By Prof. Dr. Dimiter Driankov, Dr. Hans Hellendoorn, Dr. Michael Reinfrank (auth.)
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Extra info for An Introduction to Fuzzy Control
1 NB NM zo NS PS PM PB 1 2 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Fig. 6. The fuzzy sets NB, NM, NS, ZO, PS, PM and PB on the domain [-6,6]. Typical rules of a PI-like FKBC using these linguistic notions are: if e is NB and e is ZO then u is PB if e is NM and e is ZO then u is PM if e is ZO and e is PB then u is NB where e denotes error, e change-of-error, and u denotes the control output value. We will use special names for these kinds of fuzzy sets ,with straight lines, because they return again and again in fuzzy control theory.
120}) respectively. Examples of decreasing notions on these domains are 'small', 'thin', 'cold', and 'young'. Examples of approximating notions on these domains are often difficult to express in one word. On the domain of temperature it may be 'comfortable', on the domain of age it may be 'middleaged'. Suppose one wishes to build an air conditioner, then there may be the following linguistic notions which describe the temperature to be controlled: 'hot' (Fig. 2), 'cold' (Fig. 3), and 'comfortable' (Fig.
One can, of course, ask the question of how it is that the purely experiential knowledge of the process operator is expressed in terms of such purely mathematical concepts such as error and its derivatives. Interestingly enough, the answer to this question is to be found in a publication by Bekey  that appeared a long time before the notion of a KBC was conceived. In the following we will reproduce the main findings of this publication. Consider a tracking task in which the operator is required to follow a constant velocity input (a ramp signal) with zero error.
An Introduction to Fuzzy Control by Prof. Dr. Dimiter Driankov, Dr. Hans Hellendoorn, Dr. Michael Reinfrank (auth.)