Fuzzy controllers compared with linear digital controllers

The purpose of any control system is to control the outputs of a plant in a manner described by the inputs to the control system. If a mathematical model for the plant is known, engineers can find the best linear controller to elicit the desired response. Linear controllers are well understood because they are described with solvable equations based on linear combinations of the inputs, outputs, and their derivatives. Other types of controllers are theoretically possible, but do not lend themselves to direct mathematical analysis. One such alternative to linear control is fuzzy control. Using fuzzy logic, a controller can be designed that outperforms linear controllers. The nonlinearities introduced, however, make it difficult to characterize the control system and therefore to determine relative stability or the optimality of the design