There are many concepts that are used in fuzzy sets that sometimes become useful when studying fuzzy control. The following problems introduce some of the more popular fuzzy set concepts that not treate were not treated earlier in the chapter. (a)The\support\ of a fuzzy set with membership function (x) is the(crisp) set of all points x on the universe of discourse such
Develop a graphical depiction of the operation of the fuzzy controller for the inverted pendulum similar to 3 π the one given in Figure2.1 99 on page46. For this choose(t)=andet)=, which will result in four rules being on. Be sure to show all parts of the graphical depiction
There are many concepts that are used in fuzzy logic that sometimes become useful when studying fuzzy control. The following problems introduce some of the more popular fuzzy logic oncepts that were not treated earlier in the chapter or were treated only briefly (a)The complement(\not )of a fuzzy set with a membership function has a membership function given by A(x)=1-u(x). Sketch the complement of the fuzzy set shown in Figure 2.6 on page 30 (b)There are other ways to def ine the\triangular norm\for representing
In this problem we will study the effects of adding rules to the rule- base. Suppose that we use seven triangular membership functions on each universe of discourse and make them uniformly distributed in the same manner as how we did in Exercise 2.3. In particular make the points at which the outermost input membership functions for e saturate at +r/2 and for e at tr/4 For u make the outermost ones have their peaks
problem you will study how to represent various concepts and quantify various relations with membership functions. For each part below, there is more than one correct answer. Provide one of these and justify your choice in each case. (a)Draw a membership function (and hence define a fuzzy set) that quantifies the set of all people of medium height
Questions: Why do we select fuzzy controllers in many real-world- systems? How much of the success can be attributed to the use of the mathematical model and conventional control design approach? How much should be attributed to the clever heuristic tuning that the control engineer uses upon implementation?
Fuzzy control does not exist as an isolated topic devoid of relationships to other fields, and it is important to understand how it relates to these other fields in order to strengthen your understanding of it. We have emphasized that fuzzy control has its foundations in conventional control and that there are many relationships to techniques, ideas, and methodologi there. Fuzzy control is also an\intelligent control\technique
