Page 551 - Mathematical Techniques of Fractional Order Systems

530 Mathematical Techniques of Fractional Order Systems

Rahimi et al., 2016). This chaotic behavior may cause torque ripples, insta-
bility of the motor speed, and current low-frequency oscillations which may
damage the motor (Li et al., 2002; Sun et al., 2016. Therefore, there is a
necessity for controlling this behavior to modify the motor behavior and to
prevent its damage. The control process of this unexpected behavior requires
an accurate description of the physical behavior of the motor (Li and Wu,
2016; Li et al., 2012) and an accurate estimation method of the motor para-
meters (Zribi et al., 2009; Ataei et al., 2010; Yu et al., 2011).
Currently, the nonlinear differential equations of the PMSM are modeled
as fractional order equations to simulate the nature of the motor accurately.
Where the fractional order calculus provides a profound insight into the
physical processes of the motor and requires an infinite number of terms is
the memory of all past events (Xue et al., 2015), while the integer order cal-
culus is considered as a local operator. Hence, the PMSM commensurate and
the incommensurate fractional order models have been introduced and they
are approved as more accurate and more flexible models than the integer
ones (Li and Wu, 2016; Li et al., 2012; Xue et al., 2015). The chaotic sys-
tems such as PMSM are complex and nonlinear systems that are effected by
the initial conditions. Consequently, an irregular and unpredictable behavior
results. Estimation of states of this nonlinear system to control its behavior is
difficult because it’s hard to define the parameters of such a system.
Therefore, the unknown parameters identification of the PMSM fractional
order models is a very crucial issue to control the chaotic behavior in the
motor and to protect it from damage. This motivates the authors to search
for efficient techniques to identify the models parameters accurately.
Only a few numerical techniques have been published to extract the
fractional order PMSM models parameters (Li et al., 2012; Xue et al., 2015)
at certain operating conditions. Therefore, there is a real need for efficient
and a simple parameter estimation methods to identify these parameters
accurately.
Recently, meta-heuristic optimization techniques have become a promis-
ing method in the identification of the models parameters in different fields
(Alam et al., 2015; Allam et al., 2016; Yousri et al., 2017). These algorithms
haven’t been applied in extracting the unknown parameters of these models
yet, despite their ability to optimize such a problem simply and simulta-
neously without any assumptions. This fact has motivated the authors to effi-
ciently estimate the PMSM models parameters using the meta-heuristic
algorithms for the first time.
Integration between the chaos maps and the nature-inspired algorithms to
adjust some of their parameters is becoming a new research approach
(Gandomi and Yang, 2014). This approach improves the exploration and/or
the exploitation ability of the original techniques based on the randomization
effectiveness of the chaos theory. Consequently, the accuracy and the speed
of convergence of the developed algorithms are improved as in the cases of