Engine Calibration Maps

Calibration maps are a key part of the engine plant and controller models available in the Powertrain Blockset™. Engine models use the maps to represent engine behavior and to store optimal control parameters. Using calibration maps in control design leads to flexible, efficient control algorithms and estimators that are suitable for electronic control unit (ECU) implementation.

To develop the calibration maps for engine plant and controller models in the reference applications, MathWorks^® developed and used processes to measure performance data from 1.5–L spark-ignition (SI) and compression-ignition (CI) engine models provided by Gamma Technologies LLC.

To represent the behavior of engine plants and controllers specific to your application, you can develop your own engine calibration maps. The data required for calibration typically comes from engine dynamometer tests or engine hardware design models.

Engine Plant Calibration Maps

The engine plant model calibration maps in the Powertrain Blockset SI and CI reference applications affect the engine response to control inputs (for example, spark timing, throttle position, and cam phasing).

To develop the calibration maps in the Powertrain Blockset engine plant models, MathWorks used GT-POWER models from the GT-SUITE modeling library in a Simulink^®-based virtual dynamometer. MathWorks used the Model-Based Calibration Toolbox™ to create design-of-experiment (DoE) test plans. The Simulink-based virtual dynamometer executed the DoE test plan on GT-POWER 1.5–L SI and CI reference engines. MathWorks used the Model-Based Calibration Toolbox to develop the engine plant model calibration maps from the GT-POWER.

Engine Controller Calibration Maps

The engine controller model calibration maps in the reference applications represent the optimal open-loop control commands for given engine operating points.

To develop the calibration maps for the SI engine controller, MathWorks used the GT-POWER reference engine models in a virtual engine calibration optimization (VECO) process. The process optimized the open-loop control commands for 1.5–L SI engine, subject to engine operating constraints for knock, turbocharger speed, and exhaust temperature.

To develop the calibration maps for the CI engine controller, MathWorks used the DOE test data from the GT-POWER 1.5–L CI reference model operated at minimum brake-specific fuel consumption (BSFC).

Calibration Maps in Compression-Ignition (CI) Blocks

In the engine models, the Powertrain Blockset blocks implement these calibration maps.

Calibration Maps in Spark-Ignition (SI) Blocks

In the engine models, the Powertrain Blockset blocks implement these calibration maps.

