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Unformatted text preview: 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 . 0 . 0 1 0 . 0 3 0 . 1 0 . 3 1 3 1 0 3 0 1 0 0- 4 0- 3 0- 2 0- 1 0 1 0 2 0 3 0 4 0 A n g u l a r f r e q u e n c y ( r a d / s e c ) M 2 0 l o g | H ( j M ) | 1 0 s l o p e- 2 0 d B / d e c a d e 0 . 0 1 0 . 0 3 0 . 1 0 . 3 1 3 1 0 3 0 1 0 0- 4 0- 3 0- 2 0- 1 0 1 0 2 0 3 0 4 0 A n g u l a r f r e q u e n c y ( r a d / s e c ) M s l o p e 2 0 d B / d e c a d e ( a ) ( b ) 2 0 l o g | H ( j M ) | 1 0 Massachusetts Institute of Technology Department of Mechanical Engineering 2.004 Dynamics and Control II Spring Term 2008 Lecture 34 1 Reading: Nise: 10.1 Class Handout: Sinusoidal Frequency Response 1 Bode Plots (continued In Lecture 33 we developed the following asymptotic Bode Plot s for low-order systems: Pole/Zero at the Origin: 1 H ( s ) = and H ( s ) = s s 1 copyright c D.Rowell 2008 341 0 . 0 1 0 . 0 3 0 . 1 0 . 3 1 3 1 0 3 0 1 0 0- 4 0- 3 0- 2 0- 1 0 1 0 0 . 0 1 0 . 0 3 0 . 1 0 . 3 1 3 1 0 3 0 1 0 0- 9 0- 8 0- 7 0- 6 0- 5 0- 4 0- 3 0- 2 0- 1 0 1 0 0 . 0 1 0 . 0 3 0 . 1 0 . 3 1 3 1 0 3 0 1 0 0- 1 0 1 0 2 0 3 0 4 0 0 . 0 1 0 . 0 3 0 . 1 0 . 3 1 3 1 0 3 0 1 0 0- 1 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 w t w t w t w t N o r m a l i z e d a n g u l a r f r e q u e n c y N o r m a l i z e d a n g u l a r f r e q u e n c y N o r m a l i z e d a n g u l a r f r e q u e n c y N o r m a l i z e d a n g u l a r f r e q u e n c y H ( j w ) H ( j w ) s l o p e- 2 0 d B / d e c a d e s l o p e 2 0 d B / d e c a d e 2 0 l o g | H ( j w ) | 1 0 2 0 l o g | H ( j w ) | 1 0 Single Real Pole/Zero: 1 H ( s ) = and H ( s ) = s + 1 s + 1 342 0 . 0 1 0 . 0 3 0 . 1 0 . 3 1 3 1 0 3 0 1 0 0- 1 8 0- 1 6 0- 1 4 0- 1 2 0- 1 0 0- 8 0- 6 0- 4 0- 2 0 0 . 0 1 0 . 0 3 0 . 1 0 . 3 1 3 1 0 3 0 1 0 0- 8 0- 6 0- 4 0- 2 0 2 0 0 . 0 1 0 . 0 3 0 . 1 0 . 3 1 3 1 0 3 0 1 0 0- 2 0 2 0 4 0 6 0 8 0 0 . 0 1 0 . 0 3 0 . 1 0 . 3 1 3 1 0 3 0 1 0 0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 N o r m a l i z e d a n g u l a r f r e q u e n c y N o r m a l i z e d a n g u l a r f r e q u e n c y N o r m a l i z e d a n g u l a r f r e q u e n c y N o r m a l i z e d a n g u l a r f r e q u e n c y H ( j w ) 2 0 l o g | H ( j w ) | 1 0 2 0 l o g | H ( j w ) | 1 0 H ( j w ) w / w n w / w n w / w n w / w n z = 5 z = 0 . 1 0 . 2 0 . 5 2 1 z = 0 . 1 0 . 2 0 . 5 1 2 z = 5 z = 0 . 1 z = 5 z = 5 z = 0 . 1 1 z = 0 . 1 0 . 2 0 . 5 2 z = 5 1 z = 5 z = 0 . 1 0 . 2 2 4 0 d B / d e c a d e s l o p e- 4 0 d B / d e c a d e s l o p e 0 . 5 ( a ) ( b ) Complex Conjugate...
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lecture_34 - MIT OpenCourseWare http://ocw.mit.edu 2.004...

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