# Lecture 3.1: Stability and Performance

#### 14 October 2002

 Lecture Reading FAQ Homework CDS 101

### Lecture

This lecture provides and introduction to stability and performance of (nonlinear) control systems. A formal definition of stable systems is given and phase portraits are introduced to help visualize the concepts. Local and global behavior of nonlinear systems is discussed, using a damped pendulum and the preditor-prey problem as examples. Performance of control systems is presented for both transient (step respones) and steady state (frequency domain) specifications.

\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; }

#### Handouts from lecture

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

• None

### Homework Set #3

This homework set covers stability and performance through a series of application examples. The first problem provides a set of three real-world models in which the student must identify the equilibrium points and determine stability of the equilibrium points (through simulation). The second problem explores performance specification in the conext of the cruise control example, including step response and frequency response.

• 19 Oct 02: minor changes to fix typos and clarify some statements
• Step response in 2(a) should be from 55 to 65 mph
• Problem 3(a) had some information which was not correct. It has been modified and the initial condition has been changed from y(0) = -1 to y(0) = 1.
• 16 Oct 02: handed out remaining problems (CDS 110)
• 14 Oct 02: handed out first two problems

Frequently asked questions on homework and TA hints: