a) A pair of poles of a second order system are located at - 2 ± 5j . Provide a sketch illustratingtheir locations on the Re-Im plane. Determine the natural frequency wn and the damping ratioand indicate the values on your sketch.b) If the system is subjected to a unit step input, estimate (i) rise time and (ii) overshoot as apercentage of the steady-state valuec) If specifications are to be improved (ie. faster response and lower overshoot), show thepermissible region in the Re-Im plane where the poles can be located using your sketch createdin part (a) (you can use separate sketches)d) (Note: This question is independent of parts a, b, and c) For a second order system, sketch thelocations of Five pairs of poles that represent (i) underdamped (ii) overdamped (iii) criticallydamped (iv) overdamped and (v) unstable systems, and label the poles on your sketch

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a) A pair of poles of a second order system are located at – 2±5j . Provide a sketch illustrating their locations on the Re-Im plane. Determine the natural frequency wn and the damping ratio and indicate the values on your sketch.

a) A pair of poles of a second order system are located at – 2±5j . Provide a sketch illustrating their locations on the Re-Im plane. Determine the natural frequency wn and the damping ratio and indicate the values on your sketch.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Question

a) A pair of poles of a second order system are located at - 2 ± 5j . Provide a sketch illustrating
their locations on the Re-Im plane. Determine the natural frequency wn and the damping ratio
and indicate the values on your sketch.
b) If the system is subjected to a unit step input, estimate (i) rise time and (ii) overshoot as a
percentage of the steady-state value
c) If specifications are to be improved (ie. faster response and lower overshoot), show the
permissible region in the Re-Im plane where the poles can be located using your sketch created
in part (a) (you can use separate sketches)
d) (Note: This question is independent of parts a, b, and c) For a second order system, sketch the
locations of Five pairs of poles that represent (i) underdamped (ii) overdamped (iii) critically
damped (iv) overdamped and (v) unstable systems, and label the poles on your sketch

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