Map	Used for	In	Description
Engine volumetric efficiency	SI Engine Speed-Density Air Mass Flow Model	SI Core Engine SI Controller	The engine volumetric efficiency lookup table, $f_{η_{v}}$ , is a function of intake manifold absolute pressure and engine speed $η_{v} = f_{η_{v}} (M A P, N)$ where: $η_{v}$ is engine volumetric efficiency, dimensionless. MAP is intake manifold absolute pressure, in KPa. N is engine speed, in rpm.
Cylinder volume at intake valve close table (IVC)	SI Engine Dual-Independent Cam Phaser Air Mass Flow Model	SI Core Engine SI Controller	The cylinder volume at intake valve close table (IVC), $f_{V i v c}$ is a function of the intake cam phaser angle $V_{I V C} = f_{V i v c} (φ_{I C P})$ where: $V_{I V C}$ is cylinder volume at IVC, in L. $φ_{I C P}$ is intake cam phaser angle in crank degrees of advance relative to the intake phaser park position.
Trapped mass correction	SI Engine Dual-Independent Cam Phaser Air Mass Flow Model	SI Core Engine SI Controller	The trapped mass correction factor table, $f_{T M c o r r}$ , is a function of the normalized density and engine speed $T M_{c o r r} = f_{T M c o r r} (ρ_{n o r m}, N)$ where: $T M_{c o r r}$ , is trapped mass correction multiplier, dimensionless. $ρ_{n o r m}$ is normalized density, dimensionless. N is engine speed, in rpm.
Air mass flow at cam phaser angles	SI Engine Dual-Independent Cam Phaser Air Mass Flow Model	SI Core Engine SI Controller	The phaser intake mass flow model lookup table is a function of exhaust cam phaser angles and trapped air mass flow ${\dot{m}}_{i n t k i d e a l} = f_{i n t k i d e a l} (φ_{E C P}, T M_{f l o w})$ where: ${\dot{m}}_{i n t k i d e a l}$ is engine intake port mass flow at arbitrary cam phaser angles, in g/s. $φ_{E C P}$ is exhaust cam phaser angle in crank degrees of retard relative to the exhaust phaser park position. $T M_{f l o w}$ is flow rate equivalent to corrected trapped mass at the current engine speed, in g/s.
Air mass flow correction	SI Engine Dual-Independent Cam Phaser Air Mass Flow Model	SI Core Engine SI Controller	The intake air mass flow correction lookup table, $f_{a i r c o r r}$ , is a function of ideal load and engine speed ${\dot{m}}_{a i r} = {\dot{m}}_{i n t k i d e a l} f_{a i r c o r r} (L_{i d e a l}, N)$ where: $L_{i d e a l}$ is engine load (normalized cylinder air mass) at arbitrary cam phaser angles, uncorrected for final steady-state cam phaser angles, dimensionless. N is engine speed, in rpm. ${\dot{m}}_{a i r}$ is engine intake air mass flow final correction at steady-state cam phaser angles, in g/s. ${\dot{m}}_{i n t k i d e a l}$ is engine intake port mass flow at arbitrary cam phaser angles, in g/s.
Inner torque	SI Engine Torque Structure Model	SI Core Engine SI Controller	The inner torque lookup table, $f_{T q i n r}$ , is a function of engine speed and engine load, $T q_{i n r} = f_{T q i n r} (L, N)$ , where: $T q_{i n r}$ is inner torque based on gross indicated mean effective pressure, in N·m. L is engine load at arbitrary cam phaser angles, corrected for final steady-state cam phaser angles, dimensionless. N is engine speed, in rpm.
Friction torque	SI Engine Torque Structure Model	SI Core Engine SI Controller	The friction torque lookup table, $f_{T f r i c}$ , is a function of engine speed and engine load, $T_{f r i c} = f_{T f r i c} (L, N)$ , where: $T_{f r i c}$ is friction torque offset to inner torque, in N·m. L is engine load at arbitrary cam phaser angles, corrected for final steady-state cam phaser angles, dimensionless. N is engine speed, in rpm.
Pumping torque	SI Engine Torque Structure Model	SI Core Engine SI Controller	The pumping torque lookup table, ƒ_Tpump, is a function of engine load and engine speed, `T_pump=ƒ_Tpump(L,N)`, where: T_pump is pumping torque, in N·m. L is engine load, as a normalized cylinder air mass, dimensionless. N is engine speed, in rpm.
Optimal spark advance	SI Engine Torque Structure Model	SI Core Engine SI Controller	The optimal spark lookup table, $f_{S A o p t}$ , is a function of engine speed and engine load, $S A_{o p t} = f_{S A o p t} (L, N)$ , where: SA_opt is optimal spark advance timing for maximum inner torque at stoichiometric air-fuel ratio (AFR), in deg. L is engine load at arbitrary cam phaser angles, corrected for final steady-state cam phaser angles, dimensionless. N is engine speed, in rpm.
Spark efficiency	SI Engine Torque Structure Model	SI Core Engine SI Controller	The spark efficiency lookup table, $f_{M s a}$ , is a function of the spark retard from optimal $\begin{array}{l} M_{s a} = f_{M s a} (Δ S A) \\ Δ S A = S A_{o p t} - S A \end{array}$ where: $M_{s a}$ is the spark retard efficiency multiplier, dimensionless. $Δ S A$ is the spark retard timing distance from optimal spark advance, in deg.
