Patent Publication Number: US-6698203-B2

Title: System for estimating absolute boost pressure in a turbocharged internal combustion engine

Description:
FIELD OF THE INVENTION 
     The present invention relates generally to systems for estimating turbocharger operating parameters, and more specifically to systems for estimating absolute boost pressure in a turbocharged internal combustion engine. 
     BACKGROUND AND SUMMARY OF THE INVENTION 
     Turbochargers are well known devices for pressurizing intake air entering the combustion chambers of an internal combustion engine to thereby increase the efficiency and power output of the engine. In general, pressurizing the intake air increases the quantity of air entering the engine cylinders during the intake stroke, and this allows more fuel to be utilized in establishing a desired air-to-fuel ratio. Increased available engine output torque and power is thereby realized. 
     In a turbocharged engine, the exhaust manifold of the engine is fluidly coupled to a turbine component of the turbocharger via an exhaust conduit, and the exhaust gas flowing through the exhaust conduit causes a turbine wheel within the turbine to rotate at a rate determined by the pressure and flow rate of exhaust gas. A compressor wheel within a compressor component of the turbocharger is mechanically coupled to the turbine wheel, and is therefore rotatably driven by the turbine wheel. An inlet of the compressor receives fresh ambient air, and an outlet of the compressor is fluidly coupled to the intake manifold of the engine via an intake conduit. The rotatably driven action of the compressor wheel increases the amount of intake air supplied to the intake conduit, thereby resulting in an increased, or so-called “boost”, pressure therein. 
     An exhaust gas recirculation (EGR) system implemented in such a turbocharged engine supplies controlled amounts of exhaust gas from the exhaust manifold to the intake manifold via an EGR conduit. In order to sustain positive EGR flow through the EGR conduit, it is necessary to maintain the pressure in the exhaust conduit greater than that in the intake conduit, and turbochargers in EGR-based engines must therefore typically operate at higher rotational speeds than in non EGR-based engines. In either case, however, it is desirable to have accurate knowledge of the absolute “boost” pressure within the intake manifold at all times so that the turbocharger speed may then be controlled to ensure positive EGR flow while maintaining turbocharger speed within safe operating limits. 
     In cases where implementation of an absolute boost pressure sensor is impractical or cost prohibitive, and/or in cases where redundant absolute boost pressure information is desired, what is needed is a system for accurately estimating absolute boost pressure. 
     The present invention accordingly provides a system for estimating absolute boost pressure as a function of the temperature and pressure of air entering the turbocharger compressor, the rotational speed of the turbocharger and the rotational speed of the engine. 
     These and other objects of the present invention will become more apparent from the following description of the preferred embodiment. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a diagrammatic illustration of one preferred embodiment of a system for estimating turbocharger operating parameters, in accordance with the present invention. 
     FIG. 2 is a compressor map of turbocharger compressor ratio vs. intake mass air flow illustrating some of the turbocharger operating parameter estimation concepts of the present invention. 
     FIG. 3 is a 3-D plot illustrating one preferred technique for estimating turbocharger rotational speed by mapping corrected turbocharger speed to current values of engine speed and compressor pressure ratio, in accordance with the present invention. 
     FIG. 4 is a flowchart illustrating one preferred embodiment of a software algorithm for estimating turbocharger rotational speed based on the plot of FIG. 3, in accordance with the present invention. 
     FIG. 5 is a diagrammatic illustration of one preferred embodiment of a portion of the control computer of FIG. 1 illustrating an alternate technique for estimating turbocharger rotational speed, in accordance with the present invention. 
     FIG. 6 is a plot of engine speed scaling factor vs. engine speed illustrating one preferred embodiment of the engine speed scaling factor block of FIG.  5 . 
     FIG. 7 is a 3-D plot illustrating one preferred technique for estimating absolute boost pressure by mapping compressor pressure ratio to current values of engine speed and corrected turbocharger speed, in accordance with the present invention. 
     FIG. 8 is a flowchart illustrating one preferred embodiment of a software algorithm for estimating absolute boost pressure based on the plot of FIG. 7, in accordance with the present invention. 
     FIG. 9 is a diagrammatic illustration of one preferred embodiment of a portion of the control computer of FIG. 1 illustrating an alternate technique for estimating absolute boost pressure, in accordance with the present invention. 
     FIG. 10 is a plot of engine speed scaling factor vs. engine speed illustrating one preferred embodiment of the engine speed scaling factor block of FIG.  9 . 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     For the purposes of promoting an understanding of the principles of the invention, reference will now be made to a number of preferred embodiments illustrated in the drawings and specific language will be used to describe the same. It will nevertheless be understood that no limitation of the scope of the invention is thereby intended, such alterations and further modifications in the illustrated embodiments, and such further applications of the principles of the invention as illustrated therein being contemplated as would normally occur to one skilled in the art to which the invention relates. 
     Referring now to FIG. 1, one preferred embodiment of a system  10  for estimating turbocharger operating parameters, in accordance with the present invention, is shown. System  10  includes an internal combustion engine  12  having an intake manifold  14  fluidly coupled to an outlet of a compressor  16  of a turbocharger  18  via an intake conduit  20 , wherein the compressor  16  includes a compressor inlet coupled to an intake conduit  22  for receiving fresh air therefrom. Optionally, as shown in phantom in FIG. 1, system  10  may include an intake air cooler  24  of known construction disposed in line with intake conduit  20  between the turbocharger compressor  16  and the intake manifold  14 . The turbocharger compressor  16  is mechanically coupled to a turbocharger turbine  26  via a drive shaft  25 , wherein turbine  26  includes a turbine inlet fluidly coupled to an exhaust manifold  28  of engine  12  via an exhaust conduit  30 , and further includes a turbine outlet fluidly coupled to ambient via an exhaust conduit  32 . An EGR valve  36  is disposed in line with an EGR conduit  34  disposed in fluid communication with the intake conduit  20  and the exhaust conduit  30 , and an EGR cooler  38  of known construction may optionally be disposed in line with EGR conduit  34  between EGR valve  36  and intake conduit  20  as shown in phantom in FIG.  1 . 
