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

2. Why?

3. Simulator
Simulator:

4. Problem Statement

5. Re-statement
To improve the model.

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

8. 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 ]

9. 2 Dimensions

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

11. 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

12. 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

13. 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

14. Neural Net

16. Demo

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

18. End

19. Questions/Facts