Lesson 6 - Process Control Mechanisms

Integral control exists to eliminate the steady state offset.

So how does integral control work? It keeps track of the cumulative error term over a period and uses this to compensate for the offset. It is essentially the memory of the controller.

The equation for the integral controller is as follows:

Where:

CO_I(t) = the controller output for the integral term

K_c = the controller gain

T_I = the integral time constant

It is sometimes called the “integral gain”:

  is the sum of the error term over time. (Integrals are the sum of the values of a term over time from 0 to t.)

The figure below shows how the error term is continuously calculated:

Figure: Integral error term

In order to control the impact of the integral term, we can adjust T_I. Thus, by making T_I smaller, the impact of the integral term will be larger. The figure below shows this in action:

Figure: How the integral time constant influences loop behaviour

For the blue line in the figure above, the integral term was amplified, which resulted in an overshoot. We could liken this to being in the shower and feeling ten seconds of cold water, and then overreacting by opening the tap up fully, only to be scalded. For the red line, the integral term was very small. This is similar to standing under the cold shower for two minutes before you acknowledge that it is cold.

Integral controllers do not operate on their own. Let us quickly look at what happens if you combine proportional and integral control.