IV.1.3.2 Proportional Integral Controllers

The actuating output of a PI controller is given as:

(IV.6)

where is the integral time constant (or the reset time) in minutes. The PI controller not only actuates on the basis of current error, but it also accounts for the history of all the past errors that has been encountered since the control action has started. From eq.(IV.6) the transfer function of the PI controller is

(IV.7)

In industrial lingo, the PI Controller is also termed as “Gain-Reset” controller. The reset time is a design parameter which usually varies within the range

At this point, it is worth explaining the significance of the term reset . Suppose the error between desired setpoint and process output changes by a constant step of magnitude . The effect of integral term of eqn. (IV.6) after every minutes is given as

(IV.8)

In other words, the integral action repeats the response of the proportional action every minutes and “resets” itself for an integral action. Sometimes the controllers are calibrated in terms of reciprocal of reset time, (repeats per minute). This is known as reset rate .