  faster, the lift desired value Lift_cmd is calculated by retrieving the characteristics shown using the elapsed time since engine starting and the detected coolant temperature TW. Then the program proceeds to S 124 , in which the phase desired value Cain_cmd is calculated by retrieving the characteristics shown using the elapsed time since engine starting and detected coolant temperature TW such that the pumping loss is increased and the intake air quantity is increased to promote the warm-up of the catalytic converter  36 . 
   The program then proceeds to S 126 , in which the compression ratio desired value Cr_cmd is set to a fixed value Cr_cmd_ast defined such that the exhaust gas temperature is raised by lowering the heat efficiency owing to reduced compression ratio. Since execution of the subroutine shown is commenced with starting of the engine  10  and is thereafter executed every 10 milliseconds, the time elapsed from engine starting can therefore be determined from the number of subroutine loops executed. 
   The program then proceeds to S 128 , in which the phase control, lift control and compression ratio control are conducted. Specifically, based on the desired values thus determined, the variable compression ratio mechanism  44 , variable lift mechanism  40  and variable phase mechanism  42  are controlled. 
     FIG. 22  is a subroutine flowchart showing the processing for the control. 
   Explaining this, in S 200 , the phase command value (control input) Ucain is calculated by aforesaid Eq. 2-12 to Eq. 2-35, as illustrated. 
   Outlining this with reference to  FIG. 19 , the nonlinear compensator  112  calculates the control input Ucain(k) using Eq. 2-12 to Eq. 2-14. The nonlinear characteristic correction value Cnl_adp in the equations is calculated by the nonlinear characteristic adapter  114  by using Eq. 2-15 to Eq. 2-21. 
   The linear controller (two-degrees-of-freedom response-specifying controller)  110  calculates a provisional input Usl that converges the output Cain of the variable phase mechanism (VTC)  42  (which is the controlled object) to the phase desired value Cain_cmd, in accordance with the response-specifying control algorithm (more specifically, two-degree-of-freedom response-specifying control algorithm) represented by Eq. 2-22 to Eq. 2-27. It should be noted that the sliding mode control is a response-specifying control that can specify the convergence speed of the controlled variable. The two-degree-of-freedom sliding mode control is a development of the sliding model control and is a control that can specify the follow-up speed of the controlled variable to the desired value and the convergence speed of the controlled variable when disturbance is applied, respectively and separately. 
   To be more specific, in this two-degree-of-freedom response-specifying control algorithm, first, in accordance with the first-order lag filter algorithm represented by Eq. 2-27, a filtered value (desired filter) of the phase desired value Cain_cmd_f(k) is calculated. In the equation, POLE_f is desired value filter factor and POLE referred to in Eq. 2-23, etc., switching function setting parameter, and they are set to be within a range of −1 to 0 as shown at the end of Eq. 2-27. 
   Then, in accordance with the sliding mode control algorithm represented by Eq. 2-22 to Eq. 2-26, the provisional input Usl(k) is calculated. Specifically, the provisional input Usl(k) is calculated as the sum of equivalent control input Ueq(k) and reaching law input Urch(k). 
   The equivalent control input Ueq(k) is calculated in accordance with Eq. 2-23. In the equation, c 1  is the disturbance estimation value to compensate the disturbance and modeling error, as mentioned above. 
   The reaching law input Urch(k) is a value that places the state on the switching line and is calculated according to Eq. 2-24. In the equation, Krch is predetermined reaching law gain (feedback gain) and σ(k) a switching function as defined by Eq. 2-25. Ecain(k) in Eq. 2-25 represents a follow-up error calculated by Eq. 2-26. 
   These Eq. 2-22 to Eq. 2-27 are derived in the manner mentioned below. Specifically, first, defining a system whose input is the provisional input Usl(k) and whose output is the phase Cain_est and modeling it as a discrete system model, Eq. 2-11 mentioned above can be obtained. Eq. 2-11 corresponds to a definition of the dynamic characteristics between the provisional input Usl(k) and phase Cain. 
