Chapter 1

INTRODUCTION

Brushless DC (BLDC) motors have gained significant attention in various

industrial applications due to their high efficiency, reliability, and precise speed control.
Effective speed control of BLDC motors is essential for achieving desired performance
in applications such as electric vehicles, robotics, and industrial automation [1].

Conventional speed control techniques for BLDC motors often rely on

Proportional-Integral-Derivative (PID) controllers. While PID controllers are widely used
and well-established, they may face challenges in providing robust performance and
accurate control, especially under varying load conditions and parameter uncertainties
[2].

Sliding Mode Control (SMC) has emerged as a promising control technique for
achieving robust and precise control of BLDC motors. SMC offers several advantages,
including robustness to parameter variations, insensitivity to external disturbances, and
accurate tracking of reference signals [3].

This project focuses on the speed control of a BLDC motor using a Sliding Mode
Controller. The primary objective is to design, simulate, and evaluate the performance of
the SMC in controlling the speed of the BLDC motor. The proposed SMC aims to ensure
robust performance and accurate speed control under varying load conditions and
parameter uncertainties.

Through simulation studies, the effectiveness of the Sliding Mode Controller in

achieving precise speed control and robust performance of the BLDC motor will be
demonstrated. Additionally, a comparison with conventional control techniques such as
PID controllers will be presented to highlight the advantages of the proposed SMC.

1.1 BLDC Motor Drive

BLDC motor has stationary stator windings and rotor is made up of permanent magnets.
Here three phase BLDC motor is considered for development of control technique. The
three-phase supply is derived from DC voltage source using three phase inverters [4]. The
switching pattern is governed by rotor position. For that rotor position sensors are used.
Figure 1.1 shows the three-phase inverter is feeding the stator of BLDC motor. Rotor
position is sensed by Hall Effect sensors and signals are fed to the pulse generation circuit.
It finally drives the inverter.

Fig. 1.1 BLDC Motor Drive

1.2 BLDC Motors:

Brushless DC (BLDC) motors, also known as electronically commutated motors,

are widely used in various industrial applications due to their high efficiency, reliability,
and precise speed control capabilities. Unlike brushed DC motors, BLDC motors do not
have brushes for commutation. Instead, they use an electronic commutation system that
switches the stator windings to generate the rotating magnetic field necessary for motor
operation [5], [6].

The key components of a BLDC motor include the stator, rotor, and electronic
commutation system. The stator consists of windings that produce a magnetic field when
energized with electric current. The rotor, typically made of permanent magnets, is
attracted and repelled by the magnetic field produced by the stator windings, resulting in
rotation [7], [8].
 BLDC motors offer several advantages over traditional brushed DC motors,
including higher efficiency, reduced maintenance requirements, and improved durability.
Additionally, BLDC motors provide precise speed control, making them suitable for
applications where accurate speed regulation is essential [9].

The control of BLDC motors involves regulating the speed of rotation by

adjusting the amplitude and/or frequency of the voltage applied to the motor windings.
Various control techniques, including Proportional-Integral-Derivative (PID) control,
Field-Oriented Control (FOC), and Sliding Mode Control (SMC), are employed to
achieve accurate speed control and high-performance operation of BLDC motors [10]-
[13].

In this project, the focus is on the speed control of a BLDC motor using a Sliding
Mode Controller (SMC). The SMC offers robust performance and accurate speed control,
making it suitable for applications where precise control and robustness to parameter
variations are essential.

1.3 Importance of Speed Control in BLDC Motors:

Accurate speed control is essential for optimizing the performance of Brushless

DC (BLDC) motors in various industrial applications. The ability to precisely control the
speed of a BLDC motor offers several advantages, including:

❖ Improved Efficiency:

Precise speed control allows BLDC motors to operate at optimal speeds,

maximizing efficiency and minimizing energy consumption.

❖ Enhanced Performance:

BLDC motors with accurate speed control capabilities can maintain a constant
speed or adjust their speed dynamically, enabling smooth and efficient operation in
various applications.

❖ Dynamic Response:

Speed control enables rapid changes in motor speed, allowing for quick response
to changes in load conditions or external disturbances.
❖ Torque Control:

By controlling the speed of a BLDC motor, it is also possible to regulate the torque
output, ensuring that the motor delivers the required torque for specific tasks.

❖ Precision and Accuracy:

In applications where precise control is necessary, such as robotics, automation,

and electric vehicles, accurate speed control ensures precise positioning, motion control,
and overall system performance.

❖ Reduced Wear and Tear:

Proper speed control helps in reducing mechanical stress on the motor and
associated components, extending the lifespan of the motor and improving reliability.

❖ Adaptability to Varying Loads:

BLDC motors with effective speed control can adapt to varying load conditions,
maintaining the desired speed even under changing operating conditions.

❖ Noise Reduction:

Speed control can help reduce noise and vibration in BLDC motors, leading to
quieter operation and improved user experience in applications where noise is a concern.

In this project, the focus is on developing a robust speed control system for BLDC
motors using a Sliding Mode Controller (SMC). The SMC ensures accurate and robust
speed control, making it suitable for applications where precise control and robustness to
parameter variations are essential.

1.4 Overview of Conventional Speed Control Techniques:

Various control techniques have been employed to achieve speed control in

Brushless DC (BLDC) motors. Some of the conventional speed control techniques
include:

❖ Open-Loop Control:
 In open-loop control, the speed of the BLDC motor is controlled without feedback
from the motor. A predefined voltage or pulse width modulation (PWM) signal is applied
to the motor windings to achieve the desired speed. Open-loop control is simple and cost-
effective but lacks accuracy and robustness, as it does not account for variations in load
or motor parameters [14].

❖ Proportional-Integral-Derivative (PID) Control:

PID control is a widely used closed-loop control technique that adjusts the motor
input voltage based on the error between the desired speed and the actual speed. The PID
controller continuously calculates and adjusts the control signal to minimize the error,
ensuring accurate speed control. While PID control is effective in many applications, it
may face challenges in providing robust performance and accurate control under varying
load conditions and parameter uncertainties [15].

