Supercharging pressure control method for internal combustion engines

Abstract: A method of controlling supercharging pressure in an internal combustion engine based on a basic control amount determined in dependence on operating conditions of the engine. The basic control amount is corrected in response to a difference between an actual value of the supercharging pressure and a desired value of same when the engine is in a feedback control region. The basic control amount is corrected in accordance with the change rate of the supercharging pressure when the engine is in an operating condition immediately before the feedback control region. The supercharging pressure is controlled based upon a second basic control amount when the supercharging pressure is below a predetermined value determined by the engine rotational speed and the change rate of supercharging pressure in the above operating condition. The feedback control is started on condition that the actual supercharging pressure has increased above a second predetermined value set depending upon operating parameters of the engine and a parameter representative of an environmental condition of the engine. The feedback control is started when a predetermined period of time has elapsed after the supercharging pressure has increased above the second predetermined value. The feedback control is effected when the supercharging pressure is in a steady state, while the supercharging pressure is controlled in open loop mode when it is in a transient state.

Description: This invention relates to a supercharging pressure control method for internal combustion engines, which controls the supercharger of the engine in a feedback manner responsive to the difference between the actual supercharging pressure and a desired value thereof, and more particularly to a method of this kind, which controls the supercharging pressure in a transient state immediately before and after the start of the feedback control. In order to control the supercharging pressure in an internal combustion engine for automotive vehicles to appropriate values to operating conditions of the engine, it has generally been employed to control the operating amount of the supercharger in a feedback manner responsive to the difference between the actual value of supercharging pressure and a desired value thereof. The feedback control is effective to absorb or correct variations in the operating characteristics of the supercharging pressure control system such as actuators used therein, as well as aging changes therein, thereby enabling to properly control the supercharging pressure. However, it is also well known that feedback control of supercharging pressure undergoes a time lag inherent thereto, that is, it takes time for the supercharging pressure to be brought to the desired value. Particularly in a turbocharger driven by an exhaust gas flow, such time lag is long, as is also well known. The time lag in the feedback control causes overshooting or hunting of the supercharging pressure. Particularly, in a transient state such as a state immediately after the supply of supercharging pressure to the engine has been started upon request for acceleration by the driver, the difference between the actual value of supercharging pressure and the desired value thereof is too large for the operating amount of the supercharger to be controlled in quick response to an actual change in the supercharging pressure, resulting in an excessive rise (overshooting) or an excessive drop (undershooting) in the supercharging pressure, hunting thereof, etc. As the amount of overshooting beyond the desired value is larger, the hunting time is longer, rendering the supercharging pressure control the more unstable. Excessive overshooting can cause overboosting, resulting in knocking of the engine and hence degraded driveability. To overcome the above disadvantages with the conventional feedback control, it has been proposed, e.g. by Japanese Provisional Patent Publication (Kokai) No. 61-164042, to provide two different control modes, one of which is a feedback control mode applied in a steady region where the supercharging pressure is stable, and the other is an open loop control mode applied in a transient region where the supercharging pressure is unstable, and the supercharging pressure is controlled selectively in either of the control modes depending upon which of the two regions the engine is operating in, to thereby control the supercharging pressure to the desired value with high responsiveness and high accuracy. According to the proposed method, whether or not the engine is operating in the feedback control region is determined based upon a parameter representative of load on the engine, such as intake pressure within the intake pipe. Specifically, if the engine load parameter value is higher than a predetermined value, it is determined that the engine is operating in the feedback control region. Then, the supercharging pressure is controlled in the feedback control mode. However, the proposed method still has room for further improvement, as stated below: First, if the intake pressure within the intake pipe is employed to discriminate between the feedback control region and the open loop control region, there are cases where the same control mode should not be applied even when the intake pressure assumes the same value, depending upon the changing manner of intake pressure before the same value is reached. For example, if the same feedback control gain is applied in both cases that the intake pressure gently rises, and that the intake pressure rapidly increases, overshooting or hunting can take place upon transition from the open loop control region to the feedback control region, in the latter case. Secondly, the intake pressure also varies under the influence of other factors, i.e. the operating condition of the engine, and the environmental conditions of the engine such as ambient air temperature and atmospheric pressure. If these factors are ignored in setting the timing of starting the feedback control, the feedback control is started at too early timing or at too late timing. If the feedback control is started at too early timing, the difference between the desired and actual values of supercharging pressure is still large at the start of the feedback control, resulting in overboosting or hunting, whereas if the feedback control start is made at too late timing, the aforementioned variations and aging changes in the operating characteristics of the actuators cannot be corrected for a long time before the feedback control is started. Thirdly, conventionally, the supercharging pressure or intake pressure is used for discrimination between the feedback control region and the open loop control region such that when the supercharging pressure is higher than a predetermined value lower than the desired valaue, and accordingly is deemed to be in a steady state, the feedback control is effected. However, when the supercharging pressure rises at a high rate, if the feedback control is started immediately when the supercharging pressure exceeds the predetermined value, the starting of the feedback control will cause overshooting or hunting of the supercharging pressure. A way to overcome this disadvantage would be to set the above-mentioned predetermined value of supercharging pressure at a relatively high value closer to the desired value. However, there is the possibility that the supercharging pressure is brought into a steady state even when it is still lower than the predetermined value, so that the feedback control is not started. Fourthly, since the intake pressure or supercharging pressure varies also in response to the throttle valve opening, the operating amount of the supercharger has to be controlled to different values depending upon the actual value of the throttle valve opening to maintain the same supercharging pressure. However, according to the conventional methods, even if the throttle valve is not almost fully open (the throttle valve opening is below a predetermined value), the engine is deemed to be in the steady state when the supercharging pressure exceeds a predetermined value, and then the feedback control is started. When the throttle valve becomes almost fully open thereafter, the operating amount is largely changed so as to bring the supercharging pressure to the desired value. Due to the large change in the supercharging pressure as well as to the aforementioned inherent time lag in the feedback control system, the operating amount cannot be promptly brought to a value which can maintain the supercharging pressure at the desired value, resulting in overshooting or hunting of the supercharging pressure. A way to overcome the disadvantage would be to deem that the supercharging pressure is in a steady state when the throttle valve is almost fully open, and then start the feedback control. However, according to this way, the supercharging pressure can be deemed to be in a steady state even when the actual supercharging pressure has not been increased to a sufficient level, and then the feedback control is started though the supercharging pressure is still in a transient state. This results in delayed rising of the supercharging pressure and degraded control responsiveness. JP 60259724 discloses a supercharging pressure control system to improve stability and a response characteristic in feedback control of the supercharge pressure always by a control constant of accurate value, by changing at least one of the proportional gain and the differential gain in accordance with a quantity of change in an actual supercharge pressure from the target supercharge pressure as the control constant of the feedback control of the supercharge pressure. SUMMARY OF THE INVENTION It is a first object of the invention to promptly attain a steady state of supercharging pressure, irrespective of the history of change of the intake pressure during open loop control immediately preceding the feedback control, to thereby enable starting the feedback control in a stable manner