   Next, replacing the model parameters and disturbance estimation value in Eq. 2-11 with values calculated by the model parameter scheduler  104 , assuming a model having the replaced values and applying the desired-filter-type two-degree-of-freedom sliding mode control theory such that the phase Cain follows up the phase desired value Cain_cmd based on the assumed model, Eq. 2-22 to Eq. 2-27 are obtained. 
   By virtue of the control algorithm of the above-mentioned two-degree-of-freedom response-specifying sliding mode controller (linear controller  110 ), the phase Cain can follow up the phase desired value Cain_cmd with high accuracy, while suppressing disturbance. Specifically, the follow-up ability can be specified freely by arbitrary setting the desired filter factor POLE_f in Eq. 2-27 within the aforesaid range. 
   Further, in the control algorithm represented by Eq. 2-22 to Eq. 2-26, the affection of the disturbance and modeling error can be suppressed by the disturbance estimation value. In addition, by arbitrary setting the switching-function-setting parameter within the aforesaid range, the follow-up behavior and the disturbance suppression ability can be specified freely. 
   In the flowchart of  FIG. 22 , next in S 202 , the lift control is conducted in accordance with equations mentioned there. 
   In the lift control in S 202  and compression ratio control in S 204 , instead of the aforesaid two-degree-of-freedom sliding mode control, its simplified version is used. In the lift control in S 202  and compression ratio control in S 204 , command values are calculated so as to avoid interference between the piston  26  and the intake valves  20  that could occur due to overshooting relative to the desired values. 
   Explaining this, first in S 202 , the lift command value (manipulated variable) U_Liftin is calculated in accordance with Eqs. (a) to (d) mentioned there. 
   In the simplified two-degree-of-freedom sliding mode control, as shown in Eq. (d), using a desired-value-follow-up-response-specifying parameter pole_f_lf and in accordance with the first-order lag filter algorithm, the filtered value of the lift desired value Liftin_cmd_f(k) is calculated. The desired-value-follow-up-response-specifying parameter pole_f_lf is the same as the aforesaid desired-value-filter factor. It defines the follow-up speed of the controlled variable toward the desired value and as shown, is set to a value greater than −1, but smaller than 0. 
   Next, as shown in Eq. (c), an error E_lf(k) is calculated by subtracting the filtered value of the lift desired value Liftin_cmd_f(k) from a lift detection value Liftin(k). Then, as shown in Eq. (b), the switching function σ_lk(k) is calculated by multiplying the preceding value of the error by the disturbance-suppression-response-specifying parameter pole_f and by adding the product to the current value of error. The disturbance-suppression-response-specifying parameter pole_f is the same as the switching-function-setting parameter and defines the convergence speed of the error E_lf when the disturbance is applied. As shown, it is set to a value greater than −1, but smaller than 0. 
   Then, as shown in Eq. (a), the lift command value (manipulated variable) U_Liftin is calculated by subtracting the product obtained by multiplying the switching function σ_lf(k)&#39;s integral by the second feedback gain Kadp_lf, from the product obtained by multiplying the switching function σ_lf(k) by the first feedback gain Krch_lf&#39;s minus value. 
   In Eq. (a), the right first term represents the aforesaid reaching law input and is calculated as a proportional term of the switching function as illustrated. The right second term represents the adaptive law input that places the state on the switching line, while suppressing steady-state error, and is calculated as an integral term of the switching function as illustrated. The first and second feedback gains are values set through simulation and experimentation. 
   At the same time, the lift control is conducted by operating the electric motor  40   d  of the variable lift mechanism  40  based on the calculated lift command value. 
   Next in S 204 , the compression ratio command value (manipulated variable) U_Cr is calculated in accordance with Eq. (a) to Eq. (d) shown there, and the compression ratio control is conducted by operating the hydraulic mechanism  44   e  of the variable compression ratio mechanism  44  based on the calculated compression ratio command value. 
   Since the command value calculation itself in S 204  is the same as that in S 202  except for the difference in suffix, explanation will be omitted. 
   Turning to the explanation of the flowchart of  FIG. 6 , next in S 12 , the fuel control is conducted. 