Lambda efficiency	SI Engine Torque Structure Model	SI Core Engine SI Controller	The lambda efficiency lookup table, $f_{M λ}$ , is a function of lambda, $M_{λ} = f_{M λ} (λ)$ , where: $M_{λ}$ is the lambda multiplier on inner torque to account for the air-fuel ratio (AFR) effect, dimensionless. $λ$ is lambda, AFR normalized to stoichiometric fuel AFR, dimensionless.
Simple torque	SI Engine Simple Torque Model	SI Core Engine SI Controller	For the simple torque lookup table model, the SI engine uses a lookup table map that is a function of engine speed and load, $T_{b r a k e} = f_{T n L} (L, N)$ , where: $T_{b r a k e}$ is engine brake torque after accounting for spark advance, AFR, and friction effects, in N·m. L is engine load, as a normalized cylinder air mass, dimensionless. N is engine speed, in rpm.
Hydrocarbon (HC) mass fraction	HC emissions	SI Core Engine	The SI Core Engine HC emission mass fraction lookup table is a function of engine torque and engine speed, HC Mass Fraction = ƒ(Speed, Torque), where: HC Mass Fraction is the HC emission mass fraction, dimensionless. Speed is engine speed, in rpm. Torque is engine torque, in N·m.
Carbon monoxide (CO) mass fraction	CO emissions	SI Core Engine	The SI Core Engine CO emission mass fraction lookup table is a function of engine torque and engine speed, CO Mass Fraction = ƒ(Speed, Torque), where: CO Mass Fraction is the CO emission mass fraction, dimensionless. Speed is engine speed, in rpm. Torque is engine torque, in N·m.
Nitric oxide and nitrogen dioxide (NOx) mass fraction	NOx emissions	SI Core Engine	The SI Core Engine NOx emission mass fraction lookup table is a function of engine torque and engine speed, NOx Mass Fraction = ƒ(Speed, Torque), where: NOx Mass Fraction is the NOx emission mass fraction, dimensionless. Speed is engine speed, in rpm. Torque is engine torque, in N·m.
Carbon dioxide (CO₂) mass fraction	CO₂ emissions	SI Core Engine	The SI Core Engine CO₂ emission mass fraction lookup table is a function of engine torque and engine speed, CO2 Mass Fraction = ƒ(Speed, Torque), where: CO2 Mass Fraction is the CO₂ emission mass fraction, dimensionless. Speed is engine speed, in rpm. Torque is engine torque, in N·m.
Exhaust temperature	Engine exhaust calculation as a function of engine speed and load	SI Core Engine SI Controller	The exhaust temperature lookup table, $f_{T e x h}$ , is a function of engine load and engine speed $T_{e x h} = f_{T e x h} (L, N)$ where: T_exh is engine exhaust temperature, in K. L is normalized cylinder air mass or engine load, dimensionless. N is engine speed, in rpm.
Engine torque	Engine brake torque as a function of commanded torque and engine speed	Mapped SI Engine	The engine torque lookup table is a function of commanded engine torque and engine speed, T = ƒ(T_cmd, N), where: T is engine torque, in N·m. T_cmd is commanded engine torque, in N·m. N is engine speed, in rpm.
Engine air mass flow	Engine air mass flow as a function of commanded torque and engine speed	Mapped SI Engine	The engine air mass flow lookup table is a function of commanded engine torque and engine speed, ${\dot{m}}_{i n t k}$ = ƒ(T_cmd, N), where: ${\dot{m}}_{i n t k}$ is engine air mass flow, in kg/s. T_cmd is commanded engine torque, in N·m. N is engine speed, in rpm.
Engine fuel flow	Engine fuel flow as a function of commanded torque mass and engine speed	Mapped SI Engine	The engine fuel mass flow lookup table is a function of commanded engine torque and engine speed, MassFlow = ƒ(T_cmd, N), where: MassFlow is engine fuel mass flow, in kg/s. T_cmd is commanded engine torque, in N·m. N is engine speed, in rpm.
Engine exhaust temperature	Engine exhaust temperature as a function of commanded torque and engine speed	Mapped SI Engine	The engine exhaust temperature lookup table is a function of commanded engine torque and engine speed, T_exh = ƒ(T_cmd, N), where: T_exh is exhaust temperature, in K. T_cmd is commanded engine torque, in N·m. N is engine speed, in rpm.
Brake-specific fuel consumption (BSFC) efficiency	Brake-specific fuel consumption (BSFC) as a function of commanded torque and engine speed	Mapped SI Engine	The brake-specific fuel consumption (BSFC) efficiency is a function of commanded engine torque and engine speed, BSFC = ƒ(T_cmd, N), where: BSFC is BSFC, in g/kWh. T_cmd is commanded engine torque, in N·m. N is engine speed, in rpm.
Engine-out (EO) hydrocarbon emissions	EO hydrocarbon emissions as a function of commanded torque and engine speed	Mapped SI Engine	The engine-out hydrocarbon emissions are a function of commanded engine torque and engine speed, EO HC = ƒ(T_cmd, N), where: EO HC is engine-out hydrocarbon emissions, in kg/s. T_cmd is commanded engine torque, in N·m. N is engine speed, in rpm.
