MECH 466 - Lecture2-LaplaceTransforms-2009W

Laplace ut is often omitted ut 200809 mech466

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Unformatted text preview: u(t) 2008/09 MECH466 : Automatic Control 9 Properties of Laplace transform 1. Linearity 2008/09 MECH466 : Automatic Control 10 Properties of Laplace transform 2.Time delay f(t) f(t) Proof. Proof. 0 f(t-T) f(tT t-domain Ex. s-domain Ex. 2008/09 MECH466 : Automatic Control 11 2008/09 MECH466 : Automatic Control 12 3 Properties of Laplace transform 3. Differentiation Properties of Laplace transform 4. Integration t-domain t-domain Proof. Proof. s-domain s-domain Ex. 2008/09 MECH466 : Automatic Control 13 Properties of Laplace transform 5. Final value theorem 2008/09 MECH466 : Automatic Control 14 Properties of Laplace transform 6. Initial value theorem if all the poles of sF(s) are in sF(s) the left half plane (LHP) if the limits exist. if Remark: In this theorem, it does not matter if pole location is in L...
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