- Email: [email protected]
BOOST LIMITATION IN A TORQUE BASED ENGINE MANAGEMENT SYSTEM
BOOST LIMITATION IN A TORQUE BASED ENGINE MANAGEMENT SYSTEM Jan-Ola Olsson PhD Volvo Car Corporation Powertrain Engineering Powertrain Control & Calibration Dept. 97542, VAK.HB1S 405 31 Göteborg Sweden Abstract: Turbo charged engines are gaining increasing interest for downsizing and improved fuel economy. In a modern torque based engine management system (EMS) the turbo engine provides a special challenge in estimation of maximum available torque. For the naturally aspirated engine the available torque is more or less proportional to the density of the atmosphere, however, the turbo charged engine has a more complicated relation between atmospheric conditions and maximum available torque. This paper presents a method to calculate, in real time, the reachable boost pressure with respect to turbo rotor speed and temperature after compressor. This maximum boost pressure can then be used in the EMS torque model to estimate maximum available torque. Keywords: Engine Control, Compressors, Prediction, Protection, Torque Control
1. INTRODUCTION Requirements from authorities and society call for more efficient cars. These demands are driven by fuel prices and an increasing awareness of global warming and the role of CO2 and other green house gases. Auto manufacturers have started to react on these demands by offering their customers some new alternatives: Hybrid vehicles like the Toyota Prius (Kamichi et al., 2006), extremely compact cars like Smart (Lewin, 2004), and engines for alternative fuels like Flexfuel vehicles from Ford (Cowart et al, 1995). Also important is the refinement of more conventional powertrains for improved fuel efficiency. In this area downsizing by the use of boosting techniques is playing an increasingly important role. Volkswagen has launched a small engine with compressor and turbo (Krebs et al., 2005) and BMW has launched a 3.5 liter 6 cylinder engine with turbo as an alternative to a V8 (Welter et al., 2007). Volvo has a long tradition of turbo
engines, dating back to the early eighties (Rydqvist et al., 1981). Turbo has been considered as an effective way to offer the customers a wide range of alternatives based on a few base engines. The charging system of a turbo boosted engine is extended, compared to a naturally aspirated engine, with one or two turbochargers, a charge air cooler (CAC), additional pressurized piping and a few valves for controlling the boost pressure in different operating conditions. The added hardware also adds a few constraints to the operation of the engine and the charge system. Basically these are 1) maximum rotor speed of the turbocharger, 2) maximum compressor outlet temperature and 3) maximum gage pressure. The increased charge air density also accentuates the knock problem, but this is outside the scope of the present paper. Maximum rotor speed is related to the lifetime of the turbocharger since over speeding results in excessive creeping of the material in the rotor wheels. Compressor outlet temperature is limited by the material in the compressor, the piping to the CAC or
the CAC itself. Especially if plastic pipes are used the temperature may be the limiting factor in many operating conditions. The maximum allowed gage pressure is often coupled to the allowed temperature and is governed by the lifetime of the materials seeing the hot air from the compressor. In the Engine Management System (EMS) these constraints, at every moment of operation, have to be condensed down to a maximum allowed boost pressure. Typically the system is designed with a margin to the limits at "normal" operating conditions. However, at high ambient temperature or high altitude, i.e. low atmospheric pressure, the system will be stressed and often run close to its limits. In situations like these the available torque will most probably be limited and it is then very important to fully utilize the potential of the system. In a modern torque based EMS, vehicle and transmission control functions are highly integrated with the engine control. Apart from high requirements on the estimate of the actual torque, these functions also require a good estimate of the maximum available torque. This means that also when running the engine at low load, maximum allowed boost pressure, and the torque associated to this boost, has to be calculated with high accuracy. The estimate of the maximum available torque is important to keep the good drivability of the vehicle. Typically the accelerator pedal characteristics is modified to fit the performance of the engine and the gear shifting points in an automatic transmission are shifted accordingly. The common approach to estimate the maximum allowed boost pressure and protect the charging system, is to use a 2D look up table, indexed by engine speed and atmospheric pressure, to read out
the maximum available boost. The table is then calibrated to keep the system within the limits at a selected worst case situation, i.e. a high ambient temperature. This approach protects the engine but is also very conservative, allowing the full potential to be used only at high ambient temperature. Also it does not protect the system if the selected worst case temperature would be exceeded. In this paper is proposed an algorithm that calculates the maximum allowed boost pressure, taking into account both atmospheric pressure and ambient temperature. The proposed algorithm is based on the physics of the turbo compressor as it is described by for example Heywood (1988) or Wang (2002). Also, the algorithm is not dependent of the actual operating point of the engine. 2. SYSTEM OVERVIEW The algorithm for boost limitation is developed for and applied to a Volvo turbo engine. The engine is configured similar to the engine shown in Figure 1. Following the air path the engine has a mass air flow sensor (1) placed just down stream of the air filter (not shown). The turbo compressor feeds the air through a charge air cooler (CAC) and further into the throttle body (4). Between the CAC and the throttle body the boost pressure sensor (2) is positioned. The throttle is electrically actuated and controlled by the ECU (19). In the inlet port fuel is injected by a port fuel injector (B) and mixed with the air. After passing the combustion system the exhausts are expelled to drive the turbine. Downstream of the turbine is found oxygen sensors (9) and (10) a catalyst and silencers (not shown).