Engine-out (EO) carbon monoxide emissions	EO carbon monoxide emissions as a function of commanded torque and engine speed	Mapped SI Engine	The engine-out carbon monoxide emissions are a function of commanded engine torque and engine speed, EO CO = ƒ(T_cmd, N), where: EO CO is engine-out carbon monoxide emissions, in kg/s. T_cmd is commanded engine torque, in N·m. N is engine speed, in rpm.
Engine-out (EO) nitric oxide and nitrogen dioxide emissions	EO nitric oxide and nitrogen dioxide emissions as a function of commanded torque and engine speed	Mapped SI Engine	The engine-out nitric oxide and nitrogen dioxide emissions are a function of commanded engine torque and engine speed, EO NOx = ƒ(T_cmd, N), where: EO NOx is engine-out nitric oxide and nitrogen dioxide emissions, in kg/s. T_cmd is commanded engine torque, in N·m. N is engine speed, in rpm.
Engine-out (EO) carbon dioxide emissions	EO carbon dioxide emissions as a function of commanded torque and engine speed	Mapped SI Engine	The engine-out carbon dioxide emissions are a function of commanded engine torque and engine speed, EO CO2 = ƒ(T_cmd, N), where: EO CO2 is engine-out carbon dioxide emissions, in kg/s. T_cmd is commanded engine torque, in N·m. N is engine speed, in rpm.
Wastegate area percent command	Wastegate area percent command as a function of the commanded engine load and engine speed	SI Controller	The wastegate area percent command lookup table, $f_{W A P c m d}$ , is a function of the commanded engine load and engine speed $W A P_{c m d} = f_{W A P c m d} (L_{c m d}, N)$ where: WAP_cmd is wastegate area percentage command, in percent. L_cmd=L is commanded engine load, dimensionless. N is engine speed, in rpm.
Throttle position percent command	Throttle position percent command as a function of the throttle area percentage command	SI Controller	The throttle position percent command lookup table, $f_{T P P c m d}$ , is a function of the throttle area percentage command $T P P_{c m d} = f_{T P P c m d} (T A P_{c m d})$ where: TPP_cmd is throttle position percentage command, in percent. TAP_cmd is throttle area percentage command, in percent.
Throttle area percent command	Throttle area percent command as a function of commanded load and engine speed	SI Controller	The throttle area percent command lookup table, $f_{T A P c m d}$ , is a function of commanded load and engine speed $T A P_{c m d} = f_{T A P c m d} (L_{c m d}, N)$ where: TAP_cmd is throttle area percentage command, in percent. L_cmd=L is commanded engine load, dimensionless. N is engine speed, in rpm.
Spark advance	Spark advance as a function of estimated load and engine speed	SI Controller	The spark advance lookup table is a function of estimated load and engine speed. $S A = f_{S A} (L_{e s t}, N)$ where: SA is spark advance, in crank advance degrees. L_est=L is estimated engine load, dimensionless. N is engine speed, in rpm.
Commanded lambda	Commanded lambda as a function of estimated engine load and measured engine speed	SI Controller	The commanded lambda, $λ_{c m d}$ , lookup table is a function of estimated engine load and measured engine speed $λ_{c m d} = f_{λ c m d} (L_{e s t}, N)$ where: $λ_{c m d}$ is commanded relative AFR, dimensionless. L_est=L is estimated engine load, dimensionless. N is engine speed, in rpm.
Intake cam phaser angle command	Intake cam phaser angle command as a function of the engine load and engine speed	SI Controller	The intake cam phaser angle command lookup table, $f_{I C P C M D}$ , is a function of the engine load and engine speed $φ_{I C P C M D} = f_{I C P C M D} (L_{e s t}, N)$ where: $φ_{I C P C M D}$ is commanded intake cam phaser angle, in crank degrees advance from park. L_est=L is estimated engine load, dimensionless. N is engine speed, in rpm.
Commanded engine load	Commanded engine load as a function of the commanded torque and engine speed	SI Controller	The commanded engine load lookup table, $f_{L c m d}$ , is a function of the commanded torque and engine speed $L_{c m d} = f_{L c m d} (T_{c m d}, N)$ where: L_cmd=L is commanded engine load, dimensionless. T_cmd is commanded torque, in N·m. N is engine speed, in rpm.
Exhaust cam phaser angle	Exhaust cam phaser angle as a function of the engine load and engine speed	SI Controller	The exhaust cam phaser angle command lookup table, $f_{E C P C M D}$ , is a function of the engine load and engine speed $φ_{E C P C M D} = f_{E C P C M D} (L_{e s t}, N)$ where: $φ_{E C P C M D}$ is commanded exhaust cam phaser angle, in crank degrees retard from park. L_est=L is estimated engine load, dimensionless. N is engine speed, in rpm.

