Overdamped system response



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Transcription:

Second order system response. Im(s) Underdamped Unstable Overdamped or Critically damped Undamped Re(s) Underdamped

Overdamped system response System transfer function : Impulse response : Step response :

Overdamped and critically damped system response.

Overdamped and critically damped system response. Overdamped

Overdamped and critically damped system response. Overdamped

Overdamped and critically damped system response. Critically damped

Polar vs. Cartesian representations.

Polar vs. Cartesian representations. System transfer function : All 4 cases Unless overdamped Cartesian overdamped Significance of the damping ratio : Overdamped Critically damped Underdamped Undamped

Polar vs. Cartesian representations. System transfer function : All 4 cases Unless overdamped Cartesian overdamped Significance of the damping ratio : Overdamped Critically damped Underdamped Undamped

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

Impulse response :

Increasing / Fixed Impulse Response.8.6 Amplitude.4. -. -.4.5.5.5 3 Time (sec)

Increasing / Fixed Impulse Response.8.6 Amplitude.4. -. -.4.5.5.5 3 Time (sec)

Increasing / Fixed Impulse Response.8.6 Amplitude.4. -. -.4.5.5.5 3 Time (sec)

Increasing / Fixed Impulse Response.8.6 Amplitude.4. -. -.4.5.5.5 3 Time (sec)

Increasing / Fixed. Impulse Response.8.6.4. Amplitude -. -.4 -.6 -.8 -..5.5.5 3 Time (sec)

Increasing / Fixed. Impulse Response.8.6.4. Amplitude -. -.4 -.6 -.8 -..5.5.5 3 Time (sec)

Increasing / Fixed. Impulse Response.8.6.4. Amplitude -. -.4 -.6 -.8 -..5.5.5 3 Time (sec)

Increasing / Fixed. Impulse Response.8.6.4. Amplitude -. -.4 -.6 -.8 -..5.5.5 3 Time (sec)

Increasing / Fixed 6 Impulse Response 5 4 Amplitude 3 -.5.5.5 3 3.5 4 Time (sec) 5-5 - -6-4 -

Increasing / Fixed 6 Impulse Response 5 4 Amplitude 3 -.5.5.5 3 3.5 4 Time (sec) 5-5 - -6-4 -

Increasing / Fixed 6 Impulse Response 5 4 Amplitude 3 -.5.5.5 3 3.5 4 Time (sec) 5-5 - -6-4 -

Increasing / Fixed 6 Impulse Response 5 4 Amplitude 3 -.5.5.5 3 3.5 4 Time (sec) 5-5 - -6-4 -

Increasing / Fixed 5 Impulse Response 4 3 Amplitude - - -3-4 4 6 8 6 Time (sec) 4 - -4-6 -5 5

Increasing / Fixed 5 Impulse Response 4 3 Amplitude - - -3-4 4 6 8 6 Time (sec) 4 - -4-6 -5 5

Increasing / Fixed 5 Impulse Response 4 3 Amplitude - - -3-4 4 6 8 6 Time (sec) 4 - -4-6 -5 5

Increasing / Fixed 5 Impulse Response 4 3 Amplitude - - -3-4 4 6 8 6 Time (sec) 4 - -4-6 -5 5

Second order step response Underdamped and Undamped 3 3 3 3 output +j5 zeta=.8944 5 time sec. +j5 zeta=.374 5 +j5 zeta= 5 time sec. time sec. time sec..+j5 5 3 3 4.5 3 output +j.5 zeta=.998 +j.5 zeta=.97.5 +j.5 zeta=.+j.5 5 5 time sec. time sec. time sec. time sec.

Higher frequency oscillations Faster response Slower response Unstable Lower frequency oscillations

Less damping More damping Unstable

Second order step response Time specifications..4..8.6.4..5.5.5 3

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...8.6.4..5.5.5 3

Second order step response Time specifications. Steady state value. More generally, if the numerator is not, but some :

Second order step response Time specifications. Peak time. Therefore, is the time of the occurrence of the first peak :