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Lab 02-Residues

# Lab 02-Residues - Chemical Engineering Department...

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University of Florida ECH 4323L / ECH 6326 LABORATORY 2 CALCULATION OF RESIDUES USING MATLAB Student Name:_______________________________ MATLAB can be used to calculate the residues of a rational function Y(s) = (1) where B(s) is the numerator polynomial of order m, and A(s) is the denominator polynomial of order n. The poles of the denominator polynomial are {p 1 , p 2 , p 3 , ..., p n} and can be found by taking the roots of the denominator polynomials. The poles can be real or complex, distinct or repeated. When the rational function (1) is strictly proper ( i.e., m < n) basic theory of partial- fractions expansions is as follows. When the poles are distinct (real or imaginary), the partial-fractions expansion of Y(s) is of the form Y(s) = + + + ... + (2) where r q is the residue corresponding to pole p q , k=1, 2, …, n. The residue r q is a real number when pole p q is real, and r q = β +i γ is a complex number when p q is complex. If there are repeated real poles, say p 1 =p 2 =p 3 , then Y(s) = + + + ... + (3) Finally, when the rational function is not strictly proper , ( i.e. , m n), the partial-fractions expansions includes and additional polynomial K(s), and expansions (2) and (3) must be respectively modified to the forms Y(s) = K(s) + + + + ... + (4)

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Lab 02-Residues - Chemical Engineering Department...

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