ECE 421

Homework Assignment #7
Due Thursday, March 10

The reference for this assignment is 2nd-Order Systems #4 on the Examples web page for this course. The open-loop and closed-loop systems have the standard 2nd-order expressions

The following specifications are imposed on the step response of the closed-loop system:

• settling time must be between 1 second and 4 seconds;
• overshoot must be between 10% and 20%.

TASKS:

1. Accurately sketch the region in the s-plane where the closed-loop pole with positive imaginary part must lie in order to satisfy each of these specifications. The sketch can be done by hand or in MATLAB.
2. Using MATLAB, compute and plot the step responses for each of the four closed-loop systems that correspond to the four "corners" of the acceptable region in the s-plane -- those four points where the lines representing minimum and maximum overshoot and minimum and maximum settling times intersect. The four curves should be plotted on the same graph. Plot the curves for 6 seconds, using at least 1000 values in your time vector.
3. Compute and plot the ramp responses for each of the same four systems. These four plots should be on the same graph.
4. Comment on the relationships between the closed-loop pole locations in the s-plane and the time-domain step responses. Also comment on the ramp responses relative to the values of damping ratio and undamped natural frequency and the ideal ramp signal at the reference input.

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Lastest revision on Friday, May 26, 2006 9:46 PM