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

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{{cds101-fa06}}
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{{cds101-fa08 lecture|prev=Transfer Functions|next=Loop Shaping}}
  
 
{{righttoc}}
 
{{righttoc}}
 
== Overview ==
 
== Overview ==
  
'''Monday:'''  Stability of Feedback Systems ({{cds101 handouts|L7-1_loopanal_h.pdf|Slides}}, MP3)
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The learning objectives for this week are:
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* Students should be able to draw a Nyquist curve and use the Nyquist criterion to determine stability
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* Students should be able to compute the gain a phase margin for a system using Nyquist and Bode plots
 +
 
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'''Monday:'''  Stability of Feedback Systems ({{cds101 handouts|L7-1_loopanal.pdf|Slides}}, {{cds101 mp3|cds101-2008-11-10.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.
  
'''Wednesday:''' Nyquist Analysis (Notes, MP3)
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* {{cds101 handouts|L7-1_loopanal_h.pdf|Lecture handout}}
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* MATLAB handouts: {{cds101 matlab|L7_1_loopanal.m}}, {{cds101 matlab|ambode.m}}, {{cds101 matlab|amnyquist.m}}, {{cds101 matlab|arrow.m}}
  
A more detailed description of the Nyquist criterion and its application to second order systems will be given.
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'''Wednesday:''' Nyquist Analysis ({{cds101 handouts|L7-2_nyquist.pdf|Notes}}, {{cds101 mp3|cds101-2008-11-12.mp3|MP3}})
  
'''Friday:''' Stability Margins and Loop Design (Notes, MP3)
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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 use the concepts of stability and robustness margins to perform simple control systems design in the frequency domain.
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'''Friday:''' recitations
 
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== Handouts ==
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{| width=100%
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|- valign=top
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| width=33% | Monday
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* {{cds101 handouts|L7-1_loopanal_h.pdf|Lecture handout}}
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* MATLAB handouts:
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* {{cds101 handouts|hw6.pdf|Homework #6}}
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| width=33% | Wednesday (CDS 110)
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* {{cds101 handouts|L7-2_nyquist_h.pdf|Lecture notes}}
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| width=33% | Friday
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* {{cds101 handouts|L7-3_margins_h.pdf|Lecture notes}}
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|}
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== Reading ==
 
== Reading ==
  
* {{AM06|Chapter 9 - Loop Analysis}}
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* {{AM08|Chapter 9 - Frequency Domain Analysis}}
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** CDS 101: Read sections 9.1-9.3, skipping advanced subsetions [45 min]
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** CDS 110: Read sections 9.1-9.3 [60 min]
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** CDS 210: Review AM08 Ch 9.1-9.3, read AM08 9.4-.5, DFT Ch 3 [90 min]
  
 
== 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|hw6-fa08.pdf|Homework #6}} (due 17 Nov 08): {{cds101 handouts|hw6-101-fa08.pdf|CDS 101}},  {{cds101 handouts|hw6-110-fa08.pdf|CDS 110}}, {{cds101 handouts|hw6-210-fa08.pdf|CDS 210}}
 
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<!-- Links to homework materials -->
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* {{cds101 handouts|hw7.pdf|Homework #7}}
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* Useful MATLAB commands
 
* Useful MATLAB commands
** tf - generate a transfer function from numberator/denominator coefficients
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** tf - generate a transfer function from numerator/denominator coefficients
 
** nyquist - generate a Nyquist plot for an open loop system L(s)
 
** nyquist - generate a Nyquist plot for an open loop system L(s)
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** amnyquist - same as Nyquist, but sometimes does a better job with arrows
 
** margin - generate a bode plot with gain and phase margin
 
** margin - generate a bode plot with gain and phase margin
  
 
== FAQ ==
 
== FAQ ==
 
'''Monday'''
 
'''Monday'''
<ncl>CDS 101/110 FAQ - Lecture 7-1</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</ncl>
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<ncl>CDS 101/110 FAQ - Lecture 7-2, Fall 2008</ncl>
'''Friday'''
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<ncl>CDS 101/110 FAQ - Lecture 7-3</ncl>
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'''Homework'''
 
'''Homework'''
<ncl>CDS 101/110 FAQ - Homework 6</ncl>
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<ncl>CDS 101/110 FAQ - Homework 6, Fall 2008</ncl>

Latest revision as of 05:59, 9 December 2008

CDS 101/110a Schedule Recitations FAQ ()

Overview

The learning objectives for this week are:

  • Students should be able to draw a Nyquist curve and use the Nyquist criterion to determine stability
  • Students should be able to compute the gain a phase margin for a system using Nyquist and Bode plots

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

  • K. J. Åström and R. M. Murray,, Princeton University Press, 2008..
    • CDS 101: Read sections 9.1-9.3, skipping advanced subsetions [45 min]
    • CDS 110: Read sections 9.1-9.3 [60 min]
    • CDS 210: Review AM08 Ch 9.1-9.3, read AM08 9.4-.5, DFT Ch 3 [90 min]

Homework

  • Homework #6 (due 17 Nov 08): CDS 101, CDS 110, CDS 210
  • Useful MATLAB commands
    • tf - generate a transfer function from numerator/denominator coefficients
    • nyquist - generate a Nyquist plot for an open loop system L(s)
    • amnyquist - same as Nyquist, but sometimes does a better job with arrows
    • margin - generate a bode plot with gain and phase margin

FAQ

Monday

Wednesday

Homework