Solution
David answered on
Dec 27 2021
CHAPTER 3
METHODOLOGY
3.1 Introduction
We are well aware that in today‟s scenario research methods had undergone a
tremendous change, how researchers identify a problem and then gathering information to
find a proper solution in this dynamic environment which also acts as a motivation for them
in the entire process. At this point of the time how the flow of project was performed is as
shown in the figure 3.1.
In order to have a better understanding the entire flow of the project is explained
iefly as shown below:
1. Literature Review
All information about Brushless DC (BLDC) motor, conventional PID and
Fuzzy PID were gathered first. It was necessary to understand the theoretical
concept, their mathematical modelling and their functions before getting into
our project. Most of the information was gained from papers, online journals
and standard reference books.
2. Modelling of BLDC Moto
Different types of motors were studied including the conventional (
ushed)
DC-motor where the
ushes make mechanical contact and it was noted that
though the conventional PID control ma suit for such Brushed DC motor, it
was not much efficient in the case of Brushless DC (BLDC) motor because
the response time was high and hence we need to opt for Fuzzy based PID
control for the speed control of the BLDC motor. [20]
3.2 Flowchart of the project
Figure 3.1: General Methodology of the Project
No
No
Yes
Yes
Start
Identifying the Problem & Gathering Information/ Literature
Search
Mathematical Modelling Of BLDC Motor
Study of Fuzzy Logic Controller (FLC)
Obtained
Parameters of
Speed Control
Input Parameters of FLC PID Based on „„Rule Base‟‟
Developing FLC PID Based on Simulink
Result From Fuzzy
Logic PID Controller
Result Analysis Based On FLC Simulation
End
Final Report
3.3 System configuration
3.3.1 Structure of BLDC Motor
With constant excitation, the speed and torque characteristic of BLDC is similar to
that of the shunt wound
ushed DC motor. In the case of
ushed motor, the magnets
presents in the rotor which passes through the stator poles creates a trapezoidal back EMF
in the windings of the stator. Usually the trapezoidal shape flux wave is created with a three
phase stepped waveforms with positive and negative going pulses of 120 degree duration.
[21]
BLDC motor is not a pure DC motor, just a DC pulse is given as input to the stator
winding so that a magnetic field is created in the rotor by operating at the synchronous
speed. As we can see in the figure 3.2 shown below where pole pair A is first fed with a DC
pulse which then magnetizes pole A1 as a South Pole and A2 as a North Pole thus making
the magnet to be in the initial position. When the magnet is passed through the first
magnetized pole pair we can see that the cu
ent in the pole pair A is switched off and the
next pole pair B is given with a similar DC pulse as that of pole pair. Later the magnet can
e seen rotating in the clockwise direction to align itself with that of the pole pair B. The
pulsated stator pole pairs which are in sequence with that of the magnet will continue to
otate clockwise in order to keep itself aligned with that of the energized pole pair.
Figure 3.2: Cross sectional view of BLDC motor after disassembling. [22]
Since this is a
ushless DC motor, instead of
ush commentators‟ to generate the
otating magnetic field, a six step inverter is used to generate the three phase supply and the
electronic commutation between the three pole pairs of stator coils. At a time, only two out
the three pole pairs are energized. The pulse frequency and the torque by the pulse cu
ent
control the speed of the rotor of the BLDC motor. [23]
In this chapter we will see about the structure of the BLDC motor, then the
modelling and the parameters associated with it in order to model a trapezoidal back EMF of
BLDC motor. We will then see how the conventional PID controller was used and why there
was a need to replace the conventional PID with the proposed fuzzy based PID controller. At
last we will see about the structure of the fuzzy logic control along with the design steps for
fuzzy logic control along with the Fuzzy logic editor interface tool box in MAT lab
simulation. The block diagram for the speed control of BLDC motor drive system using the
Gaussian fuzzy logic controller is as shown in the Figure 3.3.
Figure 3.3: The block diagram of speed control using Gaussian fuzzy logic controller for
BLDC motor drive system.
3.3.2 Mathematical Modelling of a BLDC moto
Based on the assumption for simplification and accuracy, the analysis of the BLDC
is done. Since the BLDC motor is an unsaturated type of motor, the self and mutual
inductance are constant for all the winding whereas the stator resistances are equal. Power
electronics or semiconductor devices encompassed inside the inverter are ideal having
negligible iron losses.[24] The back-EMF wave-forms associated with each and every
phases are equal. Hence considering the equivalent circuit of BLDC motor and VSI system
as shown in the Figure 3.4 and the assumptions, the dynamic equations of the BLDC motor
can be derived as shown below.
Va = RIa + (L – M)
+ ea (3.1)
Vb = RIb + (L – M)
+ eb (3.2)
Vc = RIc + (L – M)
+ ec (3.3)
Where
Va, Vb, Vc = Stator phase voltages across phase A, B & C respectively.
ia, ib, ic = Stator phase cu
ent across phase A, B, C respectively.
ea, eb, ec = Phase back EMF across phase A, B, C respectively.
L = Self inductance of the BLDC motor.
M = Mutual inductance of the BLDC motor.
R = Phase resistance.
