CDS 101: Principles of Feedback and Control Lecture 5.1: Controllability and State Space Feedback 28 October 2002

Lecture

This lecture introduces the concept of controllability and explores the use of state space feedback for control of linear systems. Controllability is defined as the ability to move the system from one condition to another over finite time. The controllability matrix test is given to check if a linear system is controllable, and the test is applied to several examples. The concept of (linear) state space feedback is introduced and the ability to place eigenvalues of the closed loop system arbitrarily is related to controllability. A cart and pendulum system and the preditor prey problem are used as examples.

• 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" : "

\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} ? "

No matches found

\n"; print $footer; }

Reading Material and Handouts

Handouts from lecture

• Lecture handout
• No homework this week (midterm handed out on Wednesday)

Required reading

• Packard, Poola and Horowitz, Dynamic Systems and Feedback, Section 25
  

Supplemental reading

• B. Friedland, Sections 5.1-5.4 (controllability only)
• A. D. Lewis, A Mathematical Introduction to Feedback Control, Chapter 2. [pdf]

No Homework

There is no homework set this week, due to the midterm exam.