Adaptive Cruise Control Linear Model using MPC

Hi Everyone,

I am wondering if anyone could help answer a question of mine: When using the Model Predictive Control Toolbox, specifically the Adaptive Cruise Control System block in Simulink, Matlab uses the transfer function of

I do not understand how this transfer function was developed in the first place.

I've tried to use a free body diagram like this

Which will in turn give me this differential equation:

and a transfer function such as this:

Where m is the mass of the vehicle and b is the damping coefficient. m is usually around 1000 kg and b is usually around 50 Ns/m.

I hope someone can help explain to me how the originally transfer function was found.

Thank you.