❖ Field-Oriented Control (FOC):

FOC, also known as vector control, is a sophisticated control technique that

decouples the torque and flux components of the motor current, allowing independent
control of torque and speed. FOC provides precise control over motor speed and torque
and is widely used in high-performance applications where accurate control is essential
[16].

❖ Direct Torque Control (DTC):

DTC is another advanced control technique that directly regulates the motor
torque and flux, without the need for complex coordinate transformations. DTC offers
fast dynamic response and accurate torque control, making it suitable for applications
requiring precise torque regulation.

While these conventional control techniques are effective in many applications,

they may face challenges in providing robust performance and accurate control under
varying load conditions and parameter uncertainties. In this project, use of Sliding Mode
Control (SMC) for speed control of BLDC motors is explored, aiming to achieve robust
performance and accurate speed control under varying operating conditions [17].

1.5 Sliding Mode Control (SMC):

 Sliding Mode Control (SMC) is a robust control technique widely used in various
industrial applications for its ability to provide precise control even in the presence of
parameter uncertainties and external disturbances. In SMC, the control system is designed
to force the state of the system onto a predefined manifold called the sliding surface. Once
on the sliding surface, the system's behavior is governed by a robust control law designed
to keep the system on the surface and reject disturbances [18].

The key features of Sliding Mode Control include:

❖ Robustness:

SMC is inherently robust to parameter variations, model uncertainties, and

external disturbances. The control law ensures that the system remains on the sliding
surface despite these uncertainties.

❖ Chattering:

One characteristic feature of SMC is chattering, which refers to the high-

frequency switching of the control signal near the sliding surface. While chattering can
be mitigated using various techniques, it is often considered a trade-off for the robustness
of SMC.

❖ Simple Implementation:

SMC is relatively simple to implement and does not require detailed knowledge
of the system dynamics. It is suitable for systems with nonlinearities and uncertainties.

❖ Insensitive to Modeling Errors:

SMC is less sensitive to modeling errors compared to traditional control

techniques such as PID control. It can effectively handle uncertainties in the system
model.

❖ Fast Response:

SMC provides fast and accurate response to changes in the system, making it
suitable for applications requiring rapid control action.

In the context of BLDC motor control, Sliding Mode Control offers several
advantages, including robust speed control, insensitivity to parameter variations, and
accurate tracking of reference speed.
1.6 Objectives:

Following are the objectives of the project.

1.7 Organization of Thesis:

This thesis is organized into the following chapters:

Chapter 1: Introduction

➢ Provides an overview of the project, including the importance of speed control in

BLDC motors and an introduction to Sliding Mode Control (SMC).
➢ Introduces the objectives and scope of the project.
➢ Outlines the organization of the thesis.

Chapter 2: Literature Review

➢ Presents a review of existing speed control techniques for BLDC motors.

➢ Provides an overview of Sliding Mode Control (SMC) and its application in motor
control.
➢ Summarizes previous research works on speed control of BLDC motors using SMC.

Chapter 3: BLDC Motor Modeling

➢ Describes the operation of BLDC motors.

➢ Presents the mathematical modeling of BLDC motors, including the derivation of
transfer functions.

Chapter 4: Sliding Mode Controller Design

➢ Introduces the concept of Sliding Mode Control (SMC).

➢ Details the design procedure of the SMC for BLDC motor speed control.
➢ Provides implementation details of the SMC.
Chapter 5: Simulation Results and Discussion

➢ Describes the simulation setup, including the environment used

(MATLAB/Simulink), parameters, and initial conditions.
➢ Presents the simulation results of BLDC motor speed control using SMC.
➢ Compares the performance of SMC with conventional controllers (PI, PID).
➢ Analyzes the performance under varying load conditions and parameter
uncertainties.

Chapter 6: Conclusion and Future Scope

➢ Summarizes the project and its achievements.

➢ Discusses the limitations encountered during the project.
➢ Provides recommendations for future work and research directions.

Chapter 8: References

➢ Lists the references cited throughout the thesis.

 Chapter 2

LITERATURE REVIEW
The literature review provides an overview of existing speed control techniques
for Brushless DC (BLDC) motors, with a focus on Sliding Mode Control (SMC) and its
application in motor control.

[1] P. Suganthi, S. Nagapavithra and S. Umamaheswari, "Modeling and simulation

of closed loop speed control for BLDC motor," 2017 Conference on Emerging
Devices and Smart Systems (ICEDSS), Mallasamudram, India, 2017, pp. 229-
233.

This paper addresses the importance of closed-loop speed control for Brushless
DC (BLDC) motors, which are widely utilized in various industrial sectors due to their
unique characteristics such as long life, high efficiency, and remarkable starting torque.
The abstract provides a concise overview of the paper, outlining the significance of BLDC
motors and the proposed control methods.

The authors propose a closed-loop speed control system for a BLDC motor using
classical PID controller and fuzzy logic controller. The paper compares the performance
of these two controllers in terms of stability and control efficiency. The fuzzy logic
controller is implemented using the Mamdani method of tuning. The control signals are
generated based on the feedback received from the motor, and the dynamic characteristics
such as speed, current, and back EMF are analyzed using MATLAB/SIMULINK
software [19].

[2] D. Mohanraj et al., "A Review of BLDC Motor: State of Art, Advanced Control
Techniques, and Applications," in IEEE Access, vol. 10, pp. 54833-54869, 2022.

This paper provides a thorough overview of Brushless Direct Current (BLDC)

motors, focusing on their advanced control techniques and applications. The paper
highlights the increasing significance of BLDC motors in various industries, particularly
in automotive, pumping, and rolling industries. It discusses the potential of BLDC motors
to replace traditional induction motors by 2030. The review emphasizes the challenges
faced by BLDC motors, such as fault tolerance, electromagnetic interference, and torque
ripple, and proposes closed-loop vector control as a promising solution. The paper
provides a detailed examination of various advanced control techniques for BLDC
motors, including fault tolerance control, electromagnetic interference reduction, field
orientation control (FOC), and direct torque control (DTC). It also discusses the
advantages of outer surface rotor-type BLDC motors, particularly in electric vehicle (EV)
applications, and presents simulation and hardware results to support its findings. Overall,
the paper serves as a comprehensive resource for understanding the current state of BLDC
motor technology, advanced control techniques, and their applications. It offers valuable
insights for researchers and practitioners in the field, along with identifying current
challenges and future research opportunities [20].

