Page 449 - Mathematical Techniques of Fractional Order Systems
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434 Mathematical Techniques of Fractional Order Systems
where uðx a Þ and uðx q Þ are the control inputs. This control system is single
input, so the inputs uðx a Þ and uðx q Þ are interlocked. Using the Generalized
Gronwall inequality and Laplace transform of the Mittag Leffler function,
the system was proven to converge to the equilibrium point E 1 at some con-
ditions on uðx a Þ and uðx q Þ. The first case is at uðx a Þ 5 ðm 2 55Þx a , uðx q Þ 5 0,
and m , 1. The second case is at uðx q Þ 5 ðn 2 4Þx q , uðx a Þ 5 0, and n , 4=55.
Fig. 14.13 shows the time responses on the system at the first and second
FIGURE 14.12 The BLDCM system at q 5 0:97.
FIGURE 14.13 The controlled BLDCM system at (A) the first case, m 52 10 and (B) the sec-
ond case, n 52 5.