   Specifically, this is done by sampling the output of the airflow meter  68  at every CRK signal to calculate the intake air quantity Gcyl_afm therefrom (in order to eliminate the effect of pulsation, using the value averaged over the TDC interval). Then the fuel injection quantity that achieves stoichiometric air/fuel ratio is calculated by retrieving predetermined characteristics by using the calculated intake air quantity Gcyl_afm and the detected accelerator opening AP. The injector  16  is driven based on the calculated fuel injection quantity. 
   Next in S 14 , the ignition timing control is conducted. 
     FIG. 23  is a subroutine flowchart similar to that of  FIG. 21  showing the processing for this control. 
   Explaining this, In S 300 , it is similarly determined whether at least any mechanism among the variable lift mechanism  40  and other two mechanisms is faulty. When the result is affirmative, the program proceeds to S 302 , in which fail-safe operation NE control is conducted in accordance with simplified one-degree-of-freedom sliding mode control, similarly to what has been explained with respect to  FIG. 21 . 
   Since torque control of the valve mechanisms is impossible during fail-safe operation, the processing of S 302  is for controlling the torque by determining the ignition timing so as to maintain the engine speed NE constant. 
   Explaining this, first, as indicated by Eq. (c), an error Enfs(k) is calculated by subtracting the desired engine speed NE_fs (e.g., 2,000 rpm) from the engine speed detected value NE(k) and then, as indicated by Eq. (b), the product obtained by multiplying the value of the error in the last or preceding cycle by response-specifying parameter pole## is added to the value of the error in the current cycle to calculate switching function σ##(k). 
   Next, as indicated by Equation (a), the product obtained by multiplying the integral of the switching function by second feedback gain Kadp# and the product obtained by multiplying the switching function σ##(k) by first feedback gain Krch## are subtracted from the base value lg_fs_base of fail-safe reference ignition timing lg_fs to calculate the fail-safe reference ignition timing lg_fs. 
   Next, in S 304 , the calculated fail-safe reference ignition timing is defined as an ignition command value lglog. 
   On the other hand, when the result in S 300  is negative, the program proceeds to S 306 , in which it is determined whether the engine  10  is being started. When the result is affirmative, the program proceeds to S 308 , in which the ignition command value lglog is set to ignition timing at cranking lg_crk. 
   When the result in S 306  is negative, the program proceeds to S 310 , in which it is determined whether the detected accelerator opening AP is zero. When the result is negative, which can be taken to mean that the operator wants driving power, the program proceeds to S 312 , in which ordinary control is conducted. Specifically, the ignition command value lglog is calculated by retrieving appropriate characteristics (not shown) from the detected engine speed NE and calculated intake air quantity Gcyl_afm. 
   When the result in S 30  is affirmative, the program proceeds to S 314 , in which it is determined whether the warm-up time period of the catalytic converter  36  has elapsed. When the result is affirmative, the program proceeds to S 312 , and when it is negative, the program proceeds to S 316 , in which, by processing similarly to that in S 302 , feedback control of the ignition timing is conducted in accordance with simplified sliding mode control. 
   Specifically, as indicated by Eq. (c), an error Enast(k) is calculated by subtracting the desired engine speed NE_ast (e.g., 1,500 rpm) from the engine speed detected value NE(k) and then, as indicated by Eq. (b), the product obtained by multiplying the value of the error in the preceding cycle by response-specifying parameter pole# is added to the value of the error in the current cycle to calculate switching function σ#(k). 
   Next, as indicated by Equation (a), the product obtained by multiplying the integral of the switching function by second feedback gain Kadp# and the product obtained by multiplying the switching function σ#(k) by first feedback gain Krch# are subtracted from the base value lg_ast_base of post-start reference ignition timing lg_ast to calculate the post-start reference ignition timing lg_ast (e.g., 5 degrees). The program then proceeds to  5318 , in which the ignition timing lglog is set to the calculated post-start reference ignition timing. 