without overshooting and hunting of the supercharging pressure. A second object of the invention is to start the feedback control at optimum timing in response to operating conditions of the engine and environmental conditions thereof, to thereby ensure stable starting of the feedback control without overshooting and hunting of the supercharging pressure. A third object of the invention is to start the feedback control at such suitable timing as to avoid overshooting or hunting of the supercharging pressure, even when the supercharging pressure rises at a high rate, to thereby positively stabilize the supercharging pressure at the transition to the feedback control region. A fourth object of the invention is to accurately determine a steady state of the supercharging pressure within which the feedback control is to be effected, by taking into account the throttle valve opening as well, to thereby improve the control responsiveness and prevent overshooting and hunting of the supercharging pressure at the transition to the feedback control region. To attain the above objects, the present invention provides a method of controlling supercharging pressure in an internal combustion engine having a supercharger, wherein the supercharging pressure created by the supercharger is controlled based on a basic control amount determined in dependence on operating conditions of the engine, the basic control amount being corrected in response to a difference between an actual value of the supercharging pressure and a desired value of same when the engine is in a feedback control region in which the supercharging pressure is to be controlled in feedback control mode. According to a first aspect of the invention, the method is characterized by comprising the following steps: 1) detecting a change rate of the supercharging pressure; 2) determining whether or not the engine is in an operating condition immediately before entering the feedback control region; and 3) correcting the basic control amount in accordance with the detected change rate of the supercharging pressure when the engine is in the operating condition immediately before the feedback control region. Preferably, when the detected change rate of the supercharging pressure shows that the supercharging pressure is increasing, the basic control amount is corrected so that the increase rate of the supercharging pressure is decreased, while when the detected change rate of the supercharging pressure shows that the supercharging pressure is decreasing, the basic control amount is corrected so that the decrease rate of the supercharging pressure is decreased. More preferably, the basic control amount is corrected by a larger amount as the detected change rate of the supercharging pressure is larger and/or as the detected rotational speed of said engine is higher. Further preferably, the above step (2) comprises the steps of (a) detecting the supercharging pressure, (b) detecting the opening of a throttle valve of the engine, and (c) determining that the engine is in the operating condition immediately before entering the feedback control region when the detected opening of the throttle valve is larger than a predetermined value and at the same time the detected supercharging pressure has exceeded a predetermined value which is lower than the desired value of the supercharging pressure by a predetermined amount. Preferably, the predetermined amount is determined by at least one of the rotational speed of the engine and the change rate of the supercharging pressure. For example, the predetermined amount is set to larger values as the rotational speed of the engine is higher and/or as the change rate of the supercharging pressure is larger. 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 taken on line IV - IV of Fig. 2; Figs. 5A and 5B are 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 a 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. 8; 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 correcion coefficient K DOWN applied upon departure from a particular operating condition of the engine; Fig. 12 is a flowchart showing a subroutine for determining a decremental value D T ; Fig. 13 is a diagram showing a map of the decremental value; Fig. 14 is a flowchart showing a subroutine for determining an incremental value D TRB ; (a) - (c) of Fig. 15 are diagrams showing maps of D TRB ; (a) - (c) of Fig. 16 are similar diagrams to (a) - (c) of Fig. 14, showing maps of a decremental value ΔP 2ST ; (a) - (c) of Fig. 17 are similar diagrams to (a) - (c) of Fig. 14, showing maps of a decremental value ΔP 2FB ; Fig. 18 is a diagram showing a map of a duty ratio D SCRB ; Fig. 19 is a flowchart showing a subroutine for determining feedback coefficients for determining, respectively, a proportional control term and an integral control term; Fig. 20 is a diagram showing a change in the intake pressure, which can take place when the gear position of the transmission is shifted; Fig. 21 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; Fig. 22 is a flowchart showing a main routine for controlling an electromagnetic valve in Fig. 1; Fig. 23 is a timing chart showing a change in the inatake pressure P B with the lapse of time, obtained by the control according to the first embodiment of the invention; Fig. 24 is a flowchart showing a main routine for controlling the electromagnetic control valve in Fig. 1 according to a second embodiment of the invention; Fig. 25 is a diagram showing a map of a basic duty ratio D M ; Fig. 26 is a flowchart showing a subroutine for determining the gear position of the transmission; Fig. 27 is a diagram showing a table of a predetermined value V F of the vehicle speed, applied to the subroutine of Fig. 26; Fig. 28 is a diagram showing a map of an intake air temperature-dependent correction coefficient K TATC ; Fig. 29 is a flowchart showing a subroutine for determining an open loop control region, which is executed at a step S106 in Fig. 24; Fig. 30 is a diagram showing a table of a first decremental value ΔP BSD to be applied when the transmission is in a position other than the first speed position; Fig. 31 is a diagram sowing a table of a second decremental value ΔP BFB to be applied when the transmission is in a position other than the first speed position; Fig. 32 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. 33 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. 34 is a diagram showing a map of a desired value P BREF of supercharging pressure; Fig. 35 is a diagram showing a table of a constant K P for a proportional control term K P ; Fig. 36 is a diagram showing a table of a constant K I for an integral control term K I ; Fig. 37 is a diagram showing a map of a learned correction coefficient K MOD ; Fig. 38 is a diagram showing the relationship between the intake pressure P B and the supercharging pressure control; Fig. 39 is a diagram showing the relationship between the rise rate of supercharging pressure and the feedback control-starting pressure; Fig. 40 is a diagram showing the relationship between the gear position of the transmission and the feedback control-starting pressure; Fig. 41 is a flowchart showing a subroutine for discriminating between open loop control and feedback control, depending upon the atmospheric pressure; Fig. 42 is a diagram showing another map of desired value of supercharging pressure; and (a) and (b) of Fig. 43 are timing charts showing supercharging pressure characteristics obtained by the control method of the present method and those obtained by the conventional method. 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, 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 toghether 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, and 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 ends 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 "the space area") 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 gas 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 output 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 chamber 62 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 P₂ 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 S P2 for sensing supercharging pressure P₂ 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 ϑ 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 Figs. 5A and 5B, according to a first embodiment of the invention. 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 not the engine is in starting mode, i.e. the engine is cranking. If the engine is in starting mode, the program proceeds to a step S2, where a timer t BTWC is reset. The timer t BTWC is for counting a time period t BTWCO (e.g. 96 sec.) required to determine that warming-up of the engine has been completed. Then, 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, 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 S4). 