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 q and the output is angle q. 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 θ(0) 0, and let the desired angle be ψ(t) = u(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 02 What does it approach as t gets large?