MECH 466 - Lecture3-ODEs-2009W

Inverse laplace transform m we want to know the

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Unformatted text preview: of x(t). By Laplace transform, x(t). (Total response) = (Forced response) + (Initial condition response) 2008/09 MECH466 : Automatic Control 19 2008/09 MECH466 : Automatic Control 20 5 Ex: Mechanical accelerometer Ex: Accelerometer (cont’d) Taken from Dorf & Bishop book Taken 2008/09 We would like to know how y(t) moves when unit We y(t) step f(t) is applied with zero ICs. f(t) By Newton’s law By Newton’ MECH466 : Automatic Control 21 2008/09 Ex: Mechanical accelerometer (cont’d) Suppose that b/M=3, k/M=2 and Ms=1. Suppose Partial fraction expansion Partial MECH466 : Automatic Control 22 Summary & Exercises Solution procedure to ODEs Solution 1. Laplace transform 2. Partial fraction expansion 3. Inverse Laplace transform Inverse Laplace transform Inverse Next, modeling of physical systems using Next, Laplace transform Exercises Exercises 0 Amplitude -0.1 -0.2 Read Sections 2-2 up to page 42. Read 2Solve Problems 3 & 4 in page 94 (or page 28). Solve -0.3 -0.4 -0.5 0 2008/09 MECH466 : Automatic Control 2 4 6 Tim [sec] e 8 10 23 2008/09 MECH466 : Automatic Control 24 6...
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