The so-called cruise control in a car has the task of keeping the speed constant. This can be comfortable on long trips. You set the desired speed and the system takes over.

1. Based on a simple, constant context, you will arrive at a stationary state for a unregulated, and then a regulated system. Assume that air resistance and friction for a car increase in the power of 2 of speed, as follows:

F = CV² where C = 3kg/m

What engine power F_nom is needed to maintain a speed of 30m/s?

2. Assume that the cruise control controls engine power according to the formula F_u = K_p(V_d - V). Here is V_d the desired velocity and V the real velocity. The difference between them is called the regulatory deviation. The desired velocity is 30m/s. But you do not know yet what the real speed will be, so you can't use F or V from task 1. What becomes the real velocity, V, and the regulatory deviation, e, if K_p is 0, 1000 and 2000, respectively Ns/m? Can you draw any conclusion about regulatory deviation e = V_d - V based on this?