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 S5, 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 ΔP₂ in supercharging pressure P₂, one of three time periods t FBDLY1 , t FBDLY2 and t FBDLY3 is selected as t FBDLY . The change rate ΔP₂ is calculated as the difference ( ΔP₂ = 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 Figs. 5a and 5B is carried out in synchronism with generation of TDC signal pulses. However, since the change rate ΔP₂ in supercharging pressure P₂ between two adjacent TDC signal pulses is too small for accurate detection of the change rate ΔP₂, the difference between P 2n detected in the present loop and 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 ΔP₂ 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 ΔP₂ ≦ ΔP 2PTL , t FBDLY1 is selected, if ΔP 2PTL < ΔP₂ ≦ ΔP 2PTH , t FBDLY2 is selected, and if ΔP 2PTH < ΔP₂, t FBDLY3 is selected. Further, the three time periods are in the relationship of t FBDLY1 < t FBDLY2 < t FBDLY3 . Therefore, when the change rate ΔP₂ 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 ΔP₂ 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 the starting mode, the program proceeds to a step S6, where it is determined whether or not the TDC signal pulse inputted in the present loop is the first one after control in a basic mode has been started, that is, the present loop is the first loop after the basic mode control has been started. If it is determined that the present loop is the first loop, the program proceeds to a step S7, whereas if the present loop is not the first loop, it proceeds to a step S11. At the step S7, it is determined whether or not the intake air temperature T A is above a predetermined lower value T AL (e.g. -8°C). If T A > T AL , the program proceeds to a step S8, whereas if T A ≦ T AL , it proceeds to a step S10. At the step S8, it is determined whether or not the cooling water temperature T W is above a predetermined lower value, (e.g. 60°C). If T W > T WL , the program proceeds to a step S9, whereas if T W ≦ T WL , it proceeds to the step S10. At the step S9, the timer t BTWC is set to a value FF larger than the predetermined time period t BTWCO (e.g. 96 sec.), followed by proceeding to a step S13, while at the step S10, the timer t BTWC is reset, followed by the program proceeding to the step S3. That is, if T A > T AL and at the same time T W > T WL , it is determined that the engine is in an operating condition after completion of warming-up thereof, so that the timer t BTWC is set to the time period FF larger than the predetermined time period t BTWCO , whereas if at least one of the conditions of T A ≦ T AL and T W ≦ T WL if fulfilled, the timer t BTWC is reset to start counting. Thus, the time period for determining that the warming-up of the engine has been completed starts to be counted after the basic mode control has been started. At the step S11, it is determined whether or not the intake air temperature T A is below the predetermined lower value T AL . If T A < T AL , the program proceeds to a step S2, while if T A ≧ T AL , the program proceeds to a step S12. At the step S12, it is determined whether or not the cooling water temperature T W is below the predetermined lower value T WL . If T W < T WL , the program proceeds to the step S2, while if T W ≧ T WL , the program proceeds to the step S13. That is, if it is determined at the step S6 that the present loop is not the first loop, the intake air temperature T A and the cooling water temperature T W are compared with the respective predetermined values at the steps S11 and S12, followed by the program proceeding to the step S2 or S13 in accordance with the results of respective determinations. The possible operating conditions of the engine which satisfy T W < T WL and T A < T AL 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 < T WL and/or T A < T AL , the program proceeds through the steps S2, S3 to the step S4 to set D OUT to 0%. At the step S13, it is determined whether or not the engine rotational speed N E is above a predetermined value N DO (e.g. 5000 rpm). If N E > N DO , the program proceeds to a step S14, while if N E ≦ N DO , the program skips over the step S14 to a step S15. At the step S14, it is determined whether or not the timer t BTWC has counted up the predetermined time period t BTWCO required to determine that warming-up of the engine has been completed. If t BTWC > t BTWCO , the program proceeds to the step S15, while if t BTWC ≦ t BTWCO , the program proceeds to the step S3. As described above, if the cooling water temperature T W is below the predetermined lower value T WL , the duty ratio D OUT is set to 0% to thereby decrease the supercharging pressure P₂, while even if the cooling water temperature T W is above the predetermined lower value T WL , when the engine rotational speed N E is above the predetermined value N DO , D OUT is maintained at 0% until the predetermined time period t BTWCO elapses. Consequently, even if the engine rotational speed is increased during warming-up of the engine, the supercharging pressure is not increased. At the step S15, it is determined whether or not the intake air temperature T A is above a predetermined higher value T AH (e.g. 100°C). If T A > T AH , the program proceeds to the step S3, while if T A ≦ T AH , the program proceeds to a step S16. At the next step S16, it is determined whether or not the engine coolant temperature T W exceeds a predetermined higher value T WH (e.g. 120°C). If T W > T WH , the program proceeds to the step S3. The possible operating conditions which satisfy T A > T AH and T W > 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 combustion such as misfiring. If supercharging pressure is introduced into the combustion chambers when the engine is under such unstable operating conditions, the engine operation will be made even more unstable. Therefore, at the step S4, 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 S4. At the step S16, if T W ≦ T WH , the program proceeds to a step S17. At the step S17, 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 P₂ > P 2HG , the program proceeds to the step S3. If P₂ ≦ P 2HG , the program proceeds to a step S18. The predetermined high supercharging pressure-discriminating value P 2HG is set 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 can take place, adversely affecting the durability of the engine main body E. Therefore, P 2HG is set to values lower than a medium engine rotational speed range. If the supercharging pressure P₂ which exceeds the high supercharging pressure-discriminating value P 2HG is detected, the program proceeds through the step S3 to the step S4, where the duty ratio D OUT is set to 0% whereby the supercharging pressure P₂ is decreased, and at the same time fuel injection is inhibited. At the step S18, 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 S19, 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 S20, and if the transmission is in a position other than the first speed position, the program proceeds to a step S21. At the step S20, 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 gear 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 22 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. At the step S21, 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 the 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 S22 without correcting the basic duty ratio D M . D OS and ΔP 2REFOS are predetermined decremental values. At the step S22, searched are a duty ratio correction coefficient K MODij , an atmospheric pressure-dependent correction coefficient K PATC (0.8 to 1.0), and an intake air temperature-dependent correction coefficient K TATC (0.8 to 1.3). The duty ratio correction coefficient K MODij is searched from a map of the engine rotational speed N E and the intake air temperature T A . As described later, the correction coefficient K MODij is learned when the actual supercharging pressure P₂ is within a predetermined difference range about the desired supercharging pressure value, and renewed to an up-to-date learned value. The initial value of the correction coefficient K MODij is set to 1. The atmospheric pressure-dependent correction coefficient K PATC is determined by the atmospheric pressure P A . The intake air temperature-dependent correction coefficient K TATC is determined by the intake air temperature T A . At a step S23 following the step 22, a correction coefficient K DOWN is searched in accordance with a subroutine shown in Fig. 11. This subroutine is executed by interrupting the main routine shown in Figs. 5A and 5B, in syncronism with generation of each pulse of the TDC signal. When the duty ratio D OUT is 0%, a timer t DOWN is reset. The correction coefficient K DOWN is set to an initial value upon generation of the first TDC signal pulse after the duty ratio D OUT becomes more than 0%. The initial value is determined depending on the engine rotational speed N E . When N E exceeds a predetermined value N EA , e.g. 3000rpm, the initial value is set to a value K DOWN1 , e.g. 0.5, whereas when N E is below the predetermined value N EA , it is set to a value K DOWN2 , e.g. 0.6. Further, after the predetermined time period t DOWN , e.g. 5 sec., has elapsed, the correction coefficient K DOWN is renewed by being increased by an additional value ΔK DOWN , e.g. 0.01 whenever each TDC signal pulse is generated. If the correction coefficient K DOWN exceeds 1.0, it is set to 1.0. The correction coefficient K DOWN determined as above is substituted into an equation for correcting the duty ratio D OUT to control same so as to gently vary when the duty ratio is released from a condition in which it is forced to be 0% when the engine is in a particular operating condition in which the intake air temperature T A and the cooling water temperature T W are too high or too low, and the supercharging pressure P₂ is too high. More specifically, when the engine has returned to a normal operating condition from the particular condition in which D OUT = 0%, if D OUT is immediately set to a normal value other than 0%, the D OUT value will vary unstably as the engine shifts between the normal and particular operating conditions, resulting in unstable control of the supercharging pressure. In order to avoid such unstable control, the correction coefficient K DOWN is gradually increased in each loop by e.g. 0.01, after the predetermined time period, e.g. five seconds have elapsed since the engine returned to the normal operating condition. At the step S24, 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 S25 similarly to the step S2, and then the program proceeds to a step S26. To be specific, the resetting of the timer t FBDL at the steps S3 and S25 is made in accordance with a subroutine in Fig. 6. One of three timers t FBDLY1 , t FBDLY2 , and t FBDLY3 is selected in response to the change rate ΔP₂ of the supercharging pressure P₂. The change rate ΔP₂ is determined as the difference between a value P 2n of supercharging pressure detected in the present loop and a value P 2n-6 detected in a loop corresponding to the sixth TDC signal pulse before the present TDC signal pulse, for example, whenever each TDC signal pulse is generated. This is because although the main routine of Figs. 5A and 5B is executed at every pulse of the TDC signal as mentioned before, the change rate of the supercharging pressure P₂ corresponding to the time interval between adjacent TDC signal pulses is too small for accurately determining the change rate. A predetermined lower change rate value ΔP 2PTL and a predetermined higher change rate value ΔP 2PTH are provided, which are determined from a map, not shown, in accordance with the engine rotational speed N E . When ΔP₂ ≦ ΔP 2PTL , the timer t FBDLY1 is selected, the timer t FBDLY2 when ΔP₂ ≦ ΔP 2PTH , and the timer t FBDLY3 when ΔP 2PTH < ΔP₂, respectively. The relationship between t FBDLY1 to t FBDLY3 is t FBDLY1 < t FBLY2 < t FBDLY3 . At the step S26, searched are a decremental value D T , and an incremental value D TRB . The decremental value D T is determined depending on a change rate ΔP₂ of the supercharging pressure P₂, in accordance with a subroutine in Fig. 12. 