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# lecture8 - 8 Dynamical System Analytical Description 8.1...

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1 The Transfer Function is defined as the ratio output/input in terms of the Laplace variable s. We need to perform Laplace Transform on the governing differential equations. Then we assume all initial conditions to be zero. Group some terms to form the ratio output/input. 8. Dynamical System Analytical Description 8.1 Transfer Function & Block Diagram

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2 Example ( 29 Function Transfer the is k cs ms 1 F(s) Y(s) ) s ( F ) s ( Y k cs ms ) s ( F ) s ( kY ) s ( csY ) s ( Y ms output. is y(t) and input is f(t) Here ) s ( sY y ) s ( sY dt dy L ); s ( Y s y sy ) s ( Y s dt y d L Recall ) conditions initial zero (assuming Transform Laplace Take ) t ( f ky dt dy c dt y d m : is equation al differenti the Suppose 2 2 2 o 2 ' o o 2 2 2 2 2 + + = = + + = + + = - = = - - = = + + Y(s) F(s) k cs ms 1 2 + +
3 Another Example ( 29 Function Transfer the is 1 s 3 1 U(s) Y(s) ) s ( U ) s ( Y 1 s 3 ) s ( U ) s ( Y ) s ( sY 3 conditions initial zero assume : again Note output. y(t) and input as u(t) treat and Transform Laplace Take ) t ( u y dt

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lecture8 - 8 Dynamical System Analytical Description 8.1...

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