3. Assume G(S) = = 10(s-2) (0.1s+1)(s+14s+149)(s+4s+4) a) Show the pole-zero map of this transfer function...

 

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3. Assume G(S) = = 10(s-2) (0.1s+1)(s+14s+149)(s+4s+4) a) Show the pole-zero map of this transfer function on the complex plane. Is this system stable? (5-pts) b) Express the general form of the response for this system to a unit step input. You don't need to find the coefficients of the response. (10-pts) c) Approximate this transfer function with a second order system H(s). (5-pts) d) Use partial fraction expansion to find the response of the H(s) (the approximated transfer function) to a unit step input. (10-pts) e) Verify your result in part-d by applying the initial and final value theorems. (i.e., check if the magnitudes of the response at t=0 and t=, match with the initial/final value theorem results in Laplace domain?) (5-pts) 3. Assume G(S) = = 10(s-2) (0.1s+1)(s+14s+149)(s+4s+4) a) Show the pole-zero map of this transfer function on the complex plane. Is this system stable? (5-pts) b) Express the general form of the response for this system to a unit step input. You don't need to find the coefficients of the response. (10-pts) c) Approximate this transfer function with a second order system H(s). (5-pts) d) Use partial fraction expansion to find the response of the H(s) (the approximated transfer function) to a unit step input. (10-pts) e) Verify your result in part-d by applying the initial and final value theorems. (i.e., check if the magnitudes of the response at t=0 and t=, match with the initial/final value theorem results in Laplace domain?) (5-pts)