ECU 19
18
1 5, 6 I
2
E
7
4
C
A
15
D
B
8
H
14
3
Compressor F
13 20 12
Canister
G Turbine
16 17
J
9
Fuel tank 10 Catalyst
11
Figure 1 Hardware layout of a turbo engine. In order to control the boost pressure the turbine has a wastegate (F). The wastegate valve allows exhausts to bypass the turbine, thus lowering the mechanical power extracted by the turbine wheel. The torque structure of the EMS gets a requested torque from the vehicle control system. The requested torque is translated to a required air load, taking into consideration the boundary conditions and how these will affect spark timing and fuelling. The air load, expressed as g/rev is used as a target value for the air charge control that uses the throttle as an actuator. The feedback for this system is the mass air flow sensor. Using a model of the volumetric efficiency for the engine an intake pressure equivalent to the target air load is calculated. The intake pressure is the pressure downstream of the throttle and by adding a desired throttle pressure drop the target boost pressure is calculated. When boost pressure is limited the highest possible air load is calculated. Based on this air load spark timing and fuelling are calculated and from that the maximum available torque can be estimated. This paper discusses how to calculate maximum allowable boost pressure with respect to compressor outlet temperature and rotor speed. 3. COMPRESSOR MAP The classic approach to the problem is to map maximum allowable boost during vehicle tests in
different conditions. The pressure is put into a 2D look up table indexed by engine speed and atmospheric pressure. Basically this strategy has two drawbacks 1) it does not account for ambient temperature and 2) it does not provide a base for systematic calibration. This paper suggests an approach based on the compressor performance map and the normalized variables used in this map. This means that a first calibration can easily be made from the supplier compressor data. This calibration will need to be adjusted in engine or vehicle tests. However, this work is limited to the interesting area of the compressor map and does not need to cover all possible combinations of altitude, temperature and engine speed. Figure 2 shows a compressor performance map including surge line, rotor speed lines and efficiency islands. The surge line is the black line on the left side of the operating area. This line indicates the risk of surge, compressor stalling, to the left of the line. In most applications the compressor and turbine are selected so that the compressor cannot surge other than at tip out when the throttle flow suddenly decreases. Therefore boost limitation with respect to surge is not included in this paper, but the same method as described could be applied for surge as well. The theory of how to use compressor maps is available in literature, see (Heywood 1988), but is repeated here for clarity.
4.4
4.0
n norm = 168 krpm
0.68 0.7
3.6
156
0.72
3.2
0.65
147 0.73 2.8
138
Pr
0.74 0.65
126
2.4
111
2.0
η isV = 0.75 1.6
69 1.2
0.8 0.00
0.6
93 0.6 0.55
0.5
45
0.6 0.55
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
V norm
0.18
0.20
0.22
0.24
0.26
Figure 2 An example of a compressor performance map, showing both the efficiency islands and the rotor speed lines. The compressor performance map takes two inputs: pressure ratio (y-axis) and normalized compressor flow (x-axis). From these two inputs rotor speed and compressor thermodynamic efficiency are estimated. Pressure ratio, Pr, is given by equation 1 (p0 pressure before compressor, p1 pressure after compressor):
Pr =
p1 p0
(1)
Compressor flow can be expressed as a normalized volume flow ,
Vnorm , or a normalized mass flow,
mnorm . The true dimension of the normalized flow is of course the same, but to make the numbers easier to interpret, the flow normalized to the reference condition. Volume flow, equation 2, or mass flow, equation 3, refers to the unit used at the reference condition.
Vnorm = V0
mnorm = m
Tref
(2)
T0
T0 p ref ⋅ Tref p0
In Figure 2 the unit of the volume flow is
(3) m3
s
.
