Difference between revisions of "Transfer Functions"

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{{Chapter
 
{{Chapter
 
|Chapter number=9
 
|Chapter number=9
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|Short name=xferfcns
 
|Previous chapter=Output Feedback
 
|Previous chapter=Output Feedback
 
|Next chapter=Frequency Domain Analysis
 
|Next chapter=Frequency Domain Analysis
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|First edition URL=https://www.cds.caltech.edu/~murray/amwiki/index.php?title=Transfer_Functions#Frequently_Asked_Questions
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|Chapter summary=This chapter introduces the concept of the transfer function, which is a com- pact description of the input/output relation for a linear time-invariant system. We show how to obtain transfer functions analytically and experimentally. Combining transfer functions with block diagrams gives a powerful algebraic method to analyze linear systems with many blocks. The transfer function allows new interpretations of system dynamics. We also introduce the Bode plot, a powerful graphical rep- resentation of the transfer function that was introduced by Bode to analyze and design feedback amplifiers.
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|Chapter contents=# The Loop Transfer Function
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# The Nyquist Criterion
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#* The Nyquist Plot
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#* The General Nyquist Criterion
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#* Conditional Stability
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# Stability Margins
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# Bode's Relations and Minimum Phase Systems
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# Generalized Notions of Gain and Phase
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#* System Gain and Passivity
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#* Extensions of the Nyquist Criterion
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#* Describing Functions
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# Further Reading
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:: Exercises
 
}}
 
}}

Latest revision as of 16:36, 24 November 2024

Prev: Output Feedback Chapter 9 - Transfer Functions Next: Frequency Domain Analysis
Xferfcns-firstpage.png

This chapter introduces the concept of the transfer function, which is a com- pact description of the input/output relation for a linear time-invariant system. We show how to obtain transfer functions analytically and experimentally. Combining transfer functions with block diagrams gives a powerful algebraic method to analyze linear systems with many blocks. The transfer function allows new interpretations of system dynamics. We also introduce the Bode plot, a powerful graphical rep- resentation of the transfer function that was introduced by Bode to analyze and design feedback amplifiers.

Contents

  1. The Loop Transfer Function
  2. The Nyquist Criterion
    • The Nyquist Plot
    • The General Nyquist Criterion
    • Conditional Stability
  3. Stability Margins
  4. Bode's Relations and Minimum Phase Systems
  5. Generalized Notions of Gain and Phase
    • System Gain and Passivity
    • Extensions of the Nyquist Criterion
    • Describing Functions
  6. Further Reading
Exercises
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