External Websites

Virtual Engine Calibration: Making Engine Calibration Part of the Engine Hardware Design Process

Map	Used For	In	Description
Volumetric efficiency	CI Engine Speed-Density Air Mass Flow Model	CI Core Engine CI Controller	The volumetric efficiency lookup table is a function of the intake manifold absolute pressure at intake valve closing (IVC) and engine speed $η_{v} = f_{η_{v}} (M A P, N)$ where: $η_{v}$ is engine volumetric efficiency, dimensionless. MAP is intake manifold absolute pressure, in KPa. N is engine speed, in rpm.
Optimal main start of injection (SOI) timing	CI Engine Torque Structure Model	CI Core Engine CI Controller	The optimal main start of injection (SOI) timing lookup table, ƒ_SOIc, is a function of the engine speed and injected fuel mass, SOI_c = ƒ_SOIc(F,N), where: SOI_c is optimal SOI timing, in degATDC. F is compression stroke injected fuel mass, in mg per injection. N is engine speed, in rpm.
Optimal intake manifold gas pressure	CI Engine Torque Structure Model	CI Core Engine CI Controller	The optimal intake manifold gas pressure lookup table, ƒ_MAP, is a function of the engine speed and injected fuel mass, MAP = ƒ_MAP(F,N), where: MAP is optimal intake manifold gas pressure, in Pa. F is compression stroke injected fuel mass, in mg per injection. N is engine speed, in rpm.
Optimal exhaust manifold gas pressure	CI Engine Torque Structure Model	CI Core Engine CI Controller	The optimal exhaust manifold gas pressure lookup table, ƒ_EMAP, is a function of the engine speed and injected fuel mass, EMAP = ƒ_EMAP(F,N), where: EMAP is optimal exhaust manifold gas pressure, in Pa. F is compression stroke injected fuel mass, in mg per injection. N is engine speed, in rpm.
Optimal intake manifold gas temperature	CI Engine Torque Structure Model	CI Core Engine CI Controller	The optimal intake manifold gas temperature lookup table, ƒ_MAT, is a function of the engine speed and injected fuel mass, MAT = ƒ_MAT(F,N), where: MAT is optimal intake manifold gas temperature, in K. F is compression stroke injected fuel mass, in mg per injection. N is engine speed, in rpm.
Optimal intake gas oxygen percent	CI Engine Torque Structure Model	CI Core Engine CI Controller	The optimal intake gas oxygen percent lookup table, ƒ_O2, is a function of the engine speed and injected fuel mass, O2PCT = ƒ_O2(F,N), where: O2PCT is optimal intake gas oxygen, in percent. F is compression stroke injected fuel mass, in mg per injection. N is engine speed, in rpm.
Optimal fuel rail pressure	CI Engine Torque Structure Model	CI Core Engine CI Controller	The optimal fuel rail pressure lookup table, ƒ_fuelp, is a function of the engine speed and injected fuel mass, FUELP = ƒ_fuelp(F,N), where: FUELP is optimal fuel rail pressure, in MPa. F is compression stroke injected fuel mass, in mg per injection. N is engine speed, in rpm.
Optimal gross indicated mean effective pressure	CI Engine Torque Structure Model	CI Core Engine CI Controller	The optimal gross indicated mean effective pressure lookup table, ƒ_imepg, is a function of the engine speed and injected fuel mass, IMEPG = ƒ_imepg(F,N), where: IMEPG is optimal gross indicated mean effective pressure, in Pa. F is compression stroke injected fuel mass, in mg per injection. N is engine speed, in rpm.
Optimal friction mean effective pressure	CI Engine Torque Structure Model	CI Core Engine CI Controller	The optimal friction mean effective pressure lookup table, ƒ_fmep, is a function of the engine speed and injected fuel mass, FMEP = ƒ_fmep(F,N), where: FMEP is optimal friction mean effective pressure, in Pa. F is compression stroke injected fuel mass, in mg per injection. N is engine speed, in rpm.
Optimal pumping mean effective pressure	CI Engine Torque Structure Model	CI Core Engine CI Controller	The optimal pumping mean effective pressure lookup table, ƒ_pmep, is a function of the engine speed and injected fuel mass, PMEP = ƒ_pmep(F,N), where: PMEP is optimal pumping mean effective pressure, in Pa. F is compression stroke injected fuel mass, in mg per injection. N is engine speed, in rpm.
