{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

This preview shows pages 1–5. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 Transient response and inverse Laplace trans- form Question: Given the pole-zero diagram of C ( s ), how do you get c ( t )?
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}