User`s guide

8 Model Analysis
Using Frequency-Response Plots to Validate Models
In this section...
“What Is Frequency Response?” on page 8-32
“How Frequency Response Helps to Validate Models” on page 8-33
“What D oes a Frequency-Re sponse P lot Sho w?” on page 8-34
“How to Plot Bode Plots Using the G UI” on p age 8-35
“How to Plot Bode and Nyquist Plots at the Command Line” on page 8-38
What Is Frequency Response?
Frequency response plots show the complex values of a transfer function as a
function of frequency.
Inthecaseoflineardynamicsystems, the transfer function G is essentially
an operator that takes the input u of a l inear system to the o utput y:
yGu=
For a continuous-time system, the transfer function relates the Laplace
transforms of the input U(s) and output Y(s):
Ys GsUs() () ()=
In this case, the frequency function G(iw) is the transfer f unction evaluated
on the imaginary axis s=iw.
For a discrete-time system sampled with a tim e interval T,thetransfer
function relates the Z-transforms of the input U(z) and output Y(z):
Yz GzUz() () ()=
In this case, the frequency function G(e
iwT
) is the transfer function G(z)
evaluated on the unit circle. The argument of the frequency function G(e
iwT
)
8-32