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 ΔP₂ of supercharging pressure P₂ and the engine rotational speed N E as shown in (a), (b), and (c) of Fig. 13. If ϑ TH ≦ ϑ THFB , D T is set to 0%. (a) of Fig. 13 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. 13 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. 13 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 decrimental value D T is applied, as shown in Fig. 21, when the actual supercharging pressure P₂ 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. 13 and as described above, in accordance with the engine rotational speed N E and the change rate ΔP₂ of supercharging pressure. This is because the amount of overshooting depends on the engine rotational speed N E and the change rate ΔP2 of supercharging pressure when the predetermined value P 2ST is reached. D T is set to a larger value as ΔP₂ is larger and as N E is higher. When the change rate ΔP₂ is negative, an additive or incremental value D TR , which is used in place of D T , is determined in accordance with a subroutine shown in Fig. 14. Specifically, when the control mode is open loop mode, and at the time the change rate ΔP₂ is negative, the value D TRB is set depending upon -ΔP₂ and the engine rotational speed N E such that as N E is higher, or as |ΔP₂| is larger, D TRB is set to a larger value, as shown at (a), (b) and (c) of Fig. 15. On this occasion, the subtractive or decremental value D T is set to 0. When the feedback loop control was executed in the last loop, or when the open loop control was executed in the last loop and at the same time ΔP₂ is positive, the incremental value D TRB is set to 0. In this manner, it is possible to reduce fluctuations in the supercharging pressure immediately before and/or immediately after the feedback control so that feedback control can be stably effected without hunting in the supercharging pressure, thereby stabilizing the supercharging pressure in each operating region of the engine. That is, by applying the incremental value D TRB for prevention of hunting as well as the decremental value D T for prevention of overshooting, the duty ratio D OUT is calculated, whereby further stable control of the supercharging pressure can be attained in each operating region of the engine. After the correction coefficients K MODij , K PATC , K TATC and K DOWN , the decremental value D T , and the incremental value D TRB are thus determined, the program proceeds to a step S27. At the step S27, the duty ratio D OUT is calculated by the following equation: D OUT = K TATC x K PATC x K MODij x K DOWN x (D M + D TRB - D T ) Thus, the duty ratio D OUT outputted from the step S5 is set in accordance with operating conditions of the engine, by taking into account the external factors. Further, at a step S28, the flag F is set to 1 to indicate that the engine is in the open loop control mode. Then, at steps S29 and S30, it is determined whether or not the engine is in an operating condition in which the vehicle can run with the transmission set in a second speed position. More specifically, at the step S29, it is determined whether or not the engine rotational speed N E falls within a range between a first predetermined value N SEC1 , e.g. 4500rpm, and a second value N SEC2 , e.g. 6000rpm, that is, N SEC1 ≦ N E ≦ N SEC2 . At the step S30, it is determined whether or not the vehicle speed V falls within a range between a first predetermined value V SEC1 , e.g. 70km/h, and a second predetermined value V SEC2 , e.g. 90km/h, that is, V SEC1 ≦ V ≦ V SEC2 . If the answers to the questions of the steps S29 and S30 are both Yes, the duty ratio D OUT is set to 0% at a step S31, followed by the program proceeding to a step S32. Thus, the supercharging pressure P₂ is decreased, whereby the gear shaft of the transmission, not shown, is prevented from being overloaded when it is in the second speed-holding position. If N E < N SEC1 , N SEC2 < N E , V < V SEC1 , or V SEC2 < V, the program proceeds to the step S32. At the step S32, it is determined whether or not the automatic transmission is in the first speed position. If it is in the first speed position, the program proceeds to a step S33, while it is in a position other than the first speed position, the program proceeds to a step S37, where a timer t KDF is reset, followed by the program proceeding to a step S38. At the step S33, it is determined whether or not the automatic transmission was in the first speed position in the last loop. If the answer is Yes, the program proceeds to a step S34, where it is determined whether or not the timer t KDF has counted up a predetermined time period t DKFO (e.g. 5 sec.). If t DKF > t DKFO , the program proceeds to the step S38, while if t KDF ≦ t KDFO , the program proceeds to a step S36. If it is determined at the step S33 that the automatic transmission was in a position other than the first speed position in the last loop, the timer t FBDLY is reset at a step S35, followed by the program proceeding to the step S36 where the duty ratio D OUT is set to 0%, and then to the step S38. The steps S32 - S37 are provided for the kicking-down operation. That is, by virtue of the steps, when kicking-down is made from a position other than the first speed position to the first speed position, and until a predetermined time period, e.g. 5 sec., elapses after the kicking-down, the duty ratio D OUT is maintained at 0%, thereby preventing overload on the first speed gear. At the step S38, the duty ratio D OUT is checked to make sure that it is within a predetermined range defined by upper and lower limit values. The upper and lower limit values of D OUT are set in accordance with the engine rotational speed N E . If D OUT is within the predetermined range, it is outputted at the step S5. If it is determined at the step S24 that ϑ TH > ϑ THFB , the program proceeds to a step S39 where it is determined whether or not the flag F assumed 1 in the last loop, i.e. whether or not the engine was in the open loop control mode in the last loop. If F = 1, it is determined at a step S40 whether or not the supercharging pressure P₂ 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. 16. 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 ΔP₂ 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 ΔP₂ of supercharging pressure is larger. If P₂ > P 2ST at the step S40, it is determined at a step S41 whether or not the supercharging pressure P₂ is above the 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. 17, ΔP 2FB is set in dependence on the engine rotational speed N E and the supercharging pressure change rate ΔP₂ such that it is set to a larger value as N E is higher and as the ΔP₂ is larger, in order to optimize the duty ratio control, similarly to the aforesaid ΔP 2ST , D T , and D TRB . By thus setting the feedback control-starting pressure by the use of the value ΔP 2FB , the feedback control is started at appropriate timing to prevent an abnormal rise or hunting in the supercharging pressure and hence bring the supercharging pressure to the desired value promptly after feedback control is started. At the step S41, if P₂ < P 2FB , it is decided that the engine is not in a condition where feedback control should be effected (steady state), and then the program proceeds to the aforesaid step S25, whereas if P₂ > P 2FB , the program proceeds to a step S42 to execute the feedback control. At the step S42, it is determined whether or not the delaying timer t FBDLY has counted up the preset time period t FBDLY after being reset at the step S3, S25 or S35. If it has counted up, the feedback control is continued at a step S43 et seq., whereas if it has not counted up yet, the program returns to the step S26 to execute the open loop control. Therefore, also upon the transition from open loop control to feedback control, stable control of the supercharging pressure is achieved. The curve indicated by the broken line II in Fig. 23 shows a change in the supercharging pressure, which is obtained in the case where the above described control of delaying the feedback control is not carried out. If whether or not the feedback control is to be started is decided only depending upon the state of the supercharging pressure as in the comparative example II, that is, if it is determined that the supercharging pressure P₂ is in the steady state when P₂ exceeds the predetermined value P 2FB lower than the target or desired value P 2REF by the predetermined amount ΔP 2REF , there can take place overshooting and undershooting in the supercharging pressure as shown in the figure. If the magnitude of hunting is large, it will take time for the actual supercharging pressure to be brought to the desired value, increasing the unstable time period. In contrast, according to the feedback control-delaying control by the delaying timer t FBDLY described above, even if P₂ > P 2FB has been fulfilled, the open loop control is continued before the preset time period t FBDLY elapses. In this way, since the control mode to be employed during transient state of supercharging pressure, i.e. open loop control, is continually employed under a certain condition, the magnitude of