# Cruise Control Project on Toy Car

I finished taking my control theory course, and I want to build an RC car that has cruise control. So I started off with the force analysis, and I got external forces that are constant. For example if the road is sloped, then the gravitational force is holding the car back. Another force is rolling resistance. I believe these are the only two considerable forces that will resist the car's movement; however, this does not provide a stable system.

Doing a little research online, I found that most models, if not all, say that the external forces are proportional to the velocity of the car. I understand how that can be related to the spring-damper model, but I don't see why the external forces are proportional to velocity when all the forces are constant. For instance, rolling resistance only depends on the weight/normal force of the car--not velocity. So how can I say they are variably dependent on velocity?

Also, let's assume that the forces are proportional to velocity, then how would I figure out that proportionally constant?

I am trying to create a model in simulink with some sort of controller, probably PID, then later transfer it into reality. And I am already stuck with the main system. Thanks for any help!

• not an expert in this area. But apparently the rolling resistance slightly depends on velocity too: [ref] Jul 29 '18 at 2:42
• @Alex: See my answer to electronics.stackexchange.com/questions/346730/… which may help. Bart is correct that you only need the speed setpoint and actual. Your real car knows nothing about slope, wind, tires, surface - only setpoint and speed. Jul 29 '18 at 22:36
• Regarding the force analysis, for a toy car at less than 20 kph the aerodynamic resistance will not play a significant effect. Just for reference, the aerodynamic resistance has a form of $F = \frac{1}{2}C_D \rho A v^2$. However as stated by Bart and Transistor, don't worry too much about the physical model, its best if you use error between the setpoint and speed, and play around with the parameters. Aug 17 '20 at 17:57