By Bonissone P.P.
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Verror along horizontal axis and dVerror along vertical axis. Both low level controllers are fuzzy logic proportional integral PI controllers; by appropriately adjusting the scaling factors, membership functions, and rule sets of the fuzzy PIs, one has been con gured as a coarse controller, and the other as a ne controller. The inputs of both low level fuzzy logic PI controllers are: output voltage error Verror and the change in output voltage error dVerror , where Verror is the di erence of output voltage and output voltage setpoint and dVerror is the di erence of the current and previous values of Verror .
Within this paper we will limit our scope to 42 Fuzzy Controllers FCs , reasoning systems composed of a Knowledge Base KB , an inference engine, and a defuzzi cation stage. The KB is comprised by a rule base, describing the relationship between state vector and output, and by the semantics of the linguistic terms used in the rule base. The semantics are established by scaling factors delimiting the regions of saturation and by termsets de ning a fuzzy partition in the state and output spaces Bonissone and Chiang, 1993 .
1993 we will further limit our discussion to multilayer feedforward nets. A feedforward multilayer NN is composed of a network of processing units or neurons. Each neuron performs the weighted sum of its input, using the resulting sum as the argument of a non-linear activation function. Originally the activation functions were sharp thresholds or Heavyside functions, which evolved to piecewise linear saturation functions, to di erentiable saturation functions or sigmoids , and to gaussian functions for RBFs .