Fuzzy Dynamic Parameter Adaptation in the Harmony Search Algorithm for the Optimization of the Ball and Beam Controller

Box 1

Fuzzy rules for the ball and beam controller.

1. If (in1 is in1mf1) and (in2 is in2mf1) and (in3 is in3mf1) and (in4 is in4mf1) then (out is outmf1) (1)

2. If (in1 is in1mf1) and (in2 is in2mf1) and (in3 is in3mf1) and (in4 is in4mf2) then (out is outmf2) (1)

3. If (in1 is in1mf1) and (in2 is in2mf1) and (in3 is in3mf2) and (in4 is in4mf1) then (out is outmf3) (1)

4. If (in1 is in1mf1) and (in2 is in2mf1) and (in3 is in3mf2) and (in4 is in4mf2) then (out is outmf4) (1)

5. If (in1 is in1mf1) and (in2 is in2mf2) and (in3 is in3mf1) and (in4 is in4mf1) then (out is outmf5) (1)

6. If (in1 is in1mf1) and (in2 is in2mf2) and (in3 is in3mf1) and (in4 is in4mf2) then (out is outmf6) (1)

7. If (in1 is in1mf1) and (in2 is in2mf2) and (in3 is in3mf2) and (in4 is in4mf1) then (out is outmf7) (1)

8. If (in1 is in1mf1) and (in2 is in2mf2) and (in3 is in3mf2) and (in4 is in4mf2) then (out is outmf8) (1)

9. If (in1 is in1mf2) and (in2 is in2mf1) and (in3 is in3mf1) and (in4 is in4mf1) then (out is outmf9) (1)

10. If (in1 is in1mf2) and (in2 is in2mf1) and (in3 is in3mf1) and (in4 is in4mf2) then (out is outmf10) (1)

11. If (in1 is in1mf2) and (in2 is in2mf1) and (in3 is in3mf2) and (in4 is in4mf1) then (out is outmf11) (1)

12. If (in1 is in1mf2) and (in2 is in2mf1) and (in3 is in3mf2) and (in4 is in4mf2) then (out is outmf12) (1)

13. If (in1 is in1mf2) and (in2 is in2mf2) and (in3 is in3mf1) and (in4 is in4mf1) then (out is outmf13) (1)

14. If (in1 is in1mf2) and (in2 is in2mf2) and (in3 is in3mf1) and (in4 is in4mf2) then (out is outmf14) (1)

15. If (in1 is in1mf2) and (in2 is in2mf2) and (in3 is in3mf2) and (in4 is in4mf1) then (out is outmf15) (1)

16. If (in1 is in1mf2) and (in2 is in2mf2) and (in3 is in3mf2) and (in4 is in4mf2) then (out is outmf16) (1)