## Our second model – the Alfa Romeo 147 GTA

With what we've learned so far, we're ready to develop a simple mathematical model of a real car in order to test and fine-tune the controller in a closed-loop simulation.

Luckily enough, a lot of technical detail is available nowadays on almost every car. The author likes the Alfa Romeo 147 GTA a lot, so the choice is made.

Open a new Simulink model and save it as `alfa147gta.slx`

. The model will have one input (the throttle, coming from the cruise controller) and one output (the car's speed, going to the cruise controller).

We're interested only in the longitudinal speed (a car going straight on a flat ground), and we assume the gearbox to be ideal (shifting gears in no time).

How do we compute the speed?

### Getting the speed – Newton's laws

We know that the car's speed is the integral of the acceleration in time:

Newton's second law reminds us that the acceleration is proportional to the total force applied on the car, with the mass **m** being the factor:

Since...