1. Comparison of classical state space control and fuzzy control
Felix Bierbaum

2. State space control Based on mathematical model of the physical system
Continuous time or discrete time
Laplace transforms or z-transforms

3. Fuzzy Control Based on rules No explicit mathematical model needed
Always discrete time

4. Example: Roll bite

5. Mathematical model

6. Block diagram of state space controller

7. Membership function for fuzzy variables
Fuzzy sets
HEIGT: Low (L), Little Low (LL), OK, Little High (LH) and High (H)
ANGLE: Negative (N), Negative small (NS), Zero (Z), Positive small (PS) and Positive
LEFT: Down (LD), Little Down (LLD), Still (LS), Little up (LLU) and Up (LU)
LEFT: Down (RD), Little Down (RLD), Still (RS), Little up (RLU) and Up (RU)
Membership function for fuzzy variables

8. Rule base and N NS Z PS P L LU/RU LLU/RU LLU/RLU LU/RLU LL LS/RU
LS/RLU
LLU/RS OK
LD/RU
LLD/RLU
LS/RS
LLU/RLD
LU/RD LH
LD/RLD
LLD/RS
LLD/RLD
LS/RLD
LLD/RD H
LD/RD

9. Simulation results
Height of roll bite [m] vs. time [s] using state space controller
Height of roll bite [m] vs. time [s] using fuzzy controller

10. Conclusions State space control Fuzzy Control Good performance
No mathematical model needed
No metrics for evaluation
Better performance
Mathematical model needed
Metrics for evaluation (command tracking, dynamic stiffness...)