Agriculture Reference
In-Depth Information
include a temperature regulation system that has cool/off/heat states or a mechani-
cal device that has retract/off/extend states. These controllers are often used where
the controller output is time-integrated (in the mathematical sense of the word) in
the system so that the controller output represents the time derivative of the eventual
system output. In the recent examples, the cooling or heating is time-integrated into
temperature or the retraction or extension velocity is time-integrated into position or
displacement.
A difficulty with the above-mentioned controllers is that they tend to have a trade-
off between fast response and stability. If the system is designed to respond fast,
such as with a high cooling/heating rate or high retraction/extension velocity, it is
likely that the inherent delays and inertias in the system will cause the agricultural
automation system to have overshoots, oscillatory behaviors, and/or limit cycles.
Instead of achieving the desired output, the system may oscillate above and below
the desired output value.
It is usually better when the system responds rapidly when its output needs to
change substantially and more slowly when only a little change is needed. This type
of control is called proportional control and is very popular. It requires a controller
capable of producing a wide variety of outputs. If it can produce an infinite number
of different outputs within its operating range, it exhibits continuous control. In com-
puter control, the true infinite number of outputs cannot be achieved by the controller
because of the discrete nature of the digital computer. However, the system is usually
considered as being continuous because of the large number of outputs. For example,
there are 4096 potential output levels from a 12-bit digital-to-analog converter.
In most implementations, an “error” is created by subtracting the value of the sys-
tem output from its desired value. If the error is small, the controller should do little,
and if the error is large, the controller should do more. Again, if the controller acts
fast there will be faster response, but more tendency toward oscillation and instabil-
ity. Improved performance can often be obtained by also considering the integral
or derivative of the error, thereby forming PID (proportional-integral-derivative)
control.
The proportional sensitivity of the controller to a given error is one parameter
that needs to be carefully selected to optimize system performance. For systems in
which integral and derivative actions are included, the integral and derivative gains
(the sensitivities to the integral and derivative of the error signal) also need to be
determined. There are analytical techniques to do such tuning. Alternatively, heuris-
tic techniques can be used. One common technique for tuning such controllers is the
Ziegler-Nichols method.
Controllers can be mathematically analyzed to predict and understand perfor-
mance and to enable improvements. The classical control theory was developed
in the middle of the twentieth century to analyze automation systems. It converts
the ordinary time differential equations describing dynamic systems from a time
domain to a frequency domain using Laplace transforms. Besides allowing predic-
tions of the system response to inputs, such a conversion allows the use of classi-
cal control system theory techniques. In addition to the mathematical analyses that
can be performed, there are many graphical techniques—such as pole-zero plots,
root locus plots, Bode plots, Nyquist plots, and Nichols charts—that can help with
