Problem 1. Considering the root-locus given, which is plotted for a unity feedback system for K...

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Problem 1. Considering the root-locus given, which is plotted for a unity feedback system for K > 0, (a) Obtain the open-loop transfer function. (10 pts) (b) Obtain the closed-loop transfer function. (5 pts) (c) Find the value of gain and closed-loop poles at the imaginary axis crossings. (10 pts) jo (d) Write the range of K for which the closed loop s-plane system is stable. (5 pts) (e) Write the value of gain that makes the system marginally stable. (5 pts) jl (f) What would be the period of oscillation in seconds when the system is marginally stable? (5 pts) -7 X -jl (g) What would be the settling time, peak time and percent overshoot at the gain of K = 15? (15 pts) Method: For K = 15, the closed-loop poles appear at –7.36, -0.82 + j1.81. Show if the 2d order approximation is valid. Then use the formula given at the footer. (h) Calculate the steady-state error when the input is r(t) = 0.62u(t) at the same gain (K = 15). (15 pts) Problem 1. Considering the root-locus given, which is plotted for a unity feedback system for K > 0, (a) Obtain the open-loop transfer function. (10 pts) (b) Obtain the closed-loop transfer function. (5 pts) (c) Find the value of gain and closed-loop poles at the imaginary axis crossings. (10 pts) jo (d) Write the range of K for which the closed loop s-plane system is stable. (5 pts) (e) Write the value of gain that makes the system marginally stable. (5 pts) jl (f) What would be the period of oscillation in seconds when the system is marginally stable? (5 pts) -7 X -jl (g) What would be the settling time, peak time and percent overshoot at the gain of K = 15? (15 pts) Method: For K = 15, the closed-loop poles appear at –7.36, -0.82 + j1.81. Show if the 2d order approximation is valid. Then use the formula given at the footer. (h) Calculate the steady-state error when the input is r(t) = 0.62u(t) at the same gain (K = 15). (15 pts)