This control mode results from combination of proportional and integral mode. The analytical expression for the PI mode is given by:

where pI (0) = integral term value at t = 0 (initial value)

The main advantage of this composite control mode is that one-to-one correspondence of the proportional control mode is available and integral mode eliminates the inherent offset. It can be observed from the equation that the proportional gain also changes the net integration mode gain, but the integration gain, through KI , can be independently adjusted.

The proportional mode when used alone produces offset error whenever load change occurs and nominal controller output will not provide zero error. But in PI mode, integral function provides the required new controller output, thereby allowing the error to be zero after a load change.

The integral feature effectively provides a reset of the zero error output after a load change occurs.

Accommodation of the new load condition requires a new controller output. It can be observed that the controller output is provided through a sum of proportional plus integral action that finally brings the error back to zero value.

## Application, Advantages and Disadvantages:

This composite PI mode eliminates the offset problem of proportional controller.

The mode can be used in systems with frequent or large load changes

Because of integration time the process must have relatively slow changes in load to prevent oscillations induced by the integral overshoot.

During start-up of a batch process, the integral action causes a considerable overshoot of the error and output before settling to the operation point. The PB is defined as hat positive and negative error for which the output will be driven to 0% and 100%. Therefore, the presence of an integral accumulation changes the amount of error that will bring about such saturation by the proportional term.