Internal combustion engine#

The Internal combustion engine (ICE) block is a generalized model of an internal combustion engine, the moment is calculated relative to the values of power and angular velocity in r.u. by a third-order polynomial.

A normalized throttle signal is supplied to the engine input, taking a value from 0 to 1. A moment is created at the output port, see Fig. 1 :

External_parameters — Fig. 1 - ICE block icon, external parameters#

Torque calculation for ICE with forced ignition and compression ignition

Since the calculations are carried out in r.u., the relative angular velocity is first calculated (1):

(1)#\[\omega_{о.е.} = \omega_{ДВС}/\omega_{макс.мощ.}\]

where:

\(\omega_{ICE}\) - ICE angular velocity, [rad/s];

\(\omega_{max.pow.}\) - ICE angular speed at maximum power (rotation speed at maximum power, values are converted to [rad/s] inside the block).

Power in relative units is calculated by the formula (2):

(2)#\[P_{о.е.}(\omega_{о.е.})=s_{1} \cdot \omega_{о.е.} +s_{2} \cdot \omega_{о.е.}^2+s_{3} \cdot \omega_{о.е.}^3\]

Then Тогда \(P_{s.u.}(1)\) = 1 и \(dP(1)/d\omega\) = 0.

In named units, the power is (3):

(3)#\[P_{ДВС} = P_{макс.} \cdot P_{о.е.}(\omega_{о.е.})\]

We know that ICE torque formula is (4):

(4)#\[T_{ДВС} = P_{ДВС}/\omega_{ДВС}.\]

Then, taking into account the relative units and the throttle signal, the torque formula will take the form (5):

(5)#\[T_{ДВС}=\frac{P_{макс.}⋅P_{о.е.}(ω_{о.е.} )}{ω_{о.е.}⋅ω_{макс.мощ.}}\cdotупр.\]

where control is a throttle input signal (port 1 signal in Fig. 1 above).

Characterization factor	Engine type: ICE with forced ignition	Engine type: ICE with compression ignition
\(s_1\)	1	0.6526
\(s_2\)	1	1.6948
\(s_3\)	-1	-1.3474

Calculation of torque for ICE with calculation of factors

This type of engine is suitable for your calculations when, instead of speed at maximum power, you know the maximum engine torque \(T_{max.}\) and its speed at maximum torque \(\omega_{max.moment}\)

In this type, the speed at maximum power is calculated using a formula (6):

(6)#\[\omega_{макс.мощ.}=\frac{3P_{макс.}+\sqrt{P_{макс.}\cdot (9\cdot P_{макс.}-8 \cdot T_{макс.}\cdot \omega_{макс.момент.})}}{4\cdot T_{макс.}}\]

Coefficients are calculated according to formulas (7), (8), (9):

(7)#\[s_1= \frac{3-4\cdot\frac{\omega_{макс.момент.}}{\omega_{макс.мощ.}}}{2\cdot(1-\frac{\omega_{макс.момент.}}{\omega_{макс.мощ.}})};\]

(8)#\[s_2=-\frac{\frac{\omega_{макс.момент.}}{\omega_{макс.мощ.}}}{\frac{\omega_{макс.момент.}}{\omega_{макс.мощ.}}-1};\]

(9)#\[s_3=\frac{1}{2\cdot(\frac{\omega_{макс.момент.}}{\omega_{макс.мощ.}}-1)}.\]

The moment is calculated using a formula (10):

(10)#\[T_{ДВС}(\omega_{о.е.}) =\frac{2\cdot T_{макс.}}{3-\frac{\omega_{макс.момент.}}{\omega_{макс.мощ.}}}(s_{1} +s_{2} \cdot \omega_{о.е.}+s_{3} \cdot \omega_{о.е.}^2) \cdot упр\]

Idling

The engine incorporates the idle control system to automatically control the throttle in order to maintain preset angular frequency. The control signal is generated in accordance with the derivative (11):

(11)#\[\frac{d(упр_{x.x.})}{dt} =\frac{0.5 \cdot (1 - \tanh 4 \frac{\omega_{ДВС}-\omega_{уст.х.х}}{\omega_{порог х.х.}} )}{\tau_{х.х.}}, \]

where:

\(\omega_{idling setpoint}\) - setpoint for idle speed;

\(\omega_{idling threshold}\) – lower threshold of idle rotation frequency;

\(\tau_{idling}\) – time constant of idle speed controller;

It should be noted that if there is an input control signal, the signal with the highest value is chosen (12):

(12)#\[упр(упр_{х.х.},упр_{вх.})=MAX(упр_{х.х.},упр_{вх.})\]

Limitations in the model

It is worth noting a couple of important limitations when modeling with this block:

The block limits the engine rotational frequency to a range above the minimum speed \(0< \omega_{min.} < \omega_{ICE}. \). However, this does not mean that the operation of ICE above the maximum power speed is permissible. After reaching the maximum power, the function \(P_{r.u.}(\omega_{r.u.}) \) will decrease and the torque may become negative. When the negative torque is reached, ICE automatically stalls: the torque and control signal become zero;
Engine power at minimum frequency \(P_{ICE} (ω_{min.} )\) shall be positive;
Engine power at maximum speed \(P_{ICE} (ω_{max.pow.} )\) shall be positive.

Important points in ICE modeling

When the angular frequency decreases below \(\omega_{min.}\), ICE gets tuned off, see Fig. 2 below, (the generated torque and control signal are 0);
ICE, as in real life, will not start by itself, to start the engine it is necessary to apply an angular speed higher than \(\omega_{min.} \), for example, at the moment of inertia connected to the engine, indicate the initial speed.

Power/torque diagram of ICE — Fig. 2 ICE power/torque diagram#

1. Properties#

Property	Default Value	Description	Units of measurement
Speed at maximum power	6858.0	-	rpm
Maximum power	230.0	-	kW
Stall speed	200.0	-	rpm
Engine time constant	0.1	-	s
Idle speed control reference	1000.0	-	rpm
Idle speed control threshold	300.0	-	rpm
Idle speed control controller time constant	0.1	-	s
Fuel consumption coefficient	0.001	-	l/s/W
Engine type: Spark-ignition; Diesel; Generic	Spark-ignition	-	-
Maximum torque, available when selecting `Engine type` - `Generic`	360.0	-	N\(\cdot\)m
Speed at maximum torque, available when selecting `Engine type` - `Generic`	4300.0	-	rpm
Stall speed threshold	10	-	rpm

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Command signal	Input	-	-	Automation
Torque	Output	-	N\(\cdot\)m	Rotational motion

In order to see the connection capabilities of the block, you need to go to page Description of block ports