Rotor speed is normalized in a similar way with respect to temperature, equation 4:
N norm = N
Tref
(4)
T0
The thermodynamic efficiency of the compressor is defined as the ratio of the isentropic enthalpy increase, ∆hS , over the true enthalpy increase, ∆h , equation 5:
η=
∆hs ∆h
(5)
For the pressures and temperatures of interest for a turbocharger compressor the air can be considered as a perfect gas, i.e. the specific heat is constant. In equation 5 the enthalpies can then be replaced by temperatures. The isentropic temperature increase can be calculated from the pressure ratio and the ratio of specific heats, γ , as in equation 6:
∆Ts = Ts1 − T0 = T0 Pr
γ −1 γ
−1
(6)
4. SOLUTION It is the maximum boost pressure that is sought by this algorithm. However, looking into the compressor performance map it is clear that the air flow is important as well, both for rotor speed and temperature. The solution therefore, has to include
the compressor flow at maximum boost, as well as the boost itself. Two assumptions are made to connect maximum air flow to maximum boost: 1) The air flow is proportional to the intake pressure and 2) the intake pressure is equal to the boost pressure at boost limited conditions. The first assumption is not very good if considering the complete operating range of the engine. However, boost limited operation occurs at high load and if calibrating the volumetric efficiency, here implemented as a filling coefficient, ν [g/(rev kPa)], for this condition the assumption is fair. The filling coefficient should be tabulated against engine speed and could include other dependencies as well, as long as the pressure itself is avoided. The second assumption is true if the EMS handles the boost limited situation in a proper way and fully opens the throttle. The mass flow into the engine at maximum boost, pb ,max [kPa], is then calculated according to equation 7 ( Ne refers to engine speed [rpm]):
mmax =
ν ⋅ Ne 60
⋅ pb ,max
(7)
From the maximum air flow into the engine the maximum normalized compressor flow can be formulated, equation 8:
m norm, max =
ν ⋅ Ne 60 60
60
⋅ p b,max
T0 p ref ⋅ = Tref p0
p b, max T0 ⋅ p ref ⋅ = Tref p0
⋅
ν ⋅ Ne
ν ⋅ Ne
⋅
p b, max T0 ⋅ p ref ⋅ Tref p0 (8)
Putting together equations 5 and 6, the temperature ratio over the compressor is calculated from pressure ratio and thermodynamic efficiency according to equation 9:
T1 = T0
p1 p0
γ −1 γ
−1
1
η
+1
(9)
p1 , mcorr p0
η = M Cη Tmax = T0
pb,max p0 pb ,max
,
ν ⋅ Ne
γ −1 γ
p0
60 −1
(10)
⋅ 1
η
p T0 ⋅ p ref ⋅ b,max Tref p0 +1 (11)
By using equation 11 for a set of pressure ratios,
pb,max p0
, and the first part of the normalized
maximum air flow,
ν ⋅ Ne 60
⋅
T0 ⋅ p ref , a Tref
corresponding set of temperature ratios,
Tmax , can T0
be produced. This set of data can be used to create a new look up table that produces maximum pressure ratio as function of allowed temperature ratio and air flow normalized according to the first part of the corrected maximum air flow. This map is illustrated in equation 12:
pb,max p0
= MT
Tmax ν ⋅ Ne T0 ⋅ p ref (12) , ⋅ T0 60 Tref
This approach is suited for implementation in an EMS system to limit boost pressure with respect to the maximum allowed temperature. Note that the normalization of the air flow means that the input to the map does not change with engine load. Figure 3 shows an example of how this strategy could be implemented in Matlab Simulink. For the maximum allowed compressor speed the calculations are similar. The main difference is that the conversion from efficiency to temperature ratio is nott needed since normalized rotor speed is read directly from the compressor map, according to equation 13:
N corr = M CN
The thermodynamic efficiency is given from the compressor performance map, equation 10 (MCη refers to the compressor map for efficiency):
η = M Cη
By applying equations 8 and 10 for maximum boost conditions, i.e. using the flow from equation 8, the following relations are found, equation 11:
p1 , mcorr p0
(13)
Figure 3 An example of a Matlab Simulink implementation of the calculation of maximum boost pressure with respect to maximum allowed temperature after compressor.
T0
= M CN
pb,max ν ⋅ Ne p T0 ⋅ ⋅ pref ⋅ b,max , 60 p0 Tref p0
(14) By using equation 14 for a set of maximum pressure ratios and normalized flows a set of corrected maximum rotor speeds is created. This data can be used to create a new map that produces maximum pressure ratio as function of corrected maximum rotor speed and normalized air flow, illustrated in equation 15:
pb,max p0
= M N N max
Tref ν ⋅ Ne T0 ⋅ ⋅ p ref , T0 60 Tref (15)
This formulation is suitable for implementation. An implementation in Matlab Simulink would be analog to the example shown in Figure 3. Obviously the two implementations would be very similar and should not be implemented as two independent functions. 5. RESULTS The strategy to limit the boost according to the equations above has been implemented and tested in vehicle. Typically the temperature limit is active only at extremely high ambient temperature or a combination of high temperature and some elevation.
Engine Speed (rpm)
Tref
In another test, Figure 5, at similar conditions the temperature limitation was disabled and the rotor speed limitation was tested from 5000 to 6500 rpm. In this test the allowed boost pressure is actually requested and the measured rotor speed can be directly compared to the maximum allowed speed. In the worst point the true rotor speed is just below 5000 rpm lower than the limit.
7000 6500 6000 5500 5000 4500
0
200
Pressure (kPa)
N max
Figure 4 shows the results from a test outside Phoenix Arizona. The graph shows the maximum boost pressure for 5500, 6000 and 6500 rpm engine speed.
10
20
30
40
50
60
70
30
40
50
60
70
50
60
70
Max Boost Measured Boost
190 180 170 160
Temp aft comp (°C)
Applying this equation for maximum rotor speed, including the speed correction from equation 4, maximum boost and the same corrected maximum air flow as used above equation 14 is achieved:
0
180
10
20
Max Temp Measured Temp
170 160 150 140
0
10
20
30
40 Time (s)
Figure 4 Vehicle test of maximum boost with respect to temperature out of compressor. Ambient conditions 40° C / 96 kPa. For rotor speed another result from high altitude is shown in Figure 6. In this test the margin is higher, up
to 15 krpm difference between maximum allowed and measured rotor speed can be seen. Please note that both functions are calibrated to provide some margin for variations in hardware.
6. DISCUSSION It could be discussed whether the temperature after the compressor, reached at steady state, should really limit the torque also in transient operation. This approach means that a customer may get a lower than necessary torque during an acceleration. The other approach, to limit the torque when the maximum temperature is actually reached, would mean that the higher torque would be available for shorter accelerations. On the other hand a customer could experience decreased torque during an ongoing acceleration or hill climbing – this could be perceived as an error state.
Engine Speed (rpm)
The first calibration was based on the compressor data provided by the supplier and this was a very good base for the calibration. However, it was found that to achieve the required accuracy the functionality has to be calibrated from vehicle test data. The resolution of the supplier data is not high enough and some systematic differences between the compressor data and the actual in vehicle compressor performance was also found. For example the choke flow limit of the compressor was found to be higher in practical tests than what was suggested by the compressor map.
The algorithm is based on well established theory for turbo compressors, but relies on sensors for atmospheric pressure, boost pressure and intake air temperature. This means that pressure drops and temperature change due to heat conduction is neglected in the function itself. In stead these effects are compensated for in the calibration of the two look up tables. This will result in systematic errors and leaves room for improvement of the algorithm. However, the size of the error has been found to be acceptable.
7000 6500 6000 5500 5000 4500
0
5
10
15
20
25
30
35
40
45
200
Pressure (kPa)
190 180
The implementation, as presented here, is based on two 2D look up tables that originate from the compressor performance map. Other researchers, e.g. Sorensen et al. (2005) have shown that the compressor performance can be described by algebraic expressions using only a few coefficients. Most probably a similar approach could be used to lower the ROM-space needed for an implementation of this algorithm. However, this might result in a somewhat higher CPU load and it may also make the calibration less intuitive.
170 Max Boost Actual Boost
160 150
0
5
10
15
20
25
30
35
40
45
15
20
25 Time (s)
30
35
40
45
Rotor speed (krpm)
170 Max Speed Measured Speed
160 150 140
0
5
10
Figure 5 Vehicle test of maximum boost with respect to turbo rotor speed. Ambient conditions 42°C / 96 kPa. Engine Speed (rpm)
7000 6000 5000 4000 20
25
30
35
40
45
Pressure (kPa)
160 150 140 130 120 110 20
Rotor speed (krpm)
160 150
Max Boost here Max Bosst Strat Actual Boost TgtBoost 25
30
35
40
45
Max Speed Measured Speed
140 130 20
25
30
35
40
Time (s)
Figure 6 Vehicle test of maximum boost with respect to turbo rotor speed. Ambient conditions 16°C / 66 kPa.
45
7. CONCLUSIONS The proposed strategy provides a comprehensive solution to limit boost pressure with respect to rotor speed and temperature out of compressor. The requirement of knowing the maximum allowed boost, and thus also the torque, even at part load is fulfilled. The accuracy for rotor speed is normally within 15 krpm and a bit worse close to the choke limit. This is considered as fully acceptable for production. The accuracy of the temperature out of the compressor is much harder to assess due to the slow response of the temperature. An estimate is that the temperature ends up within ±15°C from target. However, due to the slow response it could be argued the peak temperature very rarely is reached and therefore the calibration does not need to include all of the margin. It was found that calibration from supplier data only is not sufficient, but provides a very good base for vehicle testing.
CAC ECU EMS h
m
M N Ne P Pr T
8. ACRONYMS AND SYMBOLS Charge Air Cooler Engine Controller Unit Engine Management System Enthalpy (J/kg) Mass flow (g/s) 2D look up table (map) Rotor speed (krpm) Engine speed (rpm) Pressure (kPa) Pressure ratio (-) Temperature (K)
V
Volume flow (m3/s) γ Ratio of specific heats (-) η Thermodynamic efficiency (-) ν Filling coefficient, ~volumetric efficiency ((g/rev)/kPa) 9. REFERENCES Cowart J S, Boruta W E, Dalton J D, Dona R F, Rivard II F L, Furby R S, Piontkowski J A, Seiter R E, and Takai R M, Powertrain Development of the 1996 Ford Flexible Fuel Taurus, SAE 952751 Heywood J B, Internal Combustion Engine Fundamental, McGraw-Hill, Singapore 1988 Kamichi K, Okasaka K, Tomatsuri M, Matsubara T, Kaya Y and Asada H, Hybrid System Development for a High-Performance Rear Drive Vehicle, SAE 2006-01-1338 Krebs R, Szengel R, Middendorf H, Fleiß M, Laumann A and Voeltz S, Neuer Ottomotor mit Direkteinspritzung und Doppelaufladung von Volkswagen, MTZ 11/2005 Lewin T, Smart Thinking… The Little Car that made it Big, Motor Books International, St Paul, USA, 2004 Rydqvist J E, Sandberg L, Wallin R, A Turbocharged Engine With Microprocessor Controlled Boost Pressure, SAE 810060 Sorenson S, Hendricks E, Magnusson S, and Bertelsen A, Compact and Accurate Turbocharger Modelling for Engine Control, SAE 2005-01-1942 Wang Y Y, System for Estimating Turbocharger Rotational Speed, Patent US 6,539,714, Columbus IN USA 2002 Welter A, Bruener T, Unger H, Hoyer U and Brendel U, The New BMW Turbocharged Six-cylinder Inline Petrol Engine, MTZ 0212007
