ECE 429, Spring 2002

CONTROL SYSTEMS LAB -- UNIT A.1

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 4K/[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:

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