[3] S. Thirunavukkarasu and C. Nagarajan, "Performance Analysis of BLDC

Motor Drive for Feed Drives," 2018 Conference on Emerging Devices and
Smart Systems (ICEDSS), Tiruchengode, India, 2018, pp. 67-70.

The paper discusses the speed control of Brushless DC (BLDC) motors for feed
drives, particularly in CNC machines. BLDC motors are chosen for their brushless
operation and low power-loss characteristics. The analysis focuses on a three-phase
voltage source inverter fed BLDC motor control using Simulink/MATLAB. The
performance of the proposed model is evaluated in terms of speed and torque under
various load conditions using a PI controller. The findings emphasize the significance of
feed drive performance in CNC machines, directly impacting accuracy and repeatability.
Utilizing a PI controller, the paper assesses the speed characteristics of BLDC motors
across different speeds and loads. Results show minimal steady-state error and peak
overshoot of less than 2% across various speed states, indicating the proposed system's
effectiveness for feed drive applications. In summary, the paper provides insightful
analysis into the performance of BLDC motor drives for feed drives in CNC machines.
Through the implementation of a PI controller, precise speed control is achieved, meeting
the stringent requirements for feed drives' precision and repeatability [21].

[4] P. Sarala, S. F. Kodad and B. Sarvesh, "Analysis of closed loop current

controlled BLDC motor drive," 2016 International Conference on Electrical,
 Electronics, and Optimization Techniques (ICEEOT), Chennai, India, 2016, pp.
1464-1468

The paper delves into the analysis of closed-loop current-controlled Brushless DC

(BLDC) motor drives. The paper begins by highlighting the advantages of BLDC motors
over conventional DC motors, emphasizing their improved performance and efficiency.
It discusses the implementation of a current control scheme for BLDC motors, focusing
on both fixed and variable speed applications. Using MATLAB/Simulink, the paper
presents results for BLDC motors with open-loop and closed-loop speed control,
illustrating the motor's speed, torque, back EMF, and stator currents under various
conditions. The findings underscore the drawbacks of conventional DC motors, such as
losses and reduced efficiency due to mechanical parts like brushes and commutators. In
contrast, BLDC motors eliminate these disadvantages by employing electronic
commutation, resulting in better performance characteristics and smoother speed-torque
characteristics. The paper explains the operation of BLDC motors, both with open-loop
control and closed-loop control, particularly focusing on current control.
MATLAB/Simulink simulations validate the effectiveness of closed-loop BLDC motor
operation at fixed and variable speeds, demonstrating improved performance in terms of
speed, torque, back EMF, and stator currents. In summary, the paper provides a
comprehensive analysis of closed-loop current-controlled BLDC motor drives, offering
valuable insights into their operation and performance characteristics. The
MATLAB/Simulink simulations validate the effectiveness of closed-loop control,
making this paper a valuable resource for researchers and practitioners in the field of
BLDC motor drives and control systems [22].

[5] M. Poovizhi, M. S. Kumaran, P. Ragul, L. I. Priyadarshini and R. Logambal,

"Investigation of mathematical modelling of brushless dc motor (BLDC) drives
by using MATLAB-SIMULINK," 2017 International Conference on Power and
Embedded Drive Control (ICPEDC), Chennai, India, 2017, pp. 178-183.

This research paper aims to describe the mathematical simulation modeling of

Brushless DC (BLDC) motor drives using the MATLAB-Simulink environment. BLDC
motors find applications in various fields such as aerospace, robotics, industrial process
control, precision machine tools, automotive electronics, and household appliances. The
paper focuses on the mathematical modeling of BLDC drives controlled by pulse width
modulation (PWM) current controller technique. It provides an elaborate explanation of
the operating principle of BLDC motor drives and PWM current control techniques. The
mathematical modeling of BLDC motor drives is carried out using MATLAB-Simulink
software, allowing observation of speed and torque characteristics, as well as current and
voltage components of the inverter [23].

[6] M. A. Akhtar and S. Saha, "Reference Signal Generation for BLDC Motor
Drives based on Different Sector Identification Methodologies using Hall Based
Sensor," 2018 8th IEEE India International Conference on Power Electronics
(IICPE), Jaipur, India, 2018, pp. 1-5

The paper explores various methods for generating reference signals in BLDC
motor drives using Hall-based sensors. It discusses the significance of BLDC motors in
automotive industries, particularly in electric vehicle propulsion. The need for sector
identification for current commutation using power electronics converters is highlighted,
often achieved through Hall sensors. The paper compares existing sector identification
techniques using Hall sensors and proposes a binary to decimal converter-based method
for BLDC motor drives. Simulation and experimental results validate the effectiveness of
the different sector identification techniques. The proposed binary to decimal conversion-
based method is found to be the simplest to implement on a controller platform among
the discussed methods. Overall, the paper offers valuable insights into reference signal
generation for BLDC motor drives, providing a thorough investigation of sector
identification methodologies using Hall-based sensors [24].

[7] Devendra Potnuru, Alice Mary K., Saibabu Ch., " Design and implementation
methodology for rapid control prototyping of closed loop speed control for
BLDC motor," Journal of Electrical Systems and Information Technology,
Volume 5, Issue 1, Pages 99-111, 2018.

The paper's methodology ensures real-time performance in hardware

implementation, addressing the challenge of selecting appropriate hardware equipment
and configuring it with the controller board. By utilizing the dSPACE DS1103 controller
board, which allows for the conversion of MATLAB/Simulink blocks into DSP-enabled
embedded code, the paper offers a versatile and efficient solution for BLDC motor
control.

The proposed approach is thoroughly tested across various reference speeds,

demonstrating consistent and reliable performance. By reducing testing time and effort
for control algorithm development, the paper's methodology streamlines the
experimentation process, making it applicable not only to BLDC motors but also to other
electrical machines [25].