overshooting, etc. can be greatly reduced to a much lower level during feedback control, as compared with the comparative example II, as indicated by the solid line I in Fig. 23, thereby enabling to achieve stable and proper control of the supercharging pressure. That is, hunting as seen in the comparative example II is attenuated before the predetermined time period t FBDLY elapses, so that at a time point tC in Fig. 23 at which the time period t FBDLY elapses, the feedback control is started in a state where the difference between the actual supercharging pressure P₂ and the target value P 2REF has already become smaller. Therefore, the actual supercharging pressure can be promptly brought to the target value within a short time period. Furthermore, immediately upon the lapse of the time period t FBDLY the control mode is changed over to the feedback control mode, thereby avoiding the phenomenon that the open loop control is continued for a long time without the feedback control being started even after the engine has entered the feedback control region. Thus, smooth and prompt shifting to the feedback control can be effected without fail. Particularly, the above described delaying control by the timer t FBDLY is effective in the case where it is required to enhance the rising speed of supercharging pressure through the aforedescribed minimum opening control to improve the control responsiveness, such as at standing-start of the vehicle with the throttle value fully open or at rapid acceleration from a cruising condition. Further, since, as stated before, the time period t FBDLY per se is set to appropriate values to the change rate of supercharging pressure such that it is set to shorter values as the supercharging pressure change rate ΔP₂ is smaller (when the supercharging pressure gently changes), and it is set to longer values as the change rate ΔP₂ is larger (when the supercharging pressure suddenly changes), hunting in the supercharging pressure can be further positively prevented upon transition to the feedback control mode. Referring again to Fig. 5, at a step S44, a predetermined basic duty ratio value D SCRB as a second supercharging pressure control amount is searched which is dependent on the engine rotational speed N E , as shown in Fig. 18. The basic duty ratio value D SCRB searched is substituted into the following equation to calculate the duty ratio D OUT : D OUT = D SCRB x K TATC x K PATC Subsequently, at a step S46, a timer t FBDLY is reset, followed by the program proceeding to the step S38. The steps S44 and S45 are for achieving stable supercharging pressure control in an operating region in which the supercharging pressure P₂ is below the value P 2ST . That is, since the duty ratio D OUT is determined based upon the predetermined value D SCRB corresponding to the engine rotational speed N E , overshooting can be prevented without fail, irrespective of the change rate ΔP₂ of the supercharging pressure P₂. As described above, according to the control based on the duty ratio control-starting value P 2ST and the feedback control-starting value P 2FB , the supercharging pressure P₂ is controlled in feedback control if P₂ > P 2FB , in starting mode at the step S44 et seq if P₂ ≦ P 2ST , and based on the basic duty ratio DM if P 2ST < P₂ < P 2FB , respectively. However, since the supercharging pressure P2 varies depending on the ambient air pressure (atmospheric pressure), if the value P 2ST and P 2FB are determined only depending on the engine rotational speed N E and the supercharging pressure change rate ΔP₂, the starting control will be often executed, while the feedback mode control will not be executed as expected. To avoid this, the values P 2ST and P 2FB are corrected by the ambient air pressure. At the step S43, it is determined whether or not the absolute value of change rate ΔP₂ of supercharging pressure is above a predetermined 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 ΔP₂ is above the value G dP2 , the program returns to the step S26, and if the absolute value of ΔP₂ is equal to or lower than the value G dP2 , the program proceeds to a step S47. If the feedback control is started when |ΔP₂| > G dP2 , it may result in hunting. Therefore, the program returns to the step S26 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 S47 is provided mainly for fail-safe purposes. The feedback control is started at the step S47, 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 > ϑ THFB at the step S24. 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 > ϑ THFB , i.e. under a medium or high load operating condition, 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 . The desired supercharging pressure P 2REF is set to a lower value as the intake air temperature T A is decreased. More specifically, the increase rate of the supercharging pressure tends to be larger when the intake air temperature T A is lower. Therefore, the desired supercharging pressure is set in the above manner, whereby the minimum opening control can be terminated at appropriate timing, and hence the accelerability can be further improved. At a step S48, 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 - ΔP 2REFF is carried out at a step S49 in accordance with the subroutine shown in Fig. 8 when the operating condition of the engine is within the predetermined operating zone shown by hatching in Fig. 9, and then the program proceeds to a step S51. 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 S48 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 S50 in accordance with the subroutine shown in Fig. 10, and then the program proceeds to the step S51. 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 S51, an atmospheric pressure-dependent correction coefficient K PAP2 for correcting the supercharging pressure is determined in accordance with the atmospheric pressure P A , and then at a step S52, the following calculation is carried out: P 2REF = P 2REF x K PAP2 x K REFTB where K REFTB is a correction coefficient responsive to a knocking condition of the engine. At a step S53, it is determined whether the absolute value or the difference between the desired supercharging pressure P 2REF and the supercharging pressure P₂ 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 insensitive 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 S54, and if not, the program proceeds to a step S61. At the step S54, a proportional control term D P for correcting the duty ratio is calculated by the following equation: D P = K P x (P 2REF - P₂) where K P is a feedback coefficient for the proportional control term, and is obtained in accordance with a subroutine shown in Fig. 19. In Fig. 19, 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 S55, 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 S56, it is determined whether or not the flag F assumed 1 in the last loop, 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 S57 by the following equation: D I(n - 1) = K TATC x K PATC x D M x (K MODij - 1) After this calculation, the program proceeds to a step S58. If F = 0 at the step S56, the program skips over the step S57 to the step S58. At the step S58, an integral control term D In for the present loop is calculated by the following equation: D In = D I(n - 1) + K I + (P 2REF - P₂) where K I represents feedback coefficients K I1 - K I3 obtained when the feedback coefficient K P is calculated at the step S54 in accordance with the subroutine in Fig. 19. Then the program proceeds to a step S59, where the duty ratio D OUT is calculated by the following equation: D OUT = K TATC x K PATC x K DOWN x D M + D P + D In Then, at a step S60, the flag F is set to 0, and the program proceeds to the step S38. If it is determined at the step S53 that the absolute value of the difference between the desired supercharging pressure P 2REF and the actual supercharging pressure P₂ is smaller than the predetermined value G P2 , D P is set to 0 and D In is set to D I(n - 1) at a step S61. Then at steps S62 to S66, it is determined whether or not the atmospheric pressure P A is above a predetermined value P AMOD (e.g. 650 mmHG), 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 responsive to the knocking condition is equal to or lower than 1.0. If all these conditions are satisfied, the program proceeds to a step S67, and if any one of them is not satisfied, the program proceeds to the step S59. At the step S67, a coefficient K R for learning the correction coefficient K MODij for duty ratio is calculated by the following equation: K R = (K TATC x D M + D In )/(K TATC x D M ) At a step S68, in order to determine and learn the correction coefficient K MODij , the following calculation is carried out: K MODij = (C MOD x K R )/65536 + [(65536 - C MOD ) x K MODij )]/65536 where C MOD represents a variable set to a suitable value selected from 1 - 65536 experimentally depending on the characteristics of the supercharging pressure control system, the engine etc. At a step S69, K MODij obtained at the step S68 is subjected to limit checking. Thereafter, at the step S70 K MODij is stored in a back-up RAM, not shown, following by the program proceeding to the step S59. According to the above-described control of the duty ratio of the solenoid 70 of the electromagnetic 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 S20 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 2REFF is subtracted from the desired supercharging pressure P 2REF at the step S49 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 D M . 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. 20. As known, when the gear position of the transmission is shifted, the engine rotational speed N E is decreased. 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 P₂ does not properly correspond to the change in the engine rotational speed N E and overshooting of the supercharging pressure may arise. As shown by the broken line in Fig. 20, 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 Figs. 5A and 5B at the step S21 and at the step S50, 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 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 ΔP₂ of supercharging pressure P₂, and ΔP 2REFOS is subtracted from the desired supercharging pressure P 2REF in the feedback control mode. Thus, as shown by the solid line in Fig. 20, 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. 