On the Relation between Neuro Fuzzy and CMAC Controller

Transcription

1 On the Relation between Neuro Fuzzy and CMAC Controller Dr N.H.Siddique, School of Computing and Intelligent Systems, University of Ulster Dr Richard Mitchell, Cybernetics, School of Systems Engineering, University of Reading This paper proposes a learning mechanism where the rule base of the neuro-fuzzy controller is replaced by Albus s CMAC controller. The controller is applied to a flexible link manipulator and its performance verified. On Relation Between Neuro-Fuzzy and CMAC Controller - 1

2 Flexible Manipulator Arm dimensions: 190x19x3.2mm 3 Mass density: 2710 kg/m 3 Young Modulus: 71x109 N/m 2 On Relation Between Neuro-Fuzzy and CMAC Controller - 2

3 FLC for Flexible Manipulators Most of FLC reported for flexible manipulators are Mamdani-type FLC with 2 inputs requires n m rules, n and m are the number of primary fuzzy sets. Number of rules grows exponentially as the number of inputs increases. Performance of Mamdani-type FLC depends on the amount of time required for rule-base processing and the defuzzification methods used. On Relation Between Neuro-Fuzzy and CMAC Controller - 3

4 Elimination of Rule Base and Defuzz.. Problem of defuzzification methods eliminated by the use of Sugeno-type fuzzy systems Roger Jang first introduced an adaptive-networkbased fuzzy inference system; serves as a basis for constructing a set of fuzzy if-then rules. Sugeno type FLC consequent part represented by a parametric polynomial function No need for defuzzification of fuzzy sets in consequent On Relation Between Neuro-Fuzzy and CMAC Controller - 4

5 e A 1 Roger Jang s ANFIS Rule-base eliminated r 1 w i N w i e e Consequent parameters f i = a i *e + b i * e + c i r 2 N e A 2 B 1 r 3 N Σ Y B 2 r 4 N On Relation Between Neuro-Fuzzy and CMAC Controller - 5

6 Parameter Estimation This further imposes a set of premises and consequence parameters to be learnt/estimated Consequent paras found by LSE in forward pass Premises parameters are updated by gradient descent in the backward pass. Application of algorithms depends on trade-off: computational complexity v resulting performance. In the case of a flexible-link manipulator - online calculation involves inversion of large matrices, which degrades the ultimate performance. So.. On Relation Between Neuro-Fuzzy and CMAC Controller - 6

7 Neuro Fuzzy Controller x1 x2 A 1 µ A ( x 1 ) r 1 wi Π w i w i f i x 1 A 2 r 2 Π Input space r 3 Π Σ y x 2 B 1 M B 2 µ B ( x 2 ) r M Π On Relation Between Neuro-Fuzzy and CMAC Controller - 7

8 Albus CMAC CMAC can approximate a nonlinear function Fixed mapping transforms each µ into an N- dimensional binary association vector Mapping is a procedure of summing the weights of the association cells Output is a weighted sum Weights are to be learnt x 1 x 2 Association vector a 1 a 2 a 3 a 4 a 5 M a i M M a N weights w i k A Y Σ Y On Relation Between Neuro-Fuzzy and CMAC Controller - 8

9 Fuzzy CMAC Controller x 1 A Ψ Ψ a 1 a 2 a 3 a 4 Association memory cell w i y d Input space Ψ a 5 a 6 a 7 Σ u Manipulator y x 2 Firing strength of rules M e B Ψ a N weight adjustments On Relation Between Neuro-Fuzzy and CMAC Controller - 9

10 Manipulator Responses (same scales) N-Fuzzy FCMAC On Relation Between Neuro-Fuzzy and CMAC Controller - 10

11 End Point Vibration (Mag vs Freq) N-Fuzzy FCMAC On Relation Between Neuro-Fuzzy and CMAC Controller - 11

12 Conclusion FCMAC faster, but poorer end-point vibration Main advantage of the FCMAC scheme over the neuro-fuzzy controller is the reduced number of parameters that is to be learnt. Neuro-fuzzy controller has 27 parameters to be estimated from I/O data FCMAC has only 9 weights to learn This has further reduced the computation time during operation. On Relation Between Neuro-Fuzzy and CMAC Controller - 12