Given is a transfer function of a system: s +1 H(s) s2 + 4s + 8 a) Is this system stable? Justify b) Find the impulse response of the system h(t) c) Assuming the unit-step input to this system, what is the final value of the output y(t) of this system i.e. lim y(t) ? (hint: no need to derive y(t) i.e. the inverse Laplace Transform)? d) Assume you place a unity (negative) feed-back loop around the system. Derive the equivalent transfer function of the closed-loop system Heg (s). Ignoring any zeros and based only on the poles of the closed-loop system- what are the values of the relative damping factor 7, the relative undamped natural frequency and the relative damped natural frequency of the closed-loop system? Ignoring any zeros and based only on the poles of the closed-loop system - would you expect an overshoot when unit step input is applied to the closed-loop system Heq(s) (Justify) ?
Given is a transfer function of a system: s +1 H(s) s2 + 4s + 8 a) Is this system stable? Justify b) Find the impulse response of the system h(t) c) Assuming the unit-step input to this system, what is the final value of the output y(t) of this system i.e. lim y(t) ? (hint: no need to derive y(t) i.e. the inverse Laplace Transform)? d) Assume you place a unity (negative) feed-back loop around the system. Derive the equivalent transfer function of the closed-loop system Heg (s). Ignoring any zeros and based only on the poles of the closed-loop system- what are the values of the relative damping factor 7, the relative undamped natural frequency and the relative damped natural frequency of the closed-loop system? Ignoring any zeros and based only on the poles of the closed-loop system - would you expect an overshoot when unit step input is applied to the closed-loop system Heq(s) (Justify) ?
Introductory Circuit Analysis (13th Edition)
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Question
![Given is a transfer function of a system:
s + 1
H(s)
s2 + 4s + 8
a) Is this system stable? Justify
b) Find the impulse response of the system h(t)
c) Assuming the unit-step input to this system, what is the final value of the output y(t) of
this system i.e. lim y(t) ? (hint: no need to derive y(t) i.e. the inverse Laplace
Transform)?
d) Assume you place a unity (negative) feed-back loop around the system. Derive the
equivalent transfer function of the closed-loop system Heg (s). Ignoring any zeros and
based only on the poles of the closed-loop system- what are the values of the relative
damping factor 3, the relative undamped natural frequency and the relative damped
natural frequency of the closed-loop system? Ignoring any zeros and based only on the
poles of the closed-loop system - would you expect an overshoot when unit step input is
applied to the closed-loop system Heq(s) (Justify) ?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F672bf286-8abe-4b07-9ca1-0d5b2612956c%2F20a3fe97-2a34-4422-8322-3036d072473f%2Fa1lceeu_processed.png&w=3840&q=75)
Transcribed Image Text:Given is a transfer function of a system:
s + 1
H(s)
s2 + 4s + 8
a) Is this system stable? Justify
b) Find the impulse response of the system h(t)
c) Assuming the unit-step input to this system, what is the final value of the output y(t) of
this system i.e. lim y(t) ? (hint: no need to derive y(t) i.e. the inverse Laplace
Transform)?
d) Assume you place a unity (negative) feed-back loop around the system. Derive the
equivalent transfer function of the closed-loop system Heg (s). Ignoring any zeros and
based only on the poles of the closed-loop system- what are the values of the relative
damping factor 3, the relative undamped natural frequency and the relative damped
natural frequency of the closed-loop system? Ignoring any zeros and based only on the
poles of the closed-loop system - would you expect an overshoot when unit step input is
applied to the closed-loop system Heq(s) (Justify) ?
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