Page 65 - Instrumentation and Measurement

The above equation for PI controller output is often written as

Kp/Ki is called the integral action time Ti and so

Because of the lack of a steady state error, a PI controller can be used where there are large changes
in the process variable. However, because the integration part of the control takes time, the changes
must be relatively slow to prevent oscillations.

4.7 PID Control

Combining all three modes of control (proportional, integral and derivative) enables a controller to
be produced which has no steady state error and reduces the tendency for oscillations. Such a
controller is known as a three-mode controller or PID controller. The equation describing its action
is

controller output = Kp x error + Ki x integral of error + Kd x rate of change of error
where Kp is the proportionality constant, Ki the integral constant and Kd the derivative constant. The
above equation can be written as

A PID controller can be considered to be a proportional controller which has integral control to
eliminate the offset error and derivative control to reduce time lags.
EXAMPLE 4.7
Determine the controller output of a three-mode controller having Kp as 4, Ti as 0.2 s, Td as 0.5 s at
time (a) t = 0 and (b) t = 2 s when there is an error input which starts at 0 at time t = 0 and increases
at 1%/s (Figure 4.20).

FIGURE 4.20 Example.

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