     System  10  includes an engine controller  40  that is preferably microprocessor-based and is generally operable to control and manage the overall operation of engine  12 . Engine controller  40  includes a memory unit  45  as well as a number of inputs and outputs for interfacing with various sensors and systems coupled to engine  12 . Controller  40 , in one embodiment, may be a known control unit sometimes referred to as an electronic or engine control module (ECM), electronic or engine control unit (ECU) or the like, or may alternatively be a general purpose control circuit capable of operation as will be described hereinafter. In any case, engine controller  40  preferably includes one or more control algorithms, as will be described in greater detail hereinafter, for estimating turbocharger operating parameters based on input signals provided by a number of engine and/or turbocharger operating condition sensors. 
     Engine controller  40  includes a number of inputs for receiving signals from various sensors or sensing systems associated with system  10 . For example, system  10  includes a temperature sensor  50  that is preferably disposed in fluid communication with intake conduit  22  and electrically connected to an input (IN 1 ) of engine controller  40  via signal path  52 . Sensor  50  may be of known construction and generally operable to produce a compressor inlet temperature signal (CIT) on signal path  52  that is indicative of the temperature of ambient air entering the inlet of compressor  16  (i.e., entering the intake conduit  22 ). It is to be understood that for the purposes of the present invention, sensor  50  need not be disposed in fluid communication with intake conduit  22  and may instead be positioned in any convenient location relative to system  10  as long as sensor  50  is operable to produce a signal on signal path  52  indicative of the temperature of fresh ambient air entering conduit  22 . 
     System  10  further includes a pressure sensor  54  that is preferably disposed in fluid communication with intake conduit  22  and electrically connected to an input (IN 2 ) of engine controller  40  via signal path  56 . Sensor  54  may be of known construction and is generally operable to produce a compressor inlet pressure signal (CIP) on signal path  56  that is indicative of the pressure of ambient air entering the inlet of compressor  16  (i.e., entering intake conduit  22 ). It is to be understood that for the purposes of the present invention, sensor  54  need not be disposed in fluid communication with intake conduit  22  and may instead be positioned in any convenient location relative to system  10  as long as sensor  54  is operable to produce a signal on signal path  56  indicative of the pressure of ambient air entering conduit  22 . 
     In one embodiment, system  10  further includes a speed sensor  58  that is preferably disposed about, or in proximity with, the turbocharger drive shaft  25  and electrically connected to an input (IN 3 ) of engine controller  40  via signal path  60 . Sensor  58  may be of known construction and is generally operable to produce a turbocharger speed signal (TS) on signal path  60  that is indicative of the rotational speed of the turbocharger drive shaft  25 . In one embodiment, sensor  58  is a variable reluctance sensor operable to determine turbocharger rotational speed by sensing passage thereby of one or more detectable structures formed on shaft  25 . Alternatively, turbocharger speed sensor  58  may be any other known sensor operable as just described and suitably located relative to turbocharger drive shaft  25 . 
     In another embodiment, system  10  further includes a pressure sensor  62  that is preferably disposed in fluid communication with intake conduit  20  and electrically connected to an input (IN 4 ) of engine controller  40  via signal path  64 . Sensor  62  may be of known construction and is generally operable to produce a compressor outlet pressure signal (COP) on signal path  64  that is indicative of the pressure within intake conduit  20 . 
     System  10  further includes an engine speed sensor  66  that is electrically connected to an input (IN 5 ) of engine controller  40  via signal path  68 . In one embodiment, sensor  66  is a Hall effect sensor operable to sense passage thereby of a number of teeth formed on a gear or tone wheel rotation synchronously with the engine  12 . Alternatively, sensor  66  may be a variable reluctance sensor or other known speed sensor, and is in any case operable to produce a speed signal on signal path  68  indicative of the rotational speed of engine  12 . 
     Engine controller  40  also includes a number of outputs for controlling one or more engine control mechanism associated with engine  12  and/or system  10 . For example, engine controller  40  also includes at least one output for controlling turbocharger swallowing capacity/efficiency, wherein the term “turbocharger swallowing capacity/efficiency” is defined for purposes of the present invention as the gas flow capacity of the turbocharger turbine  26 . For example, as illustrated in FIG. 1, output OUT 1  of engine controller  40  is electrically connected to a turbocharger swallowing capacity/efficiency control mechanism  72  via signal path  70 , wherein the turbocharger swallowing capacity/efficiency control mechanism  72  is responsive to one or more turbocharger control signals to modify the swallowing capacity and/or efficiency of turbocharger  18 . 
     In general, the present invention contemplates controlling the swallowing capacity and/or efficiency of the turbocharger  18  via one or more known control mechanisms  70  under the direction of engine controller  40 . Examples of such control mechanisms include, but are not limited to, any combination of a mechanism for varying the geometry of the turbocharger turbine  26 , a wastegate disposed between conduits  30  and  32  for selectively diverting exhaust gas from the turbocharger turbine  26 , and an exhaust throttle for selectively controlling the flow rate of exhaust gas through either of conduits  30  and  32 . 
     Engine controller  40  further includes a second output (OUT 2 ) electrically connected to EGR valve  36  via signal path  74 . Controller  40  is operable, in a known manner, to control the cross-sectional flow area of valve  36  to thereby selectively control the flow of recirculated exhaust gas therethrough. 
     Based on conventional compressor flow dynamics, it is well known in the art that given any two of the following variables, the remaining may be uniquely determined: 
     
