Patent Publication Number: US-4928489-A

Title: Supercharging pressure control method for turbocharged internal combustion engines

Description:
BACKGROUND OF THE INVENTION 
     This invention relates to a supercharging control method for internal combustion engines, which is directed to improvement of the rising characteristic of supercharging pressure in the engine. 
     There have conventionally been proposed methods of controlling supercharging pressure in an internal combustion engine equipped with a supercharger capable of controlling the supercharging pressure such as a variable capacity turbocharger utilizing an exhaust gas flow for driving a turbine thereof, by means of an actuator such as a pressure-responsive type actuator including a diaphragm which operates in response to supercharging pressure or vacuum within the intake pipe of the engine, or an actuator utilizing a stepping motor. Amongst these methods, a method has been proposed by the assignee of the present application, e.g. by Japanese Provisional Patent Publication (Kokai) No. 63-129126, which controls the supercharging pressure in open loop control mode when the supercharging pressure is in a transient state where it drastically changes, and in feedback control mode when it is in a steady state. This proposed method is capable of controlling the supercharging pressure more stably than conventional methods by virtue of the open loop control in the transient state. However, the proposed method still has room for further improvement in respect of the accelerability of the engine. 
     Specifically, according to the proposed method, the open loop control is executed at acceleration of the engine, which is a transient state and in which the supercharging pressure should be promptly increased. During the open loop control, a basic control amount by which the supercharging pressure is controlled is determined in accordance with operating conditions of the engine, e.g. as a function of throttIe valve opening and engine rotational speed, by the use of a map of these parameters, or like means, and the determined basic control amount is directly applied to the open loop control. However, according to this control manner it is difficult to properly control the supercharging pressure in the case where it is increasing at a progressively increasing rate. 
     Generally, when the accelerator pedal of a vehicle is stepped on for acceleration of the vehicle, the supercharging pressure does not rise at a constant rate, but it rises initially at a low rate and then at a progressively increasing rate, sometimes resulting in an excessive rise rate. This phenomenon is more conspicuous at sudden standing start of the vehicle or at rapid acceleration where usually the supercharging pressure is controlled to increase to a high value at a high rate so as to enhance the control responsiveness. However, such an excessive rise rate of supercharging pressure at acceleration can cause a sudden increase in the engine torque, which spoils the feeling of smooth acceleration and can also cause spinning of wheels of the vehicle. Further, in transition to the feedback control mode the excessive rise rate of supercharging pressure can cause overboosting, which in turn can cause knocking of the engine, also spoiling the driveabilitY at acceleration. 
     On the other hand, if the rise rate of supercharging pressure is too low at acceleration, this gives the driver a feeling of insufficient acceleration, failing to obtain a feeling of smooth acceleration. 
     SUMMARY OF THE INVENTION 
     It is the object of the invention to provide a supercharging pressure control method for an internal combustion engine, which is capable of properly controlling the supercharging pressure at acceleration of the engine in such a manner that a sudden change in the supercharging pressure or overboosting thereof may not take place. thereby optimizing the rise characteristic of the supercharging pressure and hence achieving smooth acceleration of the engine. 
     To attain the above object, the present invention provides a method of controlling supercharging pressure in an internal combustion engine by means of a basic control amount dependent upon operating conditions of the engine. 
     The method according to the invention is characterized by comprising the following steps: 
     (1) detecting a change rate of the supercharging pressure; and 
     (2) when the supercharging pressure is in a transient state where it is increasing, correcting the basic control amount in response to the detected change rate of the supercharging pressure, in a manner such that the supercharging pressure increases at a predetermined rate. 
     The basic control amount is corrected such that the increase rate of the supercharging pressure is decreased as the detected change rate of the supercharging pressure in the transient state is larger. 
     The above and other objects, features, and advantages of the invention will be more apparent from the ensuing detailed description taken in conjunction with the accompanying drawings. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a schematic view showing the whole arrangement of the intake system and the exhaust system of an internal combustion engine to which is applied the method according to the invention; 
     FIG. 2 is an enlarged longitudinal cross-sectional view of a variable capacity turbocharger in FIG. 1; 
     FIG. 3 is a transverse cross-sectional view taken on line III--III of FIG. 2; 
     FIG. 4 is a transverse cross-sectional view take on line IV--IV of FIG. 2; 
     FIGS. 5A, 5B and 5C, collectively referred to as FIG. 5, constitute a flowchart showing a main routine for controlling an electromagnetic control valve in FIG. 1, according to a first embodiment of the invention; 
     FIG. 6 is a flowchart showing a subroutine for selecting a time period to be counted by a timer; 
     FIG. 7 is a graph showing the relationship between a high supercharging pressure-discriminating value P 2HG  and the engine rotational speed Ne; 
     FIG. 8 is a flowchart showing a subroutine for subtraction from a basic duty ratio and from desired supercharging pressure, which is executed when the transmission is in the first speed position; 
     FIG. 9 is a diagram showing a predetermined operating zone to be discriminated in the subroutine shown in FIG. 10; 
     FIG. 10 is a flowchart showing a subroutine for subtraction from the basic duty ratio and from the desired supercharging pressure, which is executed when the transmission is in a position other than the first speed position; 
     FIG. 11 is a flowchart showing a subroutine for determining a decremental value D T  ; 
     FIGS. 12(a) to 12(c) is a diagram showing maps of the decremental value; 
     FIG. 13 is a flowchart showing a subroutine for determining an incremental value D TRB  ; 
     FIGS. 14(a) to 14(c) are diagrams showing maps of D TRB  ; 
     FIGS. 15(a) to 15(c) are similar diagrams to FIGS. 14(a) to 14(c), showing maps of a decremental valve /P 2ST  ; 
     FIGS. 16(a) to 16(c) are similar diagrams to FIGS. 14(a) to 14(c) of FIG. 14, showing maps of a decremental valve /P 2FB  ; 
     FIG. 17 is a flowchart showing a subroutine for determining feedback coefficients for determining, respectively, a proportional control term and an integral control term; 
     FIG. 18 is a diagram showing a change in the intake pressure, which can take place when the gear position of the transmission is shifted; 
     FIG. 19 is a diagram showing changes in duty ratio and supercharging pressure, which can take place when the control mode is shifted from the open loop control mode to the feedback control mode; 
     FIGS. 20A and 20B, collectively referred to as FIG. 20, constitute a flowchart showing a main routine for controlling an electromagnetic valve in FIG. 1; 
     FIGS. 21A and 21B, collectively referred to as FIG. 21, constitute a flowchart showing a main routine for controlling the electromagnetic control valve in FIG. 1 according to a second embodiment of the invention; 
     FIG. 22 is a diagram showing a map of a basic duty ratio D M  ; 
     FIG. 23 is a flowchart showing a subroutine for determining the gear position of the transmission; 
     FIG. 24 is a diagram showing a table of a predetermined value V F  of the vehicle speed, applied to the subroutine of FIG. 23; 
     FIG. 25 is a diagram showing a map of an intake air temperature-dependent correction coefficient K TATC  ; 
     FIGS. 26A and 26B, collectively referred to as FIG. 26, constitute a flowchart showing a subroutine for determining an open loop control region, which is executed at a step S106 in FIG. 21; 
     FIG. 27 is a diagram showing a table of a first decremental value /P BSD  to be applied when the transmission is in a position other than the first speed position; 
     FIG. 28 is a diagram showing a table of a second decremental value /P BFB  to be applied when the transmission is in a position other than the first speed position; 
     FIG. 29 is a diagram showing a table of a subtraction term D T  to be applied when the transmission is in a position other than the first speed position; 
     FIG. 30 is a diagram showing a table of a subtraction term D FT  to be applied when the transmission is in the first speed position; 
     FIG. 31 is a diagram showing a map of a desired value P BREF  of supercharging pressure; 
     FIG. 32 is a diagram showing a table of a constant K P  for a proportional control term K P  ; 
     FIG. 33 is a diagram showing a table of a constant K I  for an integral control term K I  ; 
     FIG. 34 is a diagram showing a map of a learned correction coefficient K MOD  ; 
     FIG. 35 is a diagram showing the relationship between the intake pressure P B  and the supercharging pressure control; and 
     FIGS. 36(a) to 36(c) of FIG. 36 are diagrams showing changes in the values D OUT , P B  and engine torque, respectively, which are obtained by a conventional method and the method of the present invention. 
    
