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
-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)
M
-60
-50
0.1
1
10
-360
-270
-180
-90
0
(deg)
(rad/sec)

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