[8] A. T. Hafez, A. A. Sarhan and S. Givigi, "Brushless DC Motor Speed Control

Based on Advanced Sliding Mode Control (SMC) Techniques," 2019 IEEE
International Systems Conference (SysCon), Orlando, FL, USA, 2019, pp. 1-6.

The paper focuses on the design and implementation methodology for rapid
control prototyping of closed-loop speed control for Brushless DC Motors (BLDCM),
emphasizing the use of advanced Sliding Mode Control (SMC) techniques. It highlights
the benefits of BLDC motors, such as their simple design, high torque, long-term usage,
and speed stability, which make them suitable for various industrial applications. Despite
these advantages, BLDC systems exhibit uncertainties and non-linearity. To address these
challenges, the paper introduces advanced SMC techniques, specifically adaptive SMC
(AFSMC) and fuzzy SMC (FSMC), for effective speed regulation of BLDC motors under
various conditions, including the presence of external loads. The performance of these
advanced SMC approaches is compared with that of a classical Proportional-Integral-
Derivative (PID) controller to demonstrate their superiority in improving system
characteristics such as settling time, steady-state error, rise time, and disturbance and
noise rejection.

The findings show that the proposed AFSMC and FSMC techniques significantly
enhance the performance of BLDC motor speed control across different set points and
dynamic load conditions. These techniques ensure system stability and robustness even
when facing external disturbances. Additionally, the advanced SMC approaches provide
faster system response and better steady-state conditions compared to traditional PI and
PID controllers. Overall, the paper offers a valuable contribution to the field of BLDC
motor control by demonstrating the effectiveness of advanced SMC techniques. The
detailed simulation results validate the superiority of AFSMC and FSMC over traditional
control methods, making them promising solutions for handling the non-linearities and
uncertainties inherent in BLDC motor systems [26].
 Chapter 3

BLDC MOTOR MODELING

In this chapter, we delve into the intricate aspects of Brushless DC (BLDC) motor
modeling, a crucial foundation for understanding and implementing advanced control
techniques. The modeling process is essential for designing effective control strategies
and achieving optimal performance in various applications. This chapter is structured into
three parts: a brief description of BLDC motor operation, mathematical modeling of the
BLDC motor, and the derivation of the transfer function. By exploring these components,
we aim to provide a comprehensive understanding of the dynamic behavior of BLDC
motors, paving the way for precise and efficient control implementation.

3.1 Brief Description of BLDC Motor Operation

Brushless DC (BLDC) motors, also known as electronically commutated motors

(ECMs), are renowned for their efficiency, reliability, and performance. Unlike
traditional brushed DC motors, BLDC motors operate without brushes, using electronic
commutation instead. This design choice eliminates many of the drawbacks associated
with mechanical commutation, such as wear and tear, sparking, and maintenance issues,
making BLDC motors ideal for a wide range of applications, including automotive,
aerospace, industrial automation, and consumer electronics [27].

❖ Construction and Components

A BLDC motor consists of three primary components: the stator, rotor, and the
electronic controller.

Stator: The stator is the stationary part of the motor and contains the windings. These
windings are typically arranged in a three-phase configuration, which allows for efficient
and smooth operation. The stator is made from laminated steel to minimize energy losses.
Rotor: The rotor is the rotating part of the motor and contains permanent magnets. These
magnets can be configured in various ways, such as surface-mounted or interior-mounted,
depending on the design requirements. The rotor's movement generates the torque needed
to drive the mechanical load.

Electronic Controller: The electronic controller is a crucial component that manages the
commutation process. It uses signals from sensors (or sensor less methods) to determine
the rotor's position and appropriately commutates the stator windings to produce a
rotating magnetic field.

❖ Principle of Working and Starting Mechanism

The operation of a BLDC motor is based on the interaction between the magnetic
fields generated by the stator windings and the permanent magnets on the rotor. Here's a
step-by-step description of how a BLDC motor starts and operates:

1) Initial Position Detection: At startup, the electronic controller needs to know the
initial position of the rotor to begin the commutation process. This is typically
achieved using Hall effect sensors, which are positioned around the stator. These
sensors detect the magnetic field of the rotor magnets and provide signals indicating
the rotor's position
2) Commutation Sequence Initiation: Based on the initial rotor position detected by
the Hall sensors, the controller determines the appropriate commutation sequence.
The controller then energizes specific stator windings to create a magnetic field that
interacts with the rotor magnets, producing torque.
3) Rotor Movement and Continuous Commutation: As the rotor begins to turn, the
Hall sensors continue to provide feedback to the controller about the rotor's position.
The controller uses this feedback to switch the current in the stator windings at the
right times, maintaining a rotating magnetic field that keeps the rotor spinning.
4) Acceleration to Desired Speed: The controller adjusts the frequency of the
commutation and the voltage applied to the stator windings to accelerate the motor
to the desired speed. Pulse width modulation (PWM) is commonly used to control
the voltage and, consequently, the speed and torque of the motor.
5) Steady-State Operation: Once the motor reaches the desired speed, the controller
maintains this speed by continuously adjusting the commutation sequence and
 voltage based on the feedback from the Hall sensors. The motor can operate
efficiently and smoothly, with the electronic commutation ensuring precise control
over speed and torque.
6) Load Variations and Speed Adjustments: During operation, if there are changes
in the load or if the desired speed changes, the controller adjusts the commutation
sequence and voltage accordingly. This ensures that the motor responds quickly to
changes in load and maintains the desired performance characteristics.

❖ Operational Characteristics

BLDC motors exhibit several operational characteristics that are crucial for their
performance:

Torque-Speed Relationship: BLDC motors have a linear torque-speed characteristic,

which means that the torque is proportional to the current, and the speed is proportional
to the voltage. This linearity simplifies the control strategies.

Back EMF: The back EMF generated in the stator windings is proportional to the rotor
speed and plays a critical role in sensor less control methods.

Thermal Management: Efficient thermal management is essential in BLDC motors to

maintain performance and reliability. This is typically achieved through proper design
and cooling mechanisms.

❖ Control Strategies

The control of BLDC motors involves several strategies to optimize performance

and efficiency.

Pulse Width Modulation (PWM): PWM is used to control the voltage applied to the
motor windings, allowing precise control of the motor speed and torque.

