Fuzzy Logic Controller for the Inverted Pendulum Problem . Project: Fuzzy Logic Controller for the Inverted Pendulum Problem . by Larry Bush

Why?

Simulator Simulator:

Problem Statement

Re-statement To improve the model.

Consequent MFs: cp = fn ( 17, [ -5.4 : +5.4 ] ) Evenly Spaced Horizontally Symmetrical Orthogonal Trapezoidal Support = 3 x Core

Rule-Base cmf(i, j, k, l) = cp(i + j + k + l - 3)   cmf(i, j, k, l) = cp(i + j + k + l - 3) for i, j, k, l = [ 1 : 5 ]

2 Dimensions

Rule-Base   cmf(i, j, k, l) = cp( i + (j-1) + (-k+5) + (-l+5) )

Rule-Base cmf( 1, 1, 1, 1 ) = cp( i + (j-1) + (-k+5) + (-l+5) )   cmf( 1, 1, 1, 1 ) = cp( i + (j-1) + (-k+5) + (-l+5) ) = cp( 9 ) ~ Force = 0

Rule-Base Angle is large positive. Angular Velocity is large positive. Cart Position is large negative. Cart Velocity is large negative. cmf( 5, 5, 1, 1 ) = cp( i + (j-1) + (-k+5) + (-l+5) ) = cp( 17 ) ~ Force = large positive

Rule-Base Angle is small positive. Angular Velocity is small positive. Cart Position is zero. Cart Velocity is zero. cmf( 4, 4, 3, 3 ) = cp( i + (j-1) + (-k+5) + (-l+5) ) = cp( 11 ) ~ Force = small positive

Neural Net

Demo

Take Aways Fuzzy Controllers Work 4-input, 5-MF Work the Best Computationally Expensive Difficult to Tune Automated Tuning Techniques Work

End

Questions/Facts