   As mentioned above, this embodiment provides a system for controlling the variable phase mechanism (plant)  42  of the engine  10  having the linear element and nonlinear element, and calculating control input Ucain based on the linear controller  110  that calculates a provisional input Usl to converge an output of the plant Cain to the phase desired value (desired value) Cain_cmd in accordance with response-specifying control algorithm (more specifically, two-degree-of-freedom response-specifying sliding mode control algorithm) based on the linear element, and on the nonlinear compensator (table characteristics of  FIG. 14 )  112  set to cancel the provisional input and characteristics of the nonlinear element of the plant; characterized by: the nonlinear characteristic adapter (correcting means)  114  for correcting the nonlinear compensator  112  based on an error e_nl between an output estimated value Cain_est of the plant calculated by an estimation model (estimated model; Eq. 2-1, Eq. 2-11, Eq. 3-1)  114   a  solely comprising the linear element and the output Cain of the plant. It should be noted that the linear controller  110 , etc., are, in fact, processing conducted by the ECU  80 . 
   With this, even when the nonlinear characteristics of the variable phase mechanism (plant)  42  change due to manufacturing variance or aging degradation, it becomes possible to accurately compensate the nonlinear characteristics by the nonlinear compensator  112 , and to control the plant output Cain to its desired value Cain_cmd with high accuracy and high response. 
   Further, since the nonlinear characteristic adapter (correcting means)  114  corrects the nonlinear compensator  112  in accordance with response-specifying control algorithm such that the error e_nl between the output estimated value Cain_est and the output Cain becomes zero, in addition to the effects mentioned above, it becomes possible to improve the control ability, since it becomes possible to make the correction of the nonlinear compensator  112  immediately without causing overshooting to occur. 
   Further, since the system further includes: means (linear controller  110 , more specifically the adaptive disturbance observer  102  that constitutes it) for calculating a disturbance estimated value c 1  applied to the variable phase mechanism (plant)  42 ; and the nonlinear characteristic adapter (correcting means)  114  calculates the output estimated value Cain_est based on a value Uest obtained by subtracting a term (value obtained by eliminating the term) concerning the disturbance estimated value c 1  from the control input Ucain (according to Eq. 2-19), in addition to the effects mentioned above, it becomes possible to prevent the plant output Cain from exhibiting overshooting relative to the desired value Cain_cmd and to further improve the control ability, since the disturbance compensation by the disturbance estimated value c 1  by the adaptive disturbance observer  102  and correction by the nonlinear characteristic adapter  114  do not interfere with each other. 
   Further, since the plant is the variable phase mechanism  42  that variably regulates a phase of an intake valve  20  of the engine  10 , in addition to the effects mentioned above, it becomes possible to control the phase of the intake valve to a desired phase with high accuracy and high response, without causing overshooting to occur. 
   Second Embodiment 
     FIG. 24  is a schematic diagram, similar to  FIG. 19 , but showing the overall structure of a plant control system according to the second embodiment of the invention. 
   In the control system of the first embodiment, in order to prevent the output Cain_est of the controlled object model  114   a  in the nonlinear characteristic adapter  114  from being influenced by the input based on the disturbance estimated value c 1  to erroneously generate the error e_nl, the system countermeasures to eliminate the terms concerning the disturbance estimated value c 1  from the input to the controlled object model  114   a . This countermeasure is to solve the discrepancy that the actual controlled object model is applied with disturbance, but the controlled object model  114   a  is not supplied with disturbance. 
   Paying an attention on this, as shown in  FIG. 24 , it can be understood that the same effect can be realized if the controlled object model  114   a  of the nonlinear characteristic adapter  114  is applied with estimated disturbance that are equivalent to actual disturbance. In other words, using the disturbance estimated value c 1  estimated by the adaptive disturbance observer  102 , the controlled object model  114   a  of the nonlinear characteristic adapter  114  is changed as follows: 
   [Numeral 24]
 