1. INTRODUCTION Requirements from authorities and society call for more efficient cars. These demands are driven by fuel prices and an increasing awareness of global warming and the role of CO2 and other green house gases. Auto manufacturers have started to react on these demands by offering their customers some new alternatives: Hybrid vehicles like the Toyota Prius (Kamichi et al., 2006), extremely compact cars like Smart (Lewin, 2004), and engines for alternative fuels like Flexfuel vehicles from Ford (Cowart et al, 1995). Also important is the refinement of more conventional powertrains for improved fuel efficiency. In this area downsizing by the use of boosting techniques is playing an increasingly important role. Volkswagen has launched a small engine with compressor and turbo (Krebs et al., 2005) and BMW has launched a 3.5 liter 6 cylinder engine with turbo as an alternative to a V8 (Welter et al., 2007). Volvo has a long tradition of turbo
engines, dating back to the early eighties (Rydqvist et al., 1981). Turbo has been considered as an effective way to offer the customers a wide range of alternatives based on a few base engines. The charging system of a turbo boosted engine is extended, compared to a naturally aspirated engine, with one or two turbochargers, a charge air cooler (CAC), additional pressurized piping and a few valves for controlling the boost pressure in different operating conditions. The added hardware also adds a few constraints to the operation of the engine and the charge system. Basically these are 1) maximum rotor speed of the turbocharger, 2) maximum compressor outlet temperature and 3) maximum gage pressure. The increased charge air density also accentuates the knock problem, but this is outside the scope of the present paper. Maximum rotor speed is related to the lifetime of the turbocharger since over speeding results in excessive creeping of the material in the rotor wheels. Compressor outlet temperature is limited by the material in the compressor, the piping to the CAC or
the CAC itself. Especially if plastic pipes are used the temperature may be the limiting factor in many operating conditions. The maximum allowed gage pressure is often coupled to the allowed temperature and is governed by the lifetime of the materials seeing the hot air from the compressor. In the Engine Management System (EMS) these constraints, at every moment of operation, have to be condensed down to a maximum allowed boost pressure. Typically the system is designed with a margin to the limits at "normal" operating conditions. However, at high ambient temperature or high altitude, i.e. low atmospheric pressure, the system will be stressed and often run close to its limits. In situations like these the available torque will most probably be limited and it is then very important to fully utilize the potential of the system. In a modern torque based EMS, vehicle and transmission control functions are highly integrated with the engine control. Apart from high requirements on the estimate of the actual torque, these functions also require a good estimate of the maximum available torque. This means that also when running the engine at low load, maximum allowed boost pressure, and the torque associated to this boost, has to be calculated with high accuracy. The estimate of the maximum available torque is important to keep the good drivability of the vehicle. Typically the accelerator pedal characteristics is modified to fit the performance of the engine and the gear shifting points in an automatic transmission are shifted accordingly. The common approach to estimate the maximum allowed boost pressure and protect the charging system, is to use a 2D look up table, indexed by engine speed and atmospheric pressure, to read out
the maximum available boost. The table is then calibrated to keep the system within the limits at a selected worst case situation, i.e. a high ambient temperature. This approach protects the engine but is also very conservative, allowing the full potential to be used only at high ambient temperature. Also it does not protect the system if the selected worst case temperature would be exceeded. In this paper is proposed an algorithm that calculates the maximum allowed boost pressure, taking into account both atmospheric pressure and ambient temperature. The proposed algorithm is based on the physics of the turbo compressor as it is described by for example Heywood (1988) or Wang (2002). Also, the algorithm is not dependent of the actual operating point of the engine. 2. SYSTEM OVERVIEW The algorithm for boost limitation is developed for and applied to a Volvo turbo engine. The engine is configured similar to the engine shown in Figure 1. Following the air path the engine has a mass air flow sensor (1) placed just down stream of the air filter (not shown). The turbo compressor feeds the air through a charge air cooler (CAC) and further into the throttle body (4). Between the CAC and the throttle body the boost pressure sensor (2) is positioned. The throttle is electrically actuated and controlled by the ECU (19). In the inlet port fuel is injected by a port fuel injector (B) and mixed with the air. After passing the combustion system the exhausts are expelled to drive the turbine. Downstream of the turbine is found oxygen sensors (9) and (10) a catalyst and silencers (not shown).
