MECH 466 - Lecture3-ODEs-2009W

# Mech466 automatic control ode with initial conditions

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Unformatted text preview: 6 : Automatic Control ODE with initial conditions (ICs) s-domain 1. Laplace transform AE ODE 1 2 Solution to ODE 3 2008/09 MECH466 : Automatic Control Partial fraction expansion distinct roots 7 2008/09 MECH466 : Automatic Control 8 2 Properties of Laplace transform Differentiation (review) Example 1 (cont’d) 2. Partial fraction expansion t-domain unknowns Multiply both sides by s & let s go to zero: Similarly, s-domain 2008/09 MECH466 : Automatic Control 9 Example 1 (cont’d) 2008/09 MECH466 : Automatic Control 10 Example 2 (repeated roots) 3. Inverse Laplace transform ODE with initial conditions (ICs) 1. Laplace transform If we are interested in only the final value of y(t), apply y(t), Final Value Theorem: Repeated roots 2008/09 MECH466 : Automatic Control 11 2008/09 MECH466 : Automatic Control 12 3 Example 2 (cont’d) 2. Partial fraction expansion Exampl...
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