A Positioning system drives a tester in electronic manufacturing processes. The system is made of a power amplifier, a motor field circuit, and a DC motor, as shown in the block diagram: u(t) v(t) K Amplifier Field circuit i(t) Motor e(t) The inputs and outputs of these variables are related by the following differential equations: de de 1) + dr² dt = i(t) di 2) dt +5⚫i(t) = v(t) 3) v(t) Ku(t), K is a constant a) Derive a state space equation for the open-loop system. (Define states, input, output and all the matrices). b) Is the system completely controllable (reachable) and observable? c) Find eigen values of the open-loop system. d) Design a closed-loop system with state feedback and with an input r(t) as command input to the closed-loop system. e(t) is to follow r(t). e) Choose specific state feedback gains and the power amplifier gain K, such that the systems response on e(t) to a step command r(t) = 1, t≥ 0, has: 1) Zero steady state error 2) 2% settling time, T, ≤ 2 seconds 3) Overshoot ≤ 4%