    
     DETAILED DESCRIPTION 
     The invention will now be described in detail with reference to the drawings showing embodiments thereof. 
     Referring first to FIGS. 1 through 4, there is illustrated a supercharging pressure control system for an internal combustion engine, to which is applied the method according to the invention. The engine is a multiple-cylinder type which has a cylinder block E with a plurality of cylinders each provided with an intake port, neither of which is shown. Connected to the intake port of each cylinder is an intake manifold 1, to which are connected an intake pipe 2, a throttle body 3, an intercooler 4, and a variable capacity type turbocharger 5, and an air cleaner 6 in the order mentioned. Each cylinder has an exhaust port, not shown, to which is connected an exhaust manifold 7. Connected to the exhaust manifold 7 is an exhaust pipe 8 with the turbocharger 5 arranged across an intermediate portion thereof. A three-way catalytic converter 9 is arranged across the exhaust port at a location downstream of the turbocharger 5. Fuel injection valves 10 are mounted in the intake manifold 1 at locations close to the intake ports of the respective cylinders for injecting fuel toward the intake ports. 
     The turbocharger 5 is provided with a water jacket 11, an inlet of which is connected in parallel with an outlet of a water pump 13, together with an inlet of the intercooler 4. The water jacket 11 and the intercooler 4 have their outlets connected to the radiator 12. The radiator 12 is provided in addition to a radiator, not shown, for cooling coolant supplied into the interior of the cylinder block E of the engine. 
     The structure of the variable capacity type turbocharger 5 will now be explained with reference to FIGS. 2-4. The turbocharger 5 comprises a compressor casing 14, a back plate 15 closing a rear side of the compressor casing 14, a main shaft 16, a bearing casing 17 supporting the main shaft 16, and a turbine casing 18. 
     A scroll passage 19 is defined between the compressor casing 14 and the back plate 15, and an axially extending inlet passage 20 is defined through a central portion of the compressor casing 14. A compressor wheel 21 is mounted on an end of the main shaft 16 at a central portion of the scroll passage 19 and at an inner end of the inlet passage 20. 
     The compressor casing 14 and the back plate 15 are fastened together by means of bolts 22. The bearing casing 17 is joined to the back plate 15 at a central portion thereof. The bearing casing 17 is formed therein with a pair of bearing holes 23, 24 in coaxial and spaced relation to each other, through which the main shaft 16 extends. Interposed between the main shaft 16 and the bearing holes 23, 24 are radial bearings 25, 26 rotatably supporting the main shaft 16 against the bearing casing 17. Interposed between a stepped shoulder 16a of the main shaft 16 facing toward the compressor wheel 21 and the compressor wheel 21 are a collar 27, a thrust bearing 28, and a bushing 29 in the order mentioned as viewed from the stepped shoulder 16a side. By fastening a nut 30 threadedly fitted on an end portion of the main shaft 16 against an outer end of the compressor wheel 21, the main shaft 16 is located in its proper axial position and at the same time the compressor wheel 21 is mounted onto the main shaft 16. 
     A lubricating oil inlet port 32 is formed in a lateral side wall of the bearing casing 17 and connected to a lubricating oil pump, not shown, and a lubricating oil passage 33 is formed in the bearing casing 17 for guiding lubricating oil from the lubricating oil inlet port 32 to the radial bearings 25, 26 as well as to the thrust bearing 28. The bearing casing 17 has the other lateral side wall formed with a lubricating oil drain port 34 for draining lubricating oil. The drained oil is collected into an oil sump, not shown. 
     The bushing 39 extends through a through hole 35 formed in a central portion of the back plate 15. A seal ring 36 is interposed between the bushing 29 and the through hole 35 to prevent lubricating oil from flowing from the thrust bearing 28 to the compressor wheel 21. A guide plate 37 is interposed between the back plate 15 and the thrust bearing 28, through which the bushing 29 extends, so that lubricating oil flowing from the thrust bearing 28 is guided by the guide plate 37 while it is splashed in the radially outward direction. A free end portion of the guide plate 37 is curved so as to smoothly guide the lubricating oil into the lubricating oil drain port 34. 
     The bearing casing 17 is further formed therein with the aforementioned water jacket 11 disposed around the main shaft 16, a water supply port 38 for guiding water or coolant from the water pump 13 shown in FIG. 1 to the water jacket 11, and a water drain port 39 for guiding water from the water jacket 11 to the radiator 12 shown in FIG. 1. The water jacket 11 has a portion closer to the turbine casing 18 which is shaped in the form of an annulus surrounding the main shaft 16, and a portion above the lubricating oil drain port 34 and the main shaft 16, which has a generally U-shaped section in a manner downwardly diverging along the main shaft 16 as shown in FIG. 4. The water supply port 38 communicates with a lower portion of the water jacket 11, while the water drain port 39 communicates with an upper portion of the water jacket 11. 
     The turbine casing 18 is formed therein with a scroll passage 41, an inlet passage 42 tangentially extending from the scroll passage 41, and an outlet passage 43 axially extending from the scroll passage 41. 
     The bearing casing 17 and the turbine casing 18 are joined together with a back plate 44 held therebetween. That is, the two members are fastened together by tightening nuts 47 via rings 46 onto respective stud bolts 45 screwed in the turbine casing 18, with a radial flange 44a at the periphery of the back plate clamped between the two members. 
     Secured to the back plate 44 is a stationary vane member 48 which divides the interior of the scroll passage 41 into a radially outer passage 41a, and a radially inner or inlet passage 41b. The stationary vane member 48 comprises a cylindrical hub portion 48a coaxially fitted in the outlet passage 43 via a seal ring 51, an annular radial portion 48b radially outwardly extending from an axially intermediate portion of the cylindrical hub portion 48a, a plurality of, e.g. four stationary vanes 49 axially extending from an outer peripheral edge of the annular radial portion 48b and secured to the back plate 44 by means of bolts 52. A turbine wheel 50 is accommodated within the stationary vane member 48, which is secured on the other end of the main shaft 16. 
     The stationary vanes 49 are circumferentially arranged at equal intervals, each being arcuate in shape. Disposed between adjacent stationary vanes 49 are movable vanes 54 with one end thereof secured to respective rotary shafts 53 rotatably supported by the back plate 44 with their axes extending parallel with that of the main shaft 16. The movable vanes 54 act to adjust the opening area of spaces (hereinafter called &#34;the space area&#34;) between adjacent stationary and movable vanes 49, 54. 
     Each movable vane 54 is also arcuate in shape, with almost the same curvature as the stationary vanes 49, and pivotable between a fully closed position shown by the solid line in FIG. 3 and a fully open position shown by the broken line in the figure. The rotary shafts 53 are operatively connected to an actuator 60 in FIG. 1 by means of a link mechanism 55 disposed between the back plate 44 and the bearing casing 17 so that the movable vanes 54 are simultaneously controlled to open and close by the actuator 60. 
     Interposed between the back plate 44 and the bearing casing 17 is a shield plate 56 extending along a rear end face of the turbine wheel 50, for preventing the heat of exhaust gases from the engine flowing in the inlet passage 41b from being directly transmitted to the interior of the bearing casing 17. A plurality of annular grooves 58 are formed as labyrinth grooves in the outer peripheral surface of the main shaft 6 at a location corresponding to a through hole 57 formed in the bearing casing 17 and penetrated by an end of the main shaft 16. These grooves 58 serve to prevent exhaust gases from leaking into the bearing casing 17. 
     With the above described arrangement, exhaust gas emitted from the engine cylinder block E flows into the radially outer passage 41a through the inlet passage 42, and then flows into the inlet passage 41b at a flow rate corresponding to the space area between the movable vanes 54 and the stationary vanes 49, which is determined by the angle of the movable vanes 54. As the exhaust gases flows into the inlet passage 41b, it drives the turbine wheel 50 to rotate. Then, the gas is discharged through the outlet passage 43. As the space area between the movable and stationary vanes 54, 49 decreases, the rotational speed of the turbine wheel 50 and hence that of the main shaft 16 becomes higher, whereas as the opening area increases, the rotational speed becomes lower. The rotation of the turbine wheel 50 causes rotation of the compressor wheel 21 so that air introduced into the inlet passage 20 through the air cleaner 6 is compressed by the rotating compressor wheel 21 to be forced to pass through the scroll passage 19 toward the intercooler 4. When the movable vanes 54 are moved into the radially outermost position so that the space area between the movable and stationary vanes 54, 49 becomes the minimum, the supercharging pressure becomes the maximum, whereas when the movable vanes 54 assumes the radially innermost position and hence the opening area becomes the maximum, the supercharging pressure becomes the minimum. 
     Water supplied into the water jacket 11 serves to prevent the temperature of the bearing casing 17 from becoming excessively high due to increased temperature of air compressed by the turbocharger 5, while water supplied to the intercooler 4 serves to prevent increase of the intake air temperature. 
     Referring again to FIG. 1, the actuator 60, which drives the movable vanes 54 of the turbocharger 5, comprises a housing 61, a diaphragm dividing the interior of the housing 61 into a first pressure chamber 62 and a second pressure chamber 63, a return spring 65 interposed between the housing and the diaphragm 64 and urging the diaphragm 64 in a direction causing the first pressure 63 to contract, and a driving rod 66 airtightly and movably extending through the housing 61, with one end thereof connected to the diaphragm 64 and the other end to the link mechanism 55. The driving rod 66 and the link mechanism 55 are connected to each other in such a manner that when the driving rod 66 is moved by the diaphragm 64 which is displaced in a direction causing the second pressure chamber 63 to contract, the movable vanes 54 are radially inwardly pivoted in the turbine casing 18 to increase the space opening area between the movable and stationary vanes 54, 49. 
     The first pressure chamber 62 is connected to a portion of the intake passage between the turbocharger 5 and the intercooler 4 via a regulator 67, a restriction 68, and an electromagnetic control valve 69, to be supplied with supercharging pressure P 2  therefrom, and is also connected to another portion of the intake passage between the air cleaner 6 and the turbocharger 5. The electromagnetic control valve 69 is a normally-closed duty control type with a solenoid 70. As the valve-closing duty ratio for the solenoid 70 becomes smaller, the pressure within the first pressure chamber 62 increases, which is transmitted through the driving rod 66 and the link mechanism 55 to cause the movable vanes 54 to be radially inwardly pivoted, i.e. toward the closing side The second pressure chamber 63 is connected to a portion of the intake passage downstream of the throttle body 3 through a check valve 71 and an electromagnetic valve 72 to be supplied with intake pressure P B  therefrom. The electromagnetic valve 72 is a normally-closed type which becomes open when its solenoid 73 is energized. When the valve 72 is open, intake pressure P B  is supplied into the second pressure chamber 63 so that the actuator 60 drives the movable vanes 54 to be radially inwardly displaced. 
