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MIT OpenCourseWare http://ocw.mit.edu 2.004 Dynamics and Control II Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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K s + 2 s 5 s + b U ( s ) V ( s ) Y ( s ) u ( t ) v ( t ) y ( t ) I j M x x o b i n c r e a s i n g - b Massachusetts Institute of Technology Department of Mechanical Engineering 2.004 Dynamics and Control II Spring Term 2008 Lecture 22 1 Reading: Nise: 4.1 4.8 1 The Time-Domain Response of Systems with Finite Zeros Consider a system: K ( s + b ) Gs = , s 2 + 2 s + 5 we have seen that we can consider this as two cascade blocks Then if the response of the a system 1 /D ( s ) is v ( t ), then dv y ( t ) = + bv ( t ) dt and as the zero (at s = b ) moves deeper into the l.h. s -plane,, the relative contribution of the derivative term decreases and the system response tends toward a scaled version of the all pole response v ( t ). In general, the presence of the derivative terms in the response means that: 1 copyright c D.Rowell 2008 22–1
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0 1 2 3 4 5 6 7 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Step Response Time (sec) Amplitude z = -1 z = -2 z = -3 all-pole The response is faster (shorter peak-time T P and rise-time T R ).
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