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num = [1 2 3 2 1] den = [1 4 7 6 2] zeros = roots(num) Problem 4: This problem introduces several MATLAB commands that are useful for working
with the transfer function representation of a LTI system. As an example, consider a LTI system
described by the transfer function
\$4 + 283 + 382 + 2s + 1
H(\$) = 4+ 483 + 782 + 6s + 2′
a) Using the MATLAB command roots, determine the poles and the zeros of the transfer function
H(s).
b) In a previous homework we have learned that an LTI system can be represented in MATLAB
in terms of P and Q of the ODE representation of the system. Using these polynomials in
conjunction with either the step or Isim commands allows us to find the response of a LTI
system. We also have seen in class that the transfer function for the LTI system described by
the ODE
Q (D)y (t) = P(D)f(t)
is
H (s) =
Y(s)
P(s)
F(s)
Q (s )
And, so it is also possible to represent a transfer function in MATLAB using the polynomials
P and Q. In order to simplify the representation of LTI systems, MATLAB packages the
polynomials P and Q into a single structure using the command of
gt; gt; sys = tf (P, Q)
where P and Q are vectors and sys is a variable that represents the system. Now, generate a
pole-zero map of the transfer function above using the MATLAB commandEngineering Technology