Page 307 - Mathematical Techniques of Fractional Order Systems

296 Mathematical Techniques of Fractional Order Systems

(A) 10
Proposed REAL (U)
Compared REAL (U)

5

U (1) 0

–5

–10
0 2 4 6 8
Time (s)
(B)
1500
Proposed REAL (U)
Compared REAL (U)
1000

U (2) 500

0

–500
0 2 4 6 8
Time (s)
FIGURE 10.8 Real components of the input variables u 1 and u 2 .

10.5.1.2 Stabilization of the Fractional Order Complex Lorenz
Hyperchaotic System
In Fig. 10.9A and B, the real and imaginary parts of the variable x 1 are
shown, where, as can be noticed, there are less oscillations and a faster
response in comparison with the outcomes obtained by the approach
shown in Li and Li (2015) in order to drive the variables to the equilibrium
point.
Then, in Fig. 10.10, the real part of the variable x 2 is shown and as can
be noticed there is less overshoot and a faster response in comparison with
the outcomes obtained with the strategy shown in Li and Li (2015).
In Fig. 10.11A and B, the real components of the control input variables
u 1 and u 2 are shown where the control effort is smaller and a faster response
is obtained by the proposed control strategy in comparison with the strategy
shown in Li and Li (2015).