Performance Analysis of Control Strategies of

Permanent Magnet Synchronous Motor

R. M. Pindoriya, A. K. Mishra, B. S. Rajpurohit, Senior Member, IEEE, and R. Kumar
Student Member, IEEE,
Indian Institute of Technology Mandi, H imachal Pradesh, India
rajeshpindoriya@gmail.com, anshulkumarmishra@gmail.com, bsr@iitmandi.ac.in, rajeev@iitmandi.ac.in

Abstract- This paper presents the technical challenges associated a PMSM it is necessary to determine the exact rotor position.
with the proposed control techniques and an analysis performance Commonly, a position sensor, such as hall sensor, optical
of speed control of permanent magnet synchronous motor encoder, is fitted to sense the rotor position. Various types of
(PMSM), their control strategies and advance power electronics
closed loop control techniques are proposed and validated for
technologies to control PMSM. To control of PMSM drive used
PMSM, like scalar control and vector control. Vector control to
different control methods like, scalar control, direct torque control
(DTC), vector control, frequency converter method and hysteresis
PMSM is normally used to get the control, in the same way as
current control (HCC) methods are used. The speed of the PMSM that of the induction motor and DC motors, which has high
drive can be control by varying the voltage and frequency of its desirable control characteristics [1 ]-[2]. The DTC and FOC
supply. In this paper explained sinusoidal pulse width modulation methods can be performing by using vector control method [3].
(SPWM) technique to control the speed of the PMS M drive. Also The scalar and vector both controller are made based on
vector and scalar control methods are compared. Mathematical mathematical model to control of speed, current and torque of
modeling, analysis, and simulation of three-phase star connected a PMSM drive [4]-[5]. The vector control method works with
PMSM is done in MATLAB/Simulink environment. Fast response
vector quantities [6].
with negligible settling time has been obtained by SPWM method
for PMSM.
This paper describes a speed control method for a PMSM
Keywords- Direct torque control (DTC), hysteresis current drive that provides a high-performance vector control and
control (HCC), permanent magnet synchronous motor (PMSM) scalar control. By using the proposed model, sinusoidal pulse
and sinusoidal pulse width modulation (SPWM). width modulated (SPWM) [7] speed controlled 3-phase inverter
fed PMSM drive is simulated in MATLAB/Simulink
NOMENCLATURE environment. The goal of this paper is to design the equivalent
d-q model of PMSM for its vector control analysis and closed
V as' V bs' Vcs Input phase voltage (V) loop speed control of drive system. Basically speed, current and
I as' Ibs' Ics Stator phase current (A) torque control methods for PMSM is following [8]; vector
I�s' I�s' I�s Reference q,d,O axis current (A) control, scalar control, torque controller drives, hysteresis
V iq , V {s' Vc� Reference q,d,O axis voltage (V) controller, unity power factor control, angle control of air gap
Stator resistance (Ohm) flux, optimum torque per unit current control, constant power
Rs
La,Lq Stator d and q- axis self-inductance losses control, maximum efficiency control, six step voltage
in rotor reference frame (H) control, constant back electromagnetic forces (EMF) control,
J Moment of inertia (kg*m2) current controller, rotor reference frame current controller and
Actual rotor speed (rpm) stator reference current controller.
Armature flux linkage (Wb)
n. MATHEMATICAL MODEL OF PMSM
Electromagnetic torque (N*m)
Load torque (N*m)
The mathematical model of the PMSM drive is establish
Damping constant (N/rad/s)
using a 3-phase configuration along d-q axes. The assumptions
Inertial constant in normalized unit,
are; the inductance versus rotor position is sinusoidal, the effect
(per unit)
of saturation is neglected and windings of the stator are
p Number of poles
balanced with sinusoidal distributed magneto motive force
p Derivative operator dldt
(EMF) [8]. With the above acceptances, the d-q axes stator
voltages in rotor reference frame are;
I. INTRODUCTION

Currently the widely use of permanent magnet (1)

synchronous motor (PMSM) in industrial and domestic
applications due to serval methods available to control the
speed, torque and current of the motors. For proper operation of

978-1-5090-2597-8/16/$31.00 ©2016 IEEE 3224

 From (1), it is observed tbat tbe stator voltages are equal to
tbe multiply of impedance matrix, vector of current, and plus
an additional parameter due to the EMFs of the rotor flux
linkages. The expression for the electromagnetic torque
developed by tbe machine can be expressed in d-q components
Tbe value of desired mutual flux linkage is express by (9).
of tbe currents as,

(2) (9)

laIbss IIss
Eq. (3) represents tbe electromecbanical dynamic equation. Tbe reference currents are generated by using (10-12).