Cain_est( k )= a 1 sc  Cain(k−1)+ a 2 sc  Cain( k− 2)+ b 1 sc Usl ( k− 1)+ b 2 sc Usl ( k− 2)+ c 1( k )  (3-1)
 
   In this model, since the influence of disturbance is taken into amount, it becomes unnecessary to eliminate the term concerning the disturbance estimated value from the input. The equations therefore is as follows: 
   The equations for the nonlinear compensator  112  are as follows: 
   [Numeral 25]
 
 U cain( k )= dU cain( k )+ Cnl   —   adp ( k )  (3-2)
 
 dU cain( k )= Fnl ( dUsl ( k ))  (3-3)
 
 dUsl ( k )= Usl ( k )− Cnl   —   adp ( k )  (3-4)
 
   The equations for the nonlinear characteristic adapter  114  are as follows: 
   [Numeral 26]
 
 Cnl   —   adp ( k ) Cnl _base+ Dcnl ( k )  (3-5)
 
 Dcnl ( k )= Krch   —   cnl σcnl ( k )+ Kadp   —   cnl  sum —   σcnl ( k )  (3-6)
 
σ cnl ( k )= e   —   nl ( k )+POLE —   cnl e   —   nl ( k− 1)  (3-7)
 
 e   —   nl ( k )=Cain_est( k )−Cain( k )  (3-8)
 
Cain_est( k )= a 1 sc  Cain( k− 1)+ a 2 sc  Cain( k− 2)+ b 1 sc Usl ( k− 1)+ b 2 sc Usl ( k− 2)+ c 1( k )  (3-9)
 
   The characteristics of the linear controller (two-degree-of-freedom response-specifying controller)  110  are as follows: 
   [Numeral 27]
 
 Usl ( k )= U eq( k )+ U rch( k )  (3-10)
 
Equivalent Control Input
 
                   Ueq   ⁡     (   k   )       =       1     b   ⁢           ⁢   1   ⁢     sc   ⁡     (   k   )           ⁢     {         (     1   -     a   ⁢           ⁢   1   ⁢     sc   ⁡     (   k   )         -   POLE     )     ⁢           ⁢     CAIN   ⁡     (   k   )         +       (     POLE   -     a   ⁢           ⁢   2   ⁢     sc   ⁡     (   k   )           )     ⁢           ⁢     CAIN   ⁡     (     k   -   1     )         -     b   ⁢           ⁢   2   ⁢     sc   ⁡     (   k   )       ⁢     Usl   ⁡     (     k   -   1     )         -     c   ⁢           ⁢   1   ⁢     (   k   )       +     CAIN_cmd   ⁢   _f   ⁢     (   k   )       +       (     POLE   -   1     )     ⁢           ⁢   CAIN_cmd   ⁢   _f   ⁢     (     k   -   1     )       -     POLE   ⁢           ⁢   CAIN_cmd   ⁢   _f   ⁢     (     k   -   2     )         }               (     3   ⁢     -     ⁢   11     )               
Reaching Law Input
 
                   Urch   ⁡     (   k   )       =       -     Krch     b   ⁢           ⁢   1   ⁢           ⁢     sc   ⁡     (   k   )             ⁢     σ   ⁡     (   k   )                 (     3   ⁢     -     ⁢   12     )               
Switching Function
 σ( k )= E cain( k )+POLE  E cain( k− 1)  (3-13)   E cain( k )=CAIN( k )−CAIN_cmd —   f ( k− 1)  (3-14) Desired Value Filter CAIN_cmd —   f ( k )=−POLE —   f  CAIN_cmd —   f ( k− 1)+(1+POLE —   f )CAIN_cmd( k )  (3-15)     Krch: Feedback gain   POLE: Switching-function-setting parameter   POLE_f: Desired-value-filter coefficient; Here, −1&lt;POLE_f&lt;POLE&lt;0   
   The characteristics of the adaptive disturbance observer  102  are as follows: 
   [Numeral 28] 
                   c   ⁢           ⁢   1   ⁢     (   k   )       =       c   ⁢           ⁢   1   ⁢     (     k   -   1     )       +       Pdov     1   +   Pdov       ⁢   e_dov   ⁢     (   k   )                 (     3   ⁢     -     ⁢   16     )                 e _dov( k )=CAIN( k )−CAIN_hat( k )  (3-17) CAIN_hat( k )=θ T ( k )ζ( k )  (3-18) θ T ( k )=[ a 1 sc ( k ) a 2 sc ( k ) b 1 sc ( k ) b 2 sc ( k ) c 1( k− 1)] ζ T ( k )=[CAIN( k− 1)CAIN( k− 2) Usl ( k− 1) Usl ( k− 2)1]  (3-19) 
   The equations for the model parameter scheduler  104  are as follows: 
   [Numeral 29]
 
