L6-1_xferfcns

L6-1_xferfcns - CDS 101/110a: Lecture 6-1 Transfer...

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1 CDS 101/110a: Lecture 6-1 Transfer Functions Douglas MacMynowski 1 November 2010 Goals: Motivate and define the input/output transfer function of a linear system Understand the relationships among frequency response (Bode plot), transfer function, and state-space model Introduce block diagram algebra for transfer functions of interconnected systems Reading: Åström and Murray, Feedback Systems, Ch 8 Advanced : Lewis, Chapters 3-4 or DFT, Chapter 2 Frequency Domain Modeling Defn. The frequency response of a linear system is the relationship between the gain and phase of a sinusoidal input and the corresponding steady state (sinusoidal) output. 0 1 0 1 Bode plot (1940; Henrik Bode) Plot gain and phase vs input frequency Gain is plotting using log-log plot Phase is plotting with log-linear plot Frequency Response Magnitude (dB) -40 -30 -20 -10 0 10 20 0 5 10 -1 0 5 10 -1 Douglas MacMynowski, Caltech CDS CDS 101/110, 1 Nov 10 2 Can read off the system response to a sinusoid – in the lab or in simulations Linearity can construct response to any input (via Fourier decomposition) Key idea: do all computations in terms of gain and phase (frequency domain) Phase (deg) M -60 -50 0.1 1 10 -360 -270 -180 -90 0 (deg) (rad/sec)
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2 Transfer Function and Frequency Response Exponential response of a linear state space system (from convolution) Transfer function transient steady state Steady state response is proportional to exponential input => look at input/output ratio is the transfer function between input and output Frequency response Common transfer functions Douglas MacMynowski, Caltech CDS CDS 101/110, 1 Nov 10 4 gain phase
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This note was uploaded on 01/04/2012 for the course CDS 101 taught by Professor Murray,r during the Fall '08 term at Caltech.

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L6-1_xferfcns - CDS 101/110a: Lecture 6-1 Transfer...

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