# Generic Engine

Internal combustion engine with throttle and rotational inertia and time lag

## Library

Simscape / Driveline / Engines

## Description

The Generic Engine block represents a general internal combustion engine. Engine types include spark-ignition and diesel. Speed-power and speed-torque parameterizations are provided. A throttle physical signal input specifies the normalized engine torque. Optional dynamic parameters include crankshaft inertia and response time lag. A physical signal port outputs engine fuel consumption rate based on choice of fuel consumption model. Optional speed and redline controllers prevent engine stall and enable cruise control.

## Generic Engine Model

By default, the Generic Engine model uses a programmed relationship between torque and speed, modulated by the throttle signal.

### Engine Speed, Throttle, Power, and Torque

The engine model is specified by an engine power demand function g(Ω). The function provides the maximum power available for a given engine speed Ω. The block parameters (maximum power, speed at maximum power, and maximum speed) normalize this function to physical maximum torque and speed values.

The normalized throttle input signal T specifies the actual engine power. The power is delivered as a fraction of the maximum power possible in a steady state at a fixed engine speed. It modulates the actual power delivered, P, from the engine: P(Ω,T) = T·g(Ω). The engine torque is τ = P/Ω.

### Engine Power Demand

The engine power is nonzero when the speed is limited to the operating range, ΩminΩΩmax. The absolute maximum engine power Pmax defines Ω0 such that Pmax = g(Ω0). Define wΩ/Ω0 and g(Ω) ≡ Pmax·p(w). Then p(1) = 1 and dp(1)/dw = 0. The torque function is:

τ = (Pmax/Ω0)·[p(w)/w].

You can derive forms for p(w) from engine data and models. Generic Engine uses a third-order polynomial form:

p(w) = p1·w + p2·w2p3·w3

satisfying

p1 + p2p3 = 1, p1 + 2p2 – 3p3 = 0.

In typical engines, the pi are positive. This polynomial has three zeros, one at w = 0, and a conjugate pair. One of the pair is positive and physical; the other is negative and unphysical:

`${w}_{±}=\frac{1}{2}\left(-{p}_{2}±\sqrt{{p}_{2}^{2}+4{p}_{1}{p}_{3}}\right)$`

Typical Engine Power Demand Function

#### Restrictions on Engine Speed and Power

• For the engine power polynomial, there are restrictions, as shown, on the polynomial coefficients pi, to achieve a valid power-speed curve.

• If you use tabulated power or torque data, corresponding restrictions on P(Ω) remain.

Specify the speed and power as w = Ω/Ω0 and p = P(Ω)/P0 and define the boundaries as wmin = Ωmin/Ω0 and wmax = Ωmax/Ω0. Then:

• The engine speed is restricted to a positive range above the minimum speed and below the maximum speed: 0 ≤ wminwwmax.

• The engine power at minimum speed must be nonnegative: p(wmin) ≥ 0. If you use the polynomial form, this condition is a restriction on the pi:

p(wmin) = p1·wmin + p2·w2minp3·wmin3 ≥ 0.

• The engine power at maximum speed must be nonnegative: p(wmax) ≥ 0. If you use the polynomial form, this condition is a restriction on wmax: wmaxw+.

### Engine Power Forms for Different Engine Types

For the default parameterization, the block provides two choices of internal combustion engine types, each with different engine power demand parameters.

Power Demand
Coefficient
Engine Type:
Spark-IgnitionDiesel
p110.6526
p211.6948
p311.3474

### Idle Speed Controller Model

The idle speed controller adjusts the throttle signal to increase engine rotation below a reference speed according to the following expressions:

`$\Pi =\mathrm{max}\left({\Pi }_{i},{\Pi }_{c}\right)$`

and

`$\frac{d\left({\Pi }_{c}\right)}{dt}=\frac{0.5\cdot \left(1-\mathrm{tanh}\left(4\cdot \frac{\omega -{\omega }_{r}}{{\omega }_{t}}\right)\right)-{\Pi }_{c}}{\tau }$`

where:

• Π — Engine throttle

• Πi — Input throttle (port T)

• Πc — Controller throttle

• ω — Engine speed

• ωr — Idle speed reference

• ωt — Controller speed threshold

• τ — Controller time constant

The controlled throttle increases with a first-order lag from zero to one when engine speed falls below the reference speed. When the engine speed rises above the reference speed, the controlled throttle decreases from one to zero. When the difference between engine velocity and reference speed is smaller than the controller speed threshold, the tanh function smooths the time derivative of the controlled throttle. The controlled throttle is limited to the range 0–1. The engine uses the larger of the input and controlled throttle values. If engine time lag is included, the controller changes the input before the lag is computed.

### Redline Controller Model

While the idle speed controller determines the minimum throttle value for maintaining engine speed, the redline controller prevents excessive speed based on a maximum throttle input. To determine the maximum throttle value, the redline controller uses the idle speed controller model equation. However, for the redline controller:

• ωr is the redline speed reference.

• ωt is the redline speed threshold.

• τ is the redline time constant.

### Performance

To increase simulation speed, use the default option, ```No fuel consumption```, for the Fuel consumption model parameter.

If you select any other option for the Fuel consumption model, the block solves a nonlinear equation that is required for calculating fuel consumption. The block solves the equation even if the FC port, which reports the fuel consumption rate, is not connected to another block.

When the parameter is set to `No fuel consumption`, the block does not calculate fuel consumption, even if the FC port is connected to another block.

## Limitations

This block contains an engine time lag limitation.

### Engine Time Lag

Engines lag in their response to changing speed and throttle. The block optionally supports lag due to a changing throttle only. Time lag simulation increases model fidelity but reduces simulation performance.

## Ports

PortDescription
BRotational conserving port representing the engine block
FRotational Conserving port representing the engine crankshaft
TPhysical signal input port specifying the normalized engine throttle level
PPhysical signal output port reporting the instantaneous engine power, in W
FCPhysical signal output port reporting the fuel consumption rate, in kg/s

Port T accepts a signal with values in the range 0–1. The signal specifies the engine torque as a fraction of the maximum torque possible in steady state at fixed engine speed. The signal saturates at zero and one. Values below zero are interpreted as zero. Values above one are interpreted as one.

Port FC does not output data when the Fuel consumption model parameter is set to ```No fuel consumption```.

## Parameters

### Engine Torque

The table shows how the visibility of some parameters depends on the option that you choose for other parameters. To learn how to read the table, see Parameter Dependencies.

Engine Torque Parameter Dependencies

Engine Torque

Model parameterization — Choose ```Normalized 3rd-order polynomial matched to peak power```, ```Tabulated torque data```, or ```Tabulated power data```

Normalized 3rd-order polynomial matched to peak powerTabulated torque dataTabulated power data

Engine type — Choose `Spark-ignition` or `Diesel`

Speed vector

Maximum power

Torque vector

Speed at maximum power

Interpolation method — Choose `Linear` or `Smooth`

Maximum speed

Stall speed

Model parameterization

Select how to model the engine. Choose between these options, each of which enable other parameters:

• ```Normalized 3rd-order polynomial matched to peak power``` — Parametrize the engine with a power function controlled by power and speed characteristics. This is the default option.

• `Tabulated torque data` — Engine is parametrized by speed–torque table that you specify.

• `Tabulated power data` — Engine is parametrized by speed–power table that you specify.

Engine type

Choose type of internal combustion engine. Choose between `Spark-ignition`, the default option, and `Diesel`.

Selecting ```Normalized 3rd-order polynomial matched to peak power``` for the Model parameterization parameter exposes this parameter.

Maximum power

Maximum power Pmax that the engine can output. The default is `150` `kW`.

Selecting ```Normalized 3rd-order polynomial matched to peak power``` for the Model parameterization parameter exposes this parameter.

Speed at maximum power

Engine speed Ω0 at which the engine is running at maximum power. The default is `4500` `rpm`.

Selecting ```Normalized 3rd-order polynomial matched to peak power``` for the Model parameterization parameter exposes this parameter.

Maximum speed

Maximum speed Ωmax at which the engine can generate torque. The default is `6000` `rpm`.

During simulation, if Ω exceeds this maximum, the simulation stops with an error. The engine maximum speed Ωmax cannot exceed the engine speed at which the engine power becomes negative.

Selecting ```Normalized 3rd-order polynomial matched to peak power``` for the Model parameterization parameter exposes this parameter.

Stall speed

Minimum speed Ωmin at which the engine can generate torque. The default is `500` `rpm`.

During simulation, if Ω falls below this minimum, the engine torque is blended to zero.

Selecting ```Normalized 3rd-order polynomial matched to peak power``` for the Model parameterization parameter exposes this parameter.

Speed vector

Vector of values of the engine function's independent variable, the speed Ω. The default is ```[500, 1000, 2000, 3000, 4000, 5000, 6000, 7000]``` `rpm`.

The first and last speeds in the vector are interpreted as the stall speed and the maximum speed, respectively. If the speed falls below the stall speed, engine torque is blended to zero. If the speed exceeds the maximum speed, the simulation stops with an error.

Selecting `Tabulated torque data` or `Tabulated power data` for the Model parameterization parameter exposes this parameter.

Torque vector

Vector of values of the engine function's dependent variable, the torque τ. The default is ```[380, 380, 380, 380, 350, 280, 200, 80]``` `N*m`.

Selecting `Tabulated torque data` for the Model parameterization parameter exposes this parameter.

Power vector

Vector of values of the engine function's dependent variable, the power P. The default is ```[20, 40, 78, 120, 145, 148, 125, 60]``` `kW`.

Selecting `Tabulated power data` for the Model parameterization parameter exposes this parameter.

Interpolation method

Method to interpolate the engine speed–torque or speed–power function between discrete relative velocity values within the range of definition. Choose between `Linear`, the default choice, and `Smooth`.

Selecting `Tabulated torque data` or `Tabulated power data` for the Model parameterization parameter exposes this parameter.

### Dynamics

The table shows how the visibility of some parameters depends on the option that you choose for other parameters. To learn how to read the table, see Parameter Dependencies.

Dynamics Parameter Dependencies

Dynamics

Inertia — Choose `No inertia` or ```Specify inertia and initial velocity```

No inertiaSpecify inertia and initial velocity

Engine inertia

Initial velocity

Time constant — Choose ```No lag - Suitable for HIL simulation``` or ```Specify time constant and initial value```

No lag - Suitable for HIL simulationSpecify time constant and initial value

Engine time constant

Initial normalized throttle

Inertia

Select how to model the rotational inertia of the engine block. Choose between these options, each of which exposes other parameters:

• `No inertia` — Engine crankshaft is modeled with no inertia. This option is the default.

• ```Specify inertia and initial velocity``` — Engine crankshaft is modeled with rotational inertia and initial angular velocity.

Engine Inertia

Rotational inertia of the engine crankshaft. The default is `1` `kg*m^2`.

Selecting ```Specify inertia and initial velocity``` for the Inertia parameter exposes this parameter.

Initial velocity

Initial angular velocity Ω(0) of the engine crankshaft. The default is `800` `rpm`.

Selecting ```Specify inertia and initial velocity``` for the Inertia parameter exposes this parameter.

Time constant

Select how to model the time lag of the engine response. Choose between these options, each of which exposes other options:

• ```No lag — Suitable for HIL simulation``` — Engine reacts with no time lag. This option is the default.

• ```Specify time constant and initial value``` — Engine reacts with a time lag.

Selecting ```Specify time constant and initial value``` exposes other parameters.

Engine time constant

Engine time lag. The default is `0.2` `s`.

Selecting ```Specify time constant and initial value``` for the Time constant parameter exposes this parameter.

Initial normalized throttle

Initial normalized engine throttle T(0), ranging between zero and one. The default is `0`.

Selecting ```Specify time constant and initial value``` for the Time constant parameter exposes this parameter.

### Limits

Speed threshold

Width of the speed range over which the engine torque is blended to zero as Ω approaches the stall speed. The default is `100` `rpm`.

### Fuel Consumption

The table shows how the visibility of some parameters depends on the option that you choose for other parameters. To learn how to read the table, see Parameter Dependencies.

Fuel Consumption Parameter Dependencies

Fuel Consumption
Fuel consumption model — Choose `No fuel consumption`, `Constant per revolution`, ```Fuel consumption by speed and torque```, ```Brake specific fuel consumption by speed and torque```, or ```Brake specific fuel consumption by speed and brake mean effective pressure```
No fuel consumptionConstant per revolutionFuel consumption by speed and torqueBrake specific fuel consumption by speed and torqueBrake specific fuel consumption by speed and brake mean effective pressure

Fuel consumption per revolution

Displaced volume

Revolutions per cycle

Speed vector

Torque vector

Brake mean effective pressure vector

Fuel consumption table

Brake specific fuel consumption table

Interpolation method — Choose `Linear` or `Smooth`

Fuel consumption model

Select a model for calculating engine-fuel consumption. Model parameterizations are compatible with standard industrial data. Choose between these options:

• `No fuel consumption` — The default option

• `Constant per revolution`

• ```Fuel consumption by speed and torque```

• ```Brake specific fuel consumption by speed and torque```

• ```Brake specific fuel consumption by speed and brake mean effective pressure```

Some options expose other parameters. For more information, see the Fuel Consumption Parameter Dependencies table.

No fuel consumption

The block does not calculate fuel consumption even when the FC port, which reports the fuel consumption rate, is connected to another block. Selecting this option increases simulation speed.

Fuel consumption per revolution

Enter the volume of fuel consumed in one crankshaft revolution. The default is `25` `mg/rev`.

Selecting `Constant per revolution` for the Fuel consumption model parameter exposes this parameter.

Displaced volume

Enter the volume displaced by a piston stroke. The default is `400` `cm^3`.

Selecting ```Brake specific fuel consumption by speed and brake mean effective pressure``` for the Fuel consumption model parameter exposes this parameter.

Revolutions per cycle

Enter the number of crankshaft revolutions in one combustion cycle — e.g. `2` for a four-stroke engine, or `1` for a two-stroke engine. The default is `2`.

Selecting ```Brake specific fuel consumption by speed and brake mean effective pressure``` for the Fuel consumption model parameter exposes this parameter.

Speed vector

Enter vector of engine speeds used in lookup table parameterizations. Vector size must match Torque vector size. The default is `[1000, 2000, 3000, 4000, 5000, 6000]` `rpm`. Selecting ```Fuel consumption by speed and torque```, ```Brake specific fuel consumption by speed and torque```, or ```Brake specific fuel consumption by speed and brake mean effective pressure``` for the Fuel consumption model parameter exposes this parameter.

Torque vector

Enter vector of engine torques used in the lookup table parameterizations. Vector size must match Speed vector size. The default is ```[0, 80, 160, 200, 240, 320, 360, 400]``` `N*m`. Selecting ```Fuel consumption by speed and torque``` or ```Brake specific fuel consumption by speed and torque``` for the Fuel consumption model parameter exposes this parameter.

Fuel consumption table

Enter matrix with fuel consumption rates corresponding to engine speed and torque vectors. The number of rows must equal the number of elements in the Speed vector. The number of columns must equal the number of elements in the Torque vector. The default is ```[.5, .9, 1.4, 1.6, 1.9, 2.7, 3.4, 4.4; 1, 1.7, 2.7, 3.1, 3.6, 5, 6, 7.4; 1.4, 2.7, 4, 4.8, 5.6, 7.5, 8.5, 10.5; 2, 3.6, 5.8, 6.7, 8, 10.4, 11.7, 13.3; 2.5, 4.8, 7.9, 9.4, 10.8, 14, 16.2, 18.6; 3.1, 6, 10.3, 11.9, 13.8, 18.4, 22, 26.5]``` `g/s`.

Selecting ```Fuel consumption by speed and torque``` for the Fuel consumption model parameter exposes this parameter.

Brake mean effective pressure vector

Enter vector of brake mean effective pressure (BMEP) values. The default is `[0, 250, 500, 625, 750, 1000, 1150, 1250]` `kPa`. The BMEP satisfies the expression:

`$BMEP=T\cdot \left(\frac{2\pi \cdot {n}_{c}}{{V}_{d}}\right)$`

where:

• T — Output torque

• nc — Number of cycles per revolution

• Vd — Cylinder displaced volume

Selecting ```Brake specific fuel consumption by speed and brake mean effective pressure``` for the Fuel consumption model parameter exposes this parameter.

Brake specific fuel consumption table

Selecting ```Brake specific fuel consumption by speed and torque``` or ```Brake specific fuel consumption by speed and brake mean effective pressure``` for the Fuel consumption model parameter exposes this parameter.

For the ```Brake specific fuel consumption by speed and torque``` fuel model, enter the matrix with brake specific fuel consumption (BSFC) rates corresponding to engine speed and torque vectors. BSFC is the ratio of the fuel consumption rate to the output power. The number of rows must equal the number of elements in the Speed vector. The number of columns must equal the number of elements in the Torque vector.

For the ```Brake specific fuel consumption by speed and brake mean effective pressure``` fuel model, enter the matrix with brake specific fuel consumption (BSFC) rates corresponding to engine speed and brake mean effective pressure (BMEP) vectors. BSFC is the ratio of the fuel consumption rate to the output power. The number of rows must equal the number of elements in the Speed vector. The number of columns must equal the number of elements in the Brake mean effective pressure vector.

For both fuel-consumption models, the default is ```[410, 380, 300, 280, 270, 290, 320, 380; 410, 370, 290, 270, 260, 270, 285, 320; 415, 380, 290, 275, 265, 270, 270, 300; 420, 390, 310, 290, 285, 280, 280, 285; 430, 410, 340, 320, 310, 300, 310, 320; 450, 430, 370, 340, 330, 330, 350, 380]``` `g/hr/kW`.

Interpolation method

Select the interpolation method used to calculate fuel consumption at intermediate speed-torque values. Methods are `Linear` and `Smooth`. Outside the data range, fuel consumption is held constant at the last value given in the lookup table. Selecting ```Fuel consumption by speed and torque```, ```Brake specific fuel consumption by speed and torque```, or ```Brake specific fuel consumption by speed and brake mean effective pressure``` for the Fuel consumption model parameter exposes this parameter.

### Speed Control

The table shows how the visibility of some parameters depends on the option that you choose for other parameters. To learn how to read the table, see Parameter Dependencies.

Speed Control Parameter Dependencies

Speed Control

Idle speed control — Choose `Off` or `On`

OffOn

Idle speed reference

Controller time constant

Redline control

Redline control — Choose `Off` or `On`

OffOn

Redline speed

Redline time constant

Redline threshold speed

Idle speed control

Select speed control model. The options are:

• `Off` — Omit idle speed controller. Throttle input is used directly. This option is the default.

• `On` — Include idle speed controller to prevent engine stalling. This option exposes other parameters. For more information, see Idle Speed Controller Model.

Idle speed reference

Enter the value of the speed reference below which speed increases, and above which speed decreases. The default is `1000` `rpm`.

Selecting `On` for the Idle speed control parameter exposes this parameter.

Controller time constant

Enter the value of the time constant associated with an increase or decrease of the controlled throttle. The constant value must be positive. The default is `1` `s`.

Selecting `On` for the Idle speed control parameter exposes this parameter.

Controller threshold speed

Parameter used to smooth the controlled throttle value when the engine’s rotational speed crosses the idle speed reference. For more information, see Idle Speed Controller Model. Large values decrease controller responsiveness. Small values increase computational cost. This parameter must be positive. The default is `1` `rpm`.

Selecting `On` for the Idle speed control parameter exposes this parameter.

Redline control

Select redline control model. Options include `Off` and `On`.

• `Off` — Omit redline controller. Throttle depends only on the idle speed controller. This option is the default.

• `On` — Include redline controller to prevent excessive speed. This option exposes other parameters.

Redline speed

Enter the value of the speed reference above which the redline control activates. The default is `5000` `rpm`.

Selecting `On` for the Redline control parameter exposes this parameter.

Redline time constant

Enter the value of the time constant associated with an increase or decrease of the controlled throttle. The constant value must be positive. The default is `1` `s`.

Selecting `On` for the Redline control parameter exposes this parameter.

Redline threshold speed

Specify the width of the region around the redline speed where the controller goes from fully enabled to not enabled. The block uses this parameter for smoothing the controlled throttle value when the engine’s rotational speed crosses the redline speed reference. Large values decrease controller responsiveness. Small values increase computational cost. This parameter must be positive. The default is `1` `rpm`.

Selecting `On` for the Redline control parameter exposes this parameter.

## Real-Time Simulation

### Hardware-in-the-Loop Simulation

For optimal simulation performance, set the Dynamics > Time Constant parameter to ```No time constant - Suitable for HIL simulation```.

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