Overdamped system response
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1 Second order system response. Im(s) Underdamped Unstable Overdamped or Critically damped Undamped Re(s) Underdamped
2 Overdamped system response System transfer function : Impulse response : Step response :
3 Overdamped and critically damped system response.
4 Overdamped and critically damped system response. Overdamped
5 Overdamped and critically damped system response. Overdamped
6 Overdamped and critically damped system response. Critically damped
7 Polar vs. Cartesian representations.
8 Polar vs. Cartesian representations. System transfer function : All 4 cases Unless overdamped Cartesian overdamped Significance of the damping ratio : Overdamped Critically damped Underdamped Undamped
9 Polar vs. Cartesian representations. System transfer function : All 4 cases Unless overdamped Cartesian overdamped Significance of the damping ratio : Overdamped Critically damped Underdamped Undamped
10 Polar vs. Cartesian representations. System transfer function : All 4 cases Unless overdamped Cartesian overdamped Significance of the damping ratio : Overdamped Critically damped Underdamped Overdamped case: Undamped
11 Impulse response :
12 Increasing / Fixed Impulse Response.8.6 Amplitude Time (sec)
13 Increasing / Fixed Impulse Response.8.6 Amplitude Time (sec)
14 Increasing / Fixed Impulse Response.8.6 Amplitude Time (sec)
15 Increasing / Fixed Impulse Response.8.6 Amplitude Time (sec)
16 Increasing / Fixed. Impulse Response Amplitude Time (sec)
17 Increasing / Fixed. Impulse Response Amplitude Time (sec)
18 Increasing / Fixed. Impulse Response Amplitude Time (sec)
19 Increasing / Fixed. Impulse Response Amplitude Time (sec)
20 Increasing / Fixed 6 Impulse Response 5 4 Amplitude Time (sec)
21 Increasing / Fixed 6 Impulse Response 5 4 Amplitude Time (sec)
22 Increasing / Fixed 6 Impulse Response 5 4 Amplitude Time (sec)
23 Increasing / Fixed 6 Impulse Response 5 4 Amplitude Time (sec)
24 Increasing / Fixed 5 Impulse Response 4 3 Amplitude Time (sec)
25 Increasing / Fixed 5 Impulse Response 4 3 Amplitude Time (sec)
26 Increasing / Fixed 5 Impulse Response 4 3 Amplitude Time (sec)
27 Increasing / Fixed 5 Impulse Response 4 3 Amplitude Time (sec)
28 Second order step response Underdamped and Undamped output +j5 zeta= time sec. +j5 zeta= j5 zeta= 5 time sec. time sec. time sec..+j output +j.5 zeta=.998 +j.5 zeta= j.5 zeta=.+j time sec. time sec. time sec. time sec.
29 Higher frequency oscillations Faster response Slower response Unstable Lower frequency oscillations
30 Less damping More damping Unstable
31 Second order step response Time specifications
32 Second order step response Time specifications..4 Steady state value. Time to reach first peak (undamped or underdamped only). % of in excess of. Time to reach and stay within % of. Time to rise from % to 9% of
33 Second order step response Time specifications. Steady state value. More generally, if the numerator is not, but some :
34 Second order step response Time specifications. Peak time. Therefore, is the time of the occurrence of the first peak :
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