     The electromagnetic valves 69, 72 are controlled by an electronic control unit (control means) C, to which are connected a water temperature sensor S W  for sensing the temperature T W  of cooling water in a water jacket, not shown, provided in the engine cylinder block E, an intake air temperature sensor S A  for sensing the temperature T A  of intake air in the intake passage downstream of the intercooler 4, an intake pressure sensor S PA  for sensing intake pressure P A  in the intake passage at a location between the air cleaner 6 and the turbocharger 5, a supercharging pressure sensor S P2  for sensing supercharging pressure P 2  in the intake passage at a location between the turbocharger 5 and the intercooler 4, an intake pressure sensor S PB  for sensing intake pressure P B  in the intake passage downstream of the throttle body 3, an engine speed sensor S N  for sensing the rotational speed N E  of the engine, a throttle valve opening sensor S TH  for sensing the valve opening 0 TH  of a throttle valve 74 within the throttle body 3, a vehicle speed sensor S V  for sensing the speed V of a vehicle in which the engine is installed, and a gear position sensor S S  for sensing the gear position of an automatic transmission connected to the engine. The control unit C operates in response to the input signals from these sensors to control the energization and deenergization of the solenoids 70, 73 of the electromagnetic valves 69, 72. 
     Next, the manner of control by the control unit C will be described below. First, the control of duty ratio of the solenoid 70 of the electromagnetic control valve 69 will be described with reference to a main routine shown in FIG. 5. The valve-closing duty ratio D OUT  represents the ratio of valve-closing time to the time period of one cycle over which the valve 69 is opened and closed. Therefore, as the duty ratio D OUT  is larger, the opening degree of the movable vanes 54 is decreased, and D OUT  =0% corresponds to the maximum opening degree of the movable vanes 54 while D OUT  =100% corresponds to the minimum opening degree of same. 
     At a step S1, it is determined whether or no&amp; the engine is in starting mode, i.e. the engine is cranking. If the engine is in starting mode, the duty ratio D OUT  is set to 0, i.e. the electromagnetic control valve 69 is fully opened to set the maximum space area between the movable vanes 54 and the stationary vanes 49 (step S2). The engine is unstable during cranking, and if supercharging pressure is introduced into combustion chambers while the engine is in such an unstable state the engine will be more unstable. Therefore, in the above step S2, the space area between the movable vanes 54 and the stationary vanes 49 is made the maximum to thereby prevent supercharging pressure from being introduced into the combustion chambers. Further, a driver of the vehicle does not demand supercharging of intake air during cranking, and therefore it is not necessary to reduce the space area between the movable vanes 54 and the stationary vanes 49. At a step S3, a t FBDLY  timer for counting a time period t FBDLY  by which the start of the feedback control is delayed is reset, and then at a step S4, the duty ratio D OUT  is outputted. 
     The time period t FBDLY  is calculated in a manner shown in FIG. 6. Depending on the change rate ΔP 2  in supercharging pressure P 2 , one of three time periods t FBDLY1 , t FBDLY2 , and t FBDLY3  is selected as t FBDLY . The change rate ΔP 2  is calculated as the difference (ΔP 2  =P 2n  -P 2n-6 ) between the supercharging pressure P 2n  detected in the present loop and the supercharging pressure P 2n-6  detected in the sixth loop before the present loop. More specifically, the main routine shown in FIG. 5 is carried out in synchronism with generation of TDC signal pulses. However, since the change rate ΔP 2  in supercharging pressure P 2  between two adjacent TDC signal pulses is too small for accurate detection of the change rate ΔP 2 , the difference between the P 2n  detected in the present loop and the P 2n-6  detected in the sixth loop before the present loop is calculated in order to detect the supercharging characteristic or the change rate Δ P 2  more accurately. A predetermined lower change rate ΔP 2PTL  and a predetermined higher change rate ΔP 2PTH  are provided which are determined in accordance with the engine rotational speed N E . If ΔP 2  ≦ΔP 2PTL , t FBDLY1  is selected, if ΔP 2PTL  &lt;ΔP 2  ≦ΔP 2PTH , t FBDLY2  is selected, and if ΔP 2PTH  &lt;ΔP 2 , t FBDLY3  is selected. Further, the three time periods are in the relationship of t FBDLY1  &lt;t FBDLY2  &lt;t FBDLY3 . Therefore, when the change rate ΔP 2  is small, i.e. the supercharging pressure undergoes a gentle change, the delaying time is set to a smaller value, and when the change rate ΔP 2  is great, i.e. the supercharging pressure undergoes a drastic change, the delaying time is set to a larger value. This makes it possible to set the delaying time period t FBDLY  to an appropriate value when the operating mode is shifting from open loop mode to feedback control mode, to thereby positively prevent occurrence of hunting of the supercharging pressure during the transitional state of the operating mode. 
     If it is determined at the step S1 that the engine is not in starting mode, it is determined at a step S5 whether or not the engine coolant temperature T W  is below a predetermined lower value T WL . If the engine coolant temperature T W  is below the predetermined lower value T WL , the program proceeds to the step S2. The possible operating conditions of the engine which satisfy T W  &lt;T WL  are, for example, those in which the engine is at an early stage of starting or the ambient air temperature is very low. At the early stage of starting, the operation of the engine is unstable, while when the ambient air temperature is very low, the intake air density is high to increase the charging efficiency, which may result in abnormal combustion of the engine. If supercharging pressure is introduced into the combustion chambers under such a cold state of the engine, the operation of the engine may be even more unstable, and the abnormal combustion may be promoted. Further, at an extremely low temperature, there is a possibility of malfunctioning of the electromagnetic valve 69, that is, the electromagnetic valve 69 may not behave in accordance with instructions from the control unit C. Therefore, if T W  &lt;T WL , the program proceeds to the step S2 to set D OUT  to 0. 
     If it is determined at the step S5 that T W  ≧T WL , the program proceeds to a step S6, where it is determined whether or not the engine coolant temperature T W  exceeds a predetermined higher value T WH . If the engine coolant temperature T W  exceeds the predetermined higher value T WH , the program proceeds to the step S2. The possible operating conditions which satisfy T W  &gt;T WH  are, for example, those in which the engine has been continuously operating under a high load condition, or the ambient air temperature is very high, or the engine coolant system of the engine cylinder block E is malfunctioning. Under such high temperature conditions of the engine, the intake air density is low to decrease the charging efficiency, which may also result in abnormal ambition such as misfiring. If supercharging pressure is introduced into the combustion chambers then the engine is under such unstable operating conditions, the engine operation will be made even more unstable. Therefore, at the step S2, the duty ratio D OUT  is set to 0. Further, when the ambient air temperature is very high, the inductance of the solenoid 70 is liable to change, so that it may behave differently from a predetermined behavior under normal induction conditions. Also for the purpose of avoiding this, the program proceeds to the step S2. If it is determined at the step S6 that T W  ≦T WH , the program proceeds to a step S7. In other words, it is determined that the engine coolant temperature T W  is equal to or higher than the predetermined lower value T WL  and equal to or lower than the predetermined higher value T WH , the program proceeds to the step S7, and otherwise, the program proceeds to the step S2. 
     At the step S7, it is determined whether or not supercharging pressure exceeds a predetermined high supercharging pressure-discriminating value P 2HG  set as shown in FIG. 7. If P 2  &gt;P 2HG , the program proceeds to the step S2. If P 2  ≦P 2HG , the program proceeds to a step S8. The predetermined high supercharging pressure-discriminating value P 2HG  varies in accordance with the engine rotational speed N E . The value P 2HG  is provided in order that the supercharging pressure may not be higher than a limit value of the amount of advancement of ignition timing above which knocking can take place, the limit value corresponding to the engine rotational speed N E  so as to ensure attainment of the maximum output of the engine immediately under the limit value. When the engine rotational speed N E  is in a low range, where the transmission is set into a low speed position, the torque which is applied to the transmission component parts increases, whereas when the engine rotational speed N E  is in a high engine rotational speed range, knocking of the engine main body E can take place, adversely affecting the durability of the engine. Therefore, P 2HG  is set to values lower than medium engine rotational speed range. If the supercharging pressure P 2  which exceeds the high supercharging pressure-discriminating value P 2HG  is detected, the program skips over the steps S2, S3 to the step S4, where the duty ratio D OUT  is set to 0 whereby the supercharging pressure P 2  is decreased, and at the same time fuel injection is inhibited. 
     At the step S8, a basic duty ratio D M  is determined as a basic supercharging pressure control amount. The basic duty ratio D M  is searched from a map in accordance with the engine rotational speed N E  and the throttle valve opening θ TH , whereby it is made possible to accurately determine operating conditions of the engine. This is because it is impossible to accurately determine decelerating or transitional operating conditions of the engine by the use of the engine rotational speed N E  alone or the throttle valve opening θ TH  alone. In this embodiment, the throttle valve opening θ TH  is adopted as a parameter representative of load on the engine. However, it may be replaced by the intake pressure P B  or the fuel injection amount. 
     At a step S9, it is determined whether or not the automatic transmission is in a first speed position. If the automatic transmission is in the first speed position the program proceeds to a step S10, and if the transmission is in a position other than the first speed position, the program proceeds to a step S11. 
     At the step S10, subtraction is effected from the basic duty ratio D M  in accordance with a subroutine shown in FIG. 8. More specifically, a predetermined operating zone is provided as shown by hatching in FIG. 9, which is determined by the engine rotational speed N E  and the intake pressure P B , in which zone subtraction from the basic duty ratio D M  should be effected. Depending on whether or not the operating condition of the engine is within this predetermined operating zone, it is determined whether or not subtraction should be effected from the basic duty ratio D M . In FIG. 9, the torque of the engine is determined based upon the engine rotational speed N E  and the intake pressure P B , and the border line of the predetermined operating zone indicates the maximum allowable torque amount applied to the gear shaft of the transmission when the transmission is in the first speed position. In other words, in order to prevent excessive load on the rear shaft when the transmission is in the first speed position, the torque of the engine in each operating region is monitored accurately by the use of the engine rotational speed N E  and the intake pressure P B . If the operating condition of the engine is outside the predetermined operating zone. the program proceeds to a step 12 without correcting the basic duty ratio D M , whereas if the operating condition of the engine is within the predetermined operating zone, it is determined whether or not a flag F is 0, i.e. the engine is in the feedback control mode. If the engine is in the open loop control mode, subtraction of D M  =D M  -D F  is carried out. If the engine is in the feedback control mode, subtraction of P 2REF  =P 2REF  -ΔP 2REFF  is carried out. D F  is a predetermined decremental value, P 2REF  is a desired value of supercharging pressure used in the feedback control mode, and ΔP 2REFF  is also a predetermined decremental value. These values will be described in detail hereinbelow where the feedback control is described. 