Ics Is
(3) = sin(wrt + 0) (10)
2rr
= sin(wrt + 0 _
3
) (11)
Tbe 3-pbase stator voltages are obtained from (1) by using sin(wrt + 0 +
2rr
= ) (12)

V[ascbss] [
tbe inverse Park transformation as, 3

J( cos 8r sin 8r Fig. 1 shows a SPWM based vector control design and
control system for a PMSM drive. It is make a combination of
J(
=
cos(8r 3) -
2rr
sin(8r 3) -
2rr
(4) PI controllers, Park transformations, PWM and SPWM control
2rr . 2rr model.
cos(8r + 3) sm(8r + 3)

1; I:
correspondingly, the dqO currents are obtained from abc III.SPEED CONTROL METHODS OF PMSM DRIVE
currents using Park transformation as,
A. Scalar control: Tbis metbod is used wben we want to

[IIcs]
control magnitude as well as pbase quantities of PMSM. Main
cos(8r - 3) 2rr
cos(8r +
2rr
- ) disadvantages of scalar controlled drive are poor performance
sin(8r _ ;)
2
sin(8r +
2
) (5) but it will be take less time to implement it.
1 1

2 2
B. Vector control: It is work witb quantities of vector. It's
control tbe reference values by space pbasor. Tbis metbod also
From (1) and (3) tbe overall dynamic model of PMSM in known as field oriented control (FOC) because in tbe course of
implementation the identification of tbe field flux of tbe motor

I:; � I
rotor reference frame is derived by (6).
is required.
&
Lq
- G: Wr) Aat
Lq
0 C. Feedback method: In feedback metbod rotor flux vector is

[ ;' 1 G: wr)
[�+;'1
Rs sense by a flux sensor mounted in air gap or matbematically by
(P) 0 0
Lq tbe electrical macbine parameters of voltage equations.
Aat
2H
(Lq- Lq )l�s
2H
- -
B

2H
0
D. SPWM based speed controller: SPWM is tbe simplest
0 0 1 0 triangular and carrier-based modulation tecbniques for the

r� �J[�l
0 control of I-pbase and 3-pbase output voltage of inverter. It is
1 (6) a part of sbaping metbods in tbe field of power electronics and
-

Lq electrical drives, where a very bigb frequency triangular carrier

0 signal is compared with a reference signal of sinusoidal. Tbe
advantages of tbis method are very less complexity and good
Tbe simulation model of three-pbase stare connected dynamic response of drives. The number of pulses per cycle is
PMSM is make using Eq. (6). Tbe Te developed on the rotor can decided by ratio of tbe carrier frequency to modulating
be obtained as given by (7). frequency. Tbe M,. (Modulation ratio) is given by tbe relation,

frequency of carrier waveform

(7) Mr = frequency of the modulating waveform
(13)

To implement vector controlled of SPWM to speed

control ofPMSM drive system the information of rotor position
is necessary. By (7), tbe Te in PMSM can be written as,

2016 IEEE Region 10 Conference (TENCON) - Proceedings of the International Conference 3225
 Fig. I. A SPWM based vector control design and control system for a PMSM drive.

Modulation index (MI) is define, the ratio of modulating drawback with this controller is that it doesn't have a constant
reference signal to carrier signal and is written by, switching frequency as in PWM speed control.

MI= � (14)
IV. SIMULATION RESULTS AND DISCUSSIONS
Ac

Where Arthe amplitude of reference signal and A c is the

A 300 V, 3 HP, 1750 rpm sinusoidal back EMFs based
amplitude of carrier signals. If MI is medium, then the output PMSM has been simulated III MATLAB/Simulink
of sine wave is medium and vice versa. The error of the
environment. PWM switching has been used to control the
controlled signal is then compared with a very high frequency
inverter output voltage. Fig. 2 shows the waveform of three­
triangular carrier wave of desire switching frequency. The
phase stator current of PMSM, each phase is 120-degree phase
comparison will result in a pulse when the error signal is greater
shifted with respect to each other. The waveform of back-EMFs
than the triangular wave which is then used to trigger the
is same as a stator current of PMSM.
respective power devices [9]. The speed at which inverter
switches are turned on and off depends on the frequency of
switching, and it is depending on carrier frequency (fc). The
output line-to-line voltages can be defined by following
equations;

Assuming the system to be balanced the phase voltages are

computed in terms of line-to-line values with the help of (15)

v:
as = Vab-Vca
3 I
Vbc-Vab
Vbs = 3 I
v:
cs = Vca-Vbc
3 (16)

E. Hysteresis Current Controller: The implementation of basic

hysteresis current control method is based on deriving the
switching patterns to the 3-phase inverter from the compare of Fig. 2. Stator current ofPMSM.
the current signal error within a band of fixed hysteresis [10]­
[11]. The advantages of hysteresis current controllers are good
accuracy, high robustness and simple design. The major

