Page 281 - Mathematical Techniques of Fractional Order Systems

270 Mathematical Techniques of Fractional Order Systems

1.5
Reference
IOSMCPD
1
FOFSMCPD
Y–position (radian) 0 0.34
0.36
0.5
0.32
–0.5
–1 1.015 1.02

–1.5
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2
X–position (radian)
FIGURE 9.15 X Y curve for trajectory tracking (A) link-1; (B) link-2.

handling capabilities have been carried out and presented in this section.
Following are the category wise investigations carried out on IOSMCPD and
FOFSMCPD controllers to evaluate the complete performance analysis.

9.7.1 Disturbance Rejection When Disturbance Is Injected at
Controller Output

Another task of a robust control scheme is to nullify the effect of unwanted
disturbances so as to allow the reference trajectory to be followed smoothly.
In the present study, a disturbance signal is injected at the controller output
in both the feedback loops at the same time before the saturator. The distur-
bance signal is given as,
½
dtðÞ 5 Au t 2 1Þ 2 uðt 2 3ފ ð9:69Þ
ð
where, A is the amplitude of disturbances considerd for testing.
According to Eq. (9.69), a pulse signal of amplitude, A 5 0:1 N-m is con-
sidered as the disturbance signal in the present study. A complete analysis is
carried out where the obtained IAE values and objective function are
depicted in Table 9.6 and same is presented graphically in Fig. 9.16. For this
case, a trajectory tracking task, corresponding controller output and error
curves are shown in Figs. 9.17 9.19.An X Y position curve of the end-
point is also shown in Fig. 9.20 where it can be easily observed that the
FOFSMCPD controller displays a smoother curve than the IOSMCPD con-
troller. After investigating the obtained values of IAE and objective function,
it can be inferred that the FOFSMCPD controller outperforms the IOSMCPD
controller. In this study, improvements of 7.69% and 23.80% are obtained in
IAE values by the FOFSMCPD over the IOSMCPD controller in link-1 and
link-2, respectively. About 18.91% improvement in objective functions are
obtained by the FOFSMCPD controller over the IOSMCPD controller.