# ECE 429, Spring 2002

## CONTROL SYSTEMS LAB -- UNIT A.3

###
Frequency Domain Analysis and Design

Of Control Systems

1 Week

` `
**OBJECTIVE:** To use MATLAB to analyze the frequency domain response of
a third-order dynamic system, and to design a closed-loop feedback control
system using cascade compensation in order to satisfy desired frequency
domain specifications.

` `
**TASKS:**

- The plant transfer function is the one given in experiment A.1 (with
*K*
= 1). The following
specifications are imposed on the closed-loop system:
- steady-state error for a ramp input must not exceed 0.01;
- phase margin for the compensated system must be at least 40°;
- compensated gain crossover frequency must be in the range 1 - 2 r/s;
- compensated phase shift must be less negative than -180° for all frequencies
between 0.1 r/s and 4 r/s; and
- ratios of compensator zero to pole must satisfy
*alfa*_{lead} = z_{c-lead}/p_{c-lead
}> 0.05 and* alfa*_{lag} = z_{c-lag}/p_{c-lag }<
20 for
any single stage of compensation.

- Design a compensator such that the closed-loop system satisfies all of
the specifications. More than one section of compensator can be used if
necessary. The design of the compensator should be accomplished by
theoretical analysis aided by the frequency domain response capabilities of
MATLAB. Random trial and error will not be acceptable.

- Verify that the final closed-loop system satisfies all of the
requirements. Bode plots of the open-loop and closed-loop systems are
required, as well as the ramp response in the time domain. Also, plot the
step response, and determine the percent overshoot and settling time.

` `**REPORT:**
Write a report containing a description of the design problem and your
approach to designing a compensator. Include your reasons for choosing
the particular compensator type and how the compensator parameter values
were obtained. Include all plots necessary to verify that the
specifications have been satisfied. Discuss how the frequency domain
specifications given influence the time response.

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*Latest revision on
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