The document discusses underdamped second-order systems and defines key terms used to characterize their time response including: rise time, peak time, settling time, and percent overshoot. It provides examples of calculating these terms from plots of system response as well as determining system parameters like damping ratio to achieve a desired response. The document contains content on underdamped second-order systems and examples for determining time response specifications and system parameters from diagrams.

1. ME 176
Control Systems Engineering
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Time Response

2. Underdamped Second-Order Systems: Review
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3. Underdamped Second-Order Systems:
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4. Underdamped Second-Order Systems:
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Rise Time: Time required for
wave form to go from 0.1 of
the final value to 0.9 of the
final value.
Peak Time: The time required
to reach the first, or maximum
peak.
Settling Time: Time required
for the transient damped
oscillations to reach and stay
within ~2% of the steady state
value.
Percent Overshoot : Amount
that the waveform overshoots
the steady-state, or final, value
at the peak time, expressed as
a percentage of the steady-
state value.

5. Underdamped Second-Order Systems:
Peak Time: Settling Time:
Percent Overshot :
Rise Time:
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6. Underdamped Second-Order Systems: Review
= Damped Frequency of Oscillation
= Exponential Damping Frequency
= Natural Frequency
= Damping Ratio
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7. Underdamped Second-Order Systems:
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8. Examples:
1. Given the plot shown on right,
find , , , , and
2. Given diagram below, find J and
D to yield overshoot of 20% and a
settling time of 2 seconds for a step
input of torque T(t):
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9. Quiz:
1.For the system shown or the right,
a. Find the transfer function G(s) = X(s) / F(s).
b. Find , , , , and .
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