International Conference on Recent Advances in (Applied) Sciences & Engineering (Raise)12- 13April,2023
organized by Faculty Of Technology & Engineering, The Maharaja Sayajirao University Of Baroda
Closed loop speed control of BLDC motor using PI controller
Prarthana Joshi1, Pramod Modi2, Darshit Prajapati3, Piyush Dekavadiya4 and Pravin
Vadhiyar5
1
M.E.(Industrial Electronics), Department of Electrical Engineering, Faculty of Technology
& Engineering, The Maharaja Sayajirao University of Baroda, India – 390002;
Email: joshiprarthana62@gmail.com
2
Associate Professor, Department of Electrical Engineering, Faculty of Technology &
Engineering, The Maharaja Sayajirao University of Baroda, India – 390002;
Email: p.s.modi-eed@msubaroda.ac.in
3
Executive Engineer, Xylem water solutions, Vadodara – 390016;
E-mail: darshit.prajapati@xylem.com
4
Manager, Xylem water solutions, Vadodara – 390016;
E-mail: piyush.dekavadiya@xylem.com
5
Sr. Lead Hardware engineer, Xylem water solutions, Vadodara–390016;
E-mail pravin.vadhiyar@xylem.com
Abstract
In this paper, one of the commutation method of BLDC motor i.e., six step commutation
method (Trapezoidal commutation) with sensor feedback for BLDC motor is discussed.
Generalized block diagram with switching sequence of 3 phase inverter and control algorithms
for the regulation of the speed of the motor is discussed further. Advantages of BLDC motors
over other motors are fast dynamic response, high power density (output power/volume), high
efficiency, high reliability, less maintenance requirement, low weight and cost. Simulation of
this method is carried out in MATLAB Simulink software. Necessary waveforms and results
regarding simulations are also shown.
Keywords:
BLDC motor, Trapezoidal commutation, PI-controller, six step commutation method,
MATLAB Simulink
1. Introduction
In recent years BLDC motor has become popular in industry and preferred over brushed DC
motors in many applications. Brushless DC motors are type of permanent magnet
synchronous motor which contains the permanent magnet in the rotor and coils in the stator
and vice versa. Permanent magnets create the rotor flux and the energized stator windings
create electromagnetic poles. The rotor is attracted by the energized stator phase. By using
proper sequence to supply the stator phases, a rotating field on the stator is created. BLDC
motors have many advantages over other motors, such as a better speed vs. torque
characteristics, high dynamic response, high reliability, noiseless operation, higher speed
ranges, and reduction of electromagnetic interference (Yedamale, P, 2003)( Rambabu, S, 2007).
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International Conference on Recent Advances in (Applied) Sciences & Engineering (Raise)12- 13April,2023
organized by Faculty Of Technology & Engineering, The Maharaja Sayajirao University Of Baroda
In addition, the ratio of delivered torque to the size of the motor is higher, hence it is useful
in applications where space and weight are critical factors, especially in aerospace
applications and Electric vehicle applications.
2. Block diagram
A BLDC motor works on principle of Lorentz’s force law. This principle states that
whenever a current-carrying conductor is placed in a magnetic field it experiences a force.
Because of this force, the magnet will experience an equal and opposite force. Hall sensors
are used to detect the rotor position i.e., magnetic pole position. The speed of the motor can
be regulated by varying voltage across the motor. when using PWM pulses to control the six
switches of the three- phase bridge, variation of the motor voltage can be obtained byvarying
the duty cycle of the PWM signal. The speed as well as torque of the motor depends on the
strength of the magnetic field generated by the energized windings of the motor, which depend
on the current through them. Hence rotor speed can be changed by adjusting supply voltage
and current.
Figure 1 Block diagram of BLDC sensored control
As shown in the figure 1, actual speed of BLDC motor can be measured from one of
the hall sensor (or hall encoder) signal which is explained later in this paper. In case of
closed loop speed control, Actual speed is compared in comparator with the reference
speed. The difference between reference speed and desired speed is called error signal. This
error signal is given to PI controller as an input. Here conventional proportional-integral
controller is used.
Based on this data, PI controller adjusts the duty cycle of the PWM pulses of the switches
correspond to the voltage amplitude required to maintain the desired speed (Azarudeen, A.,
& Mary, D, 2017-September). Higher values of duty cycle cause more voltage to be appeared
across the motor and speed of the motor increases. Similarly, lower value of duty cycle
causes the less voltage to be appeared across the motor and speed of the motor reduces.
3. Trapezoidal commutation
Figure 2 shows the equivalent circuit of a three phase, Y connected BLDC motor driven
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International Conference on Recent Advances in (Applied) Sciences & Engineering (Raise)12- 13April,2023
organized by Faculty Of Technology & Engineering, The Maharaja Sayajirao University Of Baroda
by a three phase inverter assuming that the three phase stator windings are symmetrical and
the phase resistance and inductance are constant. ea, eb, ec represent back EMF of
respective phase.