       
         [TS/sqrt(CIT), COP/CIP, MAF*sqrt(CIT)/CIP], 
       
     
     wherein, 
     MAF is the mass flow of air entering the inlet of the turbocharger compressor  16 , 
     CIT is the temperature of air entering the compressor  16 , 
     CIP is the pressure of air entering the compressor  16 , 
     COP is the pressure of air within the intake conduit  20  (i.e., at the outlet of the turbocharger compressor), and therefore represents the absolute boost pressure within conduit  20 , and 
     TS is the rotational speed of the turbocharger  18 . In the above relationships, the term TS/sqrt(CIT) refers to a temperature-corrected turbocharger speed, hereinafter referred to as CTS, the term COP/CIP refers to a compressor pressure ratio, hereinafter represented as PR and the term MAF*sqrt(CIT)/CIP refers to a corrected compressor mass flow rate, hereinafter represented as CMAF. 
     Relationships between CTS, PR and CMAF may be represented by a compressor map of the type illustrated in FIG.  2 . Referring to FIG. 2, an example compressor map for one known turbocharged engine is shown as a plot  100  of compressor pressure ratio, PR, vs. corrected compressor mass flow rate, CMAF. The various vertically slanted/upwardly sloping lines in plot  100  represent lines of constant compressor efficiency. For example, line  104 A corresponds to 68% compressor efficiency,  104 B corresponds to 70% compressor efficiency, line  104 C corresponds to 74% compressor efficiency, etc. Conversely, the horizontal/downwardly sloping lines in plot  100  represent lines of constant temperature-corrected turbocharger rotational speed, CTS. For example, line  106 A corresponds to 68,700 RPM/sqrt(CIT), line  106 B corresponds to 78,500 RPM/sqrt(CIT), line  106 C corresponds to 88,400 RPM/sqrt(CIT), etc. Finally, the upwardly diagonal thick lines in plot  100  represent lines of constant engine rotational speed, ES. For example, line  102 A corresponds to 850 RPM, line  102 B corresponds to 1200 RPM, line  102 C corresponds to 1800 RPM, etc. 
     In relation to plot  100 , the temperature-corrected turbocharger rotational speed, CTS, can be estimated according to the equation: 
     