     At the step S11, subtraction is effected from the basic duty ratio D M  in accordance with a subroutine shown in FIG. 10. More specifically, if the throttle valve opening θ TH  is above a predetermined value θ THOS , the engine rotational speed N E  is above a predetermined value N EOS , the intake pressure P B  is above a predetermined value P BOS , change rate ΔN E  of the engine rotational speed N E  detected in the last loop is positive, and change rate ΔN E  of the engine rotational speed N E  detected in the present loop is negative, subtraction of D M  =D M  -D OS  is carried out in the open loop control mode, and subtraction of P 2REF  =P 2REF  -ΔP 2REFOS  is carried out in the feedback control mode. Otherwise, the program proceeds to the step S12 without correcting the basic duty ratio D M . D OS  and ΔP 2REFOS  are predetermined decremental values. 
     At the step S12, it is determined whether or not the throttle valve opening θ TH  is above a predetermined value θ THFB . This predetermined value θ THFB  is for determining whether the control mode should be shifted from the open loop control mode to the feedback control mode. BY adopting the throttle valve opening θ TH  as the determining parameter, it is possible to accurately determine whether the driver of the vehicle demands acceleration, i.e. supercharging. If θ TH  ≦θ THFB , i.e. if the open loop control is to be continued, the t FBDLY  timer shown in FIG. 6 is reset at a step S13, and then the program proceeds to a step S14. 
     At the step S14, a duty ratio correction coefficient K MODij  determined by the engine rotational speed N E  and the intake air temperature T A  is searched from in a map. As described later, the correction coefficient K MODij  is learned when the optimum supercharging pressure P2 is within a predetermined difference range, and renewed by learning. The initial value of the correction coefficient K MODij  is set to 1. 
     At a step S15, an atmospheric pressure-dependent correction coefficient K PATC  (0.8 to 1.0) for correcting the duty ratio is determined depending on the atmospheric pressure P A . At a step S16, an intake air temperature-dependent correction coefficient K TATC  (0.8 to 1.3) for correcting the duty ratio is determined depending on the intake air temperature T A . At a step S17, a decremental value D T  depending on the change rate ΔP 2  of supercharging pressure P 2  is determined in accordance with a subroutine shown in FIG. 11. More specifically, if the throttle valve opening θ TH  is larger than the predetermined value θ THFB , the decremental value D T  is determined by the change rate ΔP 2  of supercharging pressure P 2  and the engine rotational speed N E  as shown in (a), (b), and (c) of FIG. 12. If θ TH  ≦θ THFB , D T  is set to 0%. 
     (a) of FIG. 12 shows a map of the decremental value D T  selected when the engine rotational speed N E  is equal to or lower than a predetermined first changeover engine rotational speed N FB1  (e.g. 3000 rpm). (b) of FIG. 12 shows a map of the decremental value D T  selected when the engine rotational speed N E  is above the first changeover engine rotational speed N FB1  and equal to or lower than a predetermined second changeover engine rotational speed N FB2  (e.g. 4500 rpm), and (c) of FIG. 12 shows a map of the decremental value D T  selected when the engine rotational speed N E  is above the second changeover engine rotational speed N FB2 . The decremental value D T  is applied, as shown in FIG. 19, when the actual supercharging pressure P 2  becomes higher than a predetermined value P 2ST  lower than a desired value P 2REF  of supercharging pressure so that overshooting during rising of the supercharging pressure can be prevented. Further, D T  is set, as shown in FIG. 12 and as described above, in accordance with the engine rotational speed N E  and the change rate ΔP 2  of supercharging pressure. This is because the amount of overshooting depends on the engine rotational speed N E  and the change rate ΔP 2  of supercharging pressure when the predetermined value P 2ST  is reached. D T  is set to a larger value as ΔP 2  is larger and as N E  is higher. 
     At a step S18, an incremental value D TRB  is determined in accordance with a subroutine shown in FIG. 13. More specifically, if the engine is in the open loop control mode, and at the same time the change rate ΔP 2  of supercharging pressure is negative, the incremental value D TRB  is determined by ΔP 2  and the engine rotational speed N E  as shown in (a), (b), and (c) of FIG. 14, and then the decremental value D T  is set to 0%. Similarly to the decremental value D T , the incremental value D TRB  is also changed as shown in FIG. 14 depending on the engine rotational speed N E  and the change rate ΔP 2  of supercharging pressure. It is set to a larger value as N E  is higher and as |ΔP 2  | is larger, whereby it is possible to carry out duty ratio control in a manner ensuring stable supercharging pressure P2 with almost no hunting in each operating region of the engine. In other words, according to the invention, for example, from the start of acceleration of the engine until the predetermined supercharging pressure value P 2ST  is reached, the duty ratio D OUT  is set to and held at 100% to set the space area between the movable vanes 54 and the stationary vanes 49 to the minimum, to thereby increase the supercharging pressure P 2  at a high rate and hence enhance the accelerabity of the engine. After the supercharging pressure P 2  has exceeded the predetermined value P 2ST , the predetermined incremental value D TRB  is added to D M  so as to prevent hunting of supercharging pressure, which would otherwise occur in reaction to subtraction of the decremental value D T  for prevention of overshooting, whereby it is possible to carry out stable supercharging pressure control in each operating region of the engine. 
     After the correction coefficients K MODij , K PATC , and K TATC , the decremental value D T , and the incremental value D TRB  are thus determined, the program proceeds to a step S19. 
     At the step S19, the duty ratio D OUT  is calculated by the following equation: ##EQU1## 
     Further, at a step S20, the flag F is set to 0 to indicate that the engine is in the open loop control mode, and at a step S21, the duty ratio D OUT  is checked to make sure that it is within a predetermined range defined by upper and lower limit values. More specifically, the upper and lower limit values of the duty ratio D OUT  are predetermined in accordance with the engine rotational speed N E , and the calculated duty ratio D OUT  is checked so as to make sure that it is within the predetermined range. If the calculated duty ratio D OUT  is within the predetermined range, the duty ratio D OUT  is outputted at the step S4. 
     If it is determined at the step S12 that θ TH  &gt;θ THFB , the program proceeds to a step S22. where it is determined whether or not the flag F assumed in last loop was 1, i.e. the engine was in the open loop control mode in the last loop. If F=1, it is determined at a step S23 whether or not the supercharging pressure P 2  is above the duty ratio control-starting value P 2ST . The duty ratio control-starting value P 2ST  is obtained by the equation P 2ST  =P 2REF  -ΔP 2ST . ΔP 2ST  is set depending on the engine rotational speed N E , as shown in (a), (b), (c) of FIG. 15. Here, similarly to the above-described D T  and D TRB , ΔP 2ST  is set in accordance with the engine rotational speed N E  and the change rate ΔP 2  of supercharging pressure to ensure the optimum duty control. It is set to a larger value as the engine rotational speed N E  is higher and as the change rate ΔP 2  of supercharging pressure is larger. 
     If P 2  &gt;P 2ST  at the step S23, it is determined at a step S24 whether or not the supercharging pressure P 2  is above a feedback control-starting value P 2FB . The feedback control-starting supercharging pressure P 2FB  is obtained by the equation P 2FB  =P 2REF  -ΔP 2FB . As shown in (a), (b), and (c) of FIG. 16, ΔP 2FB  is set depending on the engine rotational speed N E . Similarly to the above-described ΔP 2ST , D T , and D TRB , ΔP 2FB  is determined in accordance with the engine rotational speed N E  and the change rate ΔP 2  of supercharging pressure to ensure the optimum duty ratio control. It is set to a larger value as the engine rotational speed N E  is higher and as the change rate ΔP 2  of supercharging pressure is larger. If P 2  &gt;P 2FB  at the step S24, the program proceeds to a step S25. 
     At the step S25, it is determined whether or not the delaying time period t FBDLY  has elapsed. If the delaying time period t FBDLY  has elapsed, the program proceeds to a step S26. In the meanwhile, if F=0 at the step S22, the program skips over the steps S23 to S25 to the step S26, if P 2  P 2ST  at the step S23, the program proceeds to the step S27, if P 2  ≦P 2FB  at the step S24, the program proceeds to the step S13, and if the delaying time period t FBDLY  has not elapsed at the step S25, the program proceeds to the step S14. 
     At the step S27, the duty ratio D OUT  is set to 100%, and at a step S28 the t FBDLY  timer is reset. Then the program proceeds to the step S4. 
     At the step S26, it is determined whether or not the absolute value of change rate ΔP 2  of supercharging pressure is above a supercharging pressure difference G dP2  for determining whether to start the feedback control. The supercharging pressure difference G dP2  is set, for example, at a value of 30 mmHg. If the absolute value of ΔP 2  is above the value G dP2 , the program proceeds to the step S14, and if the absolute value of ΔP 2  is equal to or lower than the value G dP2 , the program proceeds to a step S29. If the feedback control is started when |ΔP 2  |&gt;G dP2 , it may result in hunting. Therefore, the program proceeds to the step S14 to carry out the open loop control. As described above, in the open loop control, correction of the basic duty ratio D M  by D T  and D TRB  is carried out to prevent hunting and overshooting of supercharging pressure. Therefore, the step S26 is provided mainly for the fail-safe purpose. 
     The feedback control is started at the step S29, where the desired supercharging pressure P 2REF  is determined depending on the engine rotational speed N E  and the intake air temperature T A . The feedback control is started on condition that θ TH  &gt;θ THFB  at the step S12. Under this condition. the desired supercharging pressure P 2REF  is determined by the use of the engine rotational speed N E  and the intake air temperature T A  as parameters enabling accurate determination of operating conditions of the engine. If θ TH  &gt;θ THFB , i.e. under medium or high load operating conditions, the engine rotational speed N E  and the throttle valve opening θ TH  behave approximately in the same manner. Therefore, the N E  can be an effective parameter representing operating conditions of the engine. In the meanwhile, the intake air temperature T A  is the temperature of intake air downstream of the intercooler 4 as shown in FIG. 2, and therefore can be a parameter accurately representing the condition of intake air introduced into the combustion chambers. Therefore, it is possible to set the desired supercharging pressure P 2REF  to values exactly responsive to operating conditions of the engine by the use of a map determined by the engine rotational speed N E  and the intake air temperature T A . 
     At a step S30, it is determined whether or not the automatic transmission is in the first speed position. If the automatic transmission is in the first speed position, calculation of P 2REF  =P 2REF  -P 2REFF  -ΔP 2REFF  is carried out at a step S31 in accordance with the subroutine shown in FIG. 8 when the operating condition of the engine is within the predetermined operating zone known by hatching in FIG. 9, and then the program proceeds to a step S33. ΔP 2REFF  is a predetermined decremental value which is applied when the transmission is in the first speed position. If it is determined at the step S30 that the transmission is in a position other than the first speed position, calculation of P 2REF  =P 2REF  -ΔP 2REFOS  is carried out at a step S32 in accordance with the subroutine shown in FIG. 10, and then the program proceeds to the step S33. ΔP 2REFOS  is a predetermined decremental value which is applied when the transmission is in a position other than the first speed position. 
     At the step S33, an atmospheric pressure-dependent correction coefficient K PAP2  for correcting the supercharging pressure and the atmospheric pressure-dependent correction coefficient K PATC  for correcting the duty ratio are determined in accordance with the atmospheric pressure P A , and then at a step S34, the following calculation is carried out: 
     
