Page 585 - Mathematical Techniques of Fractional Order Systems

Parameters Identification of Fractional Order Chapter | 18 555

(G) Sine (H) Singer
CGWO CGWO
CGOA
CGOA
Mean convergence curve 10 0 −2 GOA Mean convergence curve 10 0 −2 GOA
GWO
GWO
10

100 200 300 400 10 100 200 300 400
Iteration number Iteration number
(I) Sinusoidal (J) Tent
CGWO CGWO
CGOA 0 CGOA
Mean convergence curve 10 0 Mean convergence curve 10 −2
GWO
GWO
GOA
GOA
10
−2
10
100 200 300 400 100 200 300 400
Iteration number Iteration number
FIGURE 18.6 (Continued).

other algorithms. Consequently, the proposed chaotic biologically inspired
optimizers are the more suitable techniques for identifying the parameters of
the incommensurate fractional order PMSM model, especially the CGWO
with almost of chaos maps and CGOA with sinusoidal map.

18.6 CONCLUSION
The commensurate and incommensurate fractional order PMSM models have
been recently proposed to provide more flexibility for the modeling of the
motor. Moreover, they provide a deeper vision of the physical behavior of
the motor. Therefore, an accurate estimation of the corresponding parameters
of these models to the chaotic behavior in the motor is the main target of
this work. For this purpose, both of the original meta-heuristic algorithms
and the modified ones through integration with chaos maps are introduced.
The proposed algorithms such as Grey Wolf Optimizer, Grasshopper
Optimizer, Chaotic Grey Wolf Optimizer, and the Chaotic Grasshopper
Optimization Algorithm were tested and evaluated to recommend the most
suitable one for this application. The main finding is that the Chaotic Grey
Wolf Optimizer with almost chaos maps and the Chaotic Grasshopper
Optimization Algorithm with the sinusoidal map are the more efficient