1. PSO-Based Neural Network Controller for Speed
Sensorless Control of PMSM
A. M. Nazelan, M. K. Osman, N. A. Salim, A. A. A. Samat and K. A. Ahmad
Faculty of Electrical, Universiti Teknologi Mara
13500 Permatang Pauh, Pulau Pinang, Malaysia
E-mail: amnazelan@gmail.com
Abstract— In this paper, estimation of rotor speed and
position by using model reference adaptive system
(MRAS) with multilayer perceptron (MLP) for PMSM
sensorless control are presented. Conventional controller
which is PI controller for adaptation scheme still hunger
with high accuracy information of PMSM for low speed
region. Based on PI controller, the MLP which is more
well-known about their learning efficiency and
performance. This paper proposes a method for training
an MLP network using Particles Swarm Optimization
(PSO) called MLP-PSO. The PSO is used to find the
optimum weights and biases in the MLP network. Finally,
the proposed method is evaluated by comparing with PI
controller in controlling the speed and position of PMSM.
Simulation results under various speed and load conditions
has shown that the MLP-PSO achieved well results than
the PI controller in terms of system parameter such as rise
time )
( r
T , settling time )
( s
T , percent overshoot )
(%OS ,
and root mean square error )
(RMSE .
Keywords— Permanent Magnet Synchronous Motor, Artificial
Neural Network, Particles Swarm Optimization, Model Reference
Adaptive Control.
I. INTRODUCTION
The Permanent Magnet Synchronous Motor (PMSM) has
been widely used for various industries of technologies in
robotics, electrical and automation. PMSM is one of famous
and frequently used in many application AC machine type
because of its high power density, large torque to inertia ratio,
high efficiency and simple structure. Also, the PMSM is good
in speed regulation [1].PMSM consists of two primary parts
which is permanent magnet that rotates called rotor and static
core surrounded by three equally space winding called stator.
In PMSM world, there have two different back EMF which
are sinusoidal and trapezoidal. In review that have been go
thru, trapezoidal commutation can be categorize as simple
method to control than sinusoidal commutation. But,
trapezoidal commutation is not good enough to provide
smooth and precise motor control of brushless dc motors,
especially at low speeds region. Sinusoidal commutation
solves this problem. Also, sinusoidal commutation produces
much less torque ripple than trapezoidal [1][2]. High quality
sensor is required as the feedback of the close loop system to
complete the circuit. But, the existence of the sensor cause the
cost and size of installation is increase. Therefore, sensorless
method is approach.
A variety technique have been develop to eliminate the
existence of sensor in PMSM. In general, technique have been
proposed is Lunberger or Kalman Filter observer (KMO),
Sliding Mode observer (SMO), Model Reference Adaptive
System (MRAS), fuzzy logic and artificial intelligent [3]. The
demand of for variable speed drives in low, medium and high
speed region for industries application was triggered many
researcher to digging another method for sensorless control
that can improve the efficiency of speed and position
estimation. Because of this, control strategy was become a
great role in order to fulfil the demands of each application.
Usually, modelling and simulation is used to design the
algorithm in order to identify the performance of proposed
method with the conventional controller. Also, the virtual
prototype are important to be done to reduce the cost of
experiment.
Generally, sensorless techniques have two different
methods which is back electromagnetic force (EMF)
estimation and signal injection method [4], [5]. Back EMF
method offer a good performance at high speed revolution per
minute (RPM) for PMSM. But, for the low speed region, the
estimation accuracy will be decrease because the parameter
reading is too small compare to the noise [6]. For signal
injection method, their offer good performances at all state
include zero speed. But, disadvantage of this method is
requiring extra hardware and delay problem according digital
implementation of the control algorithm and digital filters [7].
Therefore, this paper is focus on designing the MRAS
algorithm in order to improve the accuracy of rotor speed and
position estimation for all speed region which are low,
medium and high.
Model reference adaptive system (MRAS) consist of two
functional block which is reference model and adjustable
model [1], [8]–[10]. Main idea of this system is comparing the
reference parameter (current id & iq for this case) between
actual parameter. Error of this signal will be use to estimate
the speed and position of the PMSM. Then, the signal is inject
into the adaptation algorithm to estimate the quantity of which
is use to tune the adjustable model. This simple method only
required less of system computation [6].
