A reciprocating pump includes a housing, a rod, a bellows, and a bearing. The housing surrounds a bellows chamber and a displacement chamber. A first portion of the rod extends into the bellows chamber. The bellows has a first end connected to the housing and a second end connected to the rod. The bellows surrounds a second portion of the rod. The bellows includes a plurality of convolutions. The bearing is disposed within the bellows between the bellows and the rod.

A positioning device for a turnable table of a saw machine having a pivot shaft that pivotally connects a pair of clamping units. A pressing member with an attachment portion for attaching to a coupling unit may be formed on each clamping unit. By manipulating a trigger of the coupling unit, the pair of clamping units can be driven to rotate a pair of corresponding clench members for selectively clamping or unclamping a base of the saw machine. Thereby, the turnable table can be secured in place upon adjustment.

An oil supply device for a crankcase of an internal combustion engine feeds oil from a reservoir to a main oil duct of the crankcase. A filter switching device allows a selection from a plurality of oil filter units in the flow path of the oil to be selectively connected into the oil flow path, to set a proportion of the oil filter units to active and a proportion of the oil filter units to passive. A switching unit switches between the active and passive states and opens up a pressurized oil flow path to the active oil filter unit(s) and also a drainage flow path between the passive oil filter unit(s) and a drainage duct. An evacuation device drains or evacuates oil from the drainage duct which has accumulated at the passive oil filter unit(s).

A method to display a foot ornamentation system includes obtaining a foot ornamentation system that has a bottom band constructed from an elastomeric material for compressing the system snugly against a foot. The system has a first side panel and a second side panel that are flexible for conforming to a contour of a foot side. The system has a decorative member with an interior surface that has a smooth profile and a non-slip surface for interfacing with the foot top surface. The method includes donning the system by expanding an interior open area of the system via the stretchable bottom band then sliding over an end of a foot into a first position where the decorative member is located on a foot top surface. The method includes donning footwear with an open top that allows the system to be displayed.

An illumination system is housed in a footwear, the footwear including a sole and an upper. A structure and a liner form inner layers connected to the upper. A plurality of illumination sources are electrically connected to a power source and positioned adjacent to the liner. The illumination sources are positioned between the liner and upper. A batting is designed to be light diffusing, while the upper has a light diffusing section. The light emitted from the plurality of illumination sources is diffused as it passes through the batting and light diffusing section. Aesthetic designs can be creating, either through the arrangement of the plurality of illumination sources or the provision of a light impermeable section on the upper. The light impermeable section, in combination with the light diffusion section, can be used to form or outline an aesthetic design. The result is an internally illuminated footwear with diffused light.

A shoe ornament structure, comprises: a base layer, a sub-base layer, a ground color layer, a ornamental layer, a blocking wall and a transparent layer. The ground color layer has a predetermined thickness and is formed on the sub-base layer. The ornamental layer is formed with different grains or color or materials and located on the ground color layer. The blocking wall of a height 0.5-0.7 mm is formed on ornamental layer, and the transparent layer is formed in the area defined by the blocking wall.

The sole section of a shoe includes a midsole and an outsole, with the midsole being made from a translucent material. An illumination system is located inside the translucent midsole, causing the translucent midsole to be internally illuminated when the illumination system is active. Due to the translucent nature of the midsole light from the illumination system reflects internally throughout the midsole, increasing illumination. The light will also illuminate adjacent translucent components, such as the outsole if it is also made from a translucent material. Light from the illumination system can be blocked, such as by an opaque outsole or colored mold injection, and used to form an illuminated design or logo. By blacking out or covering sections of the translucent midsole, shapes and letters of visible light can be created in the negative space of the obstruction sections. This allows illuminated designs to easily be incorporated into footwear.

Methods are provided for cooling data centers based on a cooperative system including a plurality of Indirect Air-Side Economizers, also referred to as Recirculation Air Cooling Units, that are advantageously operated in conjunction with one or more Side Stream Filtration Units or filters inclusive to a portion of the IASE/RACUs, and one or more Make-Up Air Dehumidification/Humidification Units for the introduction of ventilation air and control of humidity within the enclosed space. An objective of the systems and methods according to this disclosure is to provide the necessary rejection of heat, removal of particulate from the air, and control of the absolute moisture content of the air within a data center.