       
           CTS=f ( PR, CMAF )  (1). 
       
     
     In embodiments of system  100  that include a mass air flow sensor disposed in fluid communication with intake conduit  22 , CTS may be derived directly from plot  100  as a function of measured values of PR and CMAF. However, in embodiments of system  100  that do not include such a mass airflow sensor, and/or in embodiments of system  100  that include an intake mass air flow estimation algorithm having less than desirable accuracy, CTS may not be derived directly as a function of PR and CMAF. 
     Observation of plot  100  of FIG. 2 reveals that the temperature-corrected turbocharger speed, CTS, is more sensitive to changes in compressor pressure ratio, PR, than to corrected compressor mass flow, CMAF, and is therefore a stronger function of PR than of CMAF. Additionally, knowledge of current engine speed, ES, enables mapping of compressor pressure ratio fluctuations to constant temperature-corrected turbocharger speed values as illustrated in FIG. 2 by constant engine speed lines  102 A- 102 C. Accordingly, the relationship of equation (1) may be simplified to the equation: 
     
       
           CTS=f ( PR, ES )  (2), 
       
     
     such that an estimated turbocharger speed (TS E ) is then defined by the equation: 
     
       
           TS   E   =sqrt ( CIT )* f [( COP/CIP ),  ES  ]  (3). 
       
     
     Referring now to FIG. 3, a three-dimensional plot  110  of the temperature-corrected turbocharger speed, CTS, compressor pressure ratio, PR, and engine speed, ES, is illustrated for an example engine including an air handling system (e.g., EGR system, turbocharger swallowing capacity/efficiency control mechanism(s)) of the type described with respect to FIG.  1 . For every given pair of PR and ES, plot  110  illustrates that there exists a uniquely determined temperature-corrected turbocharger speed value, CTS. 
     Referring now to FIG. 4, a flowchart is shown illustrating one preferred embodiment of a generalized software algorithm  150  for estimating turbocharger rotational speed, in accordance with the present invention. Algorithm  150  may be stored within memory  45  and executed in a known manner by engine controller  40 , although the present invention contemplates that algorithm  150  may be executed by another controller or processor, wherein information may be shared with engine controller  40  via a suitable data bus or link. For description purposes, however, algorithm  150  will be described as being executed by engine controller  40 . 
     Algorithm  150  begins at step  160  where controller  40  is operable to determine compressor inlet pressure, CIP, via information provided by pressure sensor  54  (FIG.  1 ). Thereafter at step  162 , controller  40  is operable to determine compressor outlet pressure, COP, via information provided by pressure sensor  62 . Thereafter at step  164 , controller  40  is operable to compute the compressor pressure ratio, PR, as a ratio of COP and CIP. 
     Following step  164 , algorithm execution advances to step  166  where controller  40  is operable to determine engine rotational speed, ES, via information provided by speed sensor  66 . Thereafter at step  168 , controller  40  is operable to determine compressor inlet temperature, CIT, via information provided by temperature sensor  50 . 
     Following step  168 , algorithm execution advances to step  170  where controller  40  is operable to determine an estimate of the turbocharger rotational speed, TS E , as a function of PR, ES and CIT. The present invention contemplates a number of techniques for executing step  170  to map the variables PR and ES of equation (3) to corresponding turbocharger rotational speed estimate values. For example, in one embodiment, the data in plot  110  may be stored in memory  45  in graphical or table form. In this embodiment, controller  40  is operable to execute step  170  by mapping current values of PR and ES to CTS using the stored information for plot  110 , and thereafter compute TS E  by multiplying the resulting CTS value by the square root of CIT. In the mapping of current values of PR and ES to CTS, estimation values in between data points may be obtained using known linear or non-linear interpolation techniques. 
     In an alternate embodiment, the three-dimensional plot  110  of FIG. 3 may be represented by a polynomial stored within memory  45 , wherein such a polynomial is solved for CTS given known values of the two remaining parameters. For example, plot  110  of FIG. 3 represents a smooth surface and can therefore be modeled as a second-order polynomial according to the equation: 
     