Main SOI timing efficiency multiplier	CI Engine Torque Structure Model	CI Core Engine CI Controller	The main start of injection (SOI) timing efficiency multiplier lookup table, ƒ_SOIeff, is a function of the engine speed and main SOI timing relative to optimal timing, SOI_eff = ƒ_SOIeff(ΔSOI,N), where: SOI_eff is main SOI timing efficiency multiplier, dimensionless. ΔSOI is main SOI timing relative to optimal timing, in degBTDC. N is engine speed, in rpm.
Intake manifold gas pressure efficiency multiplier	CI Engine Torque Structure Model	CI Core Engine CI Controller	The intake manifold gas pressure efficiency multiplier lookup table, ƒ_MAPeff, is a function of the intake manifold gas pressure ratio relative to optimal pressure ratio and lambda, MAP_eff = ƒ_MAPeff(MAP_ratio,λ), where: MAP_eff is intake manifold gas pressure efficiency multiplier, dimensionless. MAP_ratio is intake manifold gas pressure ratio relative to optimal pressure ratio, dimensionless. λ is intake manifold gas lambda, dimensionless.
Intake manifold gas temperature efficiency multiplier	CI Engine Torque Structure Model	CI Core Engine CI Controller	The intake manifold gas temperature efficiency multiplier lookup table, ƒ_MATeff, is a function of the engine speed and intake manifold gas temperature relative to optimal temperature, MAT_eff = ƒ_MATeff(ΔMAT,N), where: MAT_eff is intake manifold gas temperature efficiency multiplier, dimensionless. ΔMAT is intake manifold gas temperature relative to optimal temperature, in K. N is engine speed, in rpm.
Intake manifold gas oxygen efficiency multiplier	CI Engine Torque Structure Model	CI Core Engine CI Controller	The intake manifold gas oxygen efficiency multiplier lookup table, ƒ_O2Peff, is a function of the engine speed and intake manifold gas oxygen percent relative to optimal, O2P_eff = ƒ_O2Peff(ΔO2P,N), where: O2P_eff is intake manifold gas oxygen efficiency multiplier, dimensionless. ΔO2P is intake gas oxygen percent relative to optimal, in percent. N is engine speed, in rpm.
Indicated mean effective pressure post inject correction	CI Engine Torque Structure Model	CI Core Engine CI Controller	The indicated mean effective pressure post inject correction lookup table, ƒ_IMEPpost, is a function of the engine speed and fuel rail pressure relative to optimal breakpoints, ΔIMEP_post = ƒ_IMEPpost(ΔSOI_post,F_post), where: ΔIMEP_post is indicated mean effective pressure post inject correction, in Pa. ΔSOI_post is indicated mean effective pressure post inject start of inject timing centroid, in degATDC. F_post is indicated mean effective pressure post inject mass sum, in mg per injection.
Fuel rail pressure efficiency multiplier	CI Engine Torque Structure Model	CI Core Engine CI Controller	The fuel rail pressure efficiency multiplier lookup table, ƒ_FUELPeff, is a function of the engine speed and fuel rail pressure relative to optimal breakpoints, FUELP_eff = ƒ_FUELPeff(ΔFUELP,N), where: FUELP_eff is fuel rail pressure efficiency multiplier, dimensionless. ΔFUELP is fuel rail pressure relative to optimal, in MPa. N is engine speed, in rpm.
Engine brake torque	CI Engine Simple Torque Model	CI Core Engine CI Controller	For the simple torque lookup table model, the CI engine uses a lookup table is a function of engine speed and injected fuel mass, $T_{b r a k e} = f_{T n f} (F, N)$ , where: Tq = T_brake is engine brake torque after accounting for engine mechanical and pumping friction effects, in N·m. F is injected fuel mass, in mg per injection. N is engine speed, in rpm.
Hydrocarbon (HC) mass fraction	HC emissions	CI Core Engine	The CI Core Engine HC emission mass fraction lookup table is a function of engine torque and engine speed, HC Mass Fraction = ƒ(Speed, Torque), where: HC Mass Fraction is the HC emission mass fraction, dimensionless. Speed is engine speed, in rpm. Torque is engine torque, in N·m.
Carbon monoxide (CO) mass fraction	CO emissions	CI Core Engine	The CI Core Engine CO emission mass fraction lookup table is a function of engine torque and engine speed, CO Mass Fraction = ƒ(Speed, Torque), where: CO Mass Fraction is the CO emission mass fraction, dimensionless. Speed is engine speed, in rpm. Torque is engine torque, in N·m.
