Consider the standard unity-feedback system shown below: where P(s) = 10/s(1 + 0.1 s)(1 + 0.01s). The open loop transfer function is G(s) = P(s) C(s). The design specifications are given as follows. Spec1 For unit ramp input at r(t), the steady state error e_xx lessthanorequalto 0.005 Spec2 Phase Margin PM greaterthanorequalto 55 degreee. Spec3 For unit-step input at r(t), the response y(t) has Percent Overshoot P0 lessthanorequalto 2.5%, with t_p as small as possible. Let F(s) = 1 and C_1(s) = K. Determine the range of K values that stabilize P. Determine the minimum value K_min that satisfies Spec1. Is tin- closed-loop system stable for K_min? Draw the Nyquist plot and the Bode plot for G(s) = P(s). Determine the phase and gain margins for G(s) = K_min P(s) Let F(s) = 1 and C_2(s) = K s+ x/s + az, with a > 1. Design C_2 to meet Spec1 and satisfy PM greaterthanorequalto 30 degree. Draw the Bode plot. Comment on whether Spec2 can be satisfied with a single lead controller. Draw the step response of the closed loop with C_2. What is the steady dream error e_xx for a unit step reference input? Determine the percent overshoot P0, peak time t_p and the settling time (2%) t_x. Draw the root locus and compare the actual P0 with the approximate P0 based on the dominant closed loop poles. Let F(s) = 1 and C_3(s) = L s+ z/s + az C_2(s), where a > 1 and C_2(s) is the lead control solution in Design2 above. Determine the second lead stage of this lead-lead controller so that Spec1 and Spec2 are both satisfied. What is the steady-state error e_xx for a unit-step reference input? Determine the Percent Overshoot P0, peak-time t_p and the settling time (2%) t_x, . Is Spec3 satisfied? Let F(s) = 1 and C_4(s) = K s+z/s + az, C_2(s) where a