Problem 2: For cach of the following transfer functions of a second order system 1) G(S) = 144 92 +63 + 144 9 2) G(s) =

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Problem 2 For Cach Of The Following Transfer Functions Of A Second Order System 1 G S 144 92 63 144 9 2 G S 1 (90.95 KiB) Viewed 17 times

Problem 2: For cach of the following transfer functions of a second order system 1) G(S) = 144 92 +63 + 144 9 2) G(s) = 52 + 9s +9 3) G(S) 9 $2+2s +9 9 92 +9 4) G(8) 9 5) G(8) = 92 +63 +9 a) Compute the damping ratio &, the natural frequency wo and the poles $1,2 = -Ewo woV2 - 1. b) Describe the type of the system: over-damped, critically damped, under- damped or undamped. c) Describe if the system is: stable, marginally stable or unstable. d) Write the general form of the time domain unit-step response of each sys- tem (Note that, the Laplace transform of the unit-step response is given by Y(s) = R(s).G(s) = -.G(s). You can compute the coefficients using their gen- eral form given on the slides). e) In the cases when the system is under-damped, describe its performance characteristics: T. (settling time), T. (rise time), T, (peak time) and OS. (over- shoot).