CIFER®-MATLAB Interfaces: Development and ... - Cal Poly

Chapter 2: System Identification using CIFER ®
This chapter primarily contains information found in the CIFER ® user’s manual 5 and is intended
to give readers a solid understanding of how CIFER ® generates a frequency response. This will
help provide insight into the analysis of the validations described in Chapter 4.
CIFER ®
produces both nonparametric and parametric models for systems in the frequency
domain. The nonparametric frequency response should be considered the core of this thesis,
however parametric modeling is still very relevant to CIFER ® as a whole. A frequency response
is a complex-valued function that relates the Fourier Transform of system output to system input.
The general form of a frequency response is shown in Equation 2.1. The frequency response is a
full description of system dynamics, stable or unstable, that does not require assumptions of the
system’s structure.
( f )
( f )
Y
H ( f ) = [2.1]
X
CIFER ® uses a version of the Fast Fourier Transform (FFT) known as the Chirp-Z Transform
(CZT). This transform removes many of the restrictions placed on the discrete Fourier
Transforms and thus is very flexible as an algorithm. Users have greater freedom to specify
sample rates and resolution. The algorithm only runs on a specified frequency range, thus there
are no wasted data points. The CZT algorithm generates three important values that represent the
energy of the system as a function of frequency: input autospectrum (G xx ), output autospectrum
(G yy ), and cross spectrum (G xy ). The frequency response is then calculated using Equation 2.2,
which is unbiased for output noise and biased for input noise.
Gxy
H = [2.2]
G
xx
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