Page 9 - IJOCTA-15-3

Improving the performance of a chaotic nonlinear system of fractional-order...
control. IT2 FLC introduces a footprint of un- A suitable sliding surface is designed to stabilize
certainty, enhancing adaptability to nonlineari- the system, minimize oscillations, and improve
ties and external disturbances compared to type- adaptability under external disturbances and pa-
1 FLC. 21 This method has demonstrated superior rameter uncertainties. The results demonstrate
performance in uncertain and nonlinear systems, the superior performance of FO-SMC in mitigat-
particularly in real-world BLDC motor applica- ing chaos while ensuring system stability and ef-
tions where parameter variations are inevitable. 22 ficiency.
Despite its adaptability, IT2 FLC exhibits sig-
nificantly higher computational complexity than
conventional SMC and FO-SMC strategies, mak- 2. Mathematical modeling and chaos
ing it less practical for high-speed BLDC mo- analysis
tor control. In contrast, FO-SMC leverages frac-
2.1. Brushless direct current electric
tional calculus to incorporate memory effects, en-
motor system and assumptions
abling smoother control actions and superior ro-
bustness without additional fuzzy tuning. Al- In this study, the dynamic characteristics of a
though IT2 FLC provides an adaptive framework, BLDC motor were analyzed to establish a robust
it lacks the finite-time convergence guarantees of control strategy (Figure 1). First, the mathe-
FO-SMC, making the latter more suitable for matical model of the system is formulated, which
high-precision motor control. However, a hybrid is essential for investigating the bifurcation and
approach combining IT2 FLC and FO-SMC may chaos analysis. The system’s equilibrium points
offer a promising avenue for future research, merg- and stability properties are subsequently deter-
ing the strengths of both methodologies. 23 mined to provide insights into its nonlinear dy-
Furthermore, while widely used, traditional namics.
PID controllers struggle with parameter un-
certainties and external disturbances in BLDC
motors. 24 FOPID controllers improve upon PID
by offering better tuning flexibility and distur-
bance rejection capabilities. 22 However, they still
exhibit computational complexity and may fail to
suppress chaotic oscillations 23 completely. To ad-
dress these challenges, SMC and FO-SMC were
developed as robust control alternatives. While
SMC provides strong disturbance rejection and
finite-time convergence, it suffers from chattering,
potentially leading to mechanical wear in BLDC
motors. 25 FO-SMC mitigates this issue by incor-
porating fractional calculus, achieving smoother
control actions, enhanced robustness, and mini-
mal chattering. 26 Simulation results confirm that
FO-SMC outperforms PID, FOPID, and conven-
tional SMC in reducing steady-state error, im-
proving transient response, and minimizing con-
trol effort.
Recent research has also explored the hard-
ware implementation of advanced control tech-
niques using field-programmable gate arrays
(FPGA). Huerta-Moro et al. 24 demonstrated that
FPGA-based SMC and PID controllers for DC- Figure 1. Schematic of a brushless direct current
25
DC buck converters significantly improved re- motor
sponse time and reduced overshoot, suggesting A BLDC motor is powered by a DC elec-
their potential for real-time chaos suppression in tric source and differs from traditional DC mo-
BLDC motors. These findings reinforce the im- tors by employing a closed-loop electronic con-
portance of integrating advanced controllers with troller instead of mechanical brushes. This con-
efficient hardware platforms. troller converts the incoming DC current into mo-
This study aims to design a FO-SMC to sup- tor coils that generate magnetic fields, enabling
press chaotic behavior in a BLDC motor system. smooth and precise rotation. Unlike conventional
381