Lect3 - Dynamic Modeling, Linearization, Laplace

# Lect3 - Dynamic Modeling, Linearization, Laplace -...

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1/26/2010 1 Lecture 3 and 4 : Dynamic Modelin Lecture 3 and 4 : Dynamic Modeling Linearization, and Laplace Transformation AerE353, Spring 2010 Prof. Soon Jo Chung (sjchung@illinois.edu) Linearization (Sec. 9.2.1, p. 603)

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1/26/2010 2 Spring Damper Example is Various ways of solving system response finding solution x(t) 1. Use formulation and integration Response to Response to input initial condition Convolution Linear system: principle of superposition 2. Laplace Transform 3. Numerical Integration and use MATLAB
1/26/2010 3 Second Order System Laplace transform 2 21 2 oo oi o o dq aa a q b q dt dt b k a  static gain 2 2 1 o o o i b Q a a a Q ss 2 1 2 2 o n o a a a undamped natural freq. damping ratio =0.7071 e 22 freq magnitude =1.5 =0.7071 =0.1 5 =0.1 =1.5 time amplitud phase(deg) 0 90 180 =0.1 =0.7071 =1.5 n

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1/26/2010 4 Damping Ratio and Natural Freq Step Input Response
1/26/2010 5 Laplace Transform Attributes of linear time invariant systems

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## This note was uploaded on 04/12/2010 for the course AE 353 taught by Professor Voulgaris,p during the Spring '08 term at University of Illinois, Urbana Champaign.

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Lect3 - Dynamic Modeling, Linearization, Laplace -...

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