Nitric oxide and nitrogen dioxide (NOx) mass fraction	NOx emissions	CI Core Engine	The CI Core Engine NOx emission mass fraction lookup table is a function of engine torque and engine speed, NOx Mass Fraction = ƒ(Speed, Torque), where: NOx Mass Fraction is the NOx emission mass fraction, dimensionless. Speed is engine speed, in rpm. Torque is engine torque, in N·m.
Carbon dioxide (CO₂) mass fraction	CO₂ emissions	CI Core Engine	The CI Core Engine CO₂ emission mass fraction lookup table is a function of engine torque and engine speed, CO2 Mass Fraction = ƒ(Speed, Torque), where: CO2 Mass Fraction is the CO₂ emission mass fraction, dimensionless. Speed is engine speed, in rpm. Torque is engine torque, in N·m.
Exhaust temperature	Engine exhaust temperature as a function of injected fuel mass and engine speed	CI Core Engine CI Controller	The lookup table for the exhaust temperature is a function of injected fuel mass and engine speed $T_{e x h} = f_{T e x h} (F, N)$ where: $T_{e x h}$ is exhaust temperature, in K. F is injected fuel mass, in mg per injection. N is engine speed, in rpm.
Engine brake torque	Engine brake torque as a function of commanded fuel mass and engine speed	Mapped CI Engine	The engine brake torque lookup table is a function of commanded fuel mass and engine speed, $T_{b r a k e}$ = ƒ(F, N), where: $T_{b r a k e}$ is engine torque, in N·m. F is commanded fuel mass, in mg per injection. N is engine speed, in rpm.
Engine air mass flow	Engine air mass flow as a function of commanded fuel mass and engine speed	Mapped CI Engine	The air mass flow lookup table is a function of commanded fuel mass and engine speed, ${\dot{m}}_{i n t k}$ = ƒ(F_max, N), where: ${\dot{m}}_{i n t k}$ is engine air mass flow, in kg/s. F_max is commanded fuel mass, in mg per injection. N is engine speed, in rpm.
Engine fuel flow	Engine fuel flow as a function of commanded fuel mass and engine speed	Mapped CI Engine	The engine fuel flow lookup table is a function of commanded fuel mass and engine speed, MassFlow= ƒ(F, N), where: MassFlow is engine fuel mass flow, in kg/s. F is commanded fuel mass, in mg per injection. N is engine speed, in rpm.
Engine exhaust temperature	Engine exhaust temperature as a function of commanded fuel mass and engine speed	Mapped CI Engine	The engine exhaust temperature table is a function of commanded fuel mass and engine speed, T_exh= ƒ(F, N), where: T_exhis exhaust temperature, in K. F is commanded fuel mass, in mg per injection. N is engine speed, in rpm.
Brake-specific fuel consumption (BSFC) efficiency	BSFC efficiency as a function of commanded fuel mass and engine speed	Mapped CI Engine	The brake-specific fuel consumption (BSFC) efficiency is a function of commanded fuel mass and engine speed, BSFC= ƒ(F, N), where: BSFC is BSFC, in g/kWh. F is commanded fuel mass, in mg per injection. N is engine speed, in rpm.
Engine-out (EO) hydrocarbon emissions	EO hydrocarbon emissions as a function of commanded fuel mass and engine speed	Mapped CI Engine	The engine-out hydrocarbon emissions are a function of commanded fuel mass and engine speed, EO HC= ƒ(F, N), where: EO HC is engine-out hydrocarbon emissions, in kg/s. F is commanded fuel mass, in mg per injection. N is engine speed, in rpm.
Engine-out (EO) carbon monoxide emissions	EO carbon monoxide emissions as a function of commanded fuel mass and engine speed	Mapped CI Engine	The engine-out carbon monoxide emissions are a function of commanded fuel mass and engine speed, EO CO= ƒ(F, N), where: EO CO is engine-out carbon monoxide emissions, in kg/s. F is commanded fuel mass, in mg per injection. N is engine speed, in rpm.
Engine-out (EO) nitric oxide and nitrogen dioxide	EO nitric oxide and nitrogen dioxide emissions as a function of commanded fuel mass and engine speed	Mapped CI Engine	The engine-out nitric oxide and nitrogen dioxide emissions are a function of commanded fuel mass and engine speed, EO NOx= ƒ(F, N), where: EO NOx is engine-out nitric oxide and nitrogen dioxide emissions, in kg/s. F is commanded fuel mass, in mg per injection. N is engine speed, in rpm.
