# l7 - 16.06 Lecture 7 Transient Response Characteristics and...

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16.06 Lecture 7 Transient Response Characteristics and System Stability Karen Willcox September 17, 2003 Today’s Topics 1. Graphical determination of residues 2. System stability 3. Simple lag system 4. Quadratic lag system Reading : 4.4 1

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1 Graphical determination of residues (com- plex conjugate poles) (vdv 1.8, 1.9) (a) The technique for real poles (Lecture 7) applies here, but the residues are complex conjugates. (b) We consider ω 2 C ( s )= n (1) s ( s 2 +2 ζω n s + ω 2 n ) The symbols ζ and ω n will take on physical meaning shortly. (c) For ζ< 1, the poles of Eq. (1) are s 1 = s 2 = s 3 = The pole-zero pattern is: 2
PFE is: C ( s ) = (2) (d) Why do we consider ζ< 1 (underdamped)? Well: when ζ = 1 (critically damped): when ζ> 1 (overdamped): In either case, the poles are on the negative real axis. This is not typical for aero/astro systems. (e) Eq. (2) shows that the time response will be: If you like this stuﬀ, please read pgs. 23-25 of the text. However,

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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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l7 - 16.06 Lecture 7 Transient Response Characteristics and...

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