Systems, methods, and controllers for controlling gas-fired appliances such as warm air furnaces are disclosed. An illustrative furnace system can include a burner unit in communication with a combustion air flow conduit and heat exchanger, a variable speed inducer fan or blower adapted to provide a flow of combustion air to the burner unit, a furnace controller and motor speed control unit adapted to regulate the speed of the inducer fan or blower, and a pneumatically modulated gas valve adapted to variably output gas pressure to the burner unit based at least in part on the combustion air flow.

A condensate collector system includes a condensate collector box having at least one condensate outlet port, and a condensate trap fluidly connected to the at least one condensate outlet port. The condensate trap is configured and disposed to be selectively positioned in multiple drain orientations relative to the condensate collector box to accommodate multiple installation configurations of the multi-poise gas furnace.

A supplementary intercooler cools engine air after it has passed through the turbocharger of a vehicle's turbocharged internal combustion engine, but before it enters the engine. The unit has an inlet for capturing the turbo's air charge and an outlet for routing the air charge to the engine after passing through the intercooler. A container stores water until it is needed and a water pump transfers water from the container to the unit. This loosened bond of water is then sprayed on capacitor plates under turbo pressure to be converted into hydrogen and injected into the air intake stream making it a totally “hydrogen-on-demand” intercooler.

Novel systems and methods are described for reducing iron oxide to metallic iron in an integrated steel mill or the like that has a coke oven and/or an oxygen steelmaking furnace. More specifically, the present invention relates to novel systems and methods for reducing iron oxide to metallic iron using coke oven gas (COG) or COG and basic oxygen furnace gas (BOFG).

A method of internally restoring a pipe preferably includes the steps of isolating a leaking pipe from a system of pipes; drying an interior of a leaking pipe; measuring the airflow through the leak; cleaning the interior of the leaking pipe; presealing a leak with a leak sealing media, measuring the leak flow rate after the pre-sealing; applying an internal protective coating process; and pressure testing the leaking pipe for leaks. The pipe restoration method preferably uses a control box, a media injection system, an air compressor and a coating dispensing system at an inlet of the leaking pipe. The pipe restoration method preferably uses a coating overflow receiver, a muffler and a dust collector at an exit of the leaking pipe. After the treatments, the leaking pipe becomes a restored pipe. The restored pipe is pressure tested for leaks at a working pressure rating of the pipe.

A method of forming a cast product (30) by providing a core (52) having a plurality of sections (54) and one or more gaps (55) there-between. The core further includes an insert member (60) spanning the gap (55) between adjacent sections (54). The core (52) is located within a mold (68) and a liquid phase material is introduced into gap (55) between the core sections. The liquid phase material is solidified in the gap so as to form a cast feature of a resulting solid product and the core sections (54) are removed from the solid product (30) such that the insert member (60) remains securely held within the feature (74).

The invention relates to an ethylene cracking furnace having a multi-pass radiant coil, comprising at least one radiant section. In the radiant section there are provided with bottom burners and/or sidewall burners, and at least one set of multi-pass radiant coil longitudinally arranged in the radiant section. The multi-pass radiant coil is a four- to ten-pass type radiant coil. At least one tube of the multi-pass radiant coil is arranged to be spatially adjacent to a tube which is not consecutive to said at least one tube. With this arrangement, the thermal radiation influence between tubes with high temperature can be reduced, so that the tubes with low temperature can absorb the radiation heat from the tubes with high temperature. Therefore, the surface temperature of the tubes with high temperature can be reduced, thus extending the lifetime of the radiant coil and the operational cycle of the cracking furnace.

A button, knob or control key with an etchable support plate which is engraved on the backside with a fine symbol by laser, erosion or mechanical engraving, which only cuts into the material of the support plate, but not through the support plate. The backside of the support plate is optionally coated. A foil is applied on the laminated layer and affixed thereto. The front side of the support plate is treated with a material-removing substance. The material removal with the material-removing substance is performed until the engraving extending into the support plate is at least partially or completely exposed on the front side. Application of a protective layer to the front side of the support plate from which the material was removed. A function symbol is provided on the button such that it can be backlit. It is engraved in a fine line width providing a sharp optical definition erosion, mechanical engraving.