       
           CTS=a+b*PR+C*PR   2   +d*ES+e*ES   2   +f*PR*ES   (4), 
       
     
     wherein a, b, c, d, e and f represent model constants. In this embodiment, engine controller  40  is operable to execute step  170  of algorithm  150  by solving equation (4) as a function of current values of PR and ES, and then computing the turbocharger rotational speed estimate TS E  by multiplying the result by the square root of CIT. 
     In yet another alternate embodiment, the three-dimensional plot  110  of FIG. 3 may be modeled by a two-input neural network trained as an appropriate surface for fitting the data points of CTS according to the known variables PR and ES. In this embodiment, engine controller  40  is operable to execute step  170  of algorithm  150  by computing CTS according to the two-input neural network, and then computing the turbocharger rotational speed estimate TS E  by multiplying the result by the square root of CIT. 
     In a further alternate embodiment, the plot  110  of FIG. 3 may be modeled as a second-order polynomial for PR and a scaling function of ES according to the equation: 
     
       
           CTS= ( a+b*PR+c*PR   2 )* f ( ES )  (5), 
       
     
     wherein the term (a+b*PR+c*PR 2 ) represents the second-order PR model and f(ES) is a scaling factor depending upon the current value of engine rotational speed, and a, b and c represent model constants. In this embodiment, engine controller  40  is operable to execute step  170  of algorithm  150  by solving equation (5) for CTS, and then computing the turbocharger rotational speed estimate TS E  by multiplying the result by the square root of CIT. Referring to FIG. 5, a portion of engine controller  40  is shown illustrating one preferred software structure for computing the turbocharger rotational speed estimate, TS E , in accordance with equation (5). In this embodiment, controller  40  includes a SQRT block  180  receiving as an input the CIT signal on signal path  52  and producing as an output a value corresponding to the square root of CIT. An arithmetic block  182  receives as inputs the COP signal on signal path  64  and the CIP signal on signal path  56 , and produces as an output the pressure ratio value PR by dividing COP by CIP. 
     A compressor ratio function block  184  receives the compressor pressure ratio value, PR, and produces as an output the result of the pressure ratio polynomial (a+b*PR+c*PR 2 ) of equation (5). In one embodiment, block  184  may be implemented in the form of an equation, wherein block  184  is operable to compute (a+b*PR+c*PR 2 ) as a function of PR. Alternatively, block  184  may be implemented in graphical or table form for mapping PR values to (a+b*PR+c*PR 2 ) values. 
     An engine speed function block  186  receives the engine speed signal on signal path  68  and produces as an output the result of the engine speed scaling function of equation (5). In one embodiment, block  186  may be implemented as in the form of a scaling equation, wherein block  186  is operable to convert ES to an engine speed scaling factor in accordance with this equation. Alternatively, block  186  may be implemented in graphical or table form for mapping ES values to engine speed scaling factor values. In any case, one example engine speed scaling function  185  is illustrated in FIG. 6 along with test data  187  from which function  185  is derived. Those skilled in the art will recognize that other engine speed scaling functions may be used, wherein any such scaling function will generally be based on test data for the particular application. 
     The outputs of each of blocks  180 ,  184  and  186 , as well as a conversion factor CON (60 sec/1000 RPM) are provided as inputs to a multiplication block  188  producing as an output the turbocharger rotational speed estimate, TS E  according to the equation: 
     
       
           TS   E   =sqrt ( CIT )*( a+b*PR+c*PR   2 )* f ( ES )  (6). 
       
     
     Those skilled in the art will recognize that the accuracy of the turbocharger speed estimate, TS E , may be further improved by considering additional engine operating conditions such as, for example, intake manifold temperature and/or EGR flow rate. In general, it will be recognized that there exists a tradeoff between estimate accuracy and model complexity, and it will accordingly be appreciated that the application requirements will generally dictate the required accuracy which will, in turn, dictate the model complexity. 
     Referring again to FIG. 2, the pressure ratio, PR, can also be estimated from the compressor map plot  100  according to the equation: 
     
       
           PR=f ( CTS, CMAF )  (7). 
       
     
     In embodiments of system  100  that include a mass air flow sensor disposed in fluid communication with intake conduit  22 , PR may be derived directly from plot  100  as a function of measured values of CTS and CMAF. However, in embodiments of system  100  that do not include such a mass airflow sensor, and/or in embodiments of system  100  that include an intake mass air flow estimation algorithm having less than desirable accuracy, PR may not be derived directly as a function of PR and CMAF. 
     Observation of plot  100  of FIG. 2 reveals that the compressor pressure ratio, PR, is more sensitive to changes in temperature-corrected turbocharger speed, CTS, than to corrected compressor mass flow, CMAF, and is therefore a stronger function of CTS than of CMAF. Additionally, as described hereinabove, knowledge of current engine speed, ES, enables mapping of compressor pressure ratio fluctuations to constant temperature-corrected turbocharger speed values as illustrated in FIG. 2 by constant engine speed lines  102 A- 102 C. Accordingly, the relationship of equation (7) may be simplified to the equation: 
     
       
           PR=f ( CTS, ES )  (8), 
       
     
     such that an estimated compressor outlet pressure, COP, hereinafter estimated absolute boost pressure, ABP E  is then defined by the equation: 
     
       
           ABP   E   =CIP*f{[TS/sqrt ( CIT )],  ES}   (9). 
       
     
     Referring now to FIG. 7, a three-dimensional plot  190  of the pressure ratio, PR, temperature-corrected turbocharger speed, CTS, and engine speed, ES, is illustrated for an example engine including an air handling system (e.g., EGR system, turbocharger swallowing capacity/efficiency control mechanism(s)) of the type described with respect to FIG.  1 . For every given pair of CTS and ES, plot  190  illustrates that there exists a uniquely determined compressor pressure ratio value, PR, and therefore a uniquely determined absolute boost pressure estimate value, ABP E . 
     Referring now to FIG. 8, a flowchart is shown illustrating one preferred embodiment of a generalized software algorithm  200  for estimating absolute boost pressure, in accordance with the present invention. Algorithm  200  may be stored within memory  45  and executed in a known manner by engine controller  40 , although the present invention contemplates that algorithm  200  may be executed by another controller or processor, wherein information may be shared with engine controller  40  via a suitable data bus or link. For description purposes, however, algorithm  200  will be described as being executed by engine controller  40 . 
     Algorithm  200  begins at step  202  where controller  40  is operable to determine compressor inlet temperature, CIT, via information provided by pressure sensor  50  (FIG.  1 ). Thereafter at step  204 , controller  40  is operable to determine compressor inlet pressure, CIP, via information provided by pressure sensor  54 . Thereafter at step  206 , controller  40  is operable to determine turbocharger rotational speed, TS, via information provided by speed sensor  58 . Thereafter at step  208 , controller  40  is operable to determine engine rotational speed, ES, via information provided by speed sensor  66 . 
     Following step  208 , algorithm execution advances to step  210  where controller  40  is operable to determine an estimate of the absolute boost pressure, ABP E , as a function of CTS, ES and CIT. The present invention contemplates a number of techniques for executing step  210  to map the variables CTS and ES of equation (8) to corresponding absolute boost pressure estimate values. For example, in one embodiment, the data in plot  190  may be stored in memory  45  in graphical or table form. In this embodiment, controller  40  is operable to execute step  210  by mapping current values of CTS and ES to PR using the stored information for plot  190 , and thereafter compute ABP E  by multiplying the resulting PR value by the current value of CIP. In the mapping of current values of CTS and ES to PR, estimation values in between data points may be obtained using known linear or non-linear interpolation techniques. 
     In an alternate embodiment, the three-dimensional plot  190  of FIG. 7 may be represented by a polynomial stored within memory  45 , wherein such a polynomial is solved for PR given known values of the two remaining parameters. For example, plot  190  of FIG. 7 represents a smooth surface and can therefore be modeled as a second-order polynomial according to the equation: 
     
