Comparitive Analysis of Speed and Position Control of BLDC Motor via Field Oriented Control Using SPWM and SVPWM Schemes

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Comparitive Analysis of Speed and Position Control of BLDC Motor via
Field Oriented Control Using SPWM and SVPWM Schemes
Sanjan P S1, Dr. Madhu B R2
1Department of Electrical and Electronics, RV College of Engineering, Bangalore, India
2Assistant Professor, Department of Electrical and Electronics, RV College of Engineering, Bangalore, India
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Abstract— In this paper, a comparative analysis is carried
out on the performance of a Field Oriented Controlled (FOC)
based speed and position control of BLDC motor using
Sinusoidal Pulse Width Modulation (SPWM) and Space
Vector Pulse Width Modulation (SVPWM) schemes. FOC is
commonly used in high performance motor
driver/controller for its superior performance such as high
efficiency and lower torque ripple content, especially in
applications such as robotics, electric vehicles, power tools,
etc. Advancements in Digital Signal Processors and lower
costs have allowed this technique to be used in more high-
performance applications. The overall performance also
depends on PWM control scheme used. SPWM and SVPWM
techniques are two most commonly used techniques in
motor control and inverter control applications. Hence a
comparison study is carried out with the two schemes using
Simulink. In light loading conditions, the results show that
the performance is quite similar, but on closer inspection,
SVPWM based FOC offers better performance compared to
SPWM based FOC.
Keywords—FOC; BLDC; SVPWM; SPWM; Clarke
Transformation; Park Transformation;
I. INTRODUCTION
Over the years, Brushless DC Motors (BLDC), a type of
permanent magnet synchronous motor has gained wide
spread popularity. Now, it is commonly used in electric
vehicles, precision motor control applications such as CNCs
and robotic arms, power tools, aerospace applications,
drones etc. This is due to its high-power density, high
efficiency, more robust and reliable compared to a typical
brushed DC motor, also, high rotor speeds can be achieved
and quieter operation. Typical construction of a BLDC
motor uses an armature that is stationery with the three
phase coils arranged 120o electrical apart and permanent
magnets are attached on the rotor. Due to this type of
construction, the commutation needs to be done
electronically unlike a brushed DC motor that commutates
mechanically. In order to control a BLDC motor, the current
flowing through each coil needs to be controlled, by doing
so, the net magnetic field vector can be controlled (i.e., both
direction of rotation and magnitude). The rotor magnetic
field catches up with the net stator magnetic field vector to
produce torque, since the strength of magnetic field is
directly dependent on the current flowing in the coils, the
torque can be controlled [1-3].
Various BLDC control techniques have been defined in
literature, these include, trapezoidal control that involves
controlling the current through any two pair of coils
simultaneously, the sequence of firing is decided by a
lookup table and feedback from the hall effect sensors that
measure rotor position. Although this technique is simple to
implement, it does not provide smooth and precise motor
control. Sinusoidal control involves controlling the three
phase currents though the coils sinusoidally as the motor
rotates. This results in a smoothly rotating magnetic field
vector; therefore, it eliminates the torque ripples and
commutation spikes. One of the drawbacks with this
technique is that its performance degrades at higher speeds
because of the time variant nature of the control scheme
that causes the breakdown due to limited bandwidth of PI
(Proportional Integral) Controller. Field-oriented control,
also called as vector control is a scheme that offers great
performance and efficiency. In this technique, the stator
currents of the motor are represented in dq reference
frame. One vector corresponds to the magnetic flux of the
rotor and the other vector represents the torque. By
manipulating these vectors based on the desired output
required, the motor is controlled. A detailed explanation of
this scheme is provided in section. Although this scheme
requires high processing requirements, recent
advancements and reduction of cost in microprocessor and
power electronics technology have led to wide spread
usage of this scheme in AC motor drives [2-3].
For field-oriented control and various other industrial
application, two of the most commonly used PWM (Pulse
Width Modulation) schemes to control the inverter are
SPWM (Sinusoidal PWM) and SVPWM (Space Vector PWM).
In SPWM technique, two different signal types are used –
sinusoidal reference waveforms and a high frequency
triangular waveform (i.e., carrier waveform) for
comparison to generate pulses. In SVPWM, the rotating
space vector of either the reference voltage or current is
recomposed by taking the vector sum of available base
vectors [5-8].
Position control requires feedback of the rotor position,
usually encoders are used to sense the rotor position. There
are various types of encoders such as magnetic and optical
encoders, in this there are incremental and absolute types.
Depending on the application and accuracy it demands an
appropriate encoder is selected. An encoder can provide
information on direction of rotation, speed, amount of
rotation and position. The sensitivity of an encoder is
defined by its resolution. In general, a typical FOC based
speed and position control is shown in Fig. 1. It consists of
three control loops. Position control loop feeds the speed
control loop, this inturn feeds the current control loop [9-
12].
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 09 Issue: 06 | June 2022 www.irjet.net p-ISSN: 2395-0072

