Exercise 2.11 ( Graphical Depiction of Fuzzy Decision Decision Making graphical depiction of the operation of the fuzzy controller for the inverted pendulum similar to the one given in Figure2.19 on page 46. For this, choose e(0)=37 and d which will dt result in four rules being on. Be sure to show all parts of the graphical depiction, including an indication of your choices for e(o and d(n), the implied fuzzy sets, and the final defuzzified value (a) Use minimum for the premise and implication and cog defuzzification Use product for the premise and implication and center-averge defuzzification 0.5 chann-n-enmor i 270 tte nedre If cmmo i puge and
Exercise 2.11 (Graphical Depiction of Fuzzy Decision Decision Making): Develop a graphical depiction of the operation of the fuzzy controller for the inverted pendulum similar to the one given in Figure2.19 on page 46. For this, choose 3 ( ) 8 e t = and ( ) 16 e t d dt = , which will result in four rules being on. Be sure to show all parts of the graphical depiction, including an indication of your choices for et() and e t( ) d dt , the implied fuzzy sets, and the final defuzzified value. (a) Use minimum for the premise and implication and COG defuzzification. Use product for the premise and implication and center-averge defuzzification. Exercise2-11 (a) et( ) 2 0 possmall3 8 et( ) 2 0 possmall3 8 8 8 − zero 16 8 8 − zero 16 0 possmall 16 4 0 possmall 16 4 et( ) 2 0 poslarge 3 8 et( ) 2 0 poslarge 3 8 If error is possmall and chang-in-error is zero Then force is negsmall If error is possmall and chang-in-error is possmall Then force is neglarge If error is poslarge and chang-in-error is zero Then force is neglarge If error is poslarge and chang-in-error is possmall Then force is neglarge ut( ) neglarge -30 -10 neglarge -30 -10 neglarge -30 -10 ut( ) negsmall -20 ut( ) negsmall -20 neglarge -30 -10 ut( ) ut( ) 0.5 0.5 0.5 0.5 0.5 17.5 crisp u = − 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 de t() dt de t() dt de t() dt de t() dt
(b) Product 0.5 25 lunce s hegau Ir enmo is pull chane-inertor ip 0. posTage 0.25 ;( DIene -17.5
(b) et( ) 2 0 possmall3 8 et( ) 2 0 possmall3 8 8 8 − zero 16 8 8 − zero 16 0 possmall 16 4 0 possmall 16 4 et( ) 2 0 poslarge 3 8 et( ) 2 0 poslarge 3 8 If error is possmall and chang-in-error is zero Then force is negsmall If error is possmall and chang-in-error is possmall Then force is neglarge If error is poslarge and chang-in-error is zero Then force is neglarge If error is poslarge and chang-in-error is possmall Then force is neglarge ut( ) neglarge -30 -10 neglarge -30 -10 neglarge -30 -10 ut( ) negsmall -20 ut( ) negsmall -20 neglarge -30 -10 ut( ) ut( ) 0.25 0.25 0.25 0.25 0.5 17.5 crisp u = − 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 Product de t() dt de t() dt de t() dt de t() dt
