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filled4 - ME 475 Handouts Spring 2011 1 Slide 1 ME 475...

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Unformatted text preview: ME 475 Handouts - Spring 2011 1 Slide 1 ME 475 Session 4: Transfer Functions, Poles, and Zeros Galen King Purdue University Free & Forced Responses • Free Response ( u ( t ) = 0 & nonzero ICs ) – The response of a system to zero input and nonzero initial conditions . – Can be obtained by • Let u ( t ) = 0 and use LT and ILT to solve for the free response. • Forced Response ( zero ICs & nonzero u ( t ) ) – The response of a system to nonzero input and zero initial conditions . – Can be obtained by • Assume zero ICs and use LT and ILT to solve for the forced response (replace differentiation with s in the I/O ODE). Slide 2 ME 475 Session 4: Transfer Functions, Poles, and Zeros Galen King Purdue University Transfer Function Given a general nth order system model: The forced response (zero ICs) of the system due to input u ( t ) is: – Taking the LT of the ODE : ( ) ( 1) ( ) ( 1) 1 1 1 1 n n m m n n m m a y a y a y a y b u b u b u b u---- + + + + = + + + + ɺ ɺ ⋯ ⋯ ( 29 ( ) ( ) WHY?...
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filled4 - ME 475 Handouts Spring 2011 1 Slide 1 ME 475...

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