ECE 429, Spring 2002

CONTROL SYSTEMS LAB -- UNIT A.3

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:

1. 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.

2. 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.

3. 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.

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 Thursday, June 8, 2006 9:29 AM