ECU 19
18
1 5, 6 I
2
E
7
4
C
A
15
D
B
8
H
14
3
Compressor F
13 20 12
Canister
G Turbine
16 17
J
9
Fuel tank 10 Catalyst
11
Figure 1 Hardware layout of a turbo engine. In order to control the boost pressure the turbine has a wastegate (F). The wastegate valve allows exhausts to bypass the turbine, thus lowering the mechanical power extracted by the turbine wheel. The torque structure of the EMS gets a requested torque from the vehicle control system. The requested torque is translated to a required air load, taking into consideration the boundary conditions and how these will affect spark timing and fuelling. The air load, expressed as g/rev is used as a target value for the air charge control that uses the throttle as an actuator. The feedback for this system is the mass air flow sensor. Using a model of the volumetric efficiency for the engine an intake pressure equivalent to the target air load is calculated. The intake pressure is the pressure downstream of the throttle and by adding a desired throttle pressure drop the target boost pressure is calculated. When boost pressure is limited the highest possible air load is calculated. Based on this air load spark timing and fuelling are calculated and from that the maximum available torque can be estimated. This paper discusses how to calculate maximum allowable boost pressure with respect to compressor outlet temperature and rotor speed. 3. COMPRESSOR MAP The classic approach to the problem is to map maximum allowable boost during vehicle tests in
different conditions. The pressure is put into a 2D look up table indexed by engine speed and atmospheric pressure. Basically this strategy has two drawbacks 1) it does not account for ambient temperature and 2) it does not provide a base for systematic calibration. This paper suggests an approach based on the compressor performance map and the normalized variables used in this map. This means that a first calibration can easily be made from the supplier compressor data. This calibration will need to be adjusted in engine or vehicle tests. However, this work is limited to the interesting area of the compressor map and does not need to cover all possible combinations of altitude, temperature and engine speed. Figure 2 shows a compressor performance map including surge line, rotor speed lines and efficiency islands. The surge line is the black line on the left side of the operating area. This line indicates the risk of surge, compressor stalling, to the left of the line. In most applications the compressor and turbine are selected so that the compressor cannot surge other than at tip out when the throttle flow suddenly decreases. Therefore boost limitation with respect to surge is not included in this paper, but the same method as described could be applied for surge as well. The theory of how to use compressor maps is available in literature, see (Heywood 1988), but is repeated here for clarity.
4.4
4.0
n norm = 168 krpm
0.68 0.7
3.6
156
0.72
3.2
0.65
147 0.73 2.8
138
Pr
0.74 0.65
126
2.4
111
2.0
η isV = 0.75 1.6
69 1.2
0.8 0.00
0.6
93 0.6 0.55
0.5
45
0.6 0.55
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
V norm
0.18
0.20
0.22
0.24
0.26
Figure 2 An example of a compressor performance map, showing both the efficiency islands and the rotor speed lines. The compressor performance map takes two inputs: pressure ratio (y-axis) and normalized compressor flow (x-axis). From these two inputs rotor speed and compressor thermodynamic efficiency are estimated. Pressure ratio, Pr, is given by equation 1 (p0 pressure before compressor, p1 pressure after compressor):
Pr =
p1 p0
(1)
Compressor flow can be expressed as a normalized volume flow ,
Vnorm , or a normalized mass flow,
mnorm . The true dimension of the normalized flow is of course the same, but to make the numbers easier to interpret, the flow normalized to the reference condition. Volume flow, equation 2, or mass flow, equation 3, refers to the unit used at the reference condition.
Vnorm = V0
mnorm = m
Tref
(2)
T0
T0 p ref ⋅ Tref p0
In Figure 2 the unit of the volume flow is
(3) m3
s
.
Rotor speed is normalized in a similar way with respect to temperature, equation 4:
N norm = N
Tref
(4)
T0
The thermodynamic efficiency of the compressor is defined as the ratio of the isentropic enthalpy increase, ∆hS , over the true enthalpy increase, ∆h , equation 5:
η=
∆hs ∆h
(5)
For the pressures and temperatures of interest for a turbocharger compressor the air can be considered as a perfect gas, i.e. the specific heat is constant. In equation 5 the enthalpies can then be replaced by temperatures. The isentropic temperature increase can be calculated from the pressure ratio and the ratio of specific heats, γ , as in equation 6:
∆Ts = Ts1 − T0 = T0 Pr
γ −1 γ
−1
(6)
4. SOLUTION It is the maximum boost pressure that is sought by this algorithm. However, looking into the compressor performance map it is clear that the air flow is important as well, both for rotor speed and temperature. The solution therefore, has to include
the compressor flow at maximum boost, as well as the boost itself. Two assumptions are made to connect maximum air flow to maximum boost: 1) The air flow is proportional to the intake pressure and 2) the intake pressure is equal to the boost pressure at boost limited conditions. The first assumption is not very good if considering the complete operating range of the engine. However, boost limited operation occurs at high load and if calibrating the volumetric efficiency, here implemented as a filling coefficient, ν [g/(rev kPa)], for this condition the assumption is fair. The filling coefficient should be tabulated against engine speed and could include other dependencies as well, as long as the pressure itself is avoided. The second assumption is true if the EMS handles the boost limited situation in a proper way and fully opens the throttle. The mass flow into the engine at maximum boost, pb ,max [kPa], is then calculated according to equation 7 ( Ne refers to engine speed [rpm]):