         P.sub.2REF =P.sub.2REF ×K.sub.PAP2 ×K.sub.REFTB 
    
     where K REFTB  is a correction coefficient responsive to a knocking condition of the engine. 
     At a step S35, it is determined whether the absolute value of the difference between the desired supercharging pressure P 2REF  and the supercharging pressure P 2  detected in the present loop is equal to or higher than a predetermined value G P2 . The predetermined value G P2  is a value defining the intensive pressure width in the feedback control mode, and is set, for example, at 20 mmHg. If the absolute value of the difference between the desired supercharging pressure and the actual supercharging pressure is equal to or higher than the predetermined value G P2 , the program proceeds to a step S36, and if not, the program proceeds to a step S43. 
     At the step S36, a proportional control term D P  for correcting the duty ratio is calculated by the following equation: 
     
         D.sub.P =K.sub.P ×(P.sub.2REF -P.sub.2) 
    
     where K P  is a feedback coefficient for the proportional control term, and is obtained in accordance with a subroutine shown in FIG. 17. In FIG. 17, if the engine rotational speed N E  is equal to or lower than the first changeover engine rotational speed N FB1 , K P1  is obtained and at the same time a feedback coefficient K I1  for an integral control term, described later, is obtained. If the engine rotational speed N E  is above the first changeover engine rotational speed N FB1  and equal to or lower than the second changeover engine rotational speed N FB2  K P2  and K PI2  are obtained. If the engine rotational speed N E  is above the second changeover engine rotational speed N FB2 , K P3  and K PI3  are obtained. 
     At a step S37, similarly to the step S14, the correction coefficient K MODij  is determined in accordance with the engine rotational speed N E  and the intake air temperature T A . At a step S38, it is determined whether or not the flag F assumed in the last loop was 1, i.e whether or not the present loop is the first loop in which the feedback control mode has been started. If F=1, an integral control term D I (n-1) applied in the last loop is obtained at a step S39 by the following equation: 
     
         D.sub.I(n-1) =K.sub.TATC ×K.sub.PATC ×D.sub.M ×(K.sub.MODij -1) 
    
     After this calculation, the program proceeds to a step S40. If F=0 at the step S38, the program skips over the step S39 to the step S40. 
     At the step S40, an integral control term D In  for the present loop is calculated by the following equation: 
     
         D.sub.In =D.sub.I(n-1) +K.sub.I +(P.sub.2REF -P.sub.2) 
    
     Then the program proceeds to a step S41, where the duty ratio D OUT  is calculated by the following equation: 
     
         D.sub.OUT =K.sub.TATC ×K.sub.PATC ×D.sub.M +D.sub.P +D.sub.In 
    
     Then, at a step S42, the flag F is set to 0, and the program proceeds to the step S21. 
     If the absolute value of the difference between the desired supercharging pressure P 2REF  and the actual supercharging pressure P 2  is smaller than the predetermined value G P2 , D P  is set to 0 and D In  is set set to D I (n-1) at a step S43. Then at steps S44 to S47, it is determined whether or not the engine coolant temperature T W  is within a predetermined range, i.e. above T WMODL  and below T WMODH , whether or not a retarding amount T ZRET  is 0, i.e. whether or not the engine is not under a knocking condition, whether or not the transmission is in a position other than the first speed position, and whether or not K REFTB  is equal to or lower than 1.0. If all these conditions are satisfied, the program proceeds to a step S48, and if any one of them is not satisfied, the program proceeds to the step S41. 
     At the step S48, a coefficient K R  for learning the correction coefficient K MODij  for duty ratio is calculated by the following equation: 
     
         K.sub.R =(K.sub.TATC ×D.sub.M +D.sub.In)/(K.sub.TATC ×D.sub.M) 
    