Gaussian Fuzzy
Logic Controller
Brushless DC
Motor
Reference
Speed Output
Now the motion is defined as:-
= (
) (Te – TL - Bωr) (3.4)
ωr (3.5)
Where
Te = The electromagnetic torque
TL = Load torque (Nm)
J = Moment of inertia (kgm
2
)
B = Friction coefficient (Nms
ad)
ωm = Rotor speed in mechanical (rad/s)
ωr = Rotor speed in electrical (rad/s)
3.3.3 Modelling of a Trapezoidal Back EMF of BLDC moto
Since the rotor position has to be calculated based on the operation speed, the
trapezoidal back-EMF wave forms are modelled as a function of the rotor position. [25] So
the back EMF can be expressed as a function of rotor position (θr) as shown below.
eabc = fabc(θr) x E (3.6)
E = ke ωr (3.7)
Where
(ke) is back-EMF constant,
fabc(θr) are the function of rotor position.
Figure 3.4: Trapezoidal back-EMF and phase cu
ent waveforms of BLDC motor drive [25]
Figure 3.4 shows the trapezoidal back-EMF which is depicted as a function of rotor
position and has the amplitude. The expression of the back-EMF based on the rotor position
can be generated as shown in equations (3.8), (3.9) and (3.10) which are named as
trapezoidal shape functions with limit values between +1 and -1
fa(θr) = (3.8)
(
)θr (0 < θr ≤
)
1 (
< θr ≤ 5
)
-(
)θr + 6 (5
< θr ≤ 7
)
-1 (7
< θr ≤ 11
)
(
)θr – 12 (11
< θr ≤ 2π )
fb(θr) = (3.9)
fc(θr) = (3.10)
The electromagnetic torque is defined by using back-EMFs as follows
Ta =
(3.11)
Tb =
(3.12)
Tc =
(3.13)
-1 (0 < θr ≤
)
(
)θr – 4 (
< θr ≤ 5
)
1 (5
< θr ≤ 7
)
-(
)θr + 10 (7
< θr ≤ 11
)
-1 (11
< θr ≤ 2π )
1 (0 < θr ≤
)
-(
)θr + 2 (
< θr ≤ 5
)
-1 (5
< θr ≤ 7
)
(
)θr – 8 (7
< θr ≤ 11
)
1 (11
< θr ≤ 2π )
3.4 Topology of MOSFET based
idge rectifier:
Figure 3.5: Schematic symbol and MOSFET packaging [26]
Figure 3.6: 3 phase MOSFET based H-
idge [27]
MOSFET‟s (Metal–Oxide–Semiconductor Field-Effect Transistor) which are
prefe
ed over mechanical switches because of its smaller physical size, high switching
speeds, requires lower driving voltage. Figure 3.6 shows the 3 phase bidirectional MOSFET
switch setup for the 3 phase load which is the BLDC motor. The reason for selecting
MOSFET is because of its wide range of voltages, cu
ents and power it can handle. We are
using N-type MOSFET because of lower "ON state resistance" and less power consumption
while sourcing cu
ent to the motor Gate Drivers. Mostly MOSFET‟s don‟t need much
cu
ent or power to stay in the conducting or non conducting state. The only power being
consumed by the MOSFET is the load cu
ent that runs through small amount of resistance
etween the drain and source but they do consume cu
ent and power when in the "In
etween" stage while switching on or off. This is because of the small capacitance at the gate
that needs to be charged or discharged to change from the non conducting (cutoff) region to
the conducting (saturation) region and vice versa. [28]
3.5 PWM Control method of Bridge Rectifier:
Figure 3.7: PWM cu
ent regulation method [29]
The supply voltage is chopped at a fixed frequency with a duty cycle depending on
the cu
ent e
or. Therefore, both the cu
ent and the rate of change of cu
ent can be
controlled. The two phase supply duration is limited by the two phase commutation angles.
The main advantage of the PWM strategy is that the chopping frequency is a fixed
parameter; hence, acoustic and electromagnetic noises are relatively easy to filter. The PWM
frequency is held constant while speed is controlled vial the duty cycle of the "ON" portion
of the transistors. We will be using a PWM technique in my controller as it is better suited
for a variable speed load.
3.6 Control Circuit for BLDC Motor
When we come towards the inverter cu
ent pulses, they are triggered in a closed
loop system by a signal which represents the instantaneous angular position of the rotor.
Here it is to be noted that the frequency of the power supply is always controlled by the
motor speed.[29] The position of the rotor can be determined by the Hall Effect sensor
which is cascaded into the stator which also provides electrical signal representing the
magnetic field strength. This electrical signal amplitude or voltage changes accordingly
when the magnetic rotor passes over the sensor. The voltage control and the speed control
which is associated with that of cu
ent and voltage waveforms superimposed on the circuits
is shown in the Figure 3.8.
Figure 3.8: Voltage control & Speed control associated with cu
ent and voltage waveforms
superimposed on the circuits. [22]
BLDC motor are widely used in industrial application where most of the heavy
appliance are controlled and in order to have that control we need a better speed response but
in the case of conventional PID controller we don‟t get the desired speed response and hence
there are always lag in settling time and in order to reduce that we go for fuzzy based PID
controller in which the settling time is less and hence the speed of the BLDC motor...