21, a drop in the supercharging pressure P₂ 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 loop 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 S26 in accordance with the subroutine shown in Fig. 12. As stated before, the control 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 P₂ 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 P₂ may drop as shown by the broken line in Fig. 21, in reaction to the subtraction. However, according to the subroutine of Fig. 14, if ΔP₂ ≦ 0, D T is set to 0%, and only 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 P₂ to thereby smoothly shift the control mode to the feedback control mode while preventing occurrence of hunting of the supercharging pressure. Further, as stated before, when the supercharging pressure P₂ is still below P 2ST while ϑ TH > ϑ THFB , the control value D SCRB as the second basic supercharging pressure control amount is applied to the control of supercharging pressure. As a result, when the supercharging pressure P₂ rises at a high change rate ΔP₂ but does not yet reach the predetermined value P 2ST , it can be prevented that thereafter the supercharging pressure rises far beyond P 2ST , i.e. overshooting can be prevented. 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. In this manner, in addition to the control of operation of the electromagnetic control valve 69 for introducing supercharging pressure P₂ into the first pressure chamber 62 of the actuator 60 in accordance with the main routine shown in Figs. 5A and 5B, intake pressure P B is introduced into the second pressure chamber 63 of the actuator 60 by way of the electromagnetic control valve 72, and at the same time the electromagnetic valve 72 is controlled based on the intake pressure P B from the intake pressure sensor S PB , 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 P₂ 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 contrast, 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. Next, with reference to Fig. 22, the manner of controlling the solenoid 73 of the electromagnetic valve 72 by the control unit C will be described below. 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 cause 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 betwen when the vehicle speed V increases and when it decreases and is set to, for example, 90/87 km/h. If V > 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 value Δϑ THOP2 is provided with a hysteresis similar to that of the vehicle speed V OP3 . If Δϑ TH < 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 < 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 > 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 > V OP2 , the program proceeds to a step L9, where the t OP timer for counting a time period t OP is reset, and then the program proceeds to a step L10. If V ≦ V OP2 , the program directly proceeds to the step L10. At the step L10, it is determined whether or not the solenoid 73 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 OPO . If t OP > t OPO , the program proceeds to the step L6, whereas if t OP ≦ t OPO , 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 < 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 PB < 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 < 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 ϑ < Δϑ TH < 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 < Δϑ TH < ΔϑTHOP2, 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 Figs. 5A and 5B. 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 P₂ 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 such 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 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 < V < V OP1 , N E < N EOP , P B < P BOP , ϑ TH < ϑ THOP , and 0 < Δϑ TH < Δϑ THOP1 are satisfied, i.e. if the vehicle is gently accelerated under partial load in a similar manner to the standard Japanese 10 mode running test cycle, the solenoid 73 is energized to decrease the supercharging pressure P2, whereby pumping loss can be prevented. Fig. 24 shows a program for controlling the electromagnetic control valve 69, according to a second embodiment of the invention. The second embodiment is distinguished from the first embodiment of Figs. 5A and 5B, in that 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 fact that the feedback control of the supercharging pressure is effected in an operating condition of the engine where the throttle valve 74 is almost fully open, in which condition information relating to the superchargi8ng 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. 25 shows an example of the D M map in which the throttle valve opening ϑ TH is classified into sixteen predetermined values ϑ THV - 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. 26. 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 < 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 < V L and at the same time V < V F , it is determined that the gear position is in the first speed position. Fig. 27 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 table 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. 24, 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 tranmssion 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 in another position. By virtue of this control, when the transmission is in the first speed position, the supercharging pressure is moderately suppressed as a whole so that an abrupt increase or overboosting in the supercharging pressure can be prevented, as indicated by the solid line in Fig. 39. Furthermore, when the transmission is in a position other than the first speed position, the supercharging pressure can be controlled to a sufficiently high value, thereby enabling to attain desired accelerability, as indicated by the broken line in Fig. 39. 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. 28 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 "the change rate", 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. 29. First, at a step S201 of the Fig. 29 subroutine, it is determined whether or not the throttle valve opening ϑ TH is larger than a predetermined value ϑ THFB indicating that the throttle valve 74 is almost fully open. If 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. Therefore, it can be avoided that the throttle valve opening ϑ TH largely varies during the feedback control, for example, the throttle valve will not be opened from a half open state into a fully open state during the feedback control, whereby the feedback control can be stably effected without overshooting or hunting in the supercharging pressure, as indicated by the solid line in Fig. 43. If it is determined at the step S201 that ϑ TH > 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 S202 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 , followed by the program proceeding to a step S207. Fig. 30 shows an example of the ΔP BST table, in which two predetermined values ΔP B1 and ΔP B2 (ΔP B1 < ΔP B2 ) are provided as the change rate Δ P BST . The predetermined values ΔP BST3 -ΔP BST1 are set such that as Δ PB is larger, i.e., as the increase rate of the supercharging pressure is higher, the first subtraction value ΔP BST 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 S205 or S206. The difference P BREF - ΔP BST is hereinafter referred to as "duty ratio control-starting pressure". The desired value P BREF is set in accordance with the engine rotational speed N E , the intake air temperature T A , and the gear position of the transmission by the program of Fig. 24, as hereinafter described. Specifically, as hereinafter described, the desired intake pressure value P BREF is set to smaller values as the intake air temperature T A is lower, while it is set to a lower value when the gear position of the transmission is the first speed position than a value set when it is a higher speed position. If it is determined at the 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 DOUT is set to 100% to make the space area between the movable and stationary vanes 54, 49 the minimum, at a step S210. Thus, when P B ≦ (P BREF - 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. 38. 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. 24 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. 24. Referring again to Fig. 29, if at the step S207 the intake pressure PB 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. 31 shows an example of the ΔP BFB table, in which predetermined values ΔP BFB3 - ΔP BFB1 are provided (ΔP BFB3 < ΔP BFB2 < 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 smaller 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 "feedback control-starting pressure". 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 ) < PB ≦ (P BREF - ΔP BFB ), open loop control is effected as at the period between tA - tB in Fig. 38. By thus not executing the feedback control but carrying out the open loop control when the intake pressure P B is below the predetermined value, it is possible to increase the rising speed of the supercharging pressure and hence improve the control responsiveness as indicated by the solid lines in (a) and (b) of Fig. 43, as compared with the conventional method indicated by the broken lines in the same figures. As stated above, when the intake pressure P B is below the predetermined value, it is assumed that the supercharging pressure is not in the steady state, and then the open loop control is executed instead of the feedback control, so that the rising speed of the supercharging speed can be increased to thereby improve the control responsiveness, as shown in (a) and (b) of Fig. 43, as compared with the control according to the prior art indicated by the broken line in (a) and (b) of Fig. 43. 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. 