     where the coefficient K R  represents an amount of deviation of the supercharging pressure from the desired value due to variations caused during the mass production of the engine and the control system and/or due to aging change. 
     At a step S49, in order to determine and learn the correction coefficient K MODij , the following calculation is carried out: ##EQU2## At a step S50, the K MODij  obtained at the step S49 is stored. 
     In this equation, K MODij  of the second term on right side is a value of K MODij  obtained in the last loop and is read from a K MODij  map, hereinafter described, in accordance with the engine rotational speed N E  and the intake air temperature T A . A is a constant (e.g. 65536), and C MOD  is a variable which is set to a suitable value experimentally selected from 1-A. 
     The ratio of K R  to K MODij  varies depending uopn the value of the variable C MOD . Therefore, by setting the value of C MOD  to a value falling within the range of 1-A according to characteristics of the supercharging pressure control system, the engine, etc., the value of K MODij  can be calculated to an optimal value. 
     During the open loop control the coefficient K MODij  thus calculated during the feedback conttrol is applied in each of the predetermined regions in which the engine rotational speed N E  and the intake air temperature T A  fall. As a result, deviation of rhe supercharging pressure from the desired value can be accurately corrected in response to these engine operating parameters during the the open loop control. 
     According to the above-described control of the duty ratio of the solenoid 70 of the eleotromagnetic control valve 69, under the condition that the automatic transmission is in the first speed position, if the engine is in the open loop control mode, D F  is subtracted from the basic duty ratio D M  at the step S10 when the operating condition of the engine is in the predetermined operating zone shown in FIG. 9, and if the engine is in the feedback control mode, ΔP 2REF  is subtracted from the desired supercharging pressure P 2REF  at the step S31 when the operating condition of the engine is in the predetermined operating zone. Thus, excessive load on the automatic transmission due to sudden start of the vehicle and overload on the engine under the condition that the automatic transmission is in the first speed position can be prevented by decreasing the supercharging pressure through subtraction from the basic duty ratio DM Further, even if the control mode is shifted from the open loop control mode to the feedback control mode when the transmission is in the first speed position, occurrence of hunting in the transitional state can be prevented since subtraction from the desired supercharging pressure P 2REF  is carried out. 
     Suppose that the gear position of the transmission is shifted as shown in the lower part of FIG. 18. As known, when the gear position of the transmission is shifted, the engine rotational speed N E  is increased. However, there is a time lag before the actuator 60 starts to operate in response to a signal from the control unit C. Therefore, the supercharging pressure P 2  does not properly correspond to the engine rotational speed N E  and overshooting of the supercharging pressure may arise. As shown by the broken line in FIG. 18, when the gear position of the transmission is shifted immediately after acceleration in a medium or high engine speed range, the supercharging pressure may exceed the upper limit value P 2HG . However, in the embodiment of FIG. 5 at the step S11 and at the step S32, subtraction from the basic duty ratio D M  and subtraction from the desired supercharging pressure P 2REF  are carried out, respectively, in accordance with the subroutine shown in FIG. 10. More specifically, when the gear position of the transmission is shifted, under the conditions that the throttle valve opening θ.sub. TH is above the predetermined value θ THOS , the engine rotational speed N E  is above the predetermined value N EOS , and the intake pressure P B  is above the predetermined value P BOS , i.e. in the medium or high speed range, D OS  is subtracted from the basic duty ratio D M  in the open loop control mode depending on the change rate ΔP 2  of supercharging pressure P 2 , and ΔP 2REFOS  is subtracted from the desiored supercharging pressure P 2REF  in the feedback control mode. Thus, as shown by solid line in FIG. 18, overshooting at the time of shifting of the transmission position is greatly reduced, whereby it is possible to prevent hunting and carry out stable supercharging pressure control. 
     Further, when the control mode is shifted from the open loop control mode to the feedback control mode, as shown in FIG. 19, a drop in the supercharging pressure P 2  is prevented whereby the control mode can be smoothly shifted to the feedback control mode. More specifically, at the start of the engine, the duty ratio D OUT  is set to 0%, and in the open control mode in which the throttle valve opening θ TH  is below the predetermined value θ THFB , D T  is set to 0% at the step S18 in accordance with the subroutine shown in FIG. 13. As stated before, the oontol mode starts to shift from the open loop control mode to the feedback control mode when the throttle valve opening θ TH  has exceeded the predetermined value θ THFB . When the supercharging pressure P 2  has exceeded P 2ST  and the throttle valve opening θ TH  is above the predetermined value θ THFB , the subtraction of D M  =D M  -D T  is carried out to prevent overshooting of the supercharging pressure. 
     In some cases, if D T  alone is thus subtracted from the basic duty ratio D M , the supercharging pressure P 2  may drop as shown by broken line in FIG. 19 in reaction to the subtraction. However, according to the control method of the invention, if ΔP 2  ≦0, D T  is set to 0%, and D TRB  is added to the basic duty ratio D M . Therefore, it is possible to cope with the possible drop in the supercharging pressure P 2  to thereby smoothly shift the control mode to the feedback control mode while preventing occurrence of hunting of the supercharging pressure. 
     The aforesaid control of duty ratio of the solenoid 70 of the electromagnetic control valve 69 is carried out when the electromagnetic valve 72 is closed. If the electromagnetic valve 72 is opened, intake pressure P B  is introduced into the second pressure chamber 63 of the actuator 60, which in turn causes the movable vanes 54 of the variable capacity turbocharger 5 to operate such that the space area between the movable and stationary vanes 54, 49 is increased. 
     Next, with reference to FIG. 20, the manner of control of controlling the solenoid 73 of the electromagnetic valve 72 by the control unit C will be described below. In addition to the control of operation of the electromagnetic control valve 69 for introducing supercharging pressure P 2  into the first pressure chamber 62 of the actuator 60 in accordance with the main routine shown in FIG. 5, intake pressure P B  is introduced into the second pressure chamber 63 of the actuator 60 by way of the electromagnetic valve 72, which makes it possible to carry out more accurate control of the supercharging pressure. The reason for this is as follows. Since the supercharging pressure P 2  is detected between the variable capacity turbocharger 5 and the intercooler 4, it is impossible to detect a subtle operation of the throttle valve 74. In oontrast, since the intake pressure P B  is detected downstream of the throttle valve 74. it is possible to detect a subtle operation thereof. Thus, by the use of both the supercharging pressure sensor S P2  positively sensitive to the operation of the turbocharger 5 and the intake pressure sensor S PB  positively sensitive to the operation of the throttle valve 74, the operation of the whole intake system including the turbocharger 5 can be more accurately reflected upon the control of the supercharging pressure. 
     At a step L1, it is determined whether or not a predetermined time period, e.g. 2 minutes, has elapsed from the start of the engine. If the predetermined time period has not elapsed, the program proceeds to a step L2, where the solenoid 73 is energized, whereby the actuator 60 is operated to oause the movable vanes 49 to operate such that the space area between the movable and stationary vanes 54, 49 is increased. This can cope with the start of the engine in cold weather. Thus, excessive supercharging under cold weather is prevented, and the catalyst temperature can be gently raised. If the predetermined time period has elapsed at the step L1, the program proceeds to a step L3, where it is determined whether or not the speed V of the vehicle is above a predetermined value V OP3 , which is provided with a hysteresis between when the vehicle speed V increases and when it decreases and is set to, for example, 90/87 km/h. If V&gt;V OP3 , the program proceeds to a step L4, whereas if V≦V OP3 , the program proceeds to a step L5. 
     At the step L4, it is determined whether or not the throttle valve opening change rate Δθ TH  is below a predetermined value Δθ THOP2 . The predetermined Δθ THOP2  is provided with a hysteresis similar to that of the vehicle speed V OP3 . If Δθ TH  &lt;Δθ THOP2 , the program proceeds to a step L2, and otherwise, the program proceeds to the step L5. 
     At the step L5, it is determined whether or not the vehicle speed V is below a predetermined value V OP1 . The predetermined value V OP1  also has a hysteresis and is set to, for example, 65/63 km/h. If V&lt;V OP1 , the program proceeds to a step L7, whereas if V≧V OP1 , the program proceeds to a step L6, where the solenoid 73 is deenergized. At the step L7, it is determined whether or not the vehicle speed V is above a predetermined value V OP2 . The predetermined value V OP2  also has a hysteresis, and is set to, for example, 4/3 km/h. If V&gt;V OP2 , the program proceeds to a step L12, whereas if V≦V OP2 , the program proceeds to a step L8. 
     At the step L8, it is determined whether or not the vehicle speed V detected in the last loop is above the predetermined value V OP2 . If V&gt;V OP2 , the program prooeeds to a step L9, where the t OP  timer for counting a time period t OP  is reset, and then the program prooeeds to a step LlO. If V≦V OP2 , the program directly proceeds to the step L10. At the step L10, it is determined whether or not the solenoid was energized in the last loop. If the solenoid 73 was deenergized in the last loop, the program proceeds to the step L6, whereas if it was energized in the last loop, the program proceeds to a step L11, where it is determined whether or not the time period t OP  exceeds a predetermined time period t OP0 . If t OP  &gt;t OP0 , the program proceeds to the step L6, whereas if t OP  ≦t OP0 , the program proceeds to the step L2. 
     At the step L12, it is determined whether or not the engine rotational speed N E  is below a predetermined value N EOP . The predetermined value N EOP  has a hysteresis, and is set to, for example, 2500/2300 rpm. If N E  ≧N EOP , the program proceeds to the step L6, whereas if N E  &lt;N EOP , the program proceeds to a step L13. 
     At the step L13, it is determined whether or not the intake pressure P B  is below a predetermined value P BOP . The predetermined value P BOP  has a hysteresis, and is set to, for example, -100/-150 mmHg. If P B  ≧P BOP , the program proceeds to the step L6, whereas if P B  &lt;P BOP , the program proceeds to a step L14. 
     At the step L14, it is determined whether or not the throttle valve opening θ TH  is below a predetermined value θ THOP . The predetermined value θ THOP  is set at 20/15 degrees. If θ TH  ≧θ THOP , the program proceeds to the step L6, whereas if θ TH  &lt;θ THOP , the program proceeds to a step L15. 
     At the step L15, it is determined whether or not the throttle valve opening change rate Δθ TH  is positive and at the same time below a predetermined value Δθ THOP1  which is set such that it has a hysteresis. If 0&lt;Δθ TH  &lt;Δθ THOP1 , the program proceeds to the step L2, and otherwise, the program proceeds to the step L6. 
     According to the above-described control manner, if it is determined at the steps L3 and L4 that the vehicle speed V is higher than 90/87 km/h, and that the acceleration thereof is gentle as shown by 0&lt;Δθ TH  &lt;Δθ THOP2 , the movable vanes 54 of the turbocharger 5 are operated such that the space area between the movable vanes 54 and the stationary vanes 49 is increased, whereby pumping loss can be prevented. In other words, when the vehicle is cruising at a high speed, acceleration of the engine is not required, and if the movable vanes 54 are operated such that the supercharging pressure is increased, pumping loss may occur due to rise in the back pressure in the exhaust manifold resulting from a high engine rotational speed. 
     If it is determined at the step L5 that the vehicle is running at a speed higher than 65/63 km/h, the solenoid 73 is deenergized. This is because when the vehicle is running at such a high speed, the supercharging pressure can be sufficiently controlled by the electromagnetic control valve 69 in accordance with the routine shown in FIG. 5. Further, at the steps L7 to L11, if the vehicle is running at a speed lower than 4 or 3 km/h, i.e. it is almost stationary, and at the same time if the vehicle was almost stationary in the last loop, the t OP  timer is reset, and then until the time period, for example, one minute, has elapsed, the solenoid 73 is energized so as to operate the movable vanes 54 such that the space area between the movable and stationary vanes 54, 49 is increased. If the movable vanes 54 are in such a position as to make the space area narrower at the restart of the vehicle, the supercharging pressure P 2  is temporarily increased to apply excessive load on the starting gear etc Therefore the solenoid 73 is energized to prevent such application of the excessive load on the starting gear etc. Further, if the movable vanes 54 are in suoh a position as to make the space area narrower when the vehicle is running at a speed lower than 4 or 3 km/h, rotation of the variable capacity turbocharger 5 by inertia etc is promoted. On this occasion, the throttle valve opening θ TH  is almost fully closed, and therefore the supercharging pressure increases the pressure within the intake pipe on the upstream side of the throttle valve to cause surging of the latter pressure. Therefore, the movable vanes 54 are operated such that the space area is increased, to prevent surging of the intake pipe on the upstream side of the throttle valve to cause surging of the latter pressure. Therefore, the movable vanes 54 are operated such that the space area is increased, to prevent surging of the intake pipe pressure. In addition, the control of supercharging pressure carried out at the steps L7 to L11 contributes to rise in the catalyst temperature immediately after the start of the vehicle when the weather is cold. 