3226 2016 IEEE Region 10 Conference (TENCON) - Proceedings of the International Conference
 inverter-fed PMSM is designed and simulated using
MATLAB/Simulink platform. Authors have used mechanical
parameters of PMSM to calculate gain value of PI controller.
Even the accuracy of the method is very good as shown in the
responses that no overshoot or under shoot is found in the speed
response which is an indices for accuracy during transient. The
vector control technique working with very fast responses. So
it full fill the necessity of dynamic drives method to handle
transient response. It is minimizing the error of steady state and
gives a smooth tracking with the desired signal. It is found that
Fig. 3. Three-phase Input supply ofPMSM. application of PMSM drive in the field of submarine and
electric ship.
Fig. 3 shows the 3-phase input supply voltage of PMSM,
it is coming from PWM inverter circuit. Fig. 4 & 5 shows the VI. ACKNOWLEDGEMENT
rotor speed of PMSM at a rated torque and gain value of Kp =
0.005 & Ki = 12.00, and the speed reference is 100 and 1000 The authors are thankful to Naval Research Board,
rpm respectively. INDIA for financial support.

REFERENCES

[ I] J. Gao and J. Kang, "Modeling and simulation of pennanent magnet

synchronous motor vector control," Information Technology
Journal, vo!. 13, no. 3, pp. 578-582, Feb., 2014.
[2] Bimal K. Bose, ModemPower Electronics and AC Drives, 4th ed.,
South Asia: PearsonPrentice-Hall, 2007.
[3] Y. Van, J. Zhu, Y. Guo and H. Lu, "Modeling and simulation of
direct torque controlled PMSM drive system incorporating
structural and saturation saliencies," IEEE Int. conference on Ind.
Appl. 41st IAS Annu., vo!. I, pp. 76-83, Oct., 2006.
[4] C. Xia, J. Zhao, Y. Van and T. Shi, "A novel direct torque control
Fig. 4. Reference rotor speed is 100 rpm ofPMSM. of matrix converter-fed PMSM drives using duty cycle control for
torque ripple reduction", IEEE. Trans. Ind. Elect., vo!. 61, no. 6, pp.
2700- 2713, June, 2014.
When apply rotor refemce speed is 100 rpm that time
[5] M. Preindl and S. Bolognani, "Model predictive direct torque
motor rotor speed is same as a reference speed of PMSM, it is
control with finite control set for PMSM drive systems, Part I:
shows in figA. Maximum torque per ampere operation", IEEE Trans. Ind.
Informatics, vo!. 9, no: 4, pp. 1912-1921, Nov., 2013.
[6] A. Mishra, J. A. Makwana, P. Agarwal, and S.P. Srivastava.
"Modeling and implementation of vector control for PM
synchronous motor drive", IEEE, Int. Con/., Advances in
Engineering, Science and Management (ICAESM) '12, pp. 582- 585,
Mar. 2012.
[7] P. H. Zope, P. G. Bhangale, P. Sonare and S. R. Suralkar, "Design
and implementation of carrier based sinusoidalPWM inverter," Int.
Journal of Advanced Research in Electrical, Electronics and
Instrumentation Engineering, vo!. I, no. 4, pp. 230-236, Oct., 2012.
[8] R. Krishnan, Permanent Magnet Synchronous and Brushless DC
Fig. 5. Reference rotor speed is 1000 rpm ofPMSM. Motor Drives, CRC, 20 I O.
[9] W. R. Liou, H. M. Villaruza, M. L. Yeh andP. Roblin, "A digitally
controlled low-EMI SPWM generation method for inverter
By properly taking gain value of Kp & Ki, the speed
applications," IEEE, Trans. Ind. Informatics, vo!. 10, no. I, pp. 73-
response of PMSM is obtained. Fig. 4 & 5 shows that there is 83, Feb., 2014.
no overshoot and undershoot in the speed response of the [10] M. A. Khan and M. N. Uddin, "Perfonnance analysis and
PMSM. optimization of digitsl PWM controllers for surface-mounted
PMSM drives," IEEE, Industry Application s Society Annual
V . CONCLUSIONS Meeting (IAS) 'I2, pp.1-8, Oct., 2012.
[11] A. R. Sabitha and S. S. Beevi. "Encoderless vector control of
This paper has presented mathematical modeling,
interior PMSM with initial states," Int. Con! Automation,
simulation, and analysis of a sinusoidal pulse width modulation Computing, Communication, Control and Compressed Sensing, pp.
(SPWM) controlled technique to control speed of PMSM drive 342-345, Mar. 2013.
under different speed operating condition. The SPWM control
methodology is a good for design and analysis of PMSM drive.
The control system for three-phase star connected PWM

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