A device is provided, which makes it possible to perform a failure diagnostics for a filter more accurately even in the case of an internal combustion engine which is constructed to be capable of using both of gaseous fuel and liquid fuel. The device of the invention comprises judging means which judges any failure of the filter by comparing the added-up amount of the particulate matter contained in the exhaust gas as detected by a PM amount detecting sensor during a predetermined period and the added-up amount of the particulate matter contained in the exhaust gas as estimated by PM amount estimating means during the predetermined period, wherein the PM amount estimating means estimates the added-up amount of the particulate matter contained in the exhaust gas on the basis of the predetermined parameter and only a fuel injection amount of the liquid fuel out of a fuel injection amount of the gaseous fuel and the fuel injection amount of the liquid fuel.

A combustion speed, for example, is estimated or evaluated, with a required accuracy, more simply than the conventional art, while reducing man-hours to produce a heat generation rate waveform of an internal combustion engine. An increase rate of a heat generation rate relative to a change in a crank angle in a heat generation rate increasing period (e.g., a first-half combustion period a) in which the heat generation rate increases after ignition of an air-fuel mixture is defined as a heat generation rate gradient b/a that is one of characteristic values of the heat generation rate waveform. The heat generation rate gradient is estimated based on a fuel density (e.g., fuel density ρfuel@dQpeak at heat generation rate maximum time) at a predetermined time set in advance in the heat generation rate increasing period so as to produce the heat generation rate waveform using the estimated heat generation rate gradient.

A drying furnace (20) for drying an object (11) by hot air is provided with a heater (36, 38, 43, 45) that applies radiant heat to a hard-heating region (35, 42) having a larger heat capacity than the other region (37, 44) in the object (11) so as to heat the hard-heating region (35, 42) to a temperature approximate to a temperature of the other region (37, 44).

A conveyor for a sheet glass tempering furnace, comprising a roller conveyor and an inclined airborne conveyor, as well as support and transport rollers at a lower edge of the airborne conveyor. The roller conveyor includes a horizontal level conveyor and an adapter conveyor between the horizontal level conveyor and the airborne conveyor. The adapter conveyor features a horizontal level upstream end and an inclined downstream end, the inclination angle of which matches substantially that of the airborne conveyor. The adapter conveyor has its rollers increase in inclination step by step when proceeding from the up-stream end towards the downstream end.

A vacuum roll includes an inner rotor, an intermediate stator, and an outer shell roll. The inner rotor has open and closed portions and is adapted to rotate within the intermediate stator which is rotationally fixed and also has open and closed portions. The outer shell roll has open and closed portions and is adapted to move around the intermediate stator. Together the inner rotor and the intermediate stator define an internal rotary valve interface adapted to control fluid communication between the interior chamber and the outer shell.

A method of manufacturing a valve for an internal combustion engine, comprises: (i) a primary step of forging a bulging portion at one end of a rod material to form a generally disk-shape valve head of the valve having a tapered periphery; (ii) an thickness adjustment step of machining an excessively thick portion of the valve head; and (iii) a secondary step of forging a peripheral region of the valve head to create radial slip deformations therein to form a valve face of the valve head. In the step of thickness adjustment, only the front end of the disk-shape valve head is machined without harming dense grain flow lines induced in the tapered face (16a) in the primary forging while advantageously saving the valve material and reducing thickness adjustment time. In the secondary forging, the hardness of the valve face is further enhanced.

A mining shovel includes a boom and a transmission unit coupled to the boom. The transmission unit includes an outer housing, an internal motor housing disposed within the outer housing, and a venting system coupled to the outer housing to direct air through both the outer housing and the internal motor housing.

A control apparatus for an internal combustion engine having a means for performing a model calculation to calculate, as an exhaust temperature calculation value, the temperature of exhaust gas in an exhaust branch tube at the time of starting an engine, using a model representing the temperature behavior of the exhaust gas in the exhaust branch tube during stop of an engine; and an exhaust temperature actual measurement value output means for detecting the temperature of exhaust gas in the exhaust branch tube, and outputting the detected temperature as an exhaust temperature actual measurement value, wherein the model includes at least one parameter.

The invention relates to a unit for simulating the pressure and temperature conditions of an air flow drawn in by a reciprocating internal combustion engine (1) at a height above sea level, corresponding to the operating height of said reciprocating internal combustion engine (1). According to the invention, the unit comprises at least: (a) a radial inward-flow turbine (2) for expanding an air flow towards the pressure and temperature of the air drawn in by the reciprocating internal combustion engine; (b) a first container (4) and (c) a second container (5) connected to the first container (4) by means of at least a connection pipe (7) in order to balance the pressure between the two containers; (d) a centrifugal compressor (3); and (e) a vacuum pump (6) for maintaining a pressure equal to the pressure of the air flow drawn in by the reciprocating internal combustion engine (1). The invention also relates to the use of said unit for simulating the pressure and temperature conditions of the air drawn in by a reciprocating internal combustion engine.