II. MODELLING OF THE BLDC MOTOR
Let’s assume a system of BLDC motor connected via a
three-phase inverter and powered by a DC source as shown
in Fig.2. To model the motor, consider a star connected
configuration for the BLDC motor [2] and assuming a
balanced three phase system, then, R = Ra + Rb + Rc.
(1)
(2)
(3)
Fig. 2. Equivalent Circuit of BLDC Motor
In equation (1-3),
Va, Vb, Vc = phase voltages
R = Armature resistance
L = Armature self-inductance
M = Mutual inductance
Ia, ib, ic = phase current
Ea, eb, ec = motor back emf
The back emf of the motor is written as shown in (4-7)–
(4)
(5)
(6)
(7)
The electrical angle, θe = (P/2)θm, where θm is the
mechanical angle of the rotor and P are the number of pole
pairs. The function given by f in (7) gives the back emf that
is trapezoidal in nature for phase A of the motor. Kw is the
back emf constant and ω is the rotor speed.
The electromagnetic torque in both electrical form and
mechanical form is given in (8) and (9) respectively.
(8)
(9)
In this,
P = Number of pole pairs
TL = Load Torque
J = Moment of Inertia
B = Friction Constant
III. FIELD ORIENTED CONTROL
Fig.3 shows the vector representation of the stator
current in abc, alpha-beta and dq reference frames. For
conversion from abc to alpha-beta reference frame, only
two instantaneous current vectors are sufficient, in this
case phase currents of a and b. Phase c current can be
computed using the current relation shown in (10).
(10)
Using Clarke’s transformation, the phase vectors are
converted to alpha-beta orthogonal reference frame (11-
12).
(11)
Fig. 1. General Block Diagram of Position and Speed Control of BLDC Motor Using FOC

(12)
Fig. 3. Current Vector Representation Combined
Using Park’s transformation, the vectors are converted
from alpha-beta coordinate system to dq coordinate system
(13-14).
(13)
(14)
Here, θ is the instantaneous rotor position angle, also in
the dq reference frame, the quantities are time invariant. By
controlling/modifying the quadrature component of the
current, the torque can be controlled. By controlling the
direct component, the rotor flux can be controlled.
In order to maximize torque and overall efficiency, the
direct component must be ideally maintained at zero and
quadrature component is generated based on torque and
speed requirements. The reference values are compared
with actual values and via a PI controller, the corresponding
voltage is calculated. The voltage in dq reference frame is
converted back to alpha-beta coordinate system using
Inverse Park’s transformation as shown (15-16). This is
typically used to generate the gate pulses using SVPWM.
(15)
(16)
In order to convert from alpha-beta coordinate system
to abc, Inverse Clarke’s transformation is used as shown
(17-19). This is used to generate the SPWM for the inverter.
(17)
(18)
(19)
IV. SINUSOIDAL PULSE WIDTH MODULATION
Sinusoidal Pulse Width Modulation, is one of the most
commonly used technique for motor control and inverter
applications. Implementation of this technique is simple
and processing requirements are less. The sinusoidal
reference waveforms are compared with a high frequency
triangular carrier waveform to obtain the switching pulses
for the respective switches.
Space Vector Pulse Width Modulation is a more
advanced technique compared to the SPWM technique. The
added complexity offers many advantages such as better
utilization of DC bus voltage, lower harmonics and better
flexibility. Fig.4 shows a space vector representation of the
inverter system with six sectors. The reference vector
rotates with an angular velocity against the stationary
alpha-beta reference frame. By controlling the frequency
and magnitude of vref, the magnitude and frequency of the
corresponding fundamental component is varied [6-8]. The
required output voltage of each phase is shown in (20-22).
(20)
(21)
(22)
Fig. 4. Vector Representation of SVPWM
Vref is calculated using (23) and the Fig.5 visualizes the
representation of sector 1.
V. SPACE VECTOR PULSE WIDTH MODULATION
Fig. 5. Sector 1 Representation

