lecture3

lecture3 - MAE 171A Dynamic Systems Control Lecture 3...

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Unformatted text preview: MAE 171A: Dynamic Systems Control Lecture 3: Dynamical System Properties poles, zeros and impulse response Goele Pipeleers Recall from Lecture 2 . . . Models of Dynamical Systems • general procedure: physical system : lumped masses, springs, dampers ⇓ Newton’s law mathematical model : ordinary differential equation ⇓ (linearization and) Laplace transform mathematical model : transfer function • system analysis: Laplace transform and transfer function 1 Linear Time-invariant Systems Transfer Function • general formula ( m ≤ n ) G ( s ) = b m s m + b m- 1 s m- 1 + ... + b 1 s + b s n + a n- 1 s n- 1 + ... + a 1 s + a = N ( s ) D ( s ) Impulse Response • inverse Laplace transform of transfer function: g ( t ) = L- 1 { G ( s ) } • homogenous response from particular initial conditions • to compute forced response: Y ( s ) = G ( s ) U ( s ) ! y ( t ) = g ( t ) * u ( t ) 2 Zeros • complex numbers z i for which N ( z i ) = 0 and hence, G ( z i ) = 0 • determine inputs that do not pass through the system:...
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This note was uploaded on 08/08/2011 for the course MAE 171 taught by Professor Pipeleers during the Summer '11 term at UCLA.

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lecture3 - MAE 171A Dynamic Systems Control Lecture 3...

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