Biomedical Engineering Reference
In-Depth Information
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FIGURE 17.1
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Transfer function from input-output
The common approach to system analysis is to determine the system's transfer
function through observation of its response to a predetermined excitation signal. Eval-
uation of the system characteristics can be performed in the time or frequency domains.
17.2 METHODS
The engineer has several methods available to him/her for evaluating the system's re-
sponse. The Root Locus Method is a graphical approach in the time domain, which gives
an indication of the effect of adjustment based on the relation between the poles of the
transient response function, and the poles and zeros of the open loop transfer function.
The roots of the characteristic equation are obtained directly to give a complete solution
for the time response of the system.
In many cases it is advantageous to obtain system performance characteristics in
terms of response at particular frequencies. Two graphical representations for transfer
function derivations are the Bode and Nyquist Methods. The Bode Plot Method yields
a plot of the magnitude of the output/input ratio versus frequency in rectangular or
logarithmic coordinates. A plot of the corresponding phase angle versus frequency is
also produced. The Nyquist Plot Method is very similar: it plots the output/input ratio
against frequency in polar coordinates. The amplitude and phase data produced with
these methods are very useful for obtaining an estimate of the system's transfer function.
They can be determined experimentally for a steady-state sinusoidal input at various fre-
quencies, from which the magnitude and phase angle diagrams are then derived directly,
leading to the synthesis of the transfer function.
Analytical techniques that fit rational polynomial transfer functions using digital
computers are very popular as they speed the evaluation process considerably. In the next
section, two functions, which provide analytical methods for measuring the time-domain
properties of signal waveforms, will be developed.
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