PID Feedback Control Loop ◾  77
8.4 Derivative Action
The derivative (rate or preact) action in a controller is for
responding to the rate of change of the error (Equation 8.3).
CO = CO b + (K c T d ) de/dt
(8.3)
where:
T d = derivative time constant
The derivative time constant, T d , determines the amount of
change in controller output as the rate of change of the error
increases or decreases. When the controller output responds
directly to the error signal as shown in Equation 8.3, a spike
or noisy movement in the process variable can be translated
into an immediate movement in the controller output.
8.5 Parallel and Series Algorithms
The simplest algorithm for a PID controller is the sum of
Equations 8.1, 8.2, and 8.3 as shown in Equation 8.4. This is
common in computer-based control systems, and all three
control actions are considered to be operating in parallel.
However, many industrial analog controllers and microprocessor DCS (distributed control system) controllers use a
capacitance lag (filter) of about 0.05 to 0.10 in series with
the process variable signal to reduce the effect of derivative
action from setpoint changes and from short time constant
noise described earlier. 1 When the derivative time constant,
T d , is set to zero, there is no difference between the controller
action of the parallel and the series algorithm with only P and
I action:
CO = K c e + (K c /T i ) ∫ e dt + (K c T d ) de/dt
(8.4)