Consider a rotating robot where you can control the angular velocity around a fixed axis.

(a) Model this as a system where the input is angular velocity and the output is angle . Give your model as an equation relating the input and output as functions of time.

(b) Is this model BIBO stable?

(c) Design a proportional controller to set the robot onto a desired angle. That is, assume that the initial angle is (0) = 0, and let the desired angle be (t) = au(t), where u is the unit step function. Find the actual angle as a function of time and the proportional controller feedback gain K. What is your output at t = 0? What does it approach as t gets large?