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    Control System MATLAB Script

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    Please see the attached file for a diagram and help with the following problems.

    Consider the closed-loop control system shown above.

    1. Develop a MATLAB script to assist in the search for a value of k so that the percent overshoot to a unit step input is greater than 1%, but less than 10%. The script should compute the closed-loop transfer function, T(s) = Y(s)/R(s), and generate the step response.

    2. Verify graphically that the steady-state error to a unit step is zero.

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    Solution Preview

    Please see the attached files for the solution. The example of how to use the MATLAB script is in the doc file.

    % The transfer function of series Gc(s)G(s)
    % G(s) = 1/(s+k)
    % Gc(s) = 10/s

    % determine k>=0 to obtain 1%<Po<10%
    % initail value
    k=0; Po=0;
    while ((Po<1)||(Po>10));
    % closed-loop transfer function
    numGc=10; denGc=[1 0]; ...

    Solution Summary

    This posting helps with control systems. This solution contains a MATLAB script for a closed-loop control system transfer function and show the steady-state error to a unit step is zero.