Simulink - Vehicle Acceleration - 4

1. Introduction
The limitation of the previous model is that the look up table was a single input or one dimension table. So although it was possible to write a table giving the engine torque at various speeds, it was not possible to allow for any variation in throttle position. By using a two dimensional look up table it is possible to have two inputs, so a table can be written with values for engine torque at different engine speeds and at different throttle positions.

2. Model Development
This model is only sightly different to the previous one. The one dimensional look up table block is replaced by the two dimensional look up table block. One input to this table is still the engine speed obtained from the feedback loop taken from the vehicle speed. The other input is from the signal builder block used to synthesise the specified throttle positions - going from shut to fully open in 1 second then remaining fully open for the remaining 9 seconds of the simulation.

The major task is to construct the contents of the look up table. Curves showing how engine torque varies with engine speed at full throttle are published for many engines, however part throttle curves are not normally available. Some estimation (or guesswork) is required to derive appropriate data. For throttle openings of 1/4, 1/2, 3/4 it is probably reasonable to assume (for engines that are not turbo-charged) that the engine torque is pro - rata that of the full throttle torque at the same engine speed. Deciding on a value at small throttle openings is less straight forward. Putting in zero torque means the simulation never gets started. putting in a small nominal value, say 1, gives a low initial acceleration. It is probably best to put a small nominal value for closed throttle and then a larger value for 0.1 fully open throttle.
One point that should be made is that in practice a car with a manual transmission will have the engine revved somewhat while the clutch is released to pull away.
The closed throttle engine torque values chosen were 10 Nm for all engine speeds. The data put in the table is given below:

Input row values (proportion of throttle opening): [0 0.25 0.5 0.75 1]
Input column values (engine rpm): [0 1500 3000 4500 6000]
Resulting output (engine torque): [10 10 10 10 10; 10 25 51 51 50; 15 90 103 102 100; 22 135 155 154 150; 30 180 205 203 195]

3. Results
Again the model is limited by only having 1 gear ratio and the engine rpm at 6 seconds is about 8000, which is too high for the engine the concerned. The time to reach 60 mph is indicated as just under 6 seconds which would not be achieved in practice!

David J Grieve, 15th October 2004.