2017 7th IEEE International Conference on Control System, Computing and Engineering (ICCSCE 2017), 24–26 November 2017, Penang, Malaysia
978-1-5386-3897-2/17/$31.00 ©2017 IEEE 366

2. Figure 2. The PMSM equivalent circuit
In this paper, the novel method that proposed is MRAS
with Multilayer Perceptron (MLP) as adaptation scheme
which estimates the speed and position for PMSM sensorless
vector control system. The proposed method are using the
PMSM itself as the reference model and the PMSM current
model as the adjustable model. Error signal which produce by
using Popov Integral Inequality is injected into the MLP
algorithm where objective of this project is to reduce the error
approx. to zero value. The results of simulation and dynamic
response is used to verify the effectiveness of proposed
method that presented in this paper.
II. PMSM MODEL
In this section, PMSM mathematical model are describe to
understand the behavior. The PMSM can be modeled in
stationary reference (α, ß) and rotor reference (d, q) as shown
in Fig. 1.
The PMSM equivalent circuit as shown in Fig. 2 are
considered in order to determine the mathematical model of
the PMSM.
q
r
Z
d
r
Z
Fig. 2 (a) and (b) is the equivalent circuit for voltage at d-axis
and q-axis. From fig.2 the voltage equation can be derived as:
q
r
d
d
d
d
dt
di
L
i
R
V
Z
)
( (1)
d
r
q
q
q
q
dt
di
L
i
R
V
Z
)
( (2)
where R is the phase resistor winding, r
Z is the electrical
angular velocity of the rotor and d
, q
is flux for d and q.
Flux equation be derived as:
m
d
d
d i
L
)
( (3)
)
( q
q
q i
L
(4)
In the equation of flux above, m
is the flux that generated by
magnetic pole and stator.
III. POSITION AND ESTIMATION METHOD
A. Model Reference Adaptive System
In 1958, Witark was proposed the first method of model
reference adaptive system (MRAS) scheme in United States
[11]. General view and idea MRAS is a closed loop system
that contains reference model and adjustable model [1], [8].
This system compare the output of plant (PMSM) with the
desired response from reference model. The parameters from
the plant will update into the system and then, the system will
determine the error between reference models. If the
parameters have an error, adjustable model will automatically
tune and counter the error to match with reference model. The
reference model is independent from the rotor speed,
calculation of variable from the terminal voltage and current.
Meanwhile, for the adaptive model is dependent on it. The
estimated rotor speed and position is generates based on
difference between these state variables [12]. Generalized of
this system is shown in Fig. 3. Input for reference and
adjustable model is same which is voltage in stationary form
(ud uq) that project from three phase (ua, ub uc).
In Figure 3, the reference and adjustable model variable is
known as x and x̂ , respectively. Reference model is develop in
ideal condition where output of the model x will be used to
compare with the measured performance of x̂ . The difference
vector of v will be used as input for the adaptive mechanism to
modify the parameters of the adjustable model.
B. Model Reference Adaptive System on Popov Integral
Inequality
Mainly, MRAS sensorless control is based rotating
reference frame. The model of the PMSM stator current
describe as follows:
Figure 3. Block diagram of MRAS control scheme
Figure 1: The stationary and synchronous frame [16]
+
-
R
Iq
Lq
Vq
(a)
MSM
(b)
R
Ld Id
+
-
Vd
Z
R
Ld Id
+
Z
-
Vd
2017 7th IEEE International Conference on Control System, Computing and Engineering (ICCSCE 2017), 24–26 November 2017, Penang, Malaysia
367

3. d
d
q
d
q
r
d
d
d
L
V
i
L
L
i
L
R
i
dt
d
Z
]
[ (5)
d
d
r
r
q
q
q
d
d
d
q
r
q i
L
L
V
i
L
R
i
L
L
i
dt
d
Z
Z
]
[ (6)
where id, iq is dq-axis stator current, ud, uq is dq-axis stator
voltage, R is stator resistance, Ld, Lq is stator inductance and ψr
is rotor permanent magnet flux. By estimating dq-axis current,
estimated speed can be formulate as follows [11]:
³
t
q
q
d
q
q
d
re d
i
i
L
f
i
i
i
i
k
0
1 )]
'
(
'
'
[
ˆ W
Z
)
0
(
ˆ
)]
ˆ
(
ˆ
ˆ
[
2 re
q
q
d
q
q
d i
i
L
f
i
i
i
i
k Z
(7)
where Ẑ is estimated rotor angular speed, d
i' , q
i' is dq-axis
stator estimated current, k1, k2 is PI regulator coefficients.