     If at the steps L12 to L15, all the conditions of V OP2  &lt;V&lt;V OP1 , N E  &lt;N EOP , P B  &lt;PBOP, θ TH  &lt;θ THOP , and 0&lt;Δθ TH  &lt;Δθ THOP1  are satisfied, i.e. if the vehicle is gently accelerated under partial load as in the 10 mode running, the solenoid 73 is energized to decrease the supercharging pressure P 2 , whereby pumping loss can be prevented. 
     FIG. 21 shows a program for controlling the electromagnetic control valve 69 according to a second embodiment of the invention. In the second embodiment, instead of using the supercharging pressure sensor S P2 , the supercharging pressure control is effected based upon the intake pressure P B  detected by the intake pressure sensor S PB . This is based on the faot that the feedback control of the supercharging pressure is effected in an operating oondition of the engine where the throttle valve 74 is almost fully open, in which condition information relating to the supercharging pressure can be obtained by the intake pressure P B . 
     At a step S101, the basic duty ratio D M  is read from a D M  map in response to the throttle valve opening θ TH  and the engine rotational speed N E . FIG. 22 shows an example of the D M  map in which the throttle valve opening θ TH  is classified into sixteen predetermined values θ THV1  -θ THV16  within a predetermined range, while the engine rotational speed N E  is classified into twenty predetermined values N V1  -N V20 . The basic duty ratio D M  is determined by means of interpolation, if θ TH  or N E  falls between respective adjacent predetermined values. By setting the basic duty ratio D M  by the use of the D M  map, the duty ratio D OUT  of the electromagnetic control valve 69 can be controlled more accurately in response to operating conditions of the engine E. 
     Next it is determined at a step S102 whether or not the gear position of the transmission is in a first speed position. This determination is carried out in accordance with a subroutine, e.g. shown in FIG. 23. In the subroutine, it is determined whether or not the speed V of the vehicle is lower than a predetermined value V L  which is normally obtained in the first speed position. If V&lt;V L , it is then determined whether or not the vehicle speed V is smaller than a predetermined value V F  corresponding to the engine rotational speed N E . If V≧V L  or V≧V F ,  it is determined that the gear position is not in the first speed position, whereas if V&lt;V L  and at the same time V&lt;V F , it is determined that the gear position is in the first speed position. 
     FIG. 24 shows a table for determining the predetermined value V F . When the transmission is in the first speed position, the ratio between the engine rotational speed N E  and the vehicle speed V is constant. The tabIe is set so as to satisfy this constant ratio relationship and provided with predetermined values N F1  -N F9  of the engine rotational speed and predetermined values V F1  -V F8  of the vehicle speed V. It is determined that the transmission is in the first speed position when the vehicle speed V is lower than the predetermined value V F  corresponding to the actual engine rotational speed N E . By virtue of the above determinations, it is possible to determine without a gear position sensor or the like whether or not the transmission is in the first speed position, irrespective of whether the transmission is manual or automatic. 
     Referring again to FIG. 21, if it is determined at the step S102 that the transmission is in the first speed position, then at a step S103 the basic duty ratio D M  determined at the step S101 is decreased by subtracting a predetermined value D F  from the basic duty ratio D M , followed by the program proceeding to a step S104. On the other hand, if the transmission is in a position other than the first speed position, the program jumps to the step S104. In this way, the basic duty ratio D M  is set to a value smaller by the predetermined value D F  when the transmission is in the first speed position than when it is not in another position. 
     At the step S104, an intake air temperature-correcting coefficient K TATC  is read from a K TATC  map in response to the engine rotational speed N E  and the intake air temperature T A . FIG. 25 shows an example of the K TATC  map, in which the engine rotational speed N E  is classified into twenty predetermined values N V1  -N V20  within a predetermined range, similarly to the D M  map, while the intake air temperature T A  is classified into eight predetermined values T AV1  -T AV8 . By virtue of the K TATC  map, the intake air temperature-correcting coefficient K TATC  is set to a suitable value. 
     Then at a step S105, the change rate ΔP B  of the intake air pressure P B , hereinafter merely called &#34;the change rate&#34;, is calculated by subtracting a value PB n-3  detected in the third loop before the present loop from a value P Bn  detected in the present loop. The change rate ΔP B  is applied to setting of constants used for calculating the duty ratio D OUT , as hereinafter described in detail, whereby the increase rate of the supercharging pressure is controlled to a desired value. 
     Next, at a step S106, it is determined whether or not the supercharging pressure is in a range in which open loop control is to be effected. This determination is carried out in accordance with a subroutine shown in FIG. 26. 
     First, at a step S201 of the FIG. 26 subroutine, it is determined whether or not the throttIe valve opening θ TH  is larger than a predetermined value θ THFB  indicating that the throttle valve 74 is almost full open. lf θ TH  ≦θ THFB , that is, if the throttle valve 74 is not almost fully open, it is determined that the open loop control should be effected, followed by the program proceeding to a step S216 et seq, hereinafter referred to. That is, feedback control is effected only when the throttle valve 74 is almost fully open. 
     If it is determined at the step S201 that θ TH  &gt;θ THFB , it is determined at a step S202 whether or not, a flag F set in the last loop at a step S203 or S221, hereinafter referred to, is equal to a value of 1, i.e. the open loop control was effected in the last loop. If the feedback control was effected in the last loop, it is judged at the step S203 that the feedback control should be continued, and the flag F is set to a value of 0, followed by termination of the program. 
     If it is determined at the step 202 that the open loop control was effected, the program proceeds to a step S204 in which it is determined whether or not the transmission is in the first speed position. If the transmission is not in the first speed position, a first subtraction value ΔP BST  is obtained at a step S205 from a ΔP BST  table applied in a position other than the first speed position, in accordance with the change rate ΔP B , folIowed by the program proceeding to a step S207. FIG. 27 shows an example of the ΔP BST  table, in which two predetermined values ΔP B1  and ΔP B2  (ΔP B1  &lt;ΔP B2 ) are provided as the change rate ΔP BST . The predetermined values ΔP BST3  -ΔP BST1  are set such that as ΔP B  is larger, i.e., as the increase rate of the supercharging pressure is higher, the first subtraction value ΔPBST is set to a larger value. 
     If it is determined at the step S204 that the transmission is in the first speed position, the first subtraction value ΔP BST  is set to a predetermined value ΔP BSTF  applied in the first speed position. The predetermined value ΔP BSTF  is set at a larger value than the value ΔP BST  obtained from the ΔP BST  map applied in a position other than the first speed position. 
     Then, it is determined at the step S207 whether or not the intake pressure P B  is higher than the difference P BREF  -ΔP BST  between a desired value P BREF  and the first subtraction value ΔP BST  obtained at the step S2O5 or S206. The difference P BREF  -ΔP BST  is hereinafter referred to as &#34;duty ratio control-starting pressure&#34;. The desired value P BREF  is set in accordance with tbe engine rotational speed N E , the intake air temperature T A , and tbe gear position of the transmission by the program of FIG. 21, as hereinafter described. 
     If it is determined at tbe step S207 that the intake pressure P B  is below the duty ratio control-starting pressure P BREF , a proportional control term D R  and an integral control term D I , which are applied to the feedback control, are both set to a value of 0.0, at steps S208, S209, and the duty ratio D OUT  is set to 100% to make the space area between the movabIe and stationary vanes 54, 49 the minimum, at a step S210. Thus, when P B  ≦(B REF  -ΔP BST ), the space area between the movable and stationary vanes is set to the minimum, as at the period between t0-tA in FIG. 35. In this way, the increase rate of supercharging pressure in a low range is made the maximum so as for the supercharging pressure to be quickly increased to the desired value, thereby enhancing the responsiveness of the supercharging control. 
     Next, at a step S211, a t FBDLY  timer for delaying the feedback control is reset, and then the program proceeds to a step S118 in FIG. 21 to supply the control valve 69 with a driving signal corresponding to the determined duty ratio D OUT , followed by termination of the program of FIG. 21. 
     Referring again to FIG. 26, if at the step S207 the intake pressure P B  is higher than the duty ratio control-starting pressure (P BREF  -ΔP BST ), it is determined whether or not the transmission is in the first speed position, at a step S212. If the transmission is in a position other than the first speed position, a second subtraction value ΔP BFB  is determined from a ΔP BFB  table applied in a position other than the first speed position, in accordance with the change rate ΔP B , and then the program proceeds to a step S215, hereinafter described. 
     FIG. 28 shows an example of the ΔP BFB  table, in which, just like the table of FIG. 27, predetermined values ΔP BFEB3  -ΔP BFB1  are provided (ΔP BFB3  &lt;ΔP BFB2  &lt;ΔP BFB1 ), which are set such that as the change rate ΔP B  is larger, the second subtraction value ΔP BFB  is set to a larger value. 
     If it is determined at the step S212 that the transmission is in the first speed position, the second subtraction value ΔP BFB  is set to a predetermined value ΔP BFBF  for the first speed position, at a step S214, and then the program proceeds to a step 215. The predetermined value ΔP BFBF  is set at a value larger than ΔP BFBF  applied in a position other than the first speed position, determined at the step S213. 
     At the next step S215, it is determined whether or not the intake pressure P B  is higher than the difference (P BREF  -ΔP BFB ) between the desired value P BREF  and the second subtraction value ΔP BFB  obtained at the step S213 or S214. The difference (P BREF  -ΔP BFB ) is hereinafter referred to as &#34;feedback control-starting pressure&#34;. If the intake pressure P B  is lower than the feedback control-starting pressure (P BREF  -ΔP BFB ), it is judged that the feedback control should not be effected, and then the program proceeds to a step S216 et seq. If the answer at the step S215 is no, that is, if (P BREF  -ΔP BST )&lt;PB≦(P BREF  -ΔP BFB ), open loop control is effected as at period between tA-tB in FIG. 35. 
     At the step S216, the t FBDLY  timer is reset, like the step S211, and at a step S217, it is determined whether or not the transmission is in the first speed position. If the answer is no, a subtraction term D T  is determined from a D T  table applied in a position other than the first speed position, at a step S218, followed by the program proceeding to a step S221, hereinafter referred to. 
     FIG. 29 shows an example of the D T  table, in which predetermined values D T1  -D T3  (D T1  &lt;D T2  &lt;D T3 ) are set such that as the change rate ΔP B  is larger, the subtraction value D T  is set to a larger value, just like the map of FIG. 27. 
     If at the step B2I7 it is determined that the transmission is in the first speed position, a subtraction term D FT  is determined from a D FT  table for the first speed position in accordance with the change rate ΔP B , at a step S219. FIG. 30 shows an example of the D FT  table, in which two predetermined values ΔP BF1  and ΔP BF2  (ΔP BF2  &gt;ΔP BF1 ) are provided as the change rate ΔP B , and predetermined subtraction values D FT1  -D FT3  (D FT1  &lt;D FT2  &lt;D FT3 ) are set such that as the change rate ΔP B  is larger, the subtraction term D FT  is set to a larger value. These predetermined values D FT1  -D FT3  are set at larger values than respective corresponding values D T1  -D T3  of FIG. 29 at the same change rate ΔP B . 
     Then, the subtraction term D T  is set to the determined value D FT  at a step S220, and the flag F is set to 1 to indicate that the open loop control should be executed, at a step S221, followed by termination of the program. 
     The subtraction term D T  thus set is applied to calculation of tbe duty ratio D OUT  during the open loop control at a step S128, hereinafter described, to the optimize rising characteristic of supercharging pressure. 
     If at the step S215 it is determined that the intake pressure P B  is higher than the feedback control-starting pressure (P BREF  -ΔP BFB ), it is determined at a step S222 whether or not a predetermined period of time t FBDLY  has elapsed after the t FBDLY  timer was reset at the step S211 or S216. If the predetermined time period t FBDL  has not elapsed yet, the program proceeds to the step S217 wherein the open loop control is executed, while if the time period t FBDLY  has elapsed, it is judged that the feedback control should be executed, and then the program proceeds to a step S223. In this way, even when the intake pressure P B  exceeds the feedback control-starting pressure (P BREF  -ΔP BFB ), the feedback control is not executed immediately, but the open loop control is executed until the predetermined time period t FBDLY  elapses, as at period between tB-tC in FIG. 35. Only after the lapse of t FBDLY , the feedback control is started, as at tC in FIG. 35. 
     At the step S223, an initial value of the integral control term D T  is calculated by the following equation: 
     
