A neural network controller in parallel with a proportional-plus-integral (PI) feedback controller in a control system. At least one input port of the neural network for receiving an input signal representing a condition of a process is included. A first set of data is obtained that includes a plurality of output values of the neural network obtained during a training period thereof using a plurality of first inputs representing a plurality of conditions of the process. The process/plant condition signals generally define the process/plant, and may include one set-point as well as signals generated using measured systems variables/parameters. In operation, the neural network contributes to an output of the PI controller only upon detection of at least one triggering event, at which time a value of the first set of data corresponding with the condition deviation is added-in thus, contributing to the proportional-plus-integral feedback controller. The triggering event can be characterized as (a) a change in any one of the input signals greater-than a preselected amount, or (b) a detectable process condition deviation greater-than a preselected magnitude, for which an adjustment is needed to the process/plant being controlled. Also a method for controlling a process with a neural network controller operating in parallel with a IP controller is included.