# Control System MATLAB Script

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));

k=k+0.01;

% 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.