32 shows an example of the D T table, in which predetermined values D T1 - D T3 (D T1 < D T2 < 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. 30. If at the step S217 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. 33 shows an example of the D FT table, in which two predetermined values ΔP BF1 and ΔP BF2 (ΔP BF2 > ΔP BF1 ) are provided as the change rate ΔP B , and predetermined subtraction values D FT1 - D FT3 (D FT1 < D FT2 < 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. 32 at the same change rate ΔP B . As described later, the duty ratio D OUT during the open loop control is set to a smaller value as the subtraction terms D T , D FT are set to larger values. Therefore, by setting the value of D FT to a value larger than the value of D T in response to the change rate ΔP B , the rising speed of the supercharging pressure can be suppressed in accordance with an actual change in the supercharging pressure when the automatic transmission is in the first speed position. Therefore, with the aid of the basic duty ratio D M set, depending on engine operating conditions, an abrupt increase and overboosting in the supercharging pressure can be positively prevented when the transmission is in the first speed position, as indicated by the solid line I shown in Fig. 39, while the rising rate in the supercharging pressure can be controlled to a larger value when the transmission is in a position other than the first speed position to thereby obtain desired accelerability, as indicated by the chain line II in Fig. 39. 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. In this manner, when the throttle valve 74 is almost fully open, first the minimum opening control is executed to forcibly set the duty ratio D OUT to 100% at the step S210, and therefore the open loop control is executed at the step S221 when the intake pressure P B rises to terminate the minimum opening control. Specifically, the open loop control at the step S221 is carried out at steps S125 - S129, and S118 in Fig. 24 where calculation of the duty ratio D OUT , limit checking of the calculated D OUT , and outputting of D OUT are executed. By thus executing the open loop control, the intake pressure P B is controlled to change as shown in Fig. 38. At the step S215, the magnitude of supercharging pressure, i.e. the intake pressure P B in this embodiment, is monitored as it is controlled as above. If it is determined at the step S125 that the intake pressure P B exceeds the feedback control-starting pressure (P B - ΔP BFB ), the control mode shifts to the feedback control. Also in this embodiment, the lapse of the predetermined period of time t FBDLY is determined from a count in the timer t FBDLY after it has been reset at the step S211 or S216 (in the example of Fig. 38, at a time point tA corresponding to the resetting at the step S216), at a step S222. If the answer at the step S222 is no, the program proceeds to the step S217 to continue the open loop control, whereas if the answer is yes, the program proceeds to a step S223. In this way, the feedback control is not started immediately when the intake pressure P B exceeds the feedback control-starting pressure (P BREF - ΔP BFB ), but the open loop control is continually executed until the predetermined time period t FBDLY elapses (the time period between tB - tC in Fig. 23), that is, only after the lapse of the time period t FBDLY the feedback control is started (at tC in Fig. 23). Therefore, also according to this second embodiment, similarly to the first embodiment described before, only after the supercharging pressure has been brought into a state where the magnitude of hunting or overshooting has become sufficiently small, the feedback control is started, to thereby smooth the transition to the feedback control and hence further improve the supercharging pressure control, in collaboration with setting of the target supercharging pressure (P BREF - ΔP BFB ), hereinbelow described. Since, as stated with reference to the aforesaid step S215 in Fig. 29, the feedback control-starting pressure is set not to a fixed value but to the differential value (P BREF - ΔP BFB ), that is, it is set to a variable value depending upon operating conditions of the engine and environmental conditions thereof, the supercharging pressure control is always effected in accordance with actual operating factors of the engine. The setting of the feedback control-starting pressure will now be explained with reference to Figs. 39 and 40, as well. First, the subtraction value ΔP BFB applied at the step S215 is determined from a table shown in Fig. 31, such that, as stated before, as the rise rate (gradient) of supercharging pressure is larger, the value ΔP BFB is set to smaller values (ΔP BFB1 > ΔP BFB2 > ΔP BFB3 ). As shown in Fig. 39, the value ΔPBFB is set to a larger value so that the feedback control-starting pressure (P BREF - ΔP BFB ) is set to a lower value when the rise rate of supercharging pressure is smaller as indicated by the chain line II, whereas it is set to a smaller value so that (P BREF - ΔP BFB ) is set to a higher value when the rise rate is larger as indicated by the solid line I. By thus setting the feedback control-starting pressure, the transient state of supercharging pressure is made to last longer when the rise rate of supercharging pressure is larger than when the latter is smaller, so as to start the feedback control at appropriate timing as to prevent an abnormal rise or hunting in the supercharging pressure and hence bring the supercharging pressure to the desired value promptly after feedback control is started. Further, the feedback control-starting pressure (P BREF -ΔP BFB ) is changed also depending on the gear position of the transmission. More specifically, when the transmission is in the first speed position as a lower speed position, the aforementioned step S214 is executed to set the subtraction value ΔP BFB to a larger predetermined value ΔP BFBF for the first speed position, as stated before. The set value ΔP BFB is applied at the step S215 so that the feedback control-starting pressure (P BREF -ΔP BFB ) is set to a smaller value than when the transmission is in a position other than the first speed position. The setting of the feedback control-starting pressure in dependence on the gear position of the transmission always makes it possible to shift the control mode to the feedback control at optimum timing even if the supercharging pressure rising characteristic is varied according to the gear position (Fig. 40). To be specific, in the present embodiment, when the transmission is in the first speed position, the supercharging pressure is made lower, and at the same time the rise rate of supercharging pressure is made smaller, immediately after it has been brought into a steady state from a transient state. This is because when the engine is suddenly accelerated with the throttle valve fully open from a lower speed position of the transmission, the supercharging pressure and hence the torque are suddenly increased so that driving wheels of the vehicle can spin. Therefore, according to the invention, when the transmission is in a lower speed position, the target feedback control-starting pressure is set to a lower value and further the rise rate of supercharging pressure is set to a lower value, so that as indicated by the solid line I in Fig. 40 showing an intake pressure curve obtained when the transmission is in the first speed position, a sudden rise in the supercharging pressure and overboosting thereof are prevented to restrain occurrence of a sudden rise in the torque and wheel spinning. On the other hand, when the transmission is in a position other than the first speed position, a sufficient rise in the supercharging pressure is obtained as indicated by the chain line II to thereby attain desired accelerability of the engine. At the steps S212 - S215, to effect the control dependent upon the transmission gear position, when the transmission is set into the first speed position, the feedback control-starting pressure is set to a lower value as shown in Fig. 40, to obtain the best timing of shifting to the feedback control. Furthermore, the feedback control-starting pressure (P BREF - ΔP BFB ) is set depending upon the intake air temperature T A , too. The intake air temperature T A is one of important factors affecting the supercharging pressure, in that a change in the intake air temperature T A leads to a change in the charging efficiency of the engine. If the supercharging pressure characteristic is not changed as the intake air temperature T A changes, the engine output will become excessively large when the intake air temperature T A is low, which may degrade the durability of the engine, whereas the engine output will be insufficient at a high intake air temperature T A . To cope with this, according to the invention, the feedback control-starting pressure is set in dependence on the intake air temperature T A (step S108 in Fig. 24). In the present embodiment, the intake pressure P B is used in the determination at the step S215 to eliminate the influence on the supercharging pressure characteristic by the intake air temperature T A . That is, the intake pressure P B varies with a change in the intake air temperature T A . Therefore, the feedback control-starting pressure (P BREF - ΔP BFB ) is varied in dependence on the intake air temperature T A . More specifically, as the intake air temperature T A is lower, the feedback control-starting pressure (P BREF -ΔP BFB ) is set to a lower value, whereas as the former is higher, the latter is set to a higher value. By thus setting the feedback control-starting pressure (P BREF -ΔP BFB ) in dependence on the intake air temperature T A , the feedback control can be started at appropriate timing corresponding to the intake air temperature T A . Still further, the feedback control-starting pressure (P BREF - ΔP BFB ) is set in dependence on the atmospheric pressure P A as an environmental factor, too. The manner of setting the feedback control-starting pressure in dependence on