Page 550 - Mathematical Techniques of Fractional Order Systems

Chapter 18

Parameters Identification of

Fractional Order Permanent
Magnet Synchronous Motor

Models Using Chaotic Meta-
Heuristic Algorithms

Dalia Yousri, Dalia Allam and Magdy Eteiba
Fayoum University, Fayoum, Egypt

18.1 INTRODUCTION
Nowadays, fractional calculus is considered as an effective mathematical
tool when dealing with noninteger orders derivatives and integrals. It has
became a hot topic in recent research, where the physical behavior of differ-
ent systems can be mimicked as fractional order differential equations
(Miller and Ross, 1993; Debnath, 2003, 2004). As the integer order differen-
tial equation is just a special case of the fractional one, many researchers
prefer to use the fractional calculus in modeling of many systems to
enhance their design flexibility by providing extra degrees of freedom
(Debnath, 2003). Moreover, the solution of fractional order differential
equations can be accomplished by several numerical methods (Diethelm,
2010; Petra ´ˇ s, 2011). That’s why the fractional calculus has been employed
in different fields such as electrical circuit models (Gu et al., 2016; Khateb
et al., 2016), control systems (Azar et al., 2017; Azar and Vaidyanathan,
2015a,b, 2016; Boulkroune et al., 2016a,b; Zamani et al., 2016; Xu et al.,
2016; Zhu and Azar, 2015), and electric drives (Rajagopal et al., 2016;
Zhou et al., 2015), etc.
The permanent magnet synchronous motor (PMSM) is widely used in dif-
ferent industrial applications due to its simple structure, its high efficiency,
and low manufacturing cost. However, the PMSM exhibits an undesirable
behavior which is known as a chaotic behavior at certain ranges of the load
disturbance and of the system parameters (Li et al., 2002; Liu et al., 2011;

Mathematical Techniques of Fractional Order Systems. DOI: https://doi.org/10.1016/B978-0-12-813592-1.00018-0
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