Field-Oriented Control (FOC): FOC, also known as vector control, is an advanced

control technique that decouples the torque and flux components of the stator current,
enabling precise and efficient control of the motor.
Direct Torque Control (DTC): DTC is another advanced control method that directly
controls the motor torque and flux without requiring a coordinate transformation, offering
fast dynamic response.

Mathematical Modelling of BLDC Motor

Mathematical modelling of Brushless DC (BLDC) motors is essential for

analysing their behaviour and developing control strategies. The modelling process
involves deriving the equations that describe the motor's electrical, magnetic, and
mechanical dynamics. These equations are then used to simulate the motor's performance
under different operating conditions using software tools like MATLAB/Simulink.

Electrical Modelling

The electrical model of a BLDC motor is based on the relationship between the
input voltages, the currents in the motor windings, and the back electromotive force
(EMF) generated by the rotor's motion. A three-phase BLDC motor typically has three
stator windings arranged in a star or delta configuration. For simplicity, we consider a
star-connected motor [28]- [30].

Stator Voltage Equations

The stator voltage equations for the three phases (a, b, c) can be expressed as:

𝑑𝐼𝑎
𝑉𝑎 = 𝐼𝑎 𝑅𝑠 + 𝐿 + 𝑒𝑎
𝑑𝑡

𝑑𝐼𝑏
𝑉𝑏 = 𝐼𝑏 𝑅𝑠 + 𝐿 + 𝑒𝑏
𝑑𝑡

𝑑𝐼𝑐
𝑉𝑐 = 𝐼𝑐 𝑅𝑠 + 𝐿 + 𝑒𝑐
𝑑𝑡

where:

• 𝑉𝑎 , 𝑉𝑏 , 𝑉𝑐 are the phase voltages.

• 𝐼𝑎 , 𝐼𝑏 , 𝐼𝑐 are the phase currents.

• 𝑅𝑠 is the stator resistance.

• 𝐿 is the stator inductance.

 • 𝑒𝑎 , 𝑒𝑏 , 𝑒𝑐 are the back EMFs of each phase.

Back EMF Equations

The back EMF in each phase is proportional to the rotor speed and the position of
the rotor magnets. It can be expressed as:

𝑒𝑎 = 𝑘𝑒 𝜔sin⁡(𝜃)

2𝜋
𝑒𝑏 = 𝑘𝑒 𝜔sin⁡(𝜃 − )
3

2𝜋
𝑒𝑐 = 𝑘𝑒 𝜔sin⁡(𝜃 + )
3

where:

• 𝑘𝑒 is the back EMF constant.

• 𝜔 is the rotor angular velocity.

• 𝜃 is the electrical angle of the rotor.

Combined Electrical Model

By combining the stator voltage equations and the back EMF equations, we can
write the system of differential equations that describe the electrical dynamics of the
BLDC motor:

𝑑𝐼𝑎
𝑉𝑎 = 𝐼𝑎 𝑅𝑠 + 𝐿 + 𝑘𝑒 𝜔sin⁡(𝜃)
𝑑𝑡

𝑑𝐼𝑏 2𝜋
𝑉𝑏 = 𝐼𝑏 𝑅𝑠 + 𝐿 + 𝑘𝑒 𝜔sin⁡(𝜃 − )
𝑑𝑡 3

𝑑𝐼𝑐 2𝜋
𝑉𝑐 = 𝐼𝑐 𝑅𝑠 + 𝐿 + 𝑘𝑒 𝜔sin⁡(𝜃 + )
𝑑𝑡 3

Mechanical Modelling

The mechanical model of the BLDC motor describes the relationship between the
torque generated by the motor, the load torque, and the resulting angular motion of the
rotor [31], [32].

Torque Equation
The electromagnetic torque 𝑇𝑒 generated by the BLDC motor can be expressed as:

2𝜋 2𝜋
𝑇𝑒 = 𝑘𝑡 (𝐼𝑎 sin⁡(𝜃) + 𝐼𝑏 sin⁡(𝜃 − ) + 𝐼𝑐 sin⁡(𝜃 + ))
3 3

where:

• 𝑘𝑡 is the torque constant.

Motion Equation

The motion of the rotor can be described using Newton's second law of motion:

𝑑𝜔
𝐽 + 𝐵𝜔 = 𝑇𝑒 − 𝑇𝐿
𝑑𝑡

where:

• 𝐽 is the rotor inertia.

• 𝐵 is the damping coefficient.

• 𝑇𝐿 is the load torque.

State-Space Representation

To simulate the BLDC motor using software tools, it is convenient to express the
model in state-space form. The state variables can be chosen as the phase currents 𝐼𝑎 , 𝐼𝑏 , 𝐼𝑐
and the rotor angular velocity 𝜔. The state-space equations can be written as:

𝑅𝑠 𝑘𝑒 sin⁡(𝜃)
− 0 0 − 𝑉𝑎
𝐿 𝐿
2𝜋 𝐿
𝐼𝑎 𝑅𝑠 𝑘𝑒 sin⁡(𝜃− )
3 𝐼𝑎 𝑉𝑏
0 − 0 −
𝑑 𝐼𝑏 𝐿 𝐿 𝐼 𝐿
[ ]=[ 2𝜋 ][ 𝑏 ] + [ ]
𝑑𝑡 𝐼𝑐 𝑅𝑠 𝑘𝑒 sin⁡(𝜃+ ) 𝐼 𝑉𝑐
3 𝑐
0 0 − − 𝐿
𝜔 2𝜋
𝐿
2𝜋
𝐿 𝜔 𝑇𝐿
𝑘𝑡 sin⁡(𝜃) 𝑘𝑡 sin⁡(𝜃− )
3
𝑘𝑡 sin⁡(𝜃+ )
3 𝐵 −
−𝐽 𝐽
𝐽 𝐽 𝐽

Simulink Model Implementation

To implement the BLDC motor model in MATLAB/Simulink, the state-space

equations derived above can be translated into block diagrams using built-in Simulink
blocks. The process involves:
 1. Defining the Inputs: The phase voltages 𝑉𝑎 , 𝑉𝑏 , 𝑉𝑐 and the load torque 𝑇𝐿 are
defined as input signals.

