Fuzzy input window

The two seven set fuzzy input windows shown in Figure 10.8 gives a possible 7x7 set of control rules of the form given in equation (10.21). It is convenient to tabulate the two-dimensional rulebase as shown in Figure 10.9. 

Fig. 10.8 Seven set fuzzy input windows for error (e) and rate of change of error ice). Assume that a certain rule in the rulebase is given by equation (10.22) OR IF e is A AND ce is B THEN u = C...

In Figure 10.8 and equation (10.20) the fuzzy sets that were hit in the error input window when e(t) = 2.5 were PS and PM. In the rate of change input window when ce = -0.2, the fuzzy sets to be hit were NS and Z. From Figure 10.9, the relevant rules that correspond to these hits are... 

Fuzzy inference is therefore the process of mapping membership values from the input windows, through the rulebase, to the output window(s). 

Figure 10.38 shows an input window with three triangular fuzzy sets NB, Z and PB. Each set is positioned in its regime of operation by the centre parameter c so that, for example, NB can only operate on the negative side of the universe of discourse. The width of each set is controlled by parameter ri . 

Figure 10.9 assumes that the output window contains seven fuzzy sets with the same linguistic labels as the input fuzzy sets. If the universe of discourse for the control signal u(t) is 9, then the output window is as shown in Figure 10.10. 

For the input and output fuzzy windows given in Figure 10.8 and 10.10, together with the fuzzy rulebase shown in Figure 10.9, determine... 

Fig. 10.14 Input and output fuzzy windows for the inverted pendulum problem.

---