A linear alternator assembly is provided that includes a block defining a cylinder. The cylinder block has inlet ports at which fluid enters the cylinder, exhaust ports at which fluid is exhausted from the cylinder, and a fuel port. Energizable coils surround the cylinder. A first and a second magnetic or magnetizable piston are contained within the cylinder and are positionable within the cylinder in response to energization of selective ones of the coils and combustion of fuel within the cylinder to selectively establish a four-stroke working cycle having an intake stroke, a compression stroke, an expansion stroke, and an exhaust stroke, producing at least one of compressed gas and electrical energy. The four-stroke working cycle may be varied to adapt to changes in power demanded, thereby balancing required output power with efficiency considerations.

In an internal combustion engine valve drive arrangement having cam elements which are supported on a camshaft so as to be axially displaceable and having switch gates which are coupled to the cam elements and have gate tracks with track segments and switching segments for displaceing the cam elements, the track segments and the switching segments are formed, at least in part, in partial areas of the switch gates.

A Wankel engine having an insert in the peripheral wall of the stator body, the insert being made of a material having a greater heat resistance than that of the peripheral wall, having a subchamber defined therein and having an inner surface bordering the cavity, the subchamber communicating with the cavity through at least one opening defined in the inner surface and having a shape forming a reduced cross-section adjacent the opening, a pilot fuel injector having a tip received in the subchamber, an ignition element having a tip received in the subchamber, and a main fuel injector extending through the housing and having a tip communicating with the cavity at a location spaced apart from the insert.

A flow limiter for a fuel system is provided. The flow limiter includes a self-contained portion that enables testing of the flow limiter prior to assembly into a fuel system. A housing of the flow limiter is arranged to provide reduced or no pressure differential across a wall of the housing, permitting the housing to be reduced in size and thickness and providing improved consistency of operation.

A fastening structure of a fuel delivery pipe and a cylinder head of an internal combustion engine includes three or more bosses provided on each of the cylinder head and the fuel delivery pipe, and fastening portions formed by bolting the bosses on the cylinder head to the bosses on the fuel delivery pipe. The fastening portions at both end portions of the fuel delivery pipe are less rigid than one or more fastening portions in a middle between the fastening portions positioned at both end portions of the fuel delivery pipe.

Embodiments for an engine system are provided. One example internal combustion engine having at least one cylinder head and at least two cylinders, in which each cylinder has at least one inlet opening for the supply of combustion air into the cylinder, comprises an intake line leading to each inlet opening, an overall intake line where the intake lines of at least two cylinders merge, such that a distributor junction point is formed, and a heating device arranged in the overall intake line which has at least one strip-like heating element, a first narrow side of a cross section of which faces toward intake combustion air flow, wherein the heating device is arranged adjacent to the distributor junction point at which the intake lines merge to form the overall intake line, a spacing between the heating device and the distributor junction point being smaller than the diameter of a cylinder.

A variable valve operating apparatus for an internal combustion engine includes a drive camshaft, and a driven cam lobe that is rotatably supported by the drive camshaft. The variable valve operating apparatus further includes a control sleeve that has a raceway surface, a center of which is eccentric with respect to a center of rotation of its own. The variable valve operating apparatus further includes a link mechanism that is connected to each of the drive camshaft and the driven cam lobe and has a control roller which is in contact with the raceway surface. The variable valve operating apparatus further includes an actuator that drives the control sleeve. The variable valve operating apparatus further includes a control amount of the actuator is controlled to change a moving amount of the raceway surface in the above described plane direction in accordance with an operation condition of an internal combustion engine.

A protractor for use with an external fixation frame is provided. The protractor may include a face having angle designations thereon and a set of opposed and extending flanges projecting from said face. The flanges may connect to a portion of an external fixation frame, such as a ring (or other component) of the frame. The face may also include a post member to which a rotatable dial is mounted. An elongate member may be pivotally connected to a portion of the post member and may include a clamp. The clamp may be used to connect to an alternate portion of an external fixation frame, such as a strut of the frame. Thus, the protractor may be connected to two points on an external fixation frame so as to measure the angle between such points. Related methods of using the aforementioned protractor are also disclosed.

