## Simulink - Vehicle Acceleration 3

1. Introduction
In this example, model 1 is modified to provide a more realistic variation in engine torque by using a one dimensional look up table. The data below is estimated from the following graph (which is taken from the handbook for a 1983 Porsche 944 which has a 2.5 litre engine): 2. Setting up the Model
The one dimensional linear interpolation look up table is the most simple available in Simulink. Values for the input are given and an equal number of values for the output must be given, which can be by a mathematical relationship.
For this model, having dragged the block into the model window, move the cursor over the block and click the right mouse button and click again on 'Lookup parameters'. On the top line, within the [ ] brackets, the 13 engine speeds are entered:

[0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000]
In the next line the 13 estimated torque values for these engine speeds are entered: [100 150 165 177 190 201 205 204 203 202 201 201 195] Obviously the torque is zero at zero rpm but the value of 100 allows for slipping the clutch to move off. The output (torque) from the look up table then passes through a gain block with a value of 10 (the assumed overall gear ratio) and then through another gain block (Gain 1) equal to 1/wheel radius. The output from this is the driving force from the engine at the wheel periphery. The summing point then subtracts the opposing force of the air resistance which comes from the feedback loop. This leaves the net force available to accelerate the car. This force goes through a gain block (Gain 2) to give the acceleration and this is integrated to give the velocity in m/s.
This velocity is integrated (Integrator 1) to give the distance traveled.

As in the previous models the velocity is fed back and squared in the 'Dot Product' block to give v2 which goes through the gain block (Gain 3 = 0.4375) to give the opposing air resistance. The velocity is also fed back in a second loop and multiplied by 1/wheel radius (Gain 4) to give wheel angular velocity, by the gear ratio (Gain 5 = 10) to give the engine angular velocity and by 60/2*3.14159 (Gain 6) to give the engine rpm. This then goes into the look up table to generate the engine torque.

3. Results
Because only one gear is available in this model, the engine revs exceed maximum (6000 rpm) after less than 4 seconds - however the look up table then carries out a linear extrapolation beyond the highest stated engine rpm. The time taken to reach 60 mph (26.4 m/s) of just under 5 seconds is not realistic (the engine speed is over 8000rpm!).

David Grieve, 2nd November 2004.