l6 - 16.06 Lecture 6 The s-Plane, Poles and Zeroes Karen...

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16.06 Lecture 6 The s-Plane, Poles and Zeroes Karen Willcox September 15, 2003 Today’s Topics 1. Poles and zeroes 2. Transient response and inverse Laplace transform 3. Graphical determination of residues Reading : 1.7 (from the top of pg. 14), 1.8, 1.9 1
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1 The s-plane We write C ( s )= G ( s ) R ( s ) where C , G and R are each ratios of polynomials in s , i.e. G ( s num G . den G Consider the following definitions: zeroes of C , G and R are poles of C , G and R are system zeroes and poles are system characteristic polynomial is system characteristic equation is Note that the roots of the C.E. are Since, the polynomials have real coefficients, the poles and zeros are 2
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We plot the poles and zeros in the s ( σ + ) plane. Example: 1 Assume R ( s )= s . Then the pole-zero pattern of C ( s R ( s ) G ( s ) is the superposition of the patterns of R ( s ) and G ( s ): K ( s +2) C ( s s ( s +4) 3
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2 Transient response and inverse Laplace trans- form Question: Given the pole-zero diagram of C ( s ), how do you get c ( t )?
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This note was uploaded on 11/06/2011 for the course AERO 100 taught by Professor Willcox during the Fall '03 term at MIT.

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l6 - 16.06 Lecture 6 The s-Plane, Poles and Zeroes Karen...

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