Page 278 - Mathematical Techniques of Fractional Order Systems

Design of Fractional Order Fuzzy Sliding Mode Controller Chapter | 9 267

TABLE 9.4 Optimized Gain Parameters of IOSMCPD and FOFSMCPD
Controllers
Parameters IOSMCPD FOFSMCPD
Link-1 Link-2 Link-1 Link-2
Normalized fuzzy input gain 314.42 228.73
Exponential law gains 311.74 87.60 128.16 58.92
g E
43.58 220.53 174.46 157.71

g
k
Boundary layer ΔðÞ 0.64 0.64 0.77 0.77
Sliding surface error gain λ 38.88 38.88 38.97 38.97
ðÞ
Integer / Fractional order for 1 1 0.89 0.53
derivative αðÞ

0.8
IOSMCPD
FOFSMCPD
0.6 × 10 –3
Objective function 0.4 2.2 2 96.396 96.398 96.4 96.402 96.404 96.406

1.8
1.6
0.2

0
0 10 20 30 40 50 60 70 80 90 100
Generation
FIGURE 9.10 Objective functions versus iteration curve for IOSMCPD and FOFSMCPD
controllers.
this figure that the convergence of the FOFSMCPD controller is better than
the IOSMCPD controller. The value of objective functions obtained for the
IOSMCPD controller is 0.0020 whereas for the FOFSMCPD controller it is
0.0017 for trajectory tracking task as depicted in Table 9.5. An improvement
of 18.18% is obtained in IAE by the FOFSMCPD over the IOSMCPD con-
troller for link-1 whereas link-2 offered the same IAE values by both the
controllers. About 15% improvement in objective functions has been
obtained by the FOFSMCPD on the IOSMCPD controller. Reference trajec-
tory tracking curves for both links, their controller outputs, and error curves
are shown in Figs. 9.12 9.14. A careful observation is obtained from
Fig. 9.13 that after taking the value of chatter in the account of objective