An Introduction to Fuzzy Control by Prof. Dr. Dimiter Driankov, Dr. Hans Hellendoorn, Dr.

By Prof. Dr. Dimiter Driankov, Dr. Hans Hellendoorn, Dr. Michael Reinfrank (auth.)

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Extra resources for An Introduction to Fuzzy Control

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Ll positive large positive • Constraint rule 1 if value of e( k) is in constraint region then value of L1u( k) is DC'. This rule specifies the magnitude of the additional L1U(k) to be added to the one already determined by the active rules when e(k) is in the constraint region. The second and the third rules are of the form • Constraint rule 2 if value of e( k) enters constraint region then start summing up the values of L1u( k) determined by constraint rule 1. • Constraint rule 3 if value of e(k) leaves constraint region then subtract the total value of L1u(k) determined by constraint rule 2.

These linguistic notions are meaning-dependent on the actual physical domain, for example, the domain of temperature. In fuzzy control it is usual to use linguistic notions that are meaning-independent of the particular physical do~ main. The domain described above consists of five elements. Consider now a domain consisting of seven elements which is usual in fuzzy control. The elements of the domain have names like 'Positive Big' (PB) , 'Positive Medium' (PM), 'Positive Small' (PS), 'Zero' (ZO), 'Negative Small' (NS), 'Negative Medium' (NM), and 'Negative Big' (NB) (see Chapter 4).

4 Knowledge Representation in KBCs 23 y spr---------------~=_-------- No delay monotone No delay oscillatory ysp time Medium delay monotone time Medium delay oscillatory time t--------=======--- Short delay monotone Short delay oscillatory time time Long delay monotone Long delay oscillatory Fig. 4. Open-loop process characteristics. time 24 1. Introduction squares [107]. The characteristics of the closed loop transient step response employ both of the following: • The magnitude and time of the first overshoot and first undershoot for both the process output and control variable, in a response to a step change in the set-point.

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