2. Creating the State-Space Blocks: The state-space equations are implemented

using state-space or integrator blocks in Simulink.

3. Simulating the Back EMF: The back EMF for each phase is calculated using
trigonometric function blocks that depend on the rotor position θ and angular
velocity ω.

4. Modelling the Mechanical Dynamics: The torque and motion equations are
implemented to simulate the rotor dynamics and update the rotor position and
speed.

5. Feedback and Control: Feedback loops are created to control the motor's speed
and torque, using controllers such as PID or advanced control techniques like
Sliding Mode Control (SMC).

Transfer Function Derivation

The transfer function of a Brushless DC (BLDC) motor provides a mathematical

relationship between the input and output of the motor in the frequency domain. It is a
crucial tool for analysing the system's stability and performance and for designing
appropriate control strategies. The transfer function is derived by transforming the time-
domain differential equations of the motor into the Laplace domain.

Electrical Dynamics

The electrical dynamics of a BLDC motor can be described by the voltage

equations for the stator windings. For simplicity, consider a single phase of the motor.
The voltage equation is:

𝑉(𝑠) = 𝐼(𝑠) ⋅ 𝑅𝑠 + 𝑠𝐿 ⋅ 𝐼(𝑠) + 𝐸(𝑠)

where:

• 𝑉(𝑠) is the Laplace transform of the input voltage.

• 𝐼(𝑠) is the Laplace transform of the phase current.

 • 𝑅𝑠 is the stator resistance.

• 𝐿 is the stator inductance.

• 𝐸(𝑠) is the Laplace transform of the back EMF.

The back EMF 𝐸(𝑠) is proportional to the rotor speed 𝜔(𝑠):

𝐸(𝑠) = 𝐾𝑒 ⋅ 𝜔(𝑠)

where 𝐾𝑒 is the back EMF constant.

Mechanical Dynamics

The mechanical dynamics of the BLDC motor relate the electromagnetic torque
𝑇𝑒 , load torque 𝑇𝐿 , and rotor speed 𝜔. The torque equation is:

𝑑𝜔
𝑇𝑒 = 𝐽 + 𝐵𝜔 + 𝑇𝐿
𝑑𝑡

Taking the Laplace transform, we get:

𝑇𝑒 (𝑠) = 𝐽𝑠 ⋅ 𝜔(𝑠) + 𝐵 ⋅ 𝜔(𝑠) + 𝑇𝐿 (𝑠)

The electromagnetic torque 𝑇𝑒 is proportional to the phase current 𝐼(𝑠):

𝑇𝑒 = 𝐾𝑡 ⋅ 𝐼(𝑠)

where 𝐾𝑡 is the torque constant.

Combined Transfer Function

To derive the transfer function from the input voltage 𝑉(𝑠) to the output speed
𝜔(𝑠), we need to combine the electrical and mechanical dynamics.

First, express the current 𝐼(𝑠) from the electrical equation:

𝑉(𝑠) − 𝐾𝑒 ⋅ 𝜔(𝑠)
𝐼(𝑠) =
𝑅𝑠 + 𝑠𝐿

Next, substitute 𝐼(𝑠) into the torque equation:

𝑉(𝑠) − 𝐾𝑒 ⋅ 𝜔(𝑠)
𝐾𝑡 ⋅ = 𝐽𝑠 ⋅ 𝜔(𝑠) + 𝐵 ⋅ 𝜔(𝑠) + 𝑇𝐿 (𝑠)
𝑅𝑠 + 𝑠𝐿

Assuming the load torque 𝑇𝐿 (𝑠) is zero for the transfer function derivation:
 𝑉(𝑠) − 𝐾𝑒 ⋅ 𝜔(𝑠)
𝐾𝑡 ⋅ = (𝐽𝑠 + 𝐵) ⋅ 𝜔(𝑠)
𝑅𝑠 + 𝑠𝐿

Rearrange to isolate 𝜔(𝑠):

𝐾𝑡 ⋅ 𝑉(𝑠) − 𝐾𝑡 𝐾𝑒 ⋅ 𝜔(𝑠) = (𝐽𝑠 + 𝐵)(𝑅𝑠 + 𝑠𝐿) ⋅ 𝜔(𝑠)

𝐾𝑡 ⋅ 𝑉(𝑠) = [(𝐽𝑠 + 𝐵)(𝑅𝑠 + 𝑠𝐿) + 𝐾𝑡 𝐾𝑒 ] ⋅ 𝜔(𝑠)

𝜔(𝑠)
Finally, the transfer function is:
𝑉(𝑠)

𝜔(𝑠) 𝐾𝑡
=
𝑉(𝑠) (𝐽𝑠 + 𝐵)(𝑅𝑠 + 𝑠𝐿) + 𝐾𝑡 𝐾𝑒

This transfer function describes the relationship between the input voltage 𝑉(𝑠) and the
rotor speed 𝜔(𝑠).

Simplified Transfer Function

For practical purposes, the transfer function can be simplified by combining terms
and assuming certain conditions. Let's simplify it further:

𝜔(𝑠) 𝐾𝑡
= 𝐽𝐿𝑅 2
𝑉(𝑠) 𝑠 𝑠 +(𝐽𝐿+𝐵𝑅𝑠 )𝑠+(𝐵𝑅𝑠 +𝐾𝑡 𝐾𝑒 )

This quadratic form of the denominator indicates a second-order system, where

the coefficients depend on the motor parameters 𝐽, 𝐿, 𝑅𝑠 , 𝐵, 𝐾𝑡 , and 𝐾𝑒 .
 Chapter 4

SLIDING MODE CONTROLLER DESIGN

In this chapter, we delve into the design and implementation of a Sliding Mode
Controller (SMC) specifically tailored for the speed control of Brushless DC (BLDC)
motors. Sliding Mode Control is a robust control strategy well-suited for nonlinear and
uncertain systems, such as BLDC motors [33]. This chapter is organized into three
sections: the first section provides an introduction to Sliding Mode Control, highlighting
its principles and advantages. The second section outlines the design procedure for
developing an SMC for BLDC motor speed control, detailing the steps involved in
creating an effective control strategy. The final section discusses the practical aspects of
implementing the designed SMC, including the hardware and software requirements, and
the challenges encountered during implementation. By the end of this chapter, readers
will have a comprehensive understanding of how to design and implement a Sliding Mode
Controller to achieve precise and robust speed control in BLDC motor applications .

