Week 11: Observers

6 January 2003

 Overview Reading FAQ Homework CDS 110b

Overview

Observers are used to estimate the state of a system given measurements of its inputs and outputs. We begin with the definition of observability of a linear, state space control system and give algebraic conditions for checking observability. We then construct observers for linear systems and prove the separation principle for combining observers and state space feedback.

• L11_2dfan.m - MATLAB file with ducted fan observer-based controller example (L11.2)

\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} ? "
\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; }

• Friedland, Sections 5.1, 5.3-5.4, 7.1-7.3, 8.1-8.2 (40 pages)
• Optional: remainder of Chapters 7 and 8

Homework

The problem set consists of four problems that explore observability and observers. In the first two problems, some simple systems are used to explore the basic concepts. The next two problems consider the cart-pendulum system and constructs a full order observer plus an observer-based controller for stabilizing the system.

Homework #9

• 7 Jan 03: fixed small typos, inserted missing factor of theta in problem 3