Difference between revisions of "CDS 101/110  Loop Analysis"
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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)  +  '''Wednesday:''' Nyquist Analysis ({{cds101 handoutsL72_nyquistNotes}}, 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:''' Stability Margins and Loop Design (Notes, MP3)  '''Friday:''' Stability Margins and Loop Design (Notes, MP3)  
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* {{cds101 handoutshw6.pdfHomework #6}}  * {{cds101 handoutshw6.pdfHomework #6}}  
 width=33%  Wednesday (CDS 110)   width=33%  Wednesday (CDS 110)  
−  * {{cds101 handoutsL7  +  * {{cds101 handoutsL72_nyquist.pdfLecture notes}} 
 width=33%  Friday   width=33%  Friday  
−  * {{cds101 handoutsL7  +  * Lecture notes <! {{cds101 handoutsL73_margins.pdfLecture notes}} > 
}  }  
Revision as of 15:57, 8 November 2006
See current course homepage to find most recent page available. 
CDS 101/110a  Schedule  Recitations  FAQ  AM06 (errata) 
Overview
Monday: Stability of Feedback Systems (Slides, MP3  missing last 15 mins)
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: Stability Margins and Loop Design (Notes, MP3)
In this lecture we will use the concepts of stability and robustness margins to perform simple control systems design in the frequency domain.
Handouts
Monday

Wednesday (CDS 110)  Friday

Reading
 K. J. Åström and R. M. Murray, Feedback Systems: An Introduction for Scientists and Engineers, Preprint, 2006. Chapter 9  Loop Analysis.
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.
 Homework #6
 Useful MATLAB commands
 tf  generate a transfer function from numberator/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 71</ncl> Wednesday <ncl>CDS 101/110 FAQ  Lecture 72</ncl> Friday <ncl>CDS 101/110 FAQ  Lecture 73</ncl> Homework <ncl>CDS 101/110 FAQ  Homework 6</ncl>