Page 62 - Instrumentation and Measurement

controller output = 4 x 4% = 16%

The error is still changing and so there will still be an output due to the derivative mode. This will be
given by

and so controller output = KpTd x rate of change of error
controller output = 4 x 0.4 x 2% = 3.2%

Hence the total controller output due to both modes is the sum of these two outputs and 16% +
3.2% = 19.2%.

4.6 Integral Control

Integral control is the control mode where the controller output is proportional to the integral of the
error with respect to time, i.e.

controller output α integral of error with time

and so, we can write

I controller output = Ki x integral of error with time

where Ki is the constant of proportionality and, when the controller output is expressed as a
percentage and the error as a percentage, has units of s-1.

To illustrate what is meant by the integral of the error with respect to time, consider a situation where
the error varies with time in the way shown in Figure 4.16. The value of the integral at some time t
is the area under the graph between t=0 and t. Thus, we have

controller output α area under the error graph between t=0 and t

FIGURE 4.16 Integral control.

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