An ornament for attachment to orthodontic braces, the orthodontic braces having an arch wire overlying a laterally adjacent pair of teeth, the ornament having a web having a front end and a rear end; the ornament further having a first arm fixedly attached to and extending downwardly from the web's front end; the ornament further having a second arm fixedly attached to and extending downwardly from the web's rear end; the ornament further having a channel bounded by structures including the web, the first arm, and the second arm, the channel being fitted for, upon a passage of the arch wire between the first and second arms, nestingly receiving the arch wire.

An internal combustion engine which can be miniaturized, even where it includes an oil filter between a hydraulic clutch and an oil pump, without significantly increasing the length of an oil passage for the hydraulic clutch, the oil pump and a hydraulic pressure adjustment apparatus. A second oil filter is provided on an oil pan at a lower portion of the internal combustion engine so as to be disposed at a position at which the second oil filter does not overlap with any of a controlling oil pump and a hydraulic pressure adjustment apparatus as viewed in side elevation and which is lower than those of the oil pump and the hydraulic pressure adjustment apparatus.

A control switch is connected to a power supply voltage and turns on based on a control signal to output a current. A clamp circuit is connected to a load and performs clamp control of the output voltage of the control switch. A current control element conducts or shuts off a current based on the output voltage to be clamp-controlled. A selector switch group includes switches, and performs switching based on a voltage varying with the current control by the current control element, thereby switching between paths for generating an internal power supply. The switch circuit connects or disconnects the coupling between the clamp circuit and the selector switch group.

The present invention is directed to a pillow for supporting and enclosing a portion of the head of a user, the ears in exemplary use. The pillow includes a fabric shell, which in turn encompasses padding of soft compliant material. A pivotable frame is disposed within the shell. In one embodiment, the pivotable frame includes unitary semi-rigid leg, flexible substantially along its entire length. In an alternate embodiment, the pivotable frame includes of a length of a plurality of interconnected leg and joint sections. Each of the joints is connected with two legs and defines a pivot about which the legs rotate, whereby the user can manipulate the pillow from an open state to an enclosed state around a portion of his or her head.

Burner for an oven for reheating siderurlogical products such as billets, blooms or slabs, or for heat treatment oven, which is equipped with a fuel injection device and with an oxidant feed body feeding feed orifices with oxidant, the burner having an axial direction; the injection device is designed to provide a central injection of fuel via an orifice in, or parallel to, the axial direction of the burner; the oxidant feed body includes two sets of four oxidant feed orifices, each set including two orifices situated above a horizontal plane passing through the axial direction of the burner, and two orifices situated below this plane, the orifices of a second set being further away from the horizontal plane than those of the first set, the geometric axes of the orifices of the two sets making angles of inclination with respect to the axial direction of the burner.

A casket comprises a casket shell adapted to receive the remains of a deceased having a pair of side walls, a pair of end walls, and a bottom wall, and a casket cap closable on the casket shell. A dish assembly is mounted to an underside of the cap. The dish assembly includes a cap panel comprising a sheet of magnetic material. At least one medallion having text and/or graphics representing a life aspect of the deceased is removably mounted on the cap panel. The medallion comprises a medallion blank having at least one magnet on a rear side thereof and having a recess on a front side thereof, a two-dimensional image positioned in the recess of the medallion blank, and a transparent layer of material overlying the two-dimensional image. The transparent layer of material is dome-shaped in cross section such that a peripheral outer edge of the layer is thinner than a central portion of the layer. The magnet removably secures the medallion blank to the magnetic material of the cap panel.

A method for producing a synthesis-gas product gas and a vapor stream includes catalytic steam reforming a hydrocarbonaceous feedstock in a steam reformer. The hot synthesis-gas product gas stream is cooled in a heat exchanger to form a cooled synthesis-gas product gas stream and a first partial vapor stream, which is supplied to the product vapor stream. The reforming furnace is operated so as to burn a burner feedstock in burners, cool a hot flue gas stream from the burners in a heat exchanger to form a cooled flue gas stream and a second partial vapor stream, and separate the cooled flue gas stream into a waste gas stream and a flue gas recirculation stream. The flow of the recirculated flue gas is increased with decreasing flow of the synthesis-gas product gas to obtain an approximately constant product vapor stream by increasing the second partial vapor stream.

An electrostatic spray apparatus includes an electrostatic spray gun having a first external surface and a second external surface. A first electrode is disposed on the first external surface and is configured to ionize a material and to generate a first electrical field between the first electrode and a grounded object. A second electrode is disposed on the second external surface of the apparatus and is configured to generate a second electric field between the second electrode and the grounded object.

