This document discusses using an Extended Kalman Filter (EKF) for sensorless state estimation of a Permanent Magnet Synchronous Motor (PMSM). It presents the mathematical model of a PMSM and describes a vector control system structure using field oriented control with a dual closed-loop for speed and current control. Simulation results show the EKF can accurately estimate motor speed without sensors, with only a slight lag during transients compared to actual measured speed. The EKF achieves precise position and speed estimation of the PMSM against parameter variations.

1. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) Volume 5, Issue 6, June (2014), pp. 30-34 © IAEME
30
STATE ESTIMATION OF PERMANENT MAGNET SYNCHRONOUS
MOTORS USING EXTENDED KALMAN FILTER
Siddharth Kaul1
, Raosaheb Pawar2
, Shailendra Sahu3
1, 2, 3
(Control and Automation, VIT University, Vellore Tamil Nadu India)
ABSTRACT
The estate estimation of Permanent Magnet Synchronous Motor (PMSM) is based on the
study of sensorless control using Extended Kalman filter (EKF). The sensorless control system
possesses accurate Dynamic estimation by reducing the size and increasing the efficiency of PMSM.
Similar projects have attracted many researchers’ interests. This paper would present the application
of Extended Kalman Filter (KF) in PMSM speed control system. The project worked on the areas of
the mathematical model of PMSM and will estimate the angular speed (ω) using EKF algorithm The
simulation results is expected to show that the control system will work smoothly in various speeds
with load. The project would mainly focus on the study of Permanent magnet synchronous motor and
extended Kalman filter to achieve the state estimation of PMSM.
Keywords: Extended Kalman Filter (EKF), Modeling and Simulation, Permanent Magnet
Synchronous Motors (PMSM), Sensorless Control.
I. INTRODUCTION
Permanent magnet synchronous motor (PMSM) drives are replacing dc and induction motors
drives in a variety of industrial applications, such as industrial robots and machine tools. PMSM
possesses many good performances such as simple structure, small size, high efficiency, high power
factor and low moment of inertia compared with traditional electrical synchronous motors. Because
of these advantages, PMSM are excellent for use in High-performance servo drives where a fast and
accurate torque response is required.
The main drawback of a PMSM is the position sensor. The use of such direct speed/position
sensors implies additional electronics, extra wiring, extra space, frequent maintenance and careful
mounting which detracts from the inherent robustness and reliability of the drive. For these reasons,
the development of alternative indirect methods has become an important research topic. PMSM
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2. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) Volume 5, Issue 6, June (2014), pp. 30-34 © IAEME
31
drive research is concentrated on the elimination of the mechanical sensors at the motor shaft without
weakening the dynamic performances of the drive. Many advantages of sensorless ac drives such as
reduced hardware complexity, low cost, reduced size, cable elimination, reduce IR2 loss, increased
noise immunity; increased reliability and decreased maintenance can be achieved. Sensorless motor
drives are also preferred in hostile environments, and high speed applications.
The main objective of this paper is to propose an effective Sensorless PMSM drive by using
EKF. The proposed EKF is applied to the field oriented control of the PMSM and no mechanical
parameters are involved. As a result, the EKF achieves the precise position and speed estimation of
PMSM against other parameter deviations.
II. MATHEMATICAL MODEL OF PERMANENT MAGNET SYNCHRONOUS
MOTOR (PMSM)
The mathematical model of PMSMS can be divided into three kinds of representation by the
axis systems, including the three-phase stationary coordinate system (A-B-C shafting coordinate
system), the stator phase stationary coordinate system (α-β coordinate system) and the rotor two-
phase rotating coordinate system (d-q coordinate system). The mathematical model utilized for EKF
estimation is the α-β coordinate system. Therefore, this coordinate system is represented as follow.
The voltage equations of PMSM in the α and β -coordinate system are equations (1) and (2):
ܷఈ ൌ ܴ௦݅ఈ ൅ ‫ܮ‬௦
݀݅ఈ
݀‫ݐ‬
െ ߱௥ܰ௣ߣ௥‫ߠ݊݅ݏ‬௥ ሺ1ሻ
ܷఉ ൌ ܴ௦݅ఉ ൅ ‫ܮ‬௦
݀݅ఉ
݀‫ݐ‬
൅ ߱௥ܰ௣ߣ௥ܿ‫ߠݏ݋‬௥ ሺ2ሻ
From equations (1) and (2), we have
݀݅ఈ
݀‫ݐ‬
ൌ െ
ܴ௦
‫ܮ‬௦
݅ఈ ൅ ߱௥
ܰ௣ߣ௥
‫ܮ‬௦
‫ߠ݊݅ݏ‬௥ ൅
ܷఈ
‫ܮ‬௦
ሺ3ሻ
݀݅ఉ
݀‫ݐ‬
ൌ െ
ܴ௦
‫ܮ‬௦
݅ఉ ൅ ߱௥
ܰ௣ߣ௥
‫ܮ‬௦
ܿ‫ߠݏ݋‬௥ ൅
ܷఉ
‫ܮ‬௦
ሺ4ሻ
In digital systems, the sampling cycle is very short and each samling period can be
considered as constant so we have next equation (5) and (6):
݀߱௥
݀‫ݐ‬
ൌ 0 ሺ5ሻ
݀ߠ௥
݀‫ݐ‬
ൌ ߱௥ ሺ6ሻ

3. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) Volume 5, Issue 6, June (2014), pp. 30-34 © IAEME
32
III. CONTROL SYSTEM STRUCTURE OF PERMANENT MAGNET SYNCHRONOUS
MOTOR (PMSM)
Figure 1: Vector Control System Structure of PMSM
The operation of a brushless PM motor relies on the conversion of electrical energy to
magnetic energy and then from magnetic energy to mechanical energy. It is possible to generate a
magnetic rotating field by applying sinusoidal voltages to the 3 stator phases of a 3 phase motor. A
resulting sinusoidal current flows in the coils and generates the rotating stator flux. The rotation of
the rotor shaft is then created by attraction of the permanent rotor flux with the stator flux.
Through a series of coordinate transforms, we can indirectly determine and control the time
invariant values of torque and flux with classic PI control loops. The process begins by measuring
the 3-phase motor currents. In practice, the instantaneous sum of the three current values is zero.
Therefore, by measuring only two of the three currents, we can determine the third. Because of this
fact, hardware cost can be reduced by the expense of the third current sensor.
Vector control system structure of PMSM is shown in Fig. 1, including Proportional Integral
(PI) modulator, Space Vector Pulse Width Module (SVPWM), EKF estimation module, Clark-Park
transform module, three-phase inverter and PMSM module. PMSM adopts Field Oriented Control
(FOC) controlling method with dual closed-loop control scheme of speed and current regulated by PI
modulator. System estimates rotation angle and rotation speed from EKF in real time. Here, is the
feedback variable of speed control loop and is the parameter of the Park transform and inverse
transform to implement relevant calculation.
IV. SIMULATION ANALYSIS AND EXPECTED OUTPUT
The simulation is done by understanding the system parameters and understanding the
algorithms of the Extended Kalman filter. MATLAB code was written inorder to get the expected
output as shown in the figure below.

4. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) Volume 5, Issue 6, June (2014), pp. 30-34 © IAEME
33
In the Fig. 2 shown below, the red curve presents the actual measurements from speed sensor.
As can be seen from the figure, there are system disturbances emerging in the process of system
starting and state transition. Also we can observe that the transient to stable state is very quick. In
Fig. 3, blue curve denotes the estimation of speed with EKF in sensorless condition. Comparing with
the actual speed measurements and estimations from EKF, there is a slight lag in the process of
system starting and speed transition.
Figure 1: Actual Speed Measured with Sensor
Figure 2: Estimation of Speed with Extended Kalman Filter

5. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) Volume 5, Issue 6, June (2014), pp. 30-34 © IAEME
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V. REFERENCES
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[3] Wang Chengyuan, Xia JiaKuan, Yang Junyou and et al, “Modern Moter Control
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[4] S Bolognani, L Tubiana and M Zigliotto. “Extended Kalman Filter Tuning in Sensorless
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[5] Jiang Jun, Shen Yanxia and Ji Zhicheng, “Speed and Roter Positoin Estimation for PMSM
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Navigation System”, Beijing: Science Press, April 2010, Second Edition, pp. 163-165.
[8] An Quntao, Sun Li and Li Bo, “Variable Paramters EKF for Speed Estimation of PMSM”,
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[9] T.S. Viswanath and Dr.Subhash S K, “A Graphical-Based Acceleration Stabilization in
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[10] Vishal Rathore and Dr. Manisha Dubey, “Speed Control of Asynchronous Motor using Space
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