Figure 2 Equivalent circuit of BLDC motor with 3 phase inverter
In order to run BLDC motor, an electronic commutation circuitry is required. The widely
used commutation methods for the BLDC motor are trapezoidal (or six-step), sinusoidal, and
field oriented control (FOC) (or vector control). In this paper six step commutation method
is briefly explained.
The Hall-effect sensors are the most cost effective way of rotor position sensing. Using Hall
sensor feedback signals, rotor position (position of magnetic poles) can be known. The
timing diagram of three typical Hall sensors which are separated by 120° electrically inside
the motor.
The sequence of the signals are [H1 - H2 - H3]in CW and [H3 - H2 - H1] in CCW
direction. In trapezoidal commutation, two switching power devices become ON from two
different phases of 3 phase inverter at a time in a predetermined sequence to produce
unidirectional torque on a rotor by allowing the current passing through the stator windings
of motor. This method is very popular because of the simplicity of its control algorithm
(Lee, S., Lemley, T., & Keohane, G., 2009-December). It uses a six-step switching sequence
using three Hall-effect sensors to get rotor position information. Switching sequence for
clockwise as well as anticlockwise rotation of BLDC motor are different from each other.
Figure 3 shows the hall sensor signals and a back EMF of a BLDC motor with an ideal
phase-currents. The rotor movements under stator windings produces the trapezoidal shaped
back EMF in stator windings. Also the number of switches which are turned ON during
every mode are shown. Star connected BLDC motors are generally driven by the two phase
conduction mode keeping third phase floating according to the hall sensor signals. In the
two phase conduction mode, DC current flows in to both phase windings via switches in
every sequence(mode). Thus inverter operates under 120° conduction mode, at a time only
two switches are conducting.
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International Conference on Recent Advances in (Applied) Sciences & Engineering (Raise)12- 13April,2023
organized by Faculty Of Technology & Engineering, The Maharaja Sayajirao University Of Baroda
Figure 3 Waveforms of Hall sensor signals, phase current and back EMF
Only one hall sensor signal (or hall encoder) is enough for measuring the actual speed of BLDC
motor. Actual speed (in RPM) can be obtained from the frequency of hall sensor signal
(ANandurkar, M. O. N. A. L. I., & JOSHI, S., 2016).
𝑁=
120 ∗ 𝑓
𝑃
Where,
N= Actual speed in RPM
f= Frequency of HALL sensor signal in Hz
P= Number of poles of BLDC motor
Ph-a
Ph-b
Ph-c
Sector/
Modes
1
NC
Vdc−
Vdc+
1
Q5,Q6
0
Vdc+
Vdc−
NC
2
Q6,Q1
1
0
Vdc+
NC
Vdc−
3
Q1,Q2
0
1
0
NC
Vdc+
Vdc−
4
Q2,Q3
0
1
1
Vdc−
Vdc+
NC
5
Q3,Q4
0
0
1
Vdc−
NC
Vdc+
6
Q4,Q5
H1
H2
H3
1
0
1
0
1
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MOSFET
ON
International Conference on Recent Advances in (Applied) Sciences & Engineering (Raise)12- 13April,2023
organized by Faculty Of Technology & Engineering, The Maharaja Sayajirao University Of Baroda
Table 1 CW commutation sequence for BLDC motor
Vdc+ = Connected to positive terminal of DC supply
Vdc− = Connected to negative terminal of DC supply
NC = Not connected
4. PI controller modelling
Figure 4 Block diagram of PI controller
A proportional integral control loop feedback mechanism is used here to achieve desired speed.
PI controller attempts to correct the error between reference set point and tracked variable
(actual speed) and output is corrected accordingly. The PI controller calculation includes 2
separate terms namely proportional term and integral term.
PI controller algorithm can be implemented in time domain as,
𝑡
𝑦(𝑡) = 𝐾𝑝 ∗ 𝑒(𝑡) + [𝐾𝑖 ∗ ∫ 𝑒(𝑡)]
0
Where,
Kp= Proportional Gain
Ki= Integral Gain
e(t)= Error Signal
Error signal is proceeded in PI controller for compensation and regulates duty cycle for
corresponding gate signals in inverter.
The PI controller tuning can be done using Ziegler Nichols method.
This method of Ziegler Nichols requires an open loop Transfer Function of the system (BLDC
Motor). This method is only applicable if The plants that show an S shaped characteristic
(FOPTD model- First order plus dead time) for their step response. Rules for tuning
proportional and integral gain includes determining values of proportional gain Kp and integral
time Ti based on the transient response characteristic of a given plant’s step response (Patel, V.
V., 2020).
