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 sparkignition (SI) and compressionignition (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.
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 GTPOWER models from the GTSUITE modeling library in a Simulink^{®}based virtual dynamometer. MathWorks used the ModelBased Calibration Toolbox™ to create designofexperiment (DoE) test plans. The Simulinkbased virtual dynamometer executed the DoE test plan on GTPOWER 1.5–L SI and CI reference engines. MathWorks used the ModelBased Calibration Toolbox to develop the engine plant model calibration maps from the GTPOWER.
The engine controller model calibration maps in the reference applications represent the optimal openloop control commands for given engine operating points.
To develop the calibration maps for the SI engine controller, MathWorks used the GTPOWER reference engine models in a virtual engine calibration optimization (VECO) process. The process optimized the openloop 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 GTPOWER 1.5–L CI reference model operated at minimum brakespecific fuel consumption (BSFC).
In the engine models, the Powertrain Blockset blocks implement these calibration maps.
Map  Used For  In  Description 

Volumetric efficiency  The volumetric efficiency lookup table is a function of the intake manifold absolute pressure at intake valve closing (IVC) and engine speed ${\eta}_{v}={f}_{{\eta}_{v}}(MAP,N)$ where:
 
Optimal main start of injection (SOI) timing 
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:
 
Optimal intake manifold gas pressure 
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:
 
Optimal exhaust manifold gas pressure 
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:
 
Optimal intake manifold gas temperature 
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:
 
Optimal intake gas oxygen percent 
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:
 
Optimal fuel rail pressure 
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:
 
Optimal gross indicated mean effective pressure 
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:
 
Optimal friction mean effective pressure 
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:
 
Optimal pumping mean effective pressure 
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:
 
Main SOI timing efficiency multiplier 
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:
 
Intake manifold gas pressure efficiency multiplier 
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:
 
Intake manifold gas temperature efficiency multiplier 
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:
 
Intake manifold gas oxygen efficiency multiplier 
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:
 
Indicated mean effective pressure post inject correction 
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:
 
Fuel rail pressure efficiency multiplier 
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:
 
Engine brake torque  For the simple torque lookup table model, the CI engine uses a lookup table is a function of engine speed and injected fuel mass, ${T}_{brake}={f}_{Tnf}(F,N)$, where:
 
Hydrocarbon (HC) mass fraction  HC emissions  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:
 
Carbon monoxide (CO) mass fraction  CO emissions  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:
 
Nitric oxide and nitrogen dioxide (NOx) mass fraction  NOx emissions  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:
 
Carbon dioxide (CO_{2}) mass fraction  CO_{2} emissions  The CI Core Engine CO_{2} emission mass fraction lookup table is a function of engine torque and engine speed, CO2 Mass Fraction = ƒ(Speed, Torque), where:
 
Exhaust temperature  Engine exhaust temperature as a function of injected fuel mass and engine speed  The lookup table for the exhaust temperature is a function of injected fuel mass and engine speed ${T}_{exh}={f}_{Texh}(F,N)$ where:
 
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, ${T}_{brake}$ = ƒ(F, N), where:

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, ${\dot{m}}_{intk}$ = ƒ(F_{max}, N), where:

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:

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:

Brakespecific fuel consumption (BSFC) efficiency  BSFC efficiency as a function of commanded fuel mass and engine speed  Mapped CI Engine 
The brakespecific fuel consumption (BSFC) efficiency is a function of commanded fuel mass and engine speed, BSFC= ƒ(F, N), where:

Engineout (EO) hydrocarbon emissions  EO hydrocarbon emissions as a function of commanded fuel mass and engine speed  Mapped CI Engine 
The engineout hydrocarbon emissions are a function of commanded fuel mass and engine speed, EO HC= ƒ(F, N), where:

Engineout (EO) carbon monoxide emissions  EO carbon monoxide emissions as a function of commanded fuel mass and engine speed  Mapped CI Engine 
The engineout carbon monoxide emissions are a function of commanded fuel mass and engine speed, EO CO= ƒ(F, N), where:

