lecture_32 - MIT OpenCourseWare http://ocw.mit.edu 2.004...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 . s - p l a n e p 1 ( j w- p ) p 2 s - p l a n e p 1 p 2 z 1 q q 1 2 f 1 q 1 2 1 q r s j w 1 2 | j w- p | 2 1 1 j w s j w 1 f r 2 Massachusetts Institute of Technology Department of Mechanical Engineering 2.004 Dynamics and Control II Spring Term 2008 Lecture 32 1 Reading: Nise: 10.1 Class Handout: Sinusoidal Frequency Response 1 Frequency Response and the Pole-Zero Plot (continued) We showed that if H ( j ) = K ( j z 1 )( j z 2 ) ... ( j z m 1 )( j z m ) . (1) ( j p 1 )( j p 2 ) ... ( j p n 1 )( j p n ) and if each of the vectors from the n system poles to a test point s = j has a magnitude and an angle: | j p i | = = 2 + ( i ) 2 , q i i ( s p i ) = i = tan 1 i i , and similarly for the m zeros | j z i | = r i = 2 + ( i ) 2 , i ( s z i ) = i = tan 1 i i , the value of the frequency response at the point j is r 1 ...r m | H ( j ) | = K q 1 ...q n H ( j ) = ( 1 + ... + m ) ( 1 + ... + n ) 1 copyright c D.Rowell 2008 321 s - p l a n e p 1 p 2 z 1 G G 1 2 B 1 q 1 2 1 q r j M I M B r 2 2 1.0.1 High Frequency Response In Lecture 31 we saw that at high frequencies all vectors have approximately the same length, that is and 1 lim H ( j ) = K n m | | and that all of the angles of the vectors approach / 2, with the result lim H ( j ) = ( n m ) 2 If a system has an excess of poles over the number of zeros ( n > m ) the magnitude of the frequency response tends to zero as the frequency becomes large. Similarly, if a system has an excess of zeros the gain increases without bound as the frequency of the input increases. If n = m the magnitude function tends to a constant K . 1.0.2 Low Frequency Response As we note the following Magnitude Response : The magnitude response for the s-plane is r 1 ...r m | H ( j ) | = K q 1 ...q n If any of the r i 0, then H ( j ) 0, and if any q i 0, then H ( j ) | | | | If a system has one or more zeros at the origin of the s-plane (corresponding to a pure differentiation), then the system will have zero gain at = 0. Similarly, if the system has one or more poles at the origin (corresponding to a pure integration term in the transfer function), the system has infinite gain...
View Full Document

Page1 / 8

lecture_32 - MIT OpenCourseWare http://ocw.mit.edu 2.004...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online