# Matlab to determine closed-loop transfer functions

Problem 1:

A unity negative feedback system has the open-loop transfer function.

G(s) = (s + 1)/(s3 + 4s2 + 6s + 10)

1. Using MATLAB, determine the closed-loop transfer function.

2. Using MATLAB, find the roots of the characteristic equation.

3. Is the system stable, marginally stable, or unstable?

4. Use ltiview to determine the overshoot, rise time, and settling time in response to a unit step function.

5. Use ltiview to obtain a pole/zero map.

Figure 1

Figure 1

Problem 2:

Consider the feedback and control system in Figure 1 above.

1. Using the for function, develop a MATLAB script to compute the closed-loop transfer function poles for and plot the results denoting the poles with the "X" symbol. 50≤≤K

2. Determine the maximum range of K for stability with the Routh-Hurwitz method.

3. Compute the roots of the characteristic equation when K is the minimum value allowed for stability.

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#### Solution Summary

The solution uses MATLAB to compute the unity negative feedback system as the open-loop transfer function. The roots of the characteristic equation are determined.