Engineout (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 engineout nitric oxide and nitrogen dioxide emissions are a function of commanded fuel mass and engine speed, EO NOx= ƒ(F, N), where:

Engineout (EO) carbon dioxide emissions  EO carbon dioxide emissions as a function of commanded fuel mass and engine speed  Mapped CI Engine 
The engineout carbon dioxide emissions are a function of commanded fuel mass and engine speed, EO CO2= ƒ(F, N), where:

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 $EG{R}_{cmd}={f}_{EGRcmd}(Tr{q}_{cmd},N)$ where:

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 $R{P}_{cmd}={f}_{RPcmd}(Tr{q}_{cmd},N)$ where:

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 ${F}_{cmd,tot}={f}_{Fcmd,tot}(Tr{q}_{cmd},N)$ where:

Main startofinjection (SOI) timing  SOI timing as a function of commanded fuel mass and engine speed  CI Controller  The main startofinjection (SOI) timing lookup table is a function of commanded fuel mass and engine speed $$MAINSOI=f({F}_{cmd,tot},N)$$ where:

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 $${\dot{m}}_{egr,std}=f(\frac{MAP}{{P}_{exh,est}},EGRap)$$ where:

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, $$P{r}_{turbo}=f({\dot{m}}_{airstd},{N}_{vgtcorr})$$, where:

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:

In the engine models, the Powertrain Blockset blocks implement these calibration maps.
Map  Used for  In  Description 

Engine volumetric efficiency  The engine volumetric efficiency lookup table, ${f}_{{\eta}_{v}}$, is a function of intake manifold absolute pressure and engine speed ${\eta}_{v}={f}_{{\eta}_{v}}(MAP,N)$ where:
 
Cylinder volume at intake valve close table (IVC)  The cylinder volume at intake valve close table (IVC), ${f}_{Vivc}$ is a function of the intake cam phaser angle ${V}_{IVC}={f}_{Vivc}({\phi}_{ICP})$ where:
 
Trapped mass correction  The trapped mass correction factor table, ${f}_{TMcorr}$, is a function of the normalized density and engine speed $T{M}_{corr}={f}_{TMcorr}({\rho}_{norm},N)$ where:
 
Air mass flow at cam phaser angles  The phaser intake mass flow model lookup table is a function of exhaust cam phaser angles and trapped air mass flow ${\dot{m}}_{intkideal}={f}_{intkideal}({\phi}_{ECP},T{M}_{flow})$ where:
 
Air mass flow correction  The intake air mass flow correction lookup table, ${f}_{aircorr}$, is a function of ideal load and engine speed ${\dot{m}}_{air}={\dot{m}}_{intkideal}{f}_{aircorr}({L}_{ideal},N)$ where:
 
Inner torque  The inner torque lookup table, ${f}_{Tqinr}$, is a function of engine speed and engine load, $T{q}_{inr}={f}_{Tqinr}(L,N)$, where:
 
Friction torque  The friction torque lookup table, ${f}_{Tfric}$, is a function of engine speed and engine load, $${T}_{fric}={f}_{Tfric}\left(L,N\right)$$, where:
 
Pumping torque 
The pumping torque lookup
table, ƒ_{Tpump}, is a function of engine speed and
injected fuel mass,
 
Optimal spark advance  The optimal spark lookup table, ${f}_{SAopt}$, is a function of engine speed and engine load, $S{A}_{opt}={f}_{SAopt}(L,N)$, where:
 
Spark efficiency  The spark efficiency lookup table, ${f}_{Msa}$, is a function of the spark retard from optimal $\begin{array}{l}{M}_{sa}={f}_{Msa}(\Delta SA)\\ \Delta SA=S{A}_{opt}SA\end{array}$ where:
 
Lambda efficiency  The lambda efficiency lookup table, ${f}_{M\lambda}$, is a function of lambda, ${M}_{\lambda}={f}_{M\lambda}(\lambda )$, where:
 
Simple torque  For the simple torque lookup table model, the SI engine uses a lookup table map that is a function of engine speed and load, ${T}_{brake}={f}_{TnL}(L,N)$, where:
 
