Page 284 - Mathematical Techniques of Fractional Order Systems

Design of Fractional Order Fuzzy Sliding Mode Controller Chapter | 9 273

9.7.2 Disturbance Rejection When Disturbance Is Injected at
Plant Output

Another disturbance signal is considered at the plant output to study the
effectiveness of IOSMCPD and FOFSMCPD controllers. In this context, a
sinusoidal disturbance signal as given in (9.70) is injected where amplitude
A d 5 0:1 radian and angular frequency ω d 5 0:5 pi rad/s is considered for dis-
turbance rejection study.
θ d 5 A d sin ω d tf g ð9:70Þ
Analysis is shown in terms of trajectory tracking task where the obtained
values of IAE and objective functions are shown in Table 9.7. The same
values are expressed graphically in Fig. 9.21. For this study, a trajectory
tracking curve is shown in Fig. 9.22 whereas its corresponding controller
output and error curves are shown in Figs. 9.23 and 9.24.An X Y curve is
also shown in Fig. 9.25 which confirms the superiority of the FOFSMCPD
controller over the IOSMCPD controller. After investigating the result, it can
be inferred that the FOFSMCPD controller shows 9.09% improvement in
objective function over the IOSMCPD controller. After comparing the IAE
values, 8.16% and 9.09% improvements are obtained by the FOFSMCPD
over the IOSMCPD controller in link-1 and link-2, respectively.

TABLE 9.7 IAE Values and Objective Functions for Disturbance (at Plant
Output) Rejection Task
IAE Link-1 IAE Link-2 Objective function
IOSMCPD 0.00098 0.0011 0.0022
FOFSMCPD 0.00090 0.0010 0.0020

FIGURE 9.21 IAE and objective function values for disturbance (at plant output) rejection study.