Implementation of the differential control law for industrial regulators
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As shown in the figure, it is the controller output function of the regulator under step disturbances. Why is the term representing the differential action referred to as an approximate differential action? What is its relationship with actual differential action?
Where does it say “approximate differential action”?
The amplification factor of an ideal differential amplifier should be infinite, whereas the amplification factor of actual instruments is finite. Therefore, there is a difference between the actual differential curve and the theoretical curve.
If the input is a step signal, the output of an ideal differential operator at time t=0 should be infinite, while it should be zero for t≠0; such a circuit is difficult to implement. From a control perspective, it is necessary to determine the duration of the differential lead adjustment based on the lag of the controlled object; therefore, in actual differential action, the amplitude and duration of the effect are determined by the differential amplification factor kd and Td.