By Kokileswar Bhattacharyya
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Long delay monotone 8. long delay oscillatory. The description of the open-loop process as a "short", "medium", or "long" delay is done on the basis of the ratio of the pure time delay in the process and the dominant time constant. cng delay oscillatory Fig. 4. Open-loop process characteristics. time time 24 1. Introduction squares . 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.
3 Classical Set Theory A classical set is a collection of objects of any kind. The concept of a set has become one of the most fundamental notions of mathematics. So-called set 1 According to Prof. Zadeh this example came into his mind when he had a breakfast together with Prof. Hans-J. Zimmermann. 1. 1 0 0 0 0 0 theory was founded by the German mathematician Georg Cantor (1845~ 1918). In set theory the notions 'set' and 'element' are primitive. They are not defined in terms of other concepts. Letting A be a set, "x E A" means that x is an element of the set A and "x rt A" means that x does not belong to the set A.
Such a KBS normally incorporates knowledge of different types: • Physical knowledge. • Process configuration knowledge. , work schedules, stops, repairs, etc. • Experiential knowledge about process operation in similar planning tasks. • Statistical knowledge about uncertainties in process parameters and measurements. • Simulation facilities to predict process behavior as a result of intended actions. Thus the KBS has to be able to represent and reason with conceptually different types of knowledge which involves the use of causal models, temporal and spatial data and relationships, taxonomic representations, etc.