Then, Equation (7) can be rearrange as Equation (8) as
follows:
)
0
(
ˆ
)
'
(
'
'
*
ˆ re
q
q
t
d
q
q
d
i
p
re i
i
L
i
i
i
i
s
K
K Z
Z
»
¼
º
«
¬
ª
»
¼
º
«
¬
ª
(8)
³
t
re
0
ˆ
ˆ Z
T (9)
where Tˆ is rotor position estimation.
C. Multilayer Perceptron
Multilayer perceptron (MLP) is current dynamics method
have been use in many application that perform in function
fitting, reducing system error and recognition the problem by
using supervised training algorithm such as levenberg
marquardt (LM) and particles swarm optimization (PSO)
[13][14]. Because of the effectiveness ability of learning the
complex problem, artificial neural networks (ANN) frequently
become an hot topic about prediction application of nonlinear
system.
Figure 4: Multilayer Perceptron Network Structure
Multilayer perceptron (MLP) is a class feedforward ANN
that consist of three layer of nodes. First layer known as input
layer, second hidden layer and the third is known as output
layer. Except of input layer, each node contain activation
function that use for nonlinear system. Each layer is weighted
with the appropriate value that have been found by performing
system training. Fig. 4 shows the MLP network structure. The
MLP algorithm can be formulated as:
@
¦
nh
j
j
i
ij
jk
k b
t
x
w
F
w
t
y
1
1
0
1
2
)
(
.
.
)
( (10)
where
1
ij
w and
2
jk
w represent as weights between input layer
to hidden layer and weight between hidden layer to output
layer. F,
0
i
x and
1
j
b is represent activation function, thresholds
in hidden nodes and input that supply to the input layer
respectively.
Then, equation in (8) and (10) can be combine to
perform MRAS sensorless speed control with MLP as
adaptation scheme.
@»
»
¼
º
«
«
¬
ª
¦
nh
j
j
i
ij
jk
re b
t
x
w
F
w
1
1
0
1
2
)
(
.
.
Ẑ
)
0
(
ˆ
)
'
(
'
'
. re
q
q
t
d
q
q
d i
i
L
i
i
i
i Z
»
¼
º
«
¬
ª
(11)
D. Particle Swarm Optimization
In 1995, Eberhart and Kennedy inspired by social behavior
of bird flocking and fish schooling was develop an
optimization technique known as Particles Swarm
Optimization (PSO). Due to many advantage can be found by
using this technique including simplicity and easy
implementation, this algorithm can be used widely in many
field such as classification, neural network training, machine
study, and signal procession. Also, PSO is suit to be use as
optimization parameter in many dimension and application.
[15].
PSO concept is using a number of agent (particles) that
establish a swarm moving around in the search space looking
for the best solution. Each particles in search space adjust its
‘flying’ according to its own flying experience well as the
flying experience of other particles and the best are called
(pbest). Amongst the value of pbest, there have another
categorize for the best value by the group known as gbest.
Equation in (12) and (13) is used to modify the velocity and
position of each agent based on objective function of the
system.
e
)
(
*
*
)
(
*
* 2
2
1
k
i
k
i
i
i
k
i s
gbest
rand
c
s
pbest
rand
c
v
(12)
1
1
k
i
k
i
k
i v
s
s (13)
where:
k
i
v = current velocity of agent i at iteration k
1
k
i
v = new velocity of agent i at iteration k
k
i
s = current position of agent i at iteration k
1
k
i
s = denotes the position of agent I at the next iteration
k+1
i
pbest = personal best agent i
2017 7th IEEE International Conference on Control System, Computing and Engineering (ICCSCE 2017), 24–26 November 2017, Penang, Malaysia
368

4. i
gbest = global best of the population
1
c = adjustable cognitive acceleration constant (self-
confidence)
2
c = adjustable cognitive acceleration constant (swarm
confidence)
2
,
1
rand = random number between 0 and 1
For this paper, PSO is use to optimize the value of weight
for MLP controller that can minimum the error and overshoot
of the PMSM sensorless control. There are four step for this
algorithm optimize the value of weight that illustrate in Fig. 5.
Step 1: Initial condition agent generation and declaration
For the first stage, the data is choose randomly for each agent
of input and speed for initialization. Each agent will set the
current search point to pbest and at the same time, gbest also
will determine the best value of pbest. Then, the best value
that can produce low mean square error is stored for
evaluation process.
Step 2: Each agent searching point evaluation
Second stage is evaluation for the stored value of agent where
output of the system will produce an error and overshoot. The
data will be analyze and new agent will be replace to see the
output of system behavior. If the agent is better than pbest at
this time, it will replace current value. Also, if the value of
pbest is better than gbest, it will replace current value that
stored inside gbest. Then, the best agent will stored.
