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By Saul A. Basri

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12) Expanding both sides of the equation, we get S = 2 x 2  3x 3  5u  O1 x 3  O 2 x 2 =  K ( x3  O1 x 2  O 2 x1  O 2 y d ) The u obtained from this equation will be used for the control. This controller needs access to all three states, whereas the fuzzy logic controller of [l, 14] makes use of only x1 and x 2 . To have a fair comparison, we will construct an observer to get an estimate of the state variable x 3 . A standard Luenburger observer is designed to get an estimate of x 3 . 6).

For instance, if someone says: the temperature here is high. This high temperature contains some middle and even low temperature components. From this point of view, fuzzy control uses universal or global components, not just a limited range of components as the classical variables did. With the rapid development of fuzzy technologies, different fuzzy control strategies have been developed based on different classical control methods, such as PID-fuzzy control [4], sliding-mode fuzzy control [5], neural fuzzy control, adaptor fuzzy control [6] and phase-plan mapping fuzzy control [7].

The idea of fuzzy logic was invented by Professor L. A. Zadeh of the University of California at Berkeley in 1965 [1]. This invention was not well recognized until Dr. E. H. Mamdani, who is a professor at London University, applied the fuzzy logic in a practical application to control an automatic steam engine in 1974 [2], which is almost ten years after the fuzzy theory was invented. Then, in 1976, Blue Circle Cement and SIRA in Denmark developed an industrial application to control cement kilns [3].

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