The main advantage provided by this method is that, it provides starting value of parameters
(Kp and Ki). Once we obtain these parameter values, we can further fine-tune the plant’s closed
loop response by changing the values of Kp and Ki, so as to obtain a satisfactory transient
response. By Fine-tuning, obtained parameters values provide a better result. The oscillation’s
maximum overshoot is reduced, and these are practical values that can be implemented. On an
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International Conference on Recent Advances in (Applied) Sciences & Engineering (Raise)12- 13April,2023
organized by Faculty Of Technology & Engineering, The Maharaja Sayajirao University Of Baroda
average, 25% overshoot is obtained when tuning by the ZN method. Based on the different
industrial applications of the BLDC motor, the controller could be chosen and appropriately
tuned.
5. MATLAB Simulation and Results
5.1 Simulation circuit
Figure 5 Simulation circuit is shown. Simulation is carried out in MATLAB Simulink. For
BLDC motor Permanent mag net synchronous machine block is used. In this block practical
values of BLDC motor have been inserted.
Figure 5 Simulation schematic
Parameter
Power rating
Voltage rating
Stator phase resistance
Stator phase inductance
Torque constant
Inertia
Pole pairs
-
Value
120w
24v
360mΩ
1mH
0.063 N*m/A (peak)
230*10−6 kg ∗ m2
2
Table 2 Parameters of BLDC motor
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International Conference on Recent Advances in (Applied) Sciences & Engineering (Raise)12- 13April,2023
organized by Faculty Of Technology & Engineering, The Maharaja Sayajirao University Of Baroda
5.2 Results
Figure 6 shows how back EMF signal varies with respect to change in speed of motor.
Figure 6 Actual speed with reference speed
Figure 7,8 and 9 represents back EMF signals with respect to their corresponding speeds 1000
RPM,1500 RPM and 2000 RPM. magnitude as well as frequency of back EMF signals increase
with increase in speed of motor.
Figure 7 Back EMF at 1000RPM
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International Conference on Recent Advances in (Applied) Sciences & Engineering (Raise)12- 13April,2023
organized by Faculty Of Technology & Engineering, The Maharaja Sayajirao University Of Baroda
Figure 8 Back EMF at 1500 RPM
Figure 9 Back EMF at 2000 RPM
Figure 10 will give clear idea about variation of back EMF signals at their respective speeds.
Where,
—— - Back EMF at 1000 RPM
—— - Back EMF at 1500 RPM
—— - Back EMF at 2000 RPM
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International Conference on Recent Advances in (Applied) Sciences & Engineering (Raise)12- 13April,2023
organized by Faculty Of Technology & Engineering, The Maharaja Sayajirao University Of Baroda
Figure 10 Back EMF comparison at their respective speed
6. Conclusion
In this paper one of the commutation technique for BLDC motor i.e., six step commutation is
explained. The speed control of BLDC motor using PI controller in closed loop is also shown.
Operation and working of this commutation technique and speed control scheme is verified by
simulating it in MATLAB Simulink. Results are also included in this paper
References
Yedamale, P. (2003). Brushless DC (BLDC) motor fundamentals. Microchip Technology Inc,
20(1), 3-15.
Rambabu, S. (2007). Modeling and control of a brushless DC motor. Master of Thesis In Power Control
and Drives Technology, National Institute of Technology Rourkela.
Azarudeen, A., & Mary, D. (2017, September). Performance analysis of conventional and digital PWM
control scheme for speed control of BLDC motor drives. In 2017 International Conference on Advances
in Electrical Technology for Green Energy (ICAETGT) (pp. 69-75). IEEE.
Lee, S., Lemley, T., & Keohane, G. (2009, December). A comparison study of the commutation methods
for the three-phase permanent magnet brushless dc motor. In Electrical Manufacturing Technical
Conference 2009: Electrical Manufacturing and Coil Winding Expo, EMCWA 2009 (pp. 49-55).
ANandurkar, M. O. N. A. L. I., & JOSHI, S. (2016). Brushless DC Motor Position Control Based on Hall
Effect Sensor using PI Controller.
Patel, V. K. S., & Pandey, A. K. (2013). Modeling and performance analysis of PID controlled BLDC
motor and different schemes of PWM controlled BLDC motor. International Journal of Scientific and
Research Publications, 3(4), 1-14.
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International Conference on Recent Advances in (Applied) Sciences & Engineering (Raise)12- 13April,2023
organized by Faculty Of Technology & Engineering, The Maharaja Sayajirao University Of Baroda
Lazor, M., & Štulrajter, M. (2014, May). Modified field oriented control for smooth torque operation of a
BLDC motor. In 2014 ELEKTRO (pp. 180-185). IEEE.
Patel,
V.
V.
(2020).
Ziegler-Nichols
Controller. Resonance, 25(10), 1385-1397.
Tuning
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Method:
Understanding
the
PID