Difference between revisions of "CDS 101/110  Transfer Functions"
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This lecture introduces transfer functions as a tool for analyzing feedback systems using frequency response and Bode plots. The lecture uses the example of a spring, mass, damper system to show how transfer functions can be used to compute the frequency response of an interconnected system of components. We also define poles and zeros and indicate how they affect the frequency response of a system. Finally, we introduce the general computations of block diagram algebra.  This lecture introduces transfer functions as a tool for analyzing feedback systems using frequency response and Bode plots. The lecture uses the example of a spring, mass, damper system to show how transfer functions can be used to compute the frequency response of an interconnected system of components. We also define poles and zeros and indicate how they affect the frequency response of a system. Finally, we introduce the general computations of block diagram algebra.  
−  '''Wednesday:''' Laplace Transforms ({{cds101 handoutsL62_laplace.pdfNotes}}, [  +  '''Wednesday:''' Laplace Transforms ({{cds101 handoutsL62_laplace.pdfNotes}}, [http://www.cds.caltech.edu/~murray/courses/cds101/fa06/mp3/1Nov06.mp3 MP3]) 
This lecture gives a brief introduction to the Laplace transfrom and describes how it relates to the transfer function for an input/output system.  This lecture gives a brief introduction to the Laplace transfrom and describes how it relates to the transfer function for an input/output system. 
Revision as of 23:19, 4 November 2006
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CDS 101/110a  Schedule  Recitations  FAQ  () 
Contents 
Overview
Monday: Transfer Functions (Slides, MP3)
This lecture introduces transfer functions as a tool for analyzing feedback systems using frequency response and Bode plots. The lecture uses the example of a spring, mass, damper system to show how transfer functions can be used to compute the frequency response of an interconnected system of components. We also define poles and zeros and indicate how they affect the frequency response of a system. Finally, we introduce the general computations of block diagram algebra.
Wednesday: Laplace Transforms (Notes, MP3)
This lecture gives a brief introduction to the Laplace transfrom and describes how it relates to the transfer function for an input/output system.
Friday: Bode plots (Notes, MP3)
This lecture focuses on Bode plots, including how to recognize key features of the plots and how to sketch them by hand.
Handouts
Monday  Wednesday (CDS 110)

Friday

Reading
 K. J. Åström and R. M. Murray,, Preprint, 2006..
Homework
This homework set covers basic transfer function concepts. The conceptual problems show how to create a frequency response for a complex system of components using MATLAB. The analytical problems cover basic anaytical concepts in transfer functions.
FAQ
Monday
 Can you explain the axes of the Bode plot better?
 Does pole zero cancellation happen and is it useful?
 Intermediate steps in block diagram algebra for the Engine Control of a GM Astro example?
 What is G and what is H? What is the difference in the way they are defined?
 What is meant/useful about transfer functions between 2 blocks in a block diagram?
Wednesday
Friday
Homework