Fuzzy Matrix Controllers support both linear and non-linear gain mapping. Traditional PI controllers have linear gains. Thus, Fuzzy Matrix controllers can emulate traditional PI controllers.
Linear Gain Plane Non-Linear Gain Plane
The real advantage of Fuzzy Matrix Controllers is the ability to specify a non-linear gain plane. Gain mapping is specified by membership breakpoints and rule moves. The gain plane shown below represents a 6x6 controller with two inputs. Typically the inputs are process error (PV-SP) and change in PV over change in time (dPV/dT). Controllers with 3 process inputs have a 4 dimensional gain plane, which is harder to visualize.
 

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