Generic Engine

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, Ω_min ≤ Ω ≤ Ω_max. The absolute maximum engine power P_max defines Ω₀ such that P_max = g(Ω₀). Define w ≡ Ω/Ω₀ and g(Ω) ≡ P_max·p(w). Then p(1) = 1 and dp(1)/dw = 0. The torque function is:

τ = (P_max/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·w² – p₃·w³

satisfying

p₁ + p₂ – p₃ = 1, p₁ + 2p₂ – 3p₃ = 0.

In typical engines, the p_i 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:

$w_{\pm} = \frac{1}{2} (- p_{2} \pm \sqrt{p_{2}^{2} + 4 p_{1} p_{3}})$

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 p_i, 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 w_min = Ω_min/Ω₀ and w_max = Ω_max/Ω₀. Then:

The engine speed is restricted to a positive range above the minimum speed and below the maximum speed: 0 ≤ w_min ≤ w ≤ w_max.
The engine power at minimum speed must be nonnegative: p(w_min) ≥ 0. If you use the polynomial form, this condition is a restriction on the p_i:
p(w_min) = p₁·w_min + p₂·w²_min – p₃·w_min³ ≥ 0.
The engine power at maximum speed must be nonnegative: p(w_max) ≥ 0. If you use the polynomial form, this condition is a restriction on w_max: w_max ≤ w₊.

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:
Power Demand Coefficient	Spark-Ignition	Diesel
p₁	1	0.6526
p₂	1	1.6948
p₃	1	1.3474

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:

$Π = \max (Π_{i}, Π_{c})$

and

$\frac{d (Π_{c})}{d t} = \frac{0.5 \cdot (1 - \tanh (4 \cdot \frac{ω - ω_{r}}{ω_{t}})) - Π_{c}}{τ}$

where:

Π — Engine throttle
Π_i — Input throttle (port T)
Π_c — Controller throttle
ω — Engine speed
ω_r — Idle speed reference
ω_t — 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:

ω_r is the redline speed reference.
ω_t 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

Port	Description
B	Rotational conserving port representing the engine block
F	Rotational Conserving port representing the engine crankshaft
T	Physical signal input port specifying the normalized engine throttle level
P	Physical signal output port reporting the instantaneous engine power, in W
FC	Physical 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 power	Tabulated torque data	Tabulated 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.