Engine-out (EO) carbon dioxide emissions	EO carbon dioxide emissions as a function of commanded fuel mass and engine speed	Mapped CI Engine	The engine-out carbon dioxide emissions are a function of commanded fuel mass and engine speed, EO CO2= ƒ(F, N), where: EO CO2 is engine-out carbon dioxide emissions, in kg/s. F is commanded fuel mass, in mg per injection. N is engine speed, in rpm.
Commanded exhaust gas recirculation (EGR) valve area percent	Commanded exhaust gas recirculation (EGR) valve area percent as a function of commanded torque and engine speed	CI Controller	The commanded exhaust gas recirculation (EGR) valve area percent lookup table is a function of commanded torque and engine speed $E G R_{c m d} = f_{E G R c m d} (T r q_{c m d}, N)$ where: EGR_cmd is commanded EGR valve area percent, in percent. Trq_cmd is commanded engine torque, in N·m. N is engine speed, in rpm.
Variable geometry turbocharger (VGT) rack position	Variable geometry turbocharger (VGT) rack position as a function of commanded torque and engine speed	CI Controller	The variable geometry turbocharger (VGT) rack position lookup table is a function of commanded torque and engine speed $R P_{c m d} = f_{R P c m d} (T r q_{c m d}, N)$ where: RP_cmd is VGT rack position command, in percent. Trq_cmd is commanded engine torque, in N·m. N is engine speed, in rpm.
Commanded total fuel mass per injection	Commanded total fuel mass per injection as a function of torque command and engine speed	CI Controller	The commanded total fuel mass per injection table is a function of the torque command and engine speed $F_{c m d, t o t} = f_{F c m d, t o t} (T r q_{c m d}, N)$ where: F_cmd,tot = F is commanded total fuel mass per injection, in mg per cylinder. Trq_cmd is commanded engine torque, in N·m. N is engine speed, in rpm.
Main start-of-injection (SOI) timing	SOI timing as a function of commanded fuel mass and engine speed	CI Controller	The main start-of-injection (SOI) timing lookup table is a function of commanded fuel mass and engine speed $M A I N S O I = f (F_{c m d, t o t}, N)$ where: MAINSOI is the main start-of-injection timing, in degrees crank angle after top dead center (degATDC). F_cmd,tot = F is commanded fuel mass, in mg per injection. N is engine speed, in rpm.
Standard exhaust gas recirculation (EGR) mass flow	EGR mass flow as a function of the standard flow pressure ratio and EGR valve flow area	CI Controller	The standard exhaust gas recirculation (EGR) mass flow is a lookup table that is a function of the standard flow pressure ratio and EGR valve flow area ${\dot{m}}_{e g r, s t d} = f (\frac{M A P}{P_{e x h, e s t}}, E G R a p)$ where: ${\dot{m}}_{e g r, s t d}$ is the standard EGR valve mass flow, in g/s. P_exh,est is the estimated exhaust back-pressure, in Pa. MAP is the cycle average intake manifold absolute pressure, in Pa. EGRap is the measured EGR valve area, in percent.
Turbocharger pressure ratio	Turbocharger pressure ratio as a function of the standard air mass flow and corrected turbocharger speed	CI Controller	The turbocharger pressure ratio, corrected for variable geometry turbocharger (VGT) speed, is a lookup table that is a function of the standard air mass flow and corrected turbocharger speed, $P r_{t u r b o} = f ({\dot{m}}_{a i r s t d}, N_{v g t c o r r})$ , where: Pr_turbo is the turbocharger pressure ratio, corrected for VGT speed. ${\dot{m}}_{a i r s t d}$ is the standard air mass flow, in g/s. N_vgtcorr is the corrected turbocharger speed, in rpm/K^(1/2).
Turbocharger pressure ratio correction	Turbocharger pressure ratio correction as a function of the rack position	CI Controller	The variable geometry turbocharger pressure ratio correction is a function of the rack position, Pr_vgtcorr= ƒ(VGT_pos), where: Pr_vgtcorr is the turbocharger pressure ratio correction. VGT_pos is the variable geometry turbocharger (VGT) rack position.