Difference between revisions of "CDS 101/110 - Loop Analysis"

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m (CDS 101/110, Week 7 - Loop Analysis moved to CDS 101/110 - Loop Analysis)
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{{cds101-fa07}}
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{{cds101-fa08}}
  
 
{{righttoc}}
 
{{righttoc}}
 
== Overview ==
 
== Overview ==
  
'''Monday:'''  Stability of Feedback Systems ({{cds101 handouts|L7-1_loopanal_h.pdf|Slides}}, {{cds101 mp3|cds101-2007-11-12.mp3|MP3}})
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The learning objectives for this week are:
 +
* Students should be able to construct a transfer function from a state space system
 +
* Students should be able to sketch the frequency response corresponding to a transfer function and label its key features
 +
* Students should understand the concepts of poles and zeros, and their relationship with the eigenvalues of a state space system
 +
 
 +
'''Monday:'''  Stability of Feedback Systems ({{cds101 handouts placeholder|L7-1_loopanal_h.pdf|Slides}}, {{cds101 mp3 placeholder|cds101-2007-11-12.mp3|MP3}})
  
 
This lecture describes how to analyze the stability and performance of a feedback system by looking at the open loop transfer function. We introduce the Nyquist criteria for stability and talk about the gain and phase margin as measures of robustness. The cruise control system is used as an example throughout the lecture.
 
This lecture describes how to analyze the stability and performance of a feedback system by looking at the open loop transfer function. We introduce the Nyquist criteria for stability and talk about the gain and phase margin as measures of robustness. The cruise control system is used as an example throughout the lecture.
  
* {{cds101 handouts|L7-1_loopanal_h.pdf|Lecture handout}}
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* {{cds101 handouts placeholder|L7-1_loopanal_h.pdf|Lecture handout}}
 
* MATLAB handouts: {{cds101 matlab|L7_1_loopanal.m}},  {{cds101 matlab|amnyquist.m}}, {{cds101 matlab|arrow.m}}
 
* MATLAB handouts: {{cds101 matlab|L7_1_loopanal.m}},  {{cds101 matlab|amnyquist.m}}, {{cds101 matlab|arrow.m}}
  
'''Wednesday:''' Nyquist Analysis ({{cds101 handouts|L7-2_nyquist.pdf|Notes}}, {{cds101 mp3|cds101-2007-11-14.mp3|MP3}})
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'''Wednesday:''' Nyquist Analysis ({{cds101 handouts placeholder|L7-2_nyquist.pdf|Notes}}, {{cds101 mp3 placeholder|cds101-2007-11-14.mp3|MP3}})
  
 
In this lecture we will derive the Nyquist criterion using the principle of the argument and show how to apply it to determine stability of a closed loop system. We will also see how to account for right half plane poles in the open loop transfer function. Finally, we will give a brief introduction to time delay and its effects on stability.
 
In this lecture we will derive the Nyquist criterion using the principle of the argument and show how to apply it to determine stability of a closed loop system. We will also see how to account for right half plane poles in the open loop transfer function. Finally, we will give a brief introduction to time delay and its effects on stability.
 
* {{cds101 handouts|L7-2_nyquist.pdf|Lecture notes}}
 
  
 
'''Friday:''' recitations
 
'''Friday:''' recitations
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== Reading ==
 
== Reading ==
  
* {{AM07|Chapter 9 - Loop Analysis}}
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* {{AM08|Chapter 9 - Loop Analysis}}
  
 
== Homework ==
 
== Homework ==
  
This homework set covers stability and robustness using the Nyquist criterion. The first problem consists of two sample systems for which gain and phase margin should be computed using both Nyquist and Bode plots. The second problem investigates the stability and performance of the cruise control system under different PI controllers. The CDS 110 questions explore stability in the presence of delay and the stability and control of a simple disk drive positioning system.
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* {{cds101 handouts placeholder|hw6-fa08.pdf|Homework #6}} (due 17 Nov 08)
 
 
<!-- Links to homework materials -->
 
* {{cds101 handouts|hw6.pdf|Homework #6}}
 
 
* Useful MATLAB commands
 
* Useful MATLAB commands
 
** tf - generate a transfer function from numerator/denominator coefficients
 
** tf - generate a transfer function from numerator/denominator coefficients
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== FAQ ==
 
== FAQ ==
 
'''Monday'''
 
'''Monday'''
<ncl>CDS 101/110 FAQ - Lecture 7-1, Fall 2007</ncl>
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<ncl>CDS 101/110 FAQ - Lecture 7-1, Fall 2008</ncl>
 
'''Wednesday'''
 
'''Wednesday'''
<ncl>CDS 101/110 FAQ - Lecture 7-2, Fall 2007</ncl>
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<ncl>CDS 101/110 FAQ - Lecture 7-2, Fall 2008</ncl>
 
'''Homework'''
 
'''Homework'''
<ncl>CDS 101/110 FAQ - Homework 6, Fall 2007</ncl>
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<ncl>CDS 101/110 FAQ - Homework 6, Fall 2008</ncl>

Revision as of 19:32, 1 November 2008

CDS 101/110a Schedule Recitations FAQ AM08 (errata)

Overview

The learning objectives for this week are:

  • Students should be able to construct a transfer function from a state space system
  • Students should be able to sketch the frequency response corresponding to a transfer function and label its key features
  • Students should understand the concepts of poles and zeros, and their relationship with the eigenvalues of a state space system

Monday: Stability of Feedback Systems (Slides, MP3)

This lecture describes how to analyze the stability and performance of a feedback system by looking at the open loop transfer function. We introduce the Nyquist criteria for stability and talk about the gain and phase margin as measures of robustness. The cruise control system is used as an example throughout the lecture.

Wednesday: Nyquist Analysis (Notes, MP3)

In this lecture we will derive the Nyquist criterion using the principle of the argument and show how to apply it to determine stability of a closed loop system. We will also see how to account for right half plane poles in the open loop transfer function. Finally, we will give a brief introduction to time delay and its effects on stability.

Friday: recitations

Reading

Homework

  • Homework #6 (due 17 Nov 08)
  • Useful MATLAB commands
    • tf - generate a transfer function from numerator/denominator coefficients
    • nyquist - generate a Nyquist plot for an open loop system L(s)
    • margin - generate a bode plot with gain and phase margin

FAQ

Monday <ncl>CDS 101/110 FAQ - Lecture 7-1, Fall 2008</ncl> Wednesday <ncl>CDS 101/110 FAQ - Lecture 7-2, Fall 2008</ncl> Homework <ncl>CDS 101/110 FAQ - Homework 6, Fall 2008</ncl>