Given the following unity feedback control system: R(s) Ge(s) 150 s- + 20s + 200 Y(s) You are required to design the feedback controller Gc(s) using root locus methods to meet the following criteria: i) steady state error, ess = 0 ii) the 2nd-order portion of the response should have • %OS = 8% (% overshoot) • ts,±2%= 1/5 sec (2% settling time) (a) Based on the desirable closed loop pole positions, design a PD controller K(s+a). (b) Design a PI controller in the form of (s+13)/s on the top of the PD controller designed in (a). Notice that the integrator in the PI controller takes care of the steady state error. Choice of 13 needs to have minimal effect on the transient performance design in (a). (c) Using MATLAB, simulate the step response of the above system above with the controller you designed in (a) and (b), i.e. a PID controller K(s+aXs+p)/s, and then evaluate the overshoot and settling time as comparison with the design specifications.