A heat exchange assembly includes an upper cover panel, a lower cover panel, a plurality of stacked plate assemblies, and a plurality of fins interposed between the plurality of plate assemblies. Each of the plurality of plate assemblies forms a flow passage for receiving a coolant. A continuous flow path extends through the heat exchange assembly. The flow path is in fluid communication with the flow passage of each of the plates and configured to convey air from each of the flow passages to an environment separate from the heat exchanger.

A drum assembly includes a drum, a stimulus processor assembly and a Tesla coil. The stimulus processor assembly receives a stimulus, generates an input signal, and converts the input signal to an output signal. The Tesla coil receives the output signal from the stimulus processor assembly. The Tesla coil emits an electrical discharge in response to the output signal. The electrical discharge occurs at least partially within the drum interior. The stimulus processor assembly uses a conversion algorithm to convert the input signal to an output signal. The Tesla coil can be positioned inside or outside of a drum interior of the drum. A discharge router can send the electrical discharge from the Tesla coil to the drum interior. The electrical discharge can have an intensity that is correlative to the decibel level of the stimulus. The stimulus can be generated by the drum or by a source remote from the drum.

A process train for a floating production storage and offloading installation includes a crude oil storage tank that is equipped with at least one set of electrostatic internals arranged to provide a treatment flow path isolated from a surrounding volume of the electrostatic separator section of the tank. An oil-and-water stream or mixture entering the set of electrostatic internals travels along the treatment flow path and is subjected to an electric field. The treatment flow path is in an upwardly direction toward the oil outlet section and in a downwardly opposite direction toward the water outlet section of the tank. Employing electrostatic internals within the tank permits an allowable inlet water content into the tank of up to 80%, significantly reducing the required topside processing equipment.

An introducer configured with a first curve having a first angle that traverses space of an atrial appendage, a central atrium, caudad to the coronary sinus, and a second curve that has an angle sufficient to align the introducer with an intrinsic curvature of the coronary sinus of a subject.

A first-half combustion period, for example, is estimated/evaluated, with a required accuracy, more simply than the conventional art, while reducing man-hours to produce a heat generation rate waveform of an internal combustion engine. Within a combustion period of an air-fuel mixture, a period from an ignition time FA to a heat generation rate maximum time dQpeakA where the heat generation rate is maximum is defined as the first-half combustion period a that is one of characteristic values of the heat generation rate waveform. The first-half combustion period a is estimated based on an in-cylinder volume at the heat generation rate maximum time, and furthermore by being corrected using an exponential function of the engine rotation speed with a value depending on a tumble ratio as exponent. Thus, the heat generation rate waveform is produced using the estimated first-half combustion period a.

A fuel additive and its preparation for a engine, a fuel containing the additive, a fuel additive concentrate, a method for improving performance of fuel injectors and a method for cleaning fuel injectors for an engine. The fuel additive includes a quaternary ammonium salt derived from a reaction of a hydrocarbyl substituted anhydride, a tertiary amine and a hydroxyl-containing epoxide, wherein the tertiary amine is devoid of primary and secondary amino groups.

I SHOULD like to pay tribute to Alan Wiltshire the Echo and Romsey Advertiser reporter whose death was sadly announced last week

A controller is provided, which detects operating conditions of an internal combustion engine on the basis of detection results from a group of sensors and drives an actuator that modifies an opening position of a wastegate valve on the basis of the operating conditions. When driving the wastegate valve to a fully closed opening, the controller initially drives the actuator toward a preset provisional fully closed position, and after determining on the basis of a detection result from a position sensor that an actual opening of the wastegate valve has reached the provisional fully closed opening, switches a target opening to the fully closed opening and drives the actuator accordingly.

A required opening correction amount is calculated based on a target supercharging pressure and an actual supercharging pressure, a target opening is calculated based on a required opening and the required opening correction amount, an actual operating position of a wastegate valve is determined to correspond to a fully closed position when the wastegate valve is in a fully closed condition, an actual opening of the wastegate valve is calculated based on the fully closed position and the actual operating position, an operation amount of an actuator for aligning the target opening with the actual opening is calculated based on the target opening and the actual opening, and when the target opening corresponds to the fully closed condition and the actual operating position is not decreased at or above a prescribed rate, the fully closed position is updated to the actual operating position.