The control rules (Table 1) of the general fuzzy controller indicate that changes of the control outputs are regular. Based on the figures along the leading diagonal, there is a polygonal line, which can be fitted with a smooth curve (a sigmoid function). In fact, the smooth curve can be viewed as innumerable polygonal lines with a length approaching to zero joined together. When designing fuzzy controller, the form (when the deviation is comparatively large, the control demand would be loosely considered; on the contrary, when the deviation is comparatively small, the control demand would be strictly treated) that is loosen at both sides and thick at the middle is generally adopted, which is consistent with the variation form of the sigmoid function. Thus, the sigmoid function incarnates the idea of fuzzy control on a certain extent. Moreover, the fold line surface that corresponds with the whole fuzzy rule of fuzzy control can be replaced with the curved surface composed by smooth curves, as shown in figure 7.
Fig. 7. Sigmoid curved surface
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