From Feedback Control of Computing Systems
9.3 PROPORTIONAL–DERIVATIVE CONTROL
The control actions of the proportional or integral controllers are based on the
current error or past errors. In derivative control the controller output is proportional
to the rate of change of the error. The idea behind derivative control is that
the controller should react immediately to a large change in the control error;
in essence, predicting that the error will continue to increase (or decrease) and
act accordingly. Although this quick reaction can result in fast response times,
it can also result in undesirable overreaction, especially if the system output has
The derivative control law has the form
where the derivative control gain KD defines the ratio of the input magnitude
to the change in the error (Figure 9.18). Since the derivative controller adjusts
the control input according to the speed of error variation, it is able to make an
adjustment prior to the appearance of even larger errors. Practically, the derivative
controller is never used by itself since if the error remains constant, the output
of the derivative controller would be zero.
The transfer function of a derivative controller can be found by taking the
Z-transform of Equation (9.14) with...
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