       
           PR=a+b*CTS+C*CTS   2   +d*ES+e*ES   2   +f*CTS*ES   (9), 
       
     
     wherein a, b, c, d, e and f represent model constants. In this embodiment, engine controller  40  is operable to execute step  210  of algorithm  200  by solving equation (9) as a function of current values of CTS and ES, and then computing the absolute boost pressure estimate ABP E  by multiplying the result by the current value of CIP. 
     In yet another alternate embodiment, the three-dimensional plot  190  of FIG. 7 may be modeled by a two-input neural network trained as an appropriate surface for fitting the data points of PR according to the known variables CTS and ES. In this embodiment, engine controller  40  is operable to execute step  210  of algorithm  200  by computing PR according to the two-input neural network, and then computing the absolute boost pressure estimate ABP E  by multiplying the result by the current value of CIP. 
     In a further alternate embodiment, the plot  190  of FIG. 7 may be modeled as a second order polynomial for CTS and a scaling function of ES according to the equation: 
     
       
           PR= ( a+b*CTS+c*CTS   2 )* f ( ES )  (10), 
       
     
     wherein the term (a+b*CTS+c*CTS 2 ) represents the second-order CTS model and f(ES) is a scaling factor depending upon the current value of engine rotational speed, and a, b and c represent model constants. In this embodiment, engine controller  40  is operable to execute step  210  of algorithm  200  by solving equation (10) for PR, and then computing the absolute boost pressure estimate ABP E  by multiplying the result by the current value of CIP. Referring to FIG. 9, a portion of engine controller  40  is shown illustrating one preferred software structure for computing the absolute boost pressure estimate, ABP E , in accordance with equation (10). In this embodiment, controller  40  includes a SQRT block  180  receiving as an input the CIT signal on signal path  52  and producing as an output a value corresponding to the square root of CIT. A conversion block  220  receives as an input the turbocharger rotational speed signal, TS, on signal path  60  and produces as an output a scaled value (e.g., TS/1000) of the turbocharger rotational speed signal TS. A constant block  222  produces a constant value, K (e.g., 16.667), and an arithmetic block  224  is operable to receive the outs of blocks  180 ,  220  and  222  and produce as an output the temperature-corrected turbocharger rotational speed value CTS. 
     A turbocharger speed function block  226  receives the temperature-corrected turbocharger rotational speed value, CTS, and produces as an output the result of the CTS polynomial (a+b*CTS+c*CTS 2 ) of equation (10). In one embodiment, block  226  may be implemented in the form of an equation, wherein block  226  is operable to compute (a+b*CTS+cCTS 2 ) as a function of CTS. Alternatively, block  226  may be implemented in graphical or table form for mapping CTS values to (a+b*CTS+c*CTS 2 ) values. 
     An engine speed function block  228  receives the engine speed signal on signal path  68  and produces as an output the result of the engine speed scaling function of equation (10). In one embodiment, block  228  may be implemented as in the form of a scaling equation, wherein block  228  is operable to convert ES to an engine speed scaling factor in accordance with this equation. Alternatively, block  228  may be implemented in graphical or table form for mapping ES values to engine speed scaling factor values. In any case, one example engine speed scaling function  225  is illustrated in FIG. 10 along with test data  227  from which function  225  is derived. Those skilled in the art will recognize that other engine speed scaling functions may be used, wherein any such scaling function will generally be based on test data for the particular application. 
     The outputs of each of blocks  226  and  228 , as well as the compressor inlet pressure signal, CIP, on signal path  56  are provided as inputs to a multiplication block  230  producing as an output the absolute boost pressure estimate, TS E  according to the equation: 
     
       
           ABP   E   =CIP* ( a+b*CTS+c*CTS   2 )* f ( ES )  (11). 
       
     
     Those skilled in the art will recognize that the accuracy of the absolute boost pressure estimate, ABP E , may be further improved by considering additional engine operating conditions such as, for example, intake manifold temperature and/or EGR flow rate. In general, it will be recognized that there exists a tradeoff between estimate accuracy and model complexity, and it will accordingly be appreciated that the application requirements will generally dictate the required accuracy which will, in turn, dictate the model complexity. 
     While the invention has been illustrated and described in detail in the foregoing drawings and description, the same is to be considered as illustrative and not restrictive in character, it being understood that only preferred embodiments thereof have been shown and described and that all changes and modifications that come within the spirit of the invention are desired to be protected.