Page 279 - Mathematical Techniques of Fractional Order Systems

268 Mathematical Techniques of Fractional Order Systems

0.0025
0.002
0.002 0.0017
0.0011 0.0009
0.0015

0.001 0.0007 0.0007

0.0005

0
IAE Link-1 IAE Link-2 Objective Function
IOSMCPD FOFSMCPD
FIGURE 9.11 IAE and OBF values for trajectory tracking.

TABLE 9.5 IAE Values and Objective Functions for Trajectory Tracking Task

IAE Link-1 IAE Link-2 Objective Function
IOSMCPD 0.0011 0.0007 0.0020
FOFSMCPD 0.0009 0.0007 0.0017

2.5 2.5
Reference trajectory link-1 Reference trajectory link-2
2 IOSMCPD link-1 1.5 2 IOSMCPD link-2
FOFSMCPD link-1
Angular position (radian) 0.5 1 0 Angular position (radian) 0.5 1 0
FOFSMCPD link-2
1.5

–0.5
–1
–1 –0.5
–1.5 –1.5
0 1 2 3 4 0 1 2 3 4
Time (s) Time (s)
(A) (B)
FIGURE 9.12 Trajectory tracking curves (A) link-1; (B) link-2.