CDS 101: Principles of Feedback and Control

Lecture 7.1: Loop Analysis of Feedback Systems

11 November 2002

Lecture

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.

Lecture Presentation

Mud card responses [advanced search]:

#!/usr/bin/perl # -*- perl -*- # # htdbsearch.cgi - search for matching files in a database directory # RMM, 16 Mar 97 # # This CGI script searches the description files in a directory for a # against a set of criteria # # This script should be called as # # http://machine/path/htdblist.cgi? # or # http://machine/path/htdblist.cgi?db=&args # # where is the name of the configuration file that defines # all of the information needed to generate the listing. The optional # arguments are: # # _count=NN only list the first NN entries # _tight=1 use tight listing # _ssi=1 don't print header, trailer info (for includs) # # Include the necessary libraries require "cgi-lib.pl"; require "htdblib.pl"; # Parse script arguments if (&htdbinit) { # If the form contains some values, use them to search, and return # the results. if ($in{'_dbconfig'}) { # Generate the context header for the browser print &PrintHeader; # Print out the introductory information for search if (defined &SearchHeader) {&{$SearchHeader}($DBName);} # Summarize the search that was performed $rsltheader = defined &ResultHeader ? \&ResultHeader : htdb::ResultHeader; &{$rsltheader}(%in) if (!$in{_ssi}); # Go through and look for matching files if (not &PrintMatches) { &PrintNoMatches if (!in{ssi}); } # Generate the trailer if (defined &dbtrailer) {$dbtrailer = \&DBTrailer}; if (not $dbtrailer) {$dbtrailer = \&htdb::DBTrailer;} &{$dbtrailer}($DBName) if (!in{ssi}); } else { # Check to see if there is a user function for printing the search form if (defined &SearchForm) {$searchform = \&SearchForm}; if (not $searchform) {$searchform = \&htdb::SearchForm;} # Print out the introductory information for search if (defined &SearchHeader) {&{$SearchHeader}($DBName);} # Print the search form &{$searchform}(%in); } } # # Subroutine for printing the matches that occured # sub PrintMatches { my ($num_found); # Go to the database directory and read the contents chdir $DBPath || die "Can't cd to $DBPath"; opendir(DIR, '.') || die "Can't open $DBPath"; @filenames = readdir(DIR); closedir(DIR); # Check to see if there is a user function for checking matches if (defined &CheckEntry) {$checkentry = \&CheckEntry}; if (not $checkentry) {$checkentry = \&htdb::CheckEntry;} # Check to see if there is a user function for parsing filenames if (defined &ParseFname) {$parsefname = \&ParseFname}; if (not $parsefname) {$parsefname = \&htdb::ParseFname;} # Check to see if there is a user function for printing the entry if (defined &PrintEntry) {$printentry = \&PrintEntry}; if (not $printentry) {$printentry = \&htdb::PrintEntry;} # Check to see if there is a user function for printing the entry if (defined &TightEntry) {$tightentry = \&TightEntry}; if (not $tightentry) {$tightentry = \&htdb::TightEntry;} # Open the list environment used for the results # Print the command to generate a list of elements print ($in{_tight} ? "

\n"); # Loop through the filenames in order. $getfnames = defined &GetFnames ? \&GetFnames : htdb::GetFnames; @filenames = &{$getfnames}($DBPath); for (@filenames) { # Parse the filname and extract the ID and tag information ($id, $tag) = &{$parsefname}($filename = $_); next if not $id; # Open the file and extract the contents $contents = &htdb::readfile($filename); next if not $contents; # Now see if this entry matches the criteria for a match next if not &{$checkentry}($contents, %in); # Print out the information associated with this entry $count += &{($in{_tight} ? $tightentry : $printentry)} ($filename, $contents, $id, $tag, $DBURL."/".$filename); $num_found++; # See if we are counting and stop if needed last if ($in{_count} && $count > $in{_count}); } # Close the list environment used for the results print ($in{_tight} ? "

\n" : "\n"); return $num_found; } # # Subroutine for alerting the user that no matches occured # sub PrintNoMatches { print "

No matches found

\n"; print "Sorry, no entries match your request. "; print "Please choose some different parameters and try again.

\n"; print $footer; }

Reading Material and Handouts

Handouts from lecture

The following materials were handed out in lecture. These have been updated to include any corrections.

Required reading

Astrom, Control Systems Design, Sections 3.5

Supplemental reading

Packard, Poola and Horowitz, Dynamic Systems and Feedback, Section 30-31
A. D. Lewis, A Mathematical Introduction to Feedback Control, Chapter 7[pdf]

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 the stability and control of a simple disk drive positioning system and the ducted fan.

Homework Assignment [pdf]

Modifications to the homework (link above is always the latest version):

11 Nov 02: problem set release

Frequently asked questions on homework and TA hints:

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No matches found

\n"; print "Sorry, no entries match your request. "; print "Please choose some different parameters and try again.

\n"; print $footer; }