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tut9 - -10 10 PS =[5 25 and NS =-5-25 The other two...

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EE4210 Tutorial 9 Fuzzy Associative Memory (FAM) Consider the control of an inverted pendulum with two fuzzy state variables and one fuzzy control variable. state variable θ : the angle that the pendulum shaft makes with the vertical axis. state variable Δθ : angular velocity of the pendulum. control variable υ : the motor angular velocity. Assume that the range of all these three variables is [-30, 30] and that five linguistic variables (ZE = zero, NS = negative small, NM = negative medium, PS = positive small and PM = positive medium) are used for range partition. Suppose that triangular membership function is used with the peak at the centre of each of these linguistic variables. The range of three of the linguistic variables are ZE = [
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Unformatted text preview: -10, 10], PS = [5, 25] and NS = [-5, -25]. The other two variables assume their peaks at the two extreme points, i.e., PM has a range [20, 30] with a peak at 30 while NM has a range of [-20, -30] with a peak at -30. Also assume that all the input and output has a resolution of unit degree (all fractions are round off to the nearest integer). (a) Plot and label the membership functions for each of the fuzzy variables. (b) Generate some FAM rules by using common knowledge about an inverted pendulum. (c) Suppose that the input data pair is (8, -8), i.e., θ = 8 and Δθ = -8. Compute the fuzzy centroid output using the FAM rules generated in (b)....
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