# ECE 429, Spring 2002

## CONTROL SYSTEMS LAB -- UNIT A.1

###
Review of Computer-Aided Control System

Analysis and Design Software

1 Week

` `
**OBJECTIVE:** To provide a review for students to the powerful
computer-aided control system analysis and design capabilities which are
available at the University.

` `
**TASKS:**

1. Using references for MATLAB and the computer systems in IT&E, review the
capabilities of MATLAB as a design and analysis tool. In particular,
examine the capabilities for
control system analysis and design. Specifically, look at the capabilities
of the MATLAB functions: *bode, margin, rlocus, rlocfind, series,
parallel, feedback, tf, tfdata, logspace, semilogx, step, lsim, roots, pole, tzero, damp, angle, abs, poly, polyval, pzmap, find, unwrap, linspace, conv, size, length, real, imag, sum, prod, eval*.
2. Assume that the following transfer function models a system to be
controlled which is used in a unity feedback configuration. Using the
specification that the steady-state error for a ramp input should be 0.001,
find the value of the gain * K* to achieve this. Use MATLAB to find the
closed-loop poles with that *K*. Is the closed-loop system stable?

3. Using the gain found in step 2, generate Bode plots for magnitude and phase
of the open-loop system. Find the gain and phase margins. Are your results
consistent with your analysis on system stability? Plot the closed-loop
step response.
4. Plot the root locus for this system. Determine the value of
the gain *K* at the point where the root locus branches cross the
imaginary axis, and the frequency value at the crossing.

5. Approximating *G*_{p}(*s*) as the 2^{nd}-order
system 4*K*/[s(s + 0.4)], select * K* such that the damping ratio is
0.707. Determine the closed-loop stability and the gain and phase margins with the new value of
*K* (and the complete *G*_{p}(*s*) transfer
function). Plot the step and ramp
responses. What is the steady-state error for a ramp input? Use MATLAB
to find the maximum overshoot.

` `**REPORT:**

Write a report including the plots that you made, your procedures for
selecting the values of *K*, your analyses of system stability and
performance, and a discussion of the capabilities and ease of use of MATLAB
in performing this work.

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*Latest revision on
Thursday, June 8, 2006 9:28 AM
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