mmax =
ν ⋅ Ne 60
⋅ pb ,max
(7)
From the maximum air flow into the engine the maximum normalized compressor flow can be formulated, equation 8:
m norm, max =
ν ⋅ Ne 60 60
60
⋅ p b,max
T0 p ref ⋅ = Tref p0
p b, max T0 ⋅ p ref ⋅ = Tref p0
⋅
ν ⋅ Ne
ν ⋅ Ne
⋅
p b, max T0 ⋅ p ref ⋅ Tref p0 (8)
Putting together equations 5 and 6, the temperature ratio over the compressor is calculated from pressure ratio and thermodynamic efficiency according to equation 9:
T1 = T0
p1 p0
γ −1 γ
−1
1
η
+1
(9)
p1 , mcorr p0
η = M Cη Tmax = T0
pb,max p0 pb ,max
,
ν ⋅ Ne
γ −1 γ
p0
60 −1
(10)
⋅ 1
η
p T0 ⋅ p ref ⋅ b,max Tref p0 +1 (11)
By using equation 11 for a set of pressure ratios,
pb,max p0
, and the first part of the normalized
maximum air flow,
ν ⋅ Ne 60
⋅
T0 ⋅ p ref , a Tref
corresponding set of temperature ratios,
Tmax , can T0
be produced. This set of data can be used to create a new look up table that produces maximum pressure ratio as function of allowed temperature ratio and air flow normalized according to the first part of the corrected maximum air flow. This map is illustrated in equation 12:
pb,max p0
= MT
Tmax ν ⋅ Ne T0 ⋅ p ref (12) , ⋅ T0 60 Tref
This approach is suited for implementation in an EMS system to limit boost pressure with respect to the maximum allowed temperature. Note that the normalization of the air flow means that the input to the map does not change with engine load. Figure 3 shows an example of how this strategy could be implemented in Matlab Simulink. For the maximum allowed compressor speed the calculations are similar. The main difference is that the conversion from efficiency to temperature ratio is nott needed since normalized rotor speed is read directly from the compressor map, according to equation 13:
N corr = M CN
The thermodynamic efficiency is given from the compressor performance map, equation 10 (MCη refers to the compressor map for efficiency):
η = M Cη
By applying equations 8 and 10 for maximum boost conditions, i.e. using the flow from equation 8, the following relations are found, equation 11:
p1 , mcorr p0
(13)
Figure 3 An example of a Matlab Simulink implementation of the calculation of maximum boost pressure with respect to maximum allowed temperature after compressor.
T0
= M CN
pb,max ν ⋅ Ne p T0 ⋅ ⋅ pref ⋅ b,max , 60 p0 Tref p0
(14) By using equation 14 for a set of maximum pressure ratios and normalized flows a set of corrected maximum rotor speeds is created. This data can be used to create a new map that produces maximum pressure ratio as function of corrected maximum rotor speed and normalized air flow, illustrated in equation 15:
pb,max p0
= M N N max
Tref ν ⋅ Ne T0 ⋅ ⋅ p ref , T0 60 Tref (15)
This formulation is suitable for implementation. An implementation in Matlab Simulink would be analog to the example shown in Figure 3. Obviously the two implementations would be very similar and should not be implemented as two independent functions. 5. RESULTS The strategy to limit the boost according to the equations above has been implemented and tested in vehicle. Typically the temperature limit is active only at extremely high ambient temperature or a combination of high temperature and some elevation.
Engine Speed (rpm)
Tref
In another test, Figure 5, at similar conditions the temperature limitation was disabled and the rotor speed limitation was tested from 5000 to 6500 rpm. In this test the allowed boost pressure is actually requested and the measured rotor speed can be directly compared to the maximum allowed speed. In the worst point the true rotor speed is just below 5000 rpm lower than the limit.
7000 6500 6000 5500 5000 4500
0
200
Pressure (kPa)
N max
Figure 4 shows the results from a test outside Phoenix Arizona. The graph shows the maximum boost pressure for 5500, 6000 and 6500 rpm engine speed.
10
20
30
40
50
60
70
30
40
50
60
70
50
60
70
Max Boost Measured Boost
190 180 170 160
Temp aft comp (°C)
Applying this equation for maximum rotor speed, including the speed correction from equation 4, maximum boost and the same corrected maximum air flow as used above equation 14 is achieved:
0
180
10
20
Max Temp Measured Temp
170 160 150 140
0
10
20
30
40 Time (s)
Figure 4 Vehicle test of maximum boost with respect to temperature out of compressor. Ambient conditions 40° C / 96 kPa. For rotor speed another result from high altitude is shown in Figure 6. In this test the margin is higher, up
to 15 krpm difference between maximum allowed and measured rotor speed can be seen. Please note that both functions are calibrated to provide some margin for variations in hardware.
6. DISCUSSION It could be discussed whether the temperature after the compressor, reached at steady state, should really limit the torque also in transient operation. This approach means that a customer may get a lower than necessary torque during an acceleration. The other approach, to limit the torque when the maximum temperature is actually reached, would mean that the higher torque would be available for shorter accelerations. On the other hand a customer could experience decreased torque during an ongoing acceleration or hill climbing – this could be perceived as an error state.
Engine Speed (rpm)
The first calibration was based on the compressor data provided by the supplier and this was a very good base for the calibration. However, it was found that to achieve the required accuracy the functionality has to be calibrated from vehicle test data. The resolution of the supplier data is not high enough and some systematic differences between the compressor data and the actual in vehicle compressor performance was also found. For example the choke flow limit of the compressor was found to be higher in practical tests than what was suggested by the compressor map.
The algorithm is based on well established theory for turbo compressors, but relies on sensors for atmospheric pressure, boost pressure and intake air temperature. This means that pressure drops and temperature change due to heat conduction is neglected in the function itself. In stead these effects are compensated for in the calibration of the two look up tables. This will result in systematic errors and leaves room for improvement of the algorithm. However, the size of the error has been found to be acceptable.
7000 6500 6000 5500 5000 4500
0
5
10
15
20
25
30
35
40
45
200
Pressure (kPa)
190 180
The implementation, as presented here, is based on two 2D look up tables that originate from the compressor performance map. Other researchers, e.g. Sorensen et al. (2005) have shown that the compressor performance can be described by algebraic expressions using only a few coefficients. Most probably a similar approach could be used to lower the ROM-space needed for an implementation of this algorithm. However, this might result in a somewhat higher CPU load and it may also make the calibration less intuitive.
170 Max Boost Actual Boost
160 150
0
5
10
15
20
25
30
35
40
45
15
20
25 Time (s)
30
35
40
45
Rotor speed (krpm)
170 Max Speed Measured Speed
160 150 140
0
5
10
Figure 5 Vehicle test of maximum boost with respect to turbo rotor speed. Ambient conditions 42°C / 96 kPa. Engine Speed (rpm)
7000 6000 5000 4000 20
25
30
35
40
45
Pressure (kPa)
160 150 140 130 120 110 20
Rotor speed (krpm)
160 150
Max Boost here Max Bosst Strat Actual Boost TgtBoost 25
30
35
40
45
Max Speed Measured Speed
140 130 20
25
30
35
40
Time (s)
Figure 6 Vehicle test of maximum boost with respect to turbo rotor speed. Ambient conditions 16°C / 66 kPa.
45
7. CONCLUSIONS The proposed strategy provides a comprehensive solution to limit boost pressure with respect to rotor speed and temperature out of compressor. The requirement of knowing the maximum allowed boost, and thus also the torque, even at part load is fulfilled. The accuracy for rotor speed is normally within 15 krpm and a bit worse close to the choke limit. This is considered as fully acceptable for production. The accuracy of the temperature out of the compressor is much harder to assess due to the slow response of the temperature. An estimate is that the temperature ends up within ±15°C from target. However, due to the slow response it could be argued the peak temperature very rarely is reached and therefore the calibration does not need to include all of the margin. It was found that calibration from supplier data only is not sufficient, but provides a very good base for vehicle testing.
CAC ECU EMS h
m
M N Ne P Pr T
8. ACRONYMS AND SYMBOLS Charge Air Cooler Engine Controller Unit Engine Management System Enthalpy (J/kg) Mass flow (g/s) 2D look up table (map) Rotor speed (krpm) Engine speed (rpm) Pressure (kPa) Pressure ratio (-) Temperature (K)
V
Volume flow (m3/s) γ Ratio of specific heats (-) η Thermodynamic efficiency (-) ν Filling coefficient, ~volumetric efficiency ((g/rev)/kPa) 9. REFERENCES Cowart J S, Boruta W E, Dalton J D, Dona R F, Rivard II F L, Furby R S, Piontkowski J A, Seiter R E, and Takai R M, Powertrain Development of the 1996 Ford Flexible Fuel Taurus, SAE 952751 Heywood J B, Internal Combustion Engine Fundamental, McGraw-Hill, Singapore 1988 Kamichi K, Okasaka K, Tomatsuri M, Matsubara T, Kaya Y and Asada H, Hybrid System Development for a High-Performance Rear Drive Vehicle, SAE 2006-01-1338 Krebs R, Szengel R, Middendorf H, Fleiß M, Laumann A and Voeltz S, Neuer Ottomotor mit Direkteinspritzung und Doppelaufladung von Volkswagen, MTZ 11/2005 Lewin T, Smart Thinking… The Little Car that made it Big, Motor Books International, St Paul, USA, 2004 Rydqvist J E, Sandberg L, Wallin R, A Turbocharged Engine With Microprocessor Controlled Boost Pressure, SAE 810060 Sorenson S, Hendricks E, Magnusson S, and Bertelsen A, Compact and Accurate Turbocharger Modelling for Engine Control, SAE 2005-01-1942 Wang Y Y, System for Estimating Turbocharger Rotational Speed, Patent US 6,539,714, Columbus IN USA 2002 Welter A, Bruener T, Unger H, Hoyer U and Brendel U, The New BMW Turbocharged Six-cylinder Inline Petrol Engine, MTZ 0212007