Hydrocarbon (HC) mass fraction  HC emissions  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:
 
Carbon monoxide (CO) mass fraction  CO emissions  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:
 
Nitric oxide and nitrogen dioxide (NOx) mass fraction  NOx emissions  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:
 
Carbon dioxide (CO_{2}) mass fraction  CO_{2} emissions  The SI Core Engine CO_{2} emission mass fraction lookup table is a function of engine torque and engine speed, CO2 Mass Fraction = ƒ(Speed, Torque), where:
 
Exhaust temperature  Engine exhaust calculation as a function of engine speed and load  The exhaust temperature lookup table, ${f}_{Texh}$, is a function of engine load and engine speed ${T}_{exh}={f}_{Texh}(L,N)$ where:
 
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:

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, ${\dot{m}}_{intk}$ = ƒ(T_{cmd}, N), where:

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:

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:

Brakespecific fuel consumption (BSFC) efficiency  Brakespecific fuel consumption (BSFC) as a function of commanded torque and engine speed  Mapped SI Engine 
The brakespecific fuel consumption (BSFC) efficiency is a function of commanded engine torque and engine speed, BSFC = ƒ(T_{cmd}, N), where:

Engineout (EO) hydrocarbon emissions  EO hydrocarbon emissions as a function of commanded torque and engine speed  Mapped SI Engine 
The engineout hydrocarbon emissions are a function of commanded engine torque and engine speed, EO HC = ƒ(T_{cmd}, N), where:

Engineout (EO) carbon monoxide emissions  EO carbon monoxide emissions as a function of commanded torque and engine speed  Mapped SI Engine 
The engineout carbon monoxide emissions are a function of commanded engine torque and engine speed, EO CO = ƒ(T_{cmd}, N), where:

Engineout (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 engineout nitric oxide and nitrogen dioxide emissions are a function of commanded engine torque and engine speed, EO NOx = ƒ(T_{cmd}, N), where:

Engineout (EO) carbon dioxide emissions  EO carbon dioxide emissions as a function of commanded torque and engine speed  Mapped SI Engine 
The engineout carbon dioxide emissions are a function of commanded engine torque and engine speed, EO CO2 = ƒ(T_{cmd}, N), where:

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, ${f}_{WAPcmd}$, is a function of the commanded engine load and engine speed $WA{P}_{cmd}={f}_{WAPcmd}\left({L}_{cmd},N\right)$ where:

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, ${f}_{TPPcmd}$, is a function of the throttle area percentage command $TP{P}_{cmd}={f}_{TPPcmd}\left(TA{P}_{cmd}\right)$ where:

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, ${f}_{TAPcmd}$, is a function of commanded load and engine speed $TA{P}_{cmd}={f}_{TAPcmd}\left({L}_{cmd},N\right)$ where:

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. $SA={f}_{SA}\left({L}_{est},N\right)$ where:

Commanded lambda  Commanded lambda as a function of estimated engine load and measured engine speed  SI Controller  The commanded lambda, $${\lambda}_{cmd}$$, lookup table is a function of estimated engine load and measured engine speed ${\lambda}_{cmd}={f}_{\lambda cmd}\left({L}_{est},N\right)$ where:

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, ${f}_{ICPCMD}$, is a function of the engine load and engine speed ${\phi}_{ICPCMD}={f}_{ICPCMD}\left({L}_{est},N\right)$ where:

Commanded engine load  Commanded engine load as a function of the commanded torque and engine speed  SI Controller  The commanded engine load lookup table, ${f}_{Lcmd}$, is a function of the commanded torque and engine speed ${L}_{cmd}={f}_{Lcmd}\left({T}_{cmd},N\right)$ where:

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, ${f}_{ECPCMD}$, is a function of the engine load and engine speed ${\phi}_{ECPCMD}={f}_{ECPCMD}\left({L}_{est},N\right)$ where:

CI Controller  CI Core Engine  Mapped SI Engine  Mapped CI Engine  SI Controller  SI Core Engine