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Problem 1. Consider that a feedback system has the open-loop poles of -4,-1 j and no zeros (only K). (a) Sketch the root-locus of the system. (b) Find the stability margin of the system for K >0. (C) Find the value of gain for which the closed-loop transfer function will have a real pole at -5. (d) What would be the maximum percent overshoot and settling time at this gain? Hint: Show if the 2nd order approximation is valid, then use the formula given at the footer. (e) What would be the steady-state errors when the inputs are r(t) = 0.625u(t) and 0.625tu(t)? (1) Design a PID controller to speed up the step response twice while keeping the same maximum overshoot and improving the steady-state performance. Hint: Design PD first then add a PI controller. (g) What would be the steady-state errors for the same inputs of (d) after the PID controller