# ECE 429, Spring 2002

## CONTROL SYSTEMS LAB -- UNIT A.2

###
Time Domain Analysis and Design

Of Control Systems

1 Week

` `
**OBJECTIVE:** To use MATLAB to analyze the time domain response of a
third-order dynamic system, and to design closed-loop feedback control
systems using cascade compensation in order to satisfy desired time 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;
- overshoot to a step input must not exceed 10%;
- settling time for a step input (to within 2% of the final value) must
not exceed 15 seconds; 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. Possible compensator types might include
phase lead, phase lag, lag-lead, PID, PD, or PI. 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 time-domain response
capabilities of MATLAB. Random trial and error will not be acceptable.

- Verify that the final closed-loop system satisfies the requirements.
Time domain plots of the step and ramp responses are required for this. Make sure that "steady-state" can be easily identified in each of the plots.

` `**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.

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*Latest revision on
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