Step 3: Each agent modification
By using the Equation (22) and (23), the value of each agent
are declare and will be tested for the next step.
Step 4: Each agent analysation
Finally, several test are perform before the end of the process.
If the system reach the desired output, the process will stopped
and if otherwise, the process will repeat again from the first
step until the desired output is achieved.
IV. RESULTS AND DISCUSSION
First result is shows the simulation using Heuristic-PI (H-
PI) controller and then, Particles Swarm Optimization PI
(PSO-PI) controller. Simulation is perform in the MATLAB
Simulink and time is kept 0.3sec. The result is verified based
on system performance response which are rise time (Tr),
settling time (Ts), percent overshoot (%Os) and root mean
square error (RMSE) where its verified under four (4)
different conditions.
1) Constant speed and load.
2) Constant speed and varied load.
3) Varied speed and constant load.
4) Varied speed and load.
For condition 1- Speed and load torque are constant [speed is
1500r/min and load torque is 2Nm]
Figure 6: Reference and estimated speed for PI controller for
condition 1
Figure 7: Reference and estimated speed for MLP controller for
condition 1
For condition 2- Speed is constant and load torque is varied
[speed is 1500r/min and load torque is 0-0.075sec (2Nm),
0.075-0.15sec (1Nm), 0.15-0.225sec (2Nm) and 0.225-0.3sec
(1Nm)].
Figure 8: Reference and estimated speed for PI controller for
condition 2
l d d d l
Figure 5: Particle swarm optimization steps
flowchart
2017 7th IEEE International Conference on Control System, Computing and Engineering (ICCSCE 2017), 24–26 November 2017, Penang, Malaysia
369

5. Figure 9: Reference and estimated speed for MLP controller for
condition 2
For condition 3- Speed is varied and load torque is constant
[speed is 0-0.1sec (0-1500r/min), 0.1-0.18sec (1500r/min),
0.18-0.25sec (800r/min) and 0.25-0.3sec (1500r/min) and load
torque is 2Nm].
Figure 10: Reference and estimated speed for PI controller for
condition 3
Figure 11: Reference and estimated speed for MLP controller for
condition 3
For condition 4- Speed and load torque are varied [speed is 0-
0.1sec (0-1500r/min), 0.1-0.18sec (1500r/min), 0.18-0.25sec
(800r/min) and 0.25-0.3sec (1500r/min) and load torque is 0-
0.075sec (2Nm), 0.075-0.15sec (1Nm), 0.15-0.225sec (2Nm)
and 0.225-0.3sec (1Nm)].
Figure 12: Reference and estimated speed for PI controller for
condition 4
Figure 13: Reference and estimated speed for MLP controller for
condition 4
Figure 14: Reference and estimated position for PI controller for
condition 4
Figure 15: Reference and estimated position for MLP controller for
condition 4
Table 1: Result by using PI controller for condition 1 to 4
Cond. 1 Cond. 2 Cond. 3 Cond. 4
Tr 0.025938 0.02612 0.09331 0.09281
Ts 0.037314 0.0376 0.26453 0.26227
%OS 1.5385 1.4781 1.1247 1.9414
RMSE 332.0508 332.978 78.5091 77.8655
Table 2: Result by using MLP-PSO controller for condition 1 to 4
Cond. 1 Cond. 2 Cond. 3 Cond. 4
Tr 0.038055 0.03839 0.13257 0.1274125
Ts 0.048551 0.049 0.29009 0.2932889
%OS 0.5118 0.4535 0.4259 1.8022
RMSE 325.149 326.474 59.8513 59.119
Based on the result that tabulated in Table 1 and 2 for
speed estimation, it’s clearly shows that for rise time and
settling time, Tr and Ts for PI controller produce much better
than MLP controller. But, different with the overshoot and
2017 7th IEEE International Conference on Control System, Computing and Engineering (ICCSCE 2017), 24–26 November 2017, Penang, Malaysia
370

6. root mean square, %Os and RMSE, the MLP produce better
result for speed estimation. In the meantime, result RMSE for
the position estimation that tabulated in Table 3 clearly shows
that there have significant difference where the MLP produces
lower value of RMSE than PI controller.
Table 3: Result of root mean square (RMSE) for position error
between reference and estimated for PI and MLP controller
PI MLP-PSO
RMSE 43.7159 7.1904
V. CONCLUSION
This paper are proposing a new method that can produce better
result between existing controller for the dynamic response
such as rise time, settling time, maximum overshoot and root
mean square error for PMSM sensorless based. Amongst this
two controllers, MLP-PSