Simulink - Vehicle Acceleration 5 |
2. The Model
The Matlab Simulink model is shown in the diagram below:
The entries in the 2d look up table are forclosed and fully open throttle
and for 0 and 5000 rpm. Values entered were [0 1], [0 5000] with outputs
estimated to be [0.001 0.005; 0.005 0.128]
The first gain block assumes stoichiometric combustion and multiplies the air
flow by 0.068 to give the fuel mass flow rate.
The next gain block, Gain 1, multiplies the fuel mass flow rate by 46000000
to give a value for the power theoretically available from burning fuel at the rate
it is being used. This needs to be converted to torque, which can normally be done by dividing
by the engine angular velocity. However, this does not work when the engine is
starting from rest as a division by zero stops the simulation and at low engine speeds the
torque calculated is unrealistically high. To get over this the constant is added to the
value of the engine angular velocity that is fed back, before it is inverted
with the 'Math Function'. Choosing an appropriate constant is tricky. It is
probably reasonable to choose the approximate tick over speed, say 900 rpm
(94.2 radians/s) However putting this in the model gives a high torque peak, which although
it quickly drops down, is some twice the maximum that the engine can develop.
For this reason a value equivalent to letting the clutch out at 1800 rpm (188.5 rad/s)
has been used.
Gain 2 contains a value of 0.3, to represent the overall efficiency of the engine.
Gain 3 contains a value of 10, the assumed gear ratio.
Gain 4 contains the value of 1/wheel radius to give the tractive force provided
at the tyre periphery.
The summing point subtracts the air resistance computed by the inner feed back loop,
the output is then the net force available to accelerate the vehicle.
Gain 5 is 1/equivalent mass of the vehicle, the output is the acceleration. This is fed into the
integrator and the output from this is the vehicle velocity.
3. Results
This model shows a 0 - 60 time of about 6 seconds (the engine is by this time
theoretically running above its maximum capability as there is only one gear available and
it is too low to reach 60 mph).
David J Grieve, 4th November 2004