Page 82 - Biosystems Engineering

Biosystems Analysis and Optimization 63

The response of the ground speed to the multisine excitation of
the pump setting is split up in several parts:
• Response at excited frequencies: The frequency response of the
process variable on the frequencies directly excited by the
multisine is the linear process response on that frequency.
Due to the structure of the excitation sequence, contamina-
tion of this response by harmonics is very low. Only second-
order harmonics or higher can influence the response. The
frequency response of the pump setting is also taken into
account on the excited frequencies. The pump setting is the
control variable to which the multisine is applied. In practice,
the measured pump-setting spectrum is not identical to the
applied spectrum because of timing and resolution issues.
The frequency response on the pump setting is normalized so
that it has a unit response on the first excited frequency. For
each process variable, the response on the excited frequency
is then divided by this normalized input spectrum on that
frequency in order to obtain the transfer function from the
pump setting to the process variable. The unit of this transfer
function is the unit of the gain between the pump setting and
the process variable. Because the input spectrum is more or
less zero on the nonexcited frequencies, this rescaling can
only be performed on the excited frequencies.
• Response at even nonexcited frequencies: The frequency response
on these frequencies is most probably caused by the first har-
monic of an excited frequency. If this response is clearly larger
than the noise response, there are considerable nonlinearities
present in the system.
• Response at odd nonexcited frequencies: This response shows the
presence of second- or higher-order harmonics. A clear
response on these frequencies indicates large nonlinearities.
• Noise response: Because multiple periods of the multisine are
available—in this case, four full periods—the average process
response can be calculated. Noise is defined as the variation
around this average response (standard deviation per
frequency over the four periods). This means that the system
is assumed to be constant during excitation.
A multisine excitation is not the standard input for the pump
setting. This means that some effects that are visible with this excita-
tion may not need to be modeled in the actual controller. After all,
only the effects that are encountered during normal controller oper-
ation need to be modeled. Due to nonlinear effects, the response to
a multisine excitation may differ considerably from the response to
a step input.