Proportional The error is measured, and the corrective action is proportional to the error. Gain is the term for the proportionality coefficient. Some error is inherent, but performance tends to be far superior to on-off control.
Integral control Seldom used alone and can greatly improve proportional control because the integral of the error determines the amount of corrective action. As time goes on, the integral increases such that there will be no offset.
Derivative This is not often necessary for bioprocessing where things tend to change slowly but can be essential for some chemical processes. The corrective action depends on the derivative of the error, and some chemical processes are so unstable that errors can get wild. This means that the derivative will be great such that corrective action kicks in quickly.
An algorithm is needed to select the degree of corrective action. This can be simple rules of thumb or models based on understanding of fundamentals.