(23)
In this θ = ωt = 2πft
(24)
In this Tz is the time period of the PWM signal or the
reciprocal of the switching frequency fs (i.e., Tz = 1/fs). The
angle between the sectors is given by ϕ with range between
0o to 60o.
(25)
(26-28) is used to determine the switching period.
(26)
(27)
(28)
VI. SIMULATION AND RESULTS
A. Simulation Setup
The simulation studies are carried out using Simulink. In
accordance to fig, the models for the comparison studies
using the SPWM and SVPWM based speed and position
control of BLDC motor is shown in Fig.6. The Simulink
model consists of PMBLDC motor configured for
trapezoidal back emf, stator resistance of 0.01ohms and
inductance of 40uH. For the inverter, a two-level inverter
block is used, powered by a DC source of 12V. The
transformations are directly performed using the
conversion blocks available in Simulink. The PWM scheme
is directly implemented using the PWM modulator block
that offers both SVPWM and SPWM capabilities. The PWM
scheme is changed between studies to perform the
comparison study. The switching frequency is set at 8kHz.
There are three control loops, one current control loop,
speed control loop and position control loop connected in
cascaded configuration. In order to keep track of the
position, the integral of speed is taken. A constant torque of
0.008Nm is applied on the motor with a total simulation
time of 5 seconds. Using a stair generator block, the
reference position is generated. From 0, at 0.1 seconds, the
position is set to 4 radians or 4 revolutions of the rotor
shaft. At 2 seconds, the rotor position is set to -4 radians
and is set back to 0 radians at 3.5 seconds. The PI controller
of the current control loop is tuned using a separate
MATLAB script. The speed and position control loop are
tuned by trial-and-error method. The model is run at
constant speed next to obtain the back emf and
electromagnetic torque waveforms.
B. Results
Fig.7 shows the waveforms related to the motor. In order,
the first waveform shows the back emf, the phase currents
and the electromagnetic torque. At the commanded
positions, the waveforms using both SPWM and SVPWM
look similar, upon closer inspection, the electromagnetic
torque ripple is relatively less in SVPWM scheme. During
position change, the current draw increases to reach the
desired position, the current starts dropping once the
positional error start reducing. Spikes in electromagnetic
torque is seen during position changes. Fig. 8 and Fig.9
shows the comparison between speed and position
waveforms respectively. The rotor speed waveforms show
the speed increasing during position changes and reducing
when positional error reduces. The position waveforms
show the actual position and reference position waveforms.
The control system is able to track the reference positions
accurately and no overshoots occur. A similar conclusion is
drawn by comparison of these waveforms. This similar
performance is due to the light loading conditions. Fig.10
shows a comparison of the motor parameters at constant
speed of 100 rad/sec with increased loading of 0.08Nm
compared to the 0.008Nm previously. In this case, only a
small difference is seen in the electromagnetic torque. The
back-emf at this loading is at 0.7V and the current draw is
close to 10A(peak). The overall torque ripple is less in
SVPWM compared to SPWM. This is verified by taking a
moving average of the electromagnetic torque to reduce the
noise caused by switching as shown in Fig.11. There are a
lot less variations in the SVPWM based FOC compared to
Fig. 6. Simulation Model of the FOC Based Speed and Positon Control of BLDC Motor Using SPWM and SVPWM
General Block Diagram of Position and Speed Control of BLDC Motor Using FOC

SPWM based FOC.
Fig. 8. Speed Waveform in rad/sec a) SVPWM b) SPWM
Fig. 9. Actual Position (Red) and Reference Position
(Purple) Waveform a) SVPWM b) SPWM
Fig. 7. Back EMF, Stator Current, Electromagnetic Torque Waveforms of the BLDC Motor a) SVPWM b) SPWM
General Block Diagram of Position and Speed Control of BLDC Motor Using FOC

Fig. 10. Back EMF, Stator Current, Electromagnetic Torque
Waveforms of the BLDC Motor at Constant Speed a)
SVPWM b) SPWM
Fig. 11. Electromagnetic Torque at Constant Speed a)
SVPWM b) SPWM
VII. CONCLUSIONS
The comparison study of position and speed control of
BLDC motor via FOC using SPWM and SVPWM has been
carried out using Simulink and the corresponding output
waveforms of comparison is presented. In this study, due to
light loading conditions, the performance of the FOC based
algorithm using both SPWM and SVPWM scheme are quite
similar. Small variations can be seen in the waveforms
especially comparing the electromagnetic torque, the
SVPWM performs slightly better with less torque ripple
compared to SPWM technique. The averaged torque
waveform of SVPWM is relatively smoother compared to
SPWM.
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