To develop a cruise control for a car which needs to move at a fixed set-point velocity using a PID controller.
If the inertia of the wheels is neglected, and it is assumed that air drag (which is proportional to the car’s speed at low speeds) is opposing the motion of the car, then the problem is reduced to a simple first-order system.
Thus the motion of the car can be written as, mv' + bv = u where u is the input force provided by the engine to move the car at a certain velocity. Though it is intuitive to think of an input as something related to the gas pedal, but unfortunately to represent such a system accurately the dynamics of it becomes really complicated for a task of a beginner level. So for now we will just assume that our engine can give us a certain amount of force without actually looking how that force translates to real life situations.
Mass - 1000 kg
Fixed velocity- 100 kmph
Drag coefficient - 1.2
Rise time of system (time taken to reach 90% of target velocity) is 5 sec
Maximum overshoot is less than 2 %