a1sc(k)←a1sc_map(k)  (3-20)
 
a2sc(k)←a2sc_map(k)  (3-21)
 
b1sc(k)←b1sc_map(k)×Kbsc(k)  (3-22)
 
b2sc(k)←b2sc_map(k)×Kbsc(k)  (3-23)
 
   In the operation of the plant control system according to the second embodiment, the phase command value (control input) U_cain is calculated in accordance with equations from Eq. 3-2 and on in S 200  of  FIG. 22 . 
   As mentioned above, In the plant control system according to the second embodiment, since the system further includes: means (linear controller  110 , more specifically the adaptive disturbance observer  102  that constitutes it) for calculating a disturbance estimated value c 1  applied to the variable phase mechanism (plant)  42 ; and the linear characteristic adapter (correcting means)  114  calculates the output estimated value Cain_est using the disturbance estimated value c 1 , it becomes similarly possible to prevent the plant output from exhibiting overshooting relative to the desired value and to further improve the control ability, since the disturbance compensation by the disturbance estimated value c 1  and correction of the nonlinear characteristic adapter  114  do not interfere with each other. Thus, the plant control system according to the second embodiment can obtain the same control result (shown in  FIG. 20 ) as that of the first embodiment. It should be noted that the linear controller  110 , etc., are, in fact, processing conducted by the ECU  80 . 
   Third Embodiment 
     FIG. 25  is a schematic diagram, similar to  FIG. 19 , but showing the overall structure of a plant control system according to the third embodiment of the invention. 
   The control systems of the first and second embodiments can be applied not only to the variable phase mechanism  42 , but also to the other such as the variable compression ratio mechanism  44 . As mentioned above with reference to  FIG. 2 , the quad-link variable compression ratio mechanism  44  increases or decreases the compression ratio by rotating the movable shaft  44   c   2  (shown in  FIG. 2 ) by the hydraulic mechanism  44   e.    
   At this time, as shown in  FIG. 26 , characteristics of generated force Fcr of the hydraulic mechanism  44   e  relative to the control input Ucr are nonlinear. In order to rotate the movable shaft  44   c   2  of the variable compression ratio mechanism  44  shown in  FIG. 2 , the force Fcr must be large. Since high-pressurized oil must accordingly be used, when opening area of oil passage in the control valve (not shown) is slightly changed, i.e., the plus/minus direction is changed, the characteristics of the force Fcr exhibit sharp change as shown in  FIG. 26 . 
   For that reason, the variable compression ratio mechanism  44  can also be modeled by nonlinear elements and linear elements (lag elements) that represent the characteristics shown in  FIG. 26 , and as illustrated in  FIG. 25 , can be controlled by the control system explained in the first embodiment or second embodiment. In that case, nonlinear table characteristics to be used in the nonlinear compensator  112  are those shown in  FIG. 27 . As regards equations, it suffices if Cain is replaced with Cr in the equations used in the first and second embodiments. 
   Using the control system shown in  FIG. 25 , the system according to the third embodiment can improve the control ability markedly. 
   As mentioned above, the third embodiment provides a system for controlling the variable compression ratio mechanism (plant)  44  of the engine  10  having the linear element and nonlinear element, and calculating control input Ucr based on the linear controller  110  that calculates a provisional input Usl to converge an output of the plant Cr to the compression ratio desired value (desired value) Cr_cmd in accordance with response-specifying control algorithm (more specifically, two-degree-of-freedom response-specifying sliding mode control algorithm) based on the linear element, and on the nonlinear compensator (table characteristics of  FIG. 27 )  112  set to cancel the provisional input and characteristics of the nonlinear element of the plant; characterized by: the nonlinear characteristic adapter (correcting means)  114  for correcting the nonlinear compensator  112  based on an error e_nl between an output estimated value Cr_est of the plant calculated by a controlled object (estimated model; Eq. 2-1, Eq. 2-11, Eq. 3-1)  114   a  solely comprising the linear element and the output Cr of the plant. It should be noted that the linear controller  110 , etc., are, in fact, processing conducted by the ECU  80 . 