the atmospheric pressure will now be described with reference to Figs. 41 and 42. When the vehicle is running at a high altitude where the atmospheric pressure is low and hence the air density is small, the supercharging pressure will be insufficient, failing to obtain sufficient engine output. To cope with this, according to the invention, the supercharging pressure characteristic is adapted to the atmospheric pressure. Specifically, first, the target or desired supercharging pressure is corrected in dependence on the atmospheric pressure so as to avoid insufficient engine output due to a drop in the atmospheric pressure, and secondly, the feedback control-starting pressure is varied according to the correction of the target supercharging pressure. Fig. 41 shows a program for carrying out the control dependent upon the atmospheric pressure according to the invention. The steps shown in the figure correspond to the steps S215 et seq. in Fig. 39. At a step 2101, it is determined whether or not the actual supercharging pressure is higher than the feedback control-starting pressure, i.e. the difference [P BREF(PA) - ΔP BFB ] between the target supercharging pressure P BREF(PA) and the subtraction value ΔP BFB . The target value P BREF(PA) of the intake pressure PB within the intake pipe is read from a P BREF(PA) map in Fig. 42. In the map of Fig. 42, predetermined values of the target intake pressure P BREF(PA) are provided, which correspond to respective combinations of predetermined values N V1 - N Vm of the engine rotational speed N E and predetermined values P AV1 -P AVn of the atmospheric pressure. According to the map, the target intake pressure P BREF(PA) is set to higher values as the atmospheric pressure P A is lower. At the step 2101, the differential value [P BREF(PA) - ΔP BFB ] obtained by subtracting the subtraction value ΔP BFB from a value of target intake pressure P BREF(PA) read from the map of Fig. 42 is used as the feedback control-starting pressure and compared with the actual intake pressure P B to determine whether to execute the open loop control or the feedback control. In this way, according to the invention, the target supercharging pressure is set in dependence on the atmospheric pressure P A and automatically the feedback control-starting pressure is set in accordance with the set target supercharging pressure, whereby the timing of shifting to the feedback control can be varied with a change in the atmospheric pressure P A . Referring again to the step S223, an initial value of the integral control term D T is calculated by the following equation: D I = K TATC x D M x (K MODij - 1) where K MODij is a learned correction coefficient (learned value) calculated during feedback control in accordance with the program of Fig. 24, 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, followed by termination of the program. Referring again to Fig. 24, 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. 29. 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 temperatur T A , at a step S108. Fig. 34 shows an example of the P BREF map, in which predetermined values N V1 - N V20 of the engine rotational speed N E and predetermined 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 before. By the use of the P BREF map, according to which the desired value P BREF is set to a lower value as the intake air temperature T A is lower, 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 smaller, as indicated by the solid line in Fig. 40, thereby enhancing the durability of the transmission, whereas in another gear position the supercharging pressure in steady state can be controlled to a desired higher value, as indicated by the chain line in Fig. 40. 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 G PB (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. 35 and Fig. 36 show these tables, respectively. In the K P table, two predetermined values N FBP1 and N FBP2 (N FBP2 > N FBP1 ) of the engine rotational speed N E are provided, and predetermined values K P1 - K P3 (K P1 < K P2 < K P3 ) of the constant K P are provided, which correspond, respectively, to N E < N FBP1 , N FBP1 ≦ N E < 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 rotational speed N E are provided, and predetermined values K I1 - K I3 < K I1 < K I2 ) are provided, which correspond, respectively, to N E < 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 x 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 x ΔP BD ) of the integral control term D I obtained in the last loop and the product K I x 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 OUT = D M x K TATC + D R + D 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 | < G PB at the step S112 and hence the actual intake pressure P B is substantially equal to the desired value P BREF , the proportional control term Dp is set to 0.0, and the integral control term D I 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 R = (K TATC x D M + D I )/(K TATC x D 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. Then, at a step S123 the coefficient K R obtained as above is applied to calculation of the learned correction coefficient K MODij by the use of the following equation: K MODij = C MOD /A x K R + (A- C MOD )/A x K MODij where K MODij of the second term on the 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, 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 upon 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. 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. 37 shows an example of the K MODij map, in which, like the K TATC map of Fig. 28 and the P BREF map of Fig. 34, 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. 29, 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 intergal 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 OUT = K TATC x K MODij x (D M - D T ) where D T is the subtraction term set at the step S218 or S220 of the subroutine of Fig. 29. Then, the duty ratio D OUT calculated as above 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. Although 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 invention may also be applied to other types of variable capacity type turbochargers such as a waste-gate type and a supercharging pressure-relief type, as well as to other types of superchargers than the turbocharger.

Claims: A method of controlling supercharging pressure in an internal combustion engine having a supercharger (5), wherein the supercharging pressure (P₂) created by said supercharger (5) is controlled based on a basic control amount (D M ) determined in dependence on operating conditions of said engine, said basic control amount (D M ) being corrected in response to a difference between an actual value of the supercharging pressure (P₂) and a desired value (P 2REF ) of same when said engine is in a feedback control region in which the supercharging pressure (P₂) is to be controlled in feedback control mode, the method comprising the steps of: 1)detecting a change rate (ΔP₂) of the supercharging pressure (P₂). 2) determinging whether or not said engine is in an operating condition (S₁) immediately before entering said feedback control region; and 3) correcting said basic control amount (D M ) in accordance with the detected change rate of the supercharging pressure (ΔP₂) when said engine is in said operating condition immediately before said feedback control region. A method as claimed in claim 1, wherein when the detected change rate of the supercharging pressure (ΔP₂) shows that the supercharging pressure is increasing, said basic control amount (D M ) is corrected so that the increase rate of the supercharging pressure is decreased. A method as claimed in claim 1, wherein when the detected change rate of the supercharging pressure (ΔP₂) shows that the supercharging pressure is decreasing, said basic control amount (D M ) is corrected so that the decrease rate of the supercharging pressure is decreased. A method as claimed in any of claims 1 to 3, wherein said basic control amount (D M ) is corrected by a larger amount as the detected change rate of the supercharging pressure is larger. A method as claimed in any of claims 1 - 3, including the step of detecting the rotational speed (N E ) of said engine, and wherein said basic control amount (D M ) is corrected by a larger amount as the detected rotational speed (N E ) of said engine is higher. A method as claimed in claim 4, including the step of detecting the rotational speed (N E ) of said engine, and wherein said basic control amount (D M ) is corrected by a larger amount as the detected rotational speed of said engine is higher. A method as claimed in claim 1, wherein said step (2) comprises the steps of (a) detecting the supercharging pressure (P₂), (b) detecting the opening of a throttle valve (ϑ TH ) of said engine, and (c) determining that said engine is in said operating condition immediately before entering said feedback control region when the detected opening of said throttle valve (ϑ TH ) is larger than a predetermined value (ϑ THOS ) and at the same time the detected supercharging pressure (P₂) has exceeded a predetermined value which is lower than said desired value of the supercharging pressure by a predetermined amount. A method as claimed in claim 7, wherein said predetermined amount is determined by at least one of the rotational speed (N E ) of said engine and the change rate of the supercharging pressure (ΔP₂). A method as claimed in claim 8, wherein said predetermined amount is set to larger values as the rotational speed (N E ) of said engine is higher. A method as claimed in claim 8 or claim 9, wherein said predetermined amount is set to larger values as the change rate of the supercharging pressure (ΔP₂) is larger.

Inventors: AKIYAMA EITETSU, INOUE KAZUO, KATOH ATSUSHI, KISHI NORIYUKI, KUBODERA MASAO, MUNAKATA HIROKI, AKIYAMA, EITETSU, INOUE, KAZUO, KATOH, ATSUSHI, KISHI, NORIYUKI, KUBODERA, MASAO, MUNAKATA, HIROKI
Applicants: HONDA MOTOR CO LTD, HONDA GIKEN KOGYO KABUSHIKI KAISHA
Application year: 1988
Main classification: F04F11
IPC codes: F02B37, F02D41