Page 8 - IJOCTA-15-3

A. Kaveh, M. Vahedi, M. Gandomkar / IJOCTA, Vol.15, No.3, pp.379-395 (2025)
motors offer high efficiency but require a commu- in permanent magnet synchronous motors was de-
tator and brushes, which demand regular main- veloped by Shahzad. 10 In recent years, BLDC mo-
tenance. To overcome this limitation, BLDC mo- tors have been increasingly adopted in automo-
tors have been introduced. These motors consist tive, aerospace, robotics, household appliances,
of a permanent magnet rotor and a stator winding medical devices, food and chemical processing,
similar to traditional motors, but unlike conven- electric vehicles, and computer peripherals due
tional DC motors, they do not require brushes to their high efficiency, long lifespan, and good
for commutation, as this is managed electroni- speed-torque characteristics. 11,12 The chaotic be-
cally. The inverter plays the role of the com- havior of BLDC motors was initially identified by
mutator, making these motors more efficient and Hemati, 13 and such behavior is undesirable in en-
reliable. 1–4 gineering applications because it can degrade sys-
8
tem performance. Consequently, numerous stud-
The BLDC motors offer several technical ad- ies have been conducted on chaos control in
vantages over traditional DC and induction mo- BLDC systems 14,15 and the synchronization of
tors, including a simple control system, minimal chaotic BLDC motors. 16 Chaos in BLDC mo-
need for sensors, long lifespan, low maintenance, tors leads to oscillations, acoustic noise, mechan-
a favorable torque-speed characteristic, fast dy- ical vibrations, and increased electrical energy
namic response, high efficiency, noiseless opera- consumption, ultimately reducing motor lifespan.
tion, and a wide speed range. These features Thus, studying and controlling chaos is critical for
make BLDC motors preferred for applications re- improving motor design and performance. 14–19
quiring high efficiency, low noise, and precise con-
trol. Given these benefits, BLDC motors are
Since the 1970s, researchers have extensively
widely used in high-power and high-torque appli-
studied the dynamic characteristics of electric
cations with space limitations, where their com-
motors, focusing on startup issues, speed con-
pact size, efficiency, and torque-speed character-
trol, and oscillations. These challenges, partic-
istics make them ideal. A novel sensorless control
ularly low-speed oscillations in controlled-speed
scheme proposes a terminal sliding mode observer
motors, are closely related to chaos in nonlin-
to replace mechanical sensors and improve speed
ear systems. The mathematical models for multi-
estimation in interior permanent magnet synchro- variable BLDC motors are highly nonlinear and
nous motors, ensuring observer stability. 5
strongly coupled, leading to complex dynamical
behaviors. Advances in permanent magnet ma-
Fractional calculus is increasingly being ap-
terials have further increased the use of BLDC
plied in various fields because it can provide more
motors in servo systems, high-performance drives,
accurate modeling of real systems, which often 8
and household appliances.
exhibit fractional-order dynamics. Chaos theory
is one of the key areas where fractional calculus
Various control methodologies have been pro-
plays a crucial role. Chaotic systems are highly
posed for chaos mitigation in BLDC systems,
sensitive to initial conditions, and disorganized
including proportional-integral-derivative (PID)
behavior emerges when phase plane trajectories
control, fractional-order PID (FOPID) control,
are globally bounded but locally unstable. It is
and sliding mode control (SMC). While FOPID
well established that chaos does not occur in non-
controllers enhance conventional PID strategies
linear continuous-time systems of order less than
by incorporating fractional-order terms for im-
three. Typically, chaotic systems are modeled us-
proved flexibility and disturbance rejection, their
ing three coupled differential equations that in-
6
clude fractional-order derivatives. Recent studies computational complexity necessitates advanced
have demonstrated the effectiveness of fractional- optimization techniques such as particle swarm
order sliding mode controllers (FO-SMCs) in sup- optimization or genetic algorithms for parameter
pressing chaotic oscillations while improving sys- tuning. SMC, particularly in its fractional-order
tem stability. For instance, Li et al. proposed a form (FO-SMC), has emerged as a more promis-
ing alternative due to its robustness against pa-
circulating current controller for modular multi-
rameter uncertainties, finite-time convergence,
level converters, integrating fractional-order cal-
and reduced chattering. 20
culus to enhance response speed and minimize
chattering. 7
To comprehensively address the reviewers’
The existence of chaos in motor systems was concerns, this study also evaluates the potential
first reported by Kuroe in 1989. 8,9 The first math- integration of interval type-2 (IT2) fuzzy logic
ematical model analyzing chaos and bifurcation control (FLC) with FO-SMC for BLDC motor
380