Transcription of Underdamped Unstable
1 Second order system (s)Im(s)UndampedOverdamped or Critically dampedUnderdampedUnderdampedOverdamped system responseSystem transfer function : Impulse response : Step response : Overdamped and critically damped system and critically damped system and critically damped system and critically damped system dampedPolar vs. Cartesian vs. Cartesian transfer function : Significance of the damping ratio : .. Critically UndampedAll 4 casesUnless Cartesian overdampedPolar vs. Cartesian transfer function : Significance of the damping ratio : .. Critically UndampedAll 4 casesUnless Cartesian overdampedPolar vs. Cartesian transfer function : Significance of the damping ratio : .. Critically UndampedAll 4 casesUnless overdampedOverdamped case:.. Cartesian overdampedSecond order impulse response Underdamped and UndampedImpulse response : Second order impulse response Underdamped and UndampedIncreasing / Fixed Impulse ResponseTime ( s ec ) ResponseTime ( s ec ) order impulse response Underdamped and UndampedIncreasing / Fixed Impulse ResponseTime ( s ec ) order impulse response Underdamped and UndampedIncreasing / Fixed Impulse ResponseTime ( s ec ) order impulse response Underdamped and UndampedIncreasing / Fixed Second order impulse response Underdamped and UndampedIncreasing / Fixed Impulse ResponseTime ( s ec ) order impulse response Underdamped and UndampedIncreasing / Fixed Impulse ResponseTime ( s ec ) order impulse response Underdamped and UndampedIncreasing / Fixed Impulse ResponseTime ( s ec ) order impulse response Underdamped and UndampedIncreasing / Fixed Impulse ResponseTime ( s ec ) order impulse response Underdamped and UndampedIncreasing / Fixed Impulse ResponseTime ( s ec )
2 Order impulse response Underdamped and UndampedIncreasing / Fixed Impulse ResponseTime ( s ec ) order impulse response Underdamped and UndampedIncreasing / Fixed Impulse ResponseTime ( s ec ) order impulse response Underdamped and UndampedIncreasing / Fixed Impulse ResponseTime ( s ec ) order impulse response Underdamped and UndampedIncreasing / Fixed Impulse ResponseTime ( s ec )Amplitude024681012-4-3-2-1012345-505-6- 4-20246 Second order impulse response Underdamped and UndampedIncreasing / Fixed Impulse ResponseTime ( s ec )Amplitude024681012-4-3-2-1012345-505-6- 4-20246 Second order impulse response Underdamped and UndampedIncreasing / Fixed Impulse ResponseTime ( s ec )Amplitude024681012-4-3-2-1012345-505-6- 4-20246 Second order impulse response Underdamped and UndampedIncreasing / Fixed Impulse ResponseTime ( s ec )Amplitude024681012-4-3-2-1012345-505-6- 4-20246 Second order step response Underdamped and Undamped05 2 1012305 2 1012305 2 1012305 2 1012305 2 1012305 2 10010203040 2+ 10+ + + +j5+j5zeta=0 2+j5zeta= 10+j5zeta= time sec.
3 Output time sec. time sec. time sec. time sec. time sec. time sec. time sec. output Second order impulse response Underdamped and UndampedUnstableFaster responseSlower responseHigher frequency oscillationsLower frequency oscillationsSecond order impulse response Underdamped and UndampedUnstableLess dampingMore dampingSecond order step response Time order step response Time Steady state Time to reach first peak (undamped or Underdamped only).. % of in excess of .. Time to reach and stay within 2% of .. Time to rise from 10% to 90% of .Second order step response Time state generally, if the numerator is not , but some :Second order step response Time , is the time of the occurrence of the first peak.