You have a plant which has the open loop transfer function C/M=2/(+4+3). a. Plot the root locus (either hand or MATLAB) b. Add unity feedback and a PID controller to the open loop system. Hand calculate the gain of a proportional controller to make the system critically damped? What is the approximate settling time of such a system? What is the steady-state-gain of such a system? d. e. What does the proportional gain have to be to make the system have a steady-state error which is less than 5% of the system's setpoint? f. If you replace the proportional controller with a PD controller, but keep the same proportional gain, what does the derivative gain have to be to make the system. have the same 5% steady-state error, but be critically damped? g. Plot the root locus of a system with the same PD zero in the system.