         D.sub.I =K.sub.TATC ×D.sub.M× (K.sub.MODij -1) 
    
     where K MODij  is a learned correction coefficient (learned value) calculated during feedback control in acoordance with the program of FIG. 21, as hereinafter described. 
     Then, the program proceeds to the step S203 to set the flag F to 0 to indicate that the feedback control should be executed. 
     Referring again to FIG. 21, at a step S107 following the step S106, it is determined whether or not the flag F has been set to 1 in the subroutine of FIG. 26. If the flag F has been set to 1, that is, if the feedback control should be started, the desired value P BREF  is determined from a P BREF  map in accordance with the engine rotational speed N E  and the intake air temperature T A , at a step S108. FIG. 31 shows an example of the P BREF  table, in which predetermined values N V1  -N V20  of the engine rotational speed N E  and prederermined values T AV1  -T AV8  of the intake air temperature T A  are provided and set in just the same manner as the K TATC  map mentioned above. By the use of the P BREF  map, the desired value P BREF  can be set to appropriate values to operating conditions of the engine. 
     Then, at a step S109, it is determined whether or not the transmission is in the first speed position. If the answer is yes, a predetermined value P BREFF  is subtracted from the desired value P BREF  determined at the step S108, at a step S110 to set the desired value P BREF , followed by the program proceeding to a step S111. On the other hand, if the answer is no, the program jumps from the step S109 to the step S111. In this way, the desired value P BREF  is set to a lower value in the first speed position than in a position other than the first speed position. 
     By so setting the desired value P BREF , when the transmission is in the first speed position, the supercharging pressure is controlled to a smaller value than a value assumed in another gear position, during a steady state of the supercharging pressure, so that torque applied to the transmission gear is made small, thereby enhancing the durability of the transmission, whereas in another gear position the supercharging pressure in steady state can be controlled to a desired high value. 
     At the step S111, the difference ΔP BD  (=P BREF  -P B ) between the desired value P BREF  and the actual intake pressure P B  is calculated, and then it is determined at a step S112 whether or not the absolute pressure |ΔP B  | of the determined difference ΔP BD  is larger than a predetermined value GP B  (e g. 20 mmHg). The predetermined value G PB  is a value defining the insensitive pressure width. 
     If ΔP BD  ≧G PB , respective constants K P  and K I  of the proportional control term D P  and the integral control term D I  are read, respectively, from a K P  table and a K I  table, in accordance with the engine rotational speed N, at a step S113. FIG. 32 and FIG. 33 show these tables, respectively. In the K P  table, two predetermined values N FBP1  and N FBP2  (N FBP2  &gt;N FBP1 ) of the engine rotational speed N E  are provided, and predetermined values K P1  -K P   3  (K P1  &lt;K P2  &lt;K P3 ) of the constant K P  are provided, which correspond, respectively, to N E  &lt;N FBP1 , N FBP1  ≦N E  &lt;N FBP2 , and N E  ≧N FBP2 . On the other hand, in the K I  table, two predetermined values N FBI1  and N FBI2  of the engine values K I1  -K I3  (K I3  &lt;K I1  &lt;K I2 ) are provided, which correspond, respectively, to N E  &lt;N FBI1 , N FBI1  ≦N E  ≦N FBI2 , and N E  ≧N FBI2 . 
     Then, the proportional control term D P  is set to the product K P  ×ΔP BD  of the constant K P  and the difference ΔP BD , at a step S114, and the integral control term D I  is set to the sum (=D I  +K I  ×ΔP BD ) of the integral control term D I  obtained in the last loop and the product K I  ×ΔP BD , at a step S115. 
     The proportional control term D P  and the integral control term D I  thus determined are substituted into the following equation to calculate the duty ratio D OUT  applied during the feedback control: 
     
         D.sub.OUT =D.sub.M ×K.sub.TATC +D.sub.R +D.sub.I 
    
     Then, the calculated duty ratio D OUT  is subjected to limit checking to adjust same within a predetermined range, at a step S117. A driving signal corresponding to the duty ratio D OUT  is supplied to the electromagnetic control valve 69, at the step S118, followed by termination of the program. 
     When |ΔP BD  |&lt;G PB  at the step S112 and hence the actual intake pressure P is substantially equal to the desired value P BREF , the proportional control term D is set to 0.0, and the integral control term D is set to a value of same obtained in the last loop, at respective steps S119 and S120. 
     Then. it is determined at a step S121 whether or not the transmission is in the first speed position. When the answer is yes, a coefficient K R  is calculated by the following equation at a step S122: 
     
         K.sub.R =(K.sub.TATC ×D.sub.M +D.sub.I)/(K.sub.TATC ×D.sub.M) 
    
     Then, at a step S123 the cofficient K R  obtained as above is applied to calculation of the learned correction coefficient K MODij  by the use of the K MODij  -calculating equation of the first embodiment of the invention described above. 
     Then, the learned correction coefficient K MODij  calculated as above is stored into the K MODij  map which is provided within a back-up RAM of the control unit C, at a step S124, and the program proceeds to a step S116 et seq. and is then ended. FIG. 34 shows an example of the K MODij  map, in which, like the K TATC  map of FIG. 25 and the P BREF  map of FIG. 31, the K MODij  value is classified into a plurality of predetermined values in accordance with the engine rotational speed N E  and the intake air temperature T A . The value of K MODij  is calculated and the calculated value is stored in each of a plurality of regions defined by N E  and T A . 
     When it is determined that the flag F is equal to 1, that is, when the open loop control should be executed according to the subroutine of FIG. 26, a value of the learned correction coefficient K MODij  is read from the K MODij  map in accordance with the engine rotational speed N E  and the intake air temperature T A , at a step S125, and the proportional control term D P  and the integral control term D I  are both set to 0.0, at steps S126 and S129. 
     Then, the duty ratio D OUT  applied during the open loop control is calculated by the following equation: 
     
         D.sub.OUT =K.sub.TATC ×K.sub.MODij ×(D.sub.M -D.sub.T) 
    
     where D T  is the subtraction term set at the step S218 or S220 of the subroutine of FIG. 26. 
     Then, the duty ratio D OUT  calculated as above is is subjected to limit checking to be adjusted within a range from 0% to 100% at a step S129. This is followed by execution of the step S118 and termination of the program. 
     As stated above, the learned correction coefficient K MODij  is calculated and stored during the feedback control in each of the predetermined regions in which the engine rotational speed N E  and the intake air temperature T A  fall, while during the open loop control the coefficient K MODij  calculated during the feedback conttrol is applied in each of the predetermined regions in which the engine rotational speed N E  and the intake air temperature T A  fall. As a result, deviation of the supercharging pressure from the desired value can be accurately corrected in response to these engine operating parameters during the open loop control. 
     If the transmission is determined to be in the first speed position at the step S121, the program skips over the steps S122-S124 to the step S116 to inhibit the calculation of the learned correction coefficient K MODij . As stated before, when the transmission is in the first speed position, the desired supercharging pressure value P BREF  is set to a value smaller by the predetermined value P BREFF  than when the transmission is in another position, at the step S210. As a result, the supercharging pressure can be different between when the transmission is in the first speed position and when it is in another position, even if the engine rotational speed N E  and the intake air temperature T A  fall in the same region. Therefore, when the transmission is in the first speed position, the calculation of K MODij  is inhibited as mentioned above, so as to prevent the K MODij  value from being deviated from a proper value, thereby more accurately controlling the supercharging pressure during open loop control. 
     As described before, at time points t A  -t C  in FIG. 35, the open loop control is executed. In calculating the duty ratio D OUT  applied to the open loop control at the step S128, the value D M  selected from the map described before and the value D M  calculated at the step S103 are not directly applied as the basic duty ratio D M , but the value (D M  -D T ) is applied, instead. 
     This correction of the supercharging pressure control amount is applied to the control of the rise rate of supercharging pressure in transient state during increase of the supercharging pressure. 
     The control of the rise rate will be explained in detail with reference to FIGS. 29 and 36 as well. 
     Since, as stated before, the subtraction term D T  is set in the relationship D T1  &lt;D T2  &lt;S T3  with respect to the change rate ΔP B  of intake pressure, i.e. the change rate of supercharging pressure so that it is set to larger values as the change rate ΔP B , detected at the step S105 in FIG. 21, becomes larger, that is, as the change rate of supercharging pressure becomes larger, the above-mentioned value (D M  -D T ), and accordingly the duty ratio D OUT  applied during the open loop control is controlled so as to decrease as the change rate ΔP B  becomes larger, and increase as the latter becomes smaller. As a result, the duty ratio is gradually changed in response to the aotually detected change rate ΔP B , so that the actual intake pressure P is increased at a predetermined constant rate. 
     Therefore, in a transient state such as acceleration, the rise rate of supercharging pressure can be controlled to an optimal constant value, thereby enabling to attain sufficient accelerability without excessive rise nor insufficient rise in the supercharging pressure. 
     Characteristic curves IV, V, and VI shown by the broken lines in FIGS. 36(a)-36(c) indicate changes in the value of D OUT , the supercharging pressure (intake pressure P B ), and the torque, respectively, obtained in the case where the above described control of the change rate was not applied, but the map value D M  was determined in accordance with operating conditions of the engine. According to the comparative example, an excessive rise in the supercharging pressure cannot be prevented at the time of rising thereof, often resulting in overboosting and a sudden rise in the torque. 
     In contrast, according to the rise rate control of the present invention, as indicated by the solid lines in FIGS. 36(a)-36(c), the duty ratio correction is effected in response to the actual change rate ΔP B  so that the gradient θ at the time of rising of the pressure is maintained almost constant, thus optimizing the rise characteristic of supercharging pressure. In other words, according to the invention, the gradient can be controlled to the maximum possible value insofar as there takes place no overboosting or no sudden torque change as seen in the comparative example on one hand, and insofar as there takes place no excessive smoothness in the change of supercharging pressure, which gives a feeling of insufficient acceleration, on the other hand. 
     In this manner, according to the invention, the rise characteristic of intake pressure or supercharging pressure at acceleration can be optimized. Particularly, the rise rate control according to the invention is still more effective at sudden standing-start of the vehicle with the throttle valve fully open or at sudden acceleration from a cruising state, if it is applied together with the minimum opening control (D OUT  =100%) described before to increase the rising speed of supercharging pressure and hence the control responsiveness. 
     When the transmission is in the first speed position, the subtraction term D FT  for the first speed position, referred to before, is applied to the gradient control, to obtain similar results to that stated above. The subtraction term D FT  is set to a value larger than the subtraction term for other gear positions, in view of the supercharging pressure rise characteristic assumed in the first speed position. 
     AIthough the embodiments described above are applied to a variable capacity turbocharger which has its capacity varied by means of movable vanes 54 as increase rate-varying means, the method of the variable capacity turbochargers suoh as a waste-gate type and a supercharging pressure-relief type, as well as other types of superchargers than the turbocharger.