Second order system response.UnstableRe(s)Im(s)UndampedOverdamped or Critically dampedUnderdampedUnderdampedOverdamped system responseSystem transfer function : Impulse response : Step response :Overdamped and critically damped system response.Overdamped and critically damped system response.OverdampedOverdamped and critically damped system response.OverdampedOverdamped and critically damped system response.Critically dampedPolar vs. Cartesian representations.Polar vs. Cartesian representations.System transfer function : Significance of the damping ratio : … Overdamped… Critically damped… Underdamped… UndampedAll 4 casesUnless overdamped… Cartesian overdampedPolar vs. Cartesian representations.System transfer function : Significance of the damping ratio : … Overdamped… Critically damped… Underdamped… UndampedAll 4 casesUnless overdamped… Cartesian overdampedPolar vs. Cartesian representations.System transfer function : Significance of the damping ratio : … Overdamped… Critically damped… Underdamped… UndampedAll 4 casesUnless overdampedOverdamped case:… Cartesian overdampedSecond order impulse response – Underdamped and UndampedImpulse response :Second order impulse response – Underdamped and UndampedIncreasing / Fixed Impulse ResponseTime (sec)Amplitude0 0.5 1 1.5 2 2.5 3-0.4-0.200.20.40.60.81Impulse ResponseTime (sec)Amplitude0 0.5 1 1.5 2 2.5 3-0.4-0.200.20.40.60.81Second order impulse response – Underdamped and UndampedIncreasing / FixedImpulse ResponseTime (sec)Amplitude0 0.5 1 1.5 2 2.5 3-0.4-0.200.20.40.60.81Second order impulse response – Underdamped and UndampedIncreasing / FixedImpulse ResponseTime (sec)Amplitude0 0.5 1 1.5 2 2.5 3-0.4-0.200.20.40.60.81Second order impulse response – Underdamped and UndampedIncreasing / FixedSecond order impulse response – Underdamped and UndampedIncreasing / Fixed Impulse ResponseTime (sec)Amplitude0 0.5 1 1.5 2 2.5 3-0.1-0.08-0.06-0.04-0.0200.020.040.060.080.1Second order impulse response – Underdamped and UndampedIncreasing / Fixed Impulse ResponseTime (sec)Amplitude0 0.5 1 1.5 2 2.5 3-0.1-0.08-0.06-0.04-0.0200.020.040.060.080.1Second order impulse response – Underdamped and UndampedIncreasing / Fixed Impulse ResponseTime (sec)Amplitude0 0.5 1 1.5 2 2.5 3-0.1-0.08-0.06-0.04-0.0200.020.040.060.080.1Second order impulse response – Underdamped and UndampedIncreasing / Fixed Impulse ResponseTime (sec)Amplitude0 0.5 1 1.5 2 2.5 3-0.1-0.08-0.06-0.04-0.0200.020.040.060.080.1Second order impulse response – Underdamped and UndampedIncreasing / Fixed Impulse ResponseTime (sec)Amplitude0 0.5 1 1.5 2 2.5 3 3.5 4-10123456-6 -4 -2 0 2-10-50510Second order impulse response – Underdamped and UndampedIncreasing / Fixed Impulse ResponseTime (sec)Amplitude0 0.5 1 1.5 2 2.5 3 3.5 4-10123456-6 -4 -2 0 2-10-50510Second order impulse response – Underdamped and UndampedIncreasing / Fixed Impulse ResponseTime (sec)Amplitude0 0.5 1 1.5 2 2.5 3 3.5 4-10123456-6 -4 -2 0 2-10-50510Second order impulse response – Underdamped and UndampedIncreasing / Fixed Impulse ResponseTime (sec)Amplitude0 0.5 1 1.5 2 2.5 3 3.5 4-10123456-6 -4 -2 0 2-10-50510Second order impulse response – Underdamped and UndampedIncreasing / Fixed Impulse ResponseTime (sec)Amplitude0 2 4 6 8 10 12-4-3-2-1012345-5 0 5-6-4-20246Second order impulse response – Underdamped and UndampedIncreasing / Fixed Impulse ResponseTime (sec)Amplitude0 2 4 6 8 10 12-4-3-2-1012345-5 0 5-6-4-20246Second order impulse response – Underdamped and UndampedIncreasing / Fixed Impulse ResponseTime (sec)Amplitude0 2 4 6 8 10 12-4-3-2-1012345-5 0 5-6-4-20246Second order impulse response – Underdamped and UndampedIncreasing / Fixed Impulse ResponseTime (sec)Amplitude0 2 4 6 8 10 12-4-3-2-1012345-5 0 5-6-4-20246Second order step response – Underdamped and Undamped0 5−2−101230 5−2−101230 5−2−101230 5−2−101230 5−2−101230 5−2−101230 10 2000.511.50 10 20−10010203040−2+j0.5zeta=0.97 −10+j0.5zeta=0.998 +j0.5zeta=0 0.2+j0.50.2+j5+j5zeta=0 −2+j5zeta=0.3714 −10+j5zeta=0.8944 time sec. output time sec. time sec. time sec. time sec. time sec. time sec. time sec. outputSecond order impulse response – Underdamped and UndampedUnstableFaster response Slower responseHigher frequency oscillationsLower frequency oscillationsSecond order impulse response – Underdamped and UndampedUnstableLess dampingMore dampingSecond order step response – Time specifications.0 0.5 1 1.5 2 2.5 300.20.40.60.811.21.4Second order step response – Time specifications.0 0.5 1 1.5 2 2.5 300.20.40.60.811.21.4… Steady state value.… 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 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
View Full Document
Unlocking...