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# lec3 - AE 383 SYSTEM DYNAMICS Lecture Notes 3(June 24th...

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1 AE 383 SYSTEM DYNAMICS Lecture Notes 3 (June 24 th 2006) Transfer Function Representation of Dynamic Systems Transfer function of a system is defined as the ratio of the Laplace transform of the output to the Laplace transform of the input, with zero initial conditions. Transfer Function = [ ] [ ] conditions initial zero ) ( ) ( ) ( input L output L s u s x s G = = Transfer functions are defined by only linear time-invariant systems Transfer function is a property of the system, it is independent of the magnitude and nature of the input. It does not contain any information about the physical structure of the system. Let the equation of motion for a system be (mass-spring-damper system) ) ( t u kx x b x m = + + Taking the Laplace transform with zero initial conditions: ) ( ) ( ) ( ) ( 2 s u s kx s bsx s x ms = + + Transfer function k bs ms s u s x s G + + = = 2 1 ) ( ) ( ) ( We will use Tranfer function blocks in our Simulink Simulations. State Space Representation of Dynamical Systems

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lec3 - AE 383 SYSTEM DYNAMICS Lecture Notes 3(June 24th...

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