By KE LUO )KE WA XI QI ?(KE LUO )BO GE DAN HU YU LING DENG YI

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**Extra resources for Fuzzy Controller Design Theory and Applications**

**Example text**

For some control problems, only a few rules may be sufficient to provide good control quality, while in other cases certain combinations of linguistic values at © 2006 by Taylor & Francis Group, LLC ✐ ✐ ✐ ✐ ✐ ✐ “DK6032_C002” — 2005/11/4 — 17:35 — page 21 — #13 ✐ ✐ 21 Fuzzy Controller Design controller inputs simply do not or cannot occur. Incompleteness may also reflect a lack of the operator’s knowledge about process control. Besides fuzzy propositions and relations, the consequent parts of fuzzy rules may also have functions and expressions, which explicitly determine the dependence of controller inputs and outputs.

Incompleteness may also reflect a lack of the operator’s knowledge about process control. Besides fuzzy propositions and relations, the consequent parts of fuzzy rules may also have functions and expressions, which explicitly determine the dependence of controller inputs and outputs. This type of controller is often referred to as a Takagi–Sugeno fuzzy controller (see References 23 and 12 in Chapters 1 and 2, respectively). The rules of such a controller have the form FR i : IF Rpq THEN ui = ρi (x1 , x2 , .

We have already mentioned that the design of a fuzzy controller is actually a heuristic search for the best fitted static nonlinear mapping function between controller inputs and outputs. As a result of mapping, every discrete trajectory [e(k), yf (k)] has a matching controller output series uFC (k), k = 0, 1, . . 13). This allows us to interpret the fuzzy rule table as a partitioned state space composed of a phase plane and a corresponding fuzzy control surface lying above the plane. Every controller output sequence uFC (k) belongs to this fuzzy control surface.