   With this, even when the nonlinear characteristics of the variable compression ratio mechanism (plant)  44  change due to manufacturing variance or aging degradation, it becomes possible to accurately compensate the nonlinear characteristics by the nonlinear compensator  112 , and to control the plant output Cr to its desired value Cr_cmd with high accuracy and high response. 
   Further, since the nonlinear characteristic adapter (correcting means)  114  corrects the nonlinear compensator  112  in accordance with response-specifying control algorithm such that the error e_nl between the output estimated value Cr_est and the output Cr becomes zero, in addition to the effects mentioned above, it becomes possible to improve the control ability, since it becomes possible to make the correction of the nonlinear compensator  112  immediately without causing overshooting to occur. 
   Further, since the system further includes: means (linear controller  110 , more specifically the adaptive disturbance observer  102  that constitutes it) for calculating a disturbance estimated value c 1  applied to the variable phase mechanism (plant)  42 ; and the nonlinear characteristic adapter (correcting means)  114  calculates the output estimated value Cr_est based on a value Uest obtained by subtracting a term (value obtained by eliminating the term) concerning the disturbance estimated value c 1  from the control input Ucr (according to Eq. 2-19), in addition to the effects mentioned above, it becomes possible to prevent the plant output Cr from exhibiting overshooting relative to the desired value Cr_cmd and to further improve the control ability, since the disturbance compensation by the disturbance estimated value c 1  by the adaptive disturbance observer  102  and correction by the nonlinear characteristic adapter  114  do not interfere with each other. 
   Further, since the plant is the variable compression ratio mechanism  44  that regulates the compression ratio of the engine  10 , in addition to the effects mentioned in the first and second embodiments, at the time of switching increase/decrease of the compression ratio, it becomes possible to control to change the compression ratio, not abruptly, but smoothly. 
   It should be noted in the above that it is alternatively possible to combine the third embodiment with the first or second embodiment and to control both the variable phase mechanism  42  and variable compression ratio mechanism  44  by the control system mentioned above. 
   It should also be noted in the above that, although the nonlinear characteristic correction value is calculated in accordance with the equations using the simplified sliding mode control algorithm, other back stepping control mode algorithm or PID control can instead be used. 
   It should further be noted in the above that, although the simplified sliding mode control algorithm is used in the lift control and ignition timing control, other sliding mode control can instead be used. Further, any other control including adaptive control or PID control can instead be used. 
   It should further be noted that the variable lift mechanism, variable phase mechanism and variable compression ratio mechanism are not limited to the shown examples. 
   INDUSTRIAL APPLICABILITY 
   According to the invention, in a plant control system calculating control input Ucain, Ucr based on a linear controller that calculates a provisional input Usl to converge an output of the plant to a desired value in accordance with control algorithm based on the linear element, and on a nonlinear compensator set to cancel the provisional input and characteristics of the nonlinear element of the plant; correcting means is provided for correcting the nonlinear compensator based on an error e_nl between an output estimated value Cain_est of the plant calculated by an estimation model solely comprising the linear element and the output Cain of the plant, even when the nonlinear characteristics of the plant change due to manufacturing variance or aging degradation, it becomes possible to accurately compensate the nonlinear characteristics by the nonlinear compensator, and to provide a system that controls the plant output to its desired value with high accuracy and high response.