4.1 Introduction to Sliding Mode Controller (SMC)

Sliding Mode Control (SMC) is a nonlinear control technique that has gained
significant attention due to its robustness and effectiveness in dealing with systems
characterized by uncertainties, nonlinearities, and external disturbances. The fundamental
concept behind SMC is to force the system states to reach and then slide along a
predetermined surface in the state space, known as the sliding surface, which ensures the
desired dynamic behaviour of the system [34]-[36].

➢ Fundamentals of Sliding Mode Control

The primary objective of SMC is to design a control law that drives the system's
state trajectory onto the sliding surface and maintains it there despite external
disturbances and model uncertainties. This is achieved through two main steps:
 1. Design of the Sliding Surface: The sliding surface is chosen such that the system
exhibits desirable dynamics once the trajectory reaches this surface. It is typically
defined as a function of the system's states and can be represented as:

𝜎(𝑥) = 0

where 𝜎(𝑥) is the sliding surface and xxx represents the state vector of the system.

2. Control Law Design: The control input is designed to ensure that the system's
trajectory reaches the sliding surface in finite time and remains on it thereafter.
This involves the design of a discontinuous control law, often in the form:

𝑢 = 𝑢𝑒𝑞 + 𝑢𝑠𝑤

where 𝑢𝑒𝑞 is the equivalent control, which maintains the system on the sliding
surface, and 𝑢𝑠𝑤 is the switching control, which drives the system towards the
sliding surface.

➢ Advantages of Sliding Mode Control

SMC offers several advantages that make it particularly attractive for controlling
BLDC motors [37], [38]:

1) Robustness: One of the most significant advantages of SMC is its robustness to

system uncertainties and external disturbances. Once the system's trajectory reaches
the sliding surface, the closed-loop system dynamics become insensitive to certain
types of uncertainties.
2) Finite-Time Convergence: SMC ensures finite-time convergence to the sliding
surface, which means that the desired system dynamics can be achieved in a finite
time despite disturbances.
3) Simplicity in Design: The design of SMC does not require an exact model of the
system. It only requires knowledge of the system's relative degree and the design of
the sliding surface.

➢ Sliding Mode Control for BLDC Motor Speed Control

BLDC motors, with their inherent nonlinearities and parameter variations, pose a
challenging control problem. Conventional control strategies like Proportional-Integral-
Derivative (PID) controllers may not always provide satisfactory performance under
varying operational conditions. This is where SMC proves to be highly effective. By
employing SMC, we can achieve robust speed control of BLDC motors, ensuring high
performance even in the presence of model uncertainties and external disturbances [39]-
[41].

Figure 2 shows block diagram of control scheme of BLDC motor drive. The
voltage source inverter (VSI) is used to fed BLDC motor. The inverter works as electronic
commutator, which energizes stator winding. In accordance to commutation sequence,
stator poles are created and rotor follows the same. The speed and angular position of
rotor are sensed. Hall effect sensors displaced by 120° are placed on stator itself [42].
They are used to sense rotor position. The actual speed of rotor is compared against
reference speed. The error is given to speed controller, which sets reference DC current
∗
𝐼𝐷𝐶 . The hall effect signals and current 𝐼𝐷𝐶 are used to calculate reference AC current 𝐼𝐴𝐶 .
∗
The amplitude of current𝐼𝐴𝐶 is equal to 𝐼𝐷𝐶 , whereas the frequency and shape is governed
∗
by hall effect signals. The actual AC current is now compared with 𝐼𝐴𝐶 and error is fed to
the hysteresis current controller. In turns, it generates pulse pattern that drives the inverter.

Fig. 2. Control scheme of BLDC motor drive

Sliding Mode Controller Based Speed Control

 The sliding mode controller is faster in response than PI controller. It does this
without any overshoot. Once SMC controller is designed, the performance of system
becomes independent of parameter variation. The sliding function is defined as below,

𝑠𝜔 = 𝑒𝜔 + 𝑘1 ∫ 𝑒𝜔 ⁡𝑑𝑡 (1)

∗
where 𝑒𝜔 = 𝜔𝑚 − 𝜔𝑚

∗ ∗
∴ 𝑠𝜔 = (𝜔𝑚 − 𝜔𝑚 ) + 𝑘1 ∫(𝜔𝑚 − 𝜔𝑚 )⁡𝑑𝑡 (2)

where 𝜔𝑚 is the angular speed of BLDC motor.

Taking derivative of equation 2 with respect to time,

∗
̇ + 𝑘1 (𝜔𝑚
𝑠𝜔̇ = −𝜔𝑚 − 𝜔𝑚 ) (3)

The electro-mechanical equation of BLDC motor is as below.

1
̇ = 𝐽 (𝑇𝑒 − 𝑇𝐿 − 𝐷𝜔𝑚 )
𝜔𝑚 (4)

where,

𝑇𝑒 – Electromagnetic torque

𝑇𝐿 – Load Torque

𝐷 – Damping factor

Putting equation 4 in equation 3,

1 ∗
𝑠𝜔̇ = − 𝐽 (𝑇𝑒 − 𝑇𝐿 − 𝐷𝜔𝑚 ) + 𝑘1 (𝜔𝑚 − 𝜔𝑚 ) (5)

Again, using constant plus proportional rate reaching law,

𝑠𝜔̇ = −𝑘2 𝑠𝑔𝑛(𝑠𝜔 ) − 𝑘3 𝑠𝜔 (6)

Equating equations 5 and 6 and solving for 𝑇𝑒 , we will get

∗
𝑇𝑒 = 𝐽[𝑘1 (𝜔𝑚 − 𝜔𝑚 ) + 𝑘2 𝑠𝑔𝑛(𝑠𝜔 ) + 𝑘3 𝑠𝜔 ] + 𝑇𝐿 − 𝐷𝜔𝑚 (7)

The electromagnetic torque 𝑇𝑒 is the control output of sliding mode controller as shown
in figure 3.
Fig. 3. Sliding Mode Controller

Pulse Generation

The reference AC currents calculated are compared with actual motor input AC
currents. The error is fed to the Hysteresis PWM, which is characterized by hysteresis
band. When actual current reaches to the upper band, the switch will be turned OFF. The
current starts to drop. When it comes down to the lower hysteresis band, the switch will
turn ON again. In this way, actual current is confined between upper and lower band
defined around reference current as shown figure 4.

Fig. 4. Pulse Generation by Hysteresis PWM

 Chapter 5

SIMULATION RESULTS AND DISCUSSIONS

The proposed SMC based control scheme for 3 phase BLDC motor is simulated
using MATLAB/Simulink software. The sample time is taken equal to 5 × 10−6 sec. The
parameters chosen for preparation of this simulation are presented in Table-I. The
simulation block diagram is shown in figure 5. Performance of proposed method is
checked by applying change in speed and load torque. The results are also presented,
which validates the effectiveness of the technique [43].

Table-I Motor Parameters

Parameters Value

Motor Parameters

DC Supply 320 V

Moment of Inertia (J) 0.089 𝑘𝑔. 𝑚2

Pole Pairs 4

Stator Resistance (𝑅𝑆 ) 0.2 Ω

Stator Inductance (𝐿𝑆 ) 8.5 𝑚𝐻

Flux Linkage 0.175 (𝑉. 𝑠)

SMC Controller Parameters

K1 210

K2 0.2

K3 350
Fig. 5. Simulation Block Diagram of BLDC Motor Speed Control Scheme

Response of BLDC Motor for Change in Speed with constant load torque

The performance of BLDC motor controlled using SMC controller is checked by

varying reference speed as shown in figure 6(a). The Reference speed is varied smoothly.
From starting the motor to reach new speed command of 300 rpm, the actual speed exactly
tracks reference speed. There is no overshoot observed and motor settles at new speed
immediately. The speed response is also checked during increase of reference speed from
300 rpm to 400 rpm and decrease back to 300 rpm. Here also, no overshoot exists and
motor immediately settles at new speed command. During transition phase, the actual
speed exactly matches the smooth change in reference speed.

The constant load torque of 10 N-m is applied to the motor. The motor torque is
increased more than load torque during starting and acceleration. In deceleration phase,
load drives the motor, so motor torque drops as shown in figure 6(b). As motor torque is
dependent on motor current, same changes are present in current waveform as shown in
figure 6(c).
 (a)

(b)

(c)
Fig. 6. Performance of BLDC motor during speed variations with constant load (a) Motor
speed, (b) Motor Torque and (c) Motor current
Response of BLDC Motor for Change in Load Torque with constant speed

The speed regulation is checked by giving variations in load torque. The motor speed
graph is shown in figure 7(a). The load torque is increased from 10 N-m to 12 N-m after
0.6 sec and again decreased to 8 N-m on 1.4 sec. The motor is able to provide these load
changes immediately as shown in figure 7(b). These load changes have no effect on speed
regulation. Motor continues to run at constant speed. The motor current follows changes
in load torque as shown in figure 7(c).

(a)

(b)
 (c)

Fig. 7. Performance of BLDC motor during load torque variations with constant speed (a)
Motor speed, (b) Motor Torque and (c) Motor current
 Chapter 6

CONCLUSION AND FUTURE SCOPE

Conclusion:

The simulation results validate the effectiveness of the Sliding Mode Control (SMC) for
controlling the speed of a BLDC motor under varying operational conditions. The SMC
controller demonstrates excellent performance in tracking reference speed commands
with high accuracy. When the reference speed is varied, the motor responds promptly
without any overshoot, and the actual speed closely follows the reference speed. The
motor also shows quick settling to the new speed command, highlighting the robust nature
of the SMC controller.

The ability of the BLDC motor to maintain speed stability even when subjected to
changes in load torque further underscores the reliability of the SMC approach. Despite
significant load variations, the motor maintains constant speed, demonstrating the
controller's robustness against disturbances. The motor's torque and current responses
adapt well to these changes, confirming the SMC's capability to handle dynamic
conditions effectively.

Overall, the SMC controller provides superior speed regulation and disturbance rejection
for the BLDC motor, ensuring stable and accurate performance across different scenarios.
This makes it a highly suitable control strategy for applications requiring precise and
reliable motor control.

Future Scope:

Following is the future scope of this project.

1) Hardware Implementation: While the current study focuses on simulation results,

future work could involve the implementation of the Sliding Mode Controller (SMC)
on an actual BLDC motor setup. This would validate the simulation findings and
address any real-world challenges such as noise, non-idealities, and hardware
limitations.
2) SMC Tuning for Different Motor Types: Extending the SMC design to other types
of motors, such as Permanent Magnet Synchronous Motors (PMSMs) or Induction
Motors, could provide insights into the versatility and adaptability of the control
strategy.
3) Integration with Advanced Control Techniques: Combining SMC with other
advanced control methods like Model Predictive Control (MPC) or Artificial
Intelligence (AI)-based approaches could enhance the performance of BLDC motor
drives, particularly in complex, multi-variable systems.
4) Energy Efficiency Optimization: Future research could focus on optimizing the
energy efficiency of BLDC motors controlled by SMC, especially under varying load
and speed conditions. This would be particularly beneficial for applications like
electric vehicles where energy consumption is critical.
5) Robustness to External Disturbances: Investigating the robustness of SMC under
more extreme conditions, such as high external disturbances or faults in the motor
drive system, could lead to further refinements in controller design.
6) Comparison with Emerging Control Strategies: Continuous benchmarking
against emerging control strategies, such as deep learning-based controllers or
advanced adaptive controllers, would keep the SMC approach relevant and
competitive in the field.
7) Long-term Reliability Studies: Conducting long-term studies on the reliability and
maintenance aspects of SMC-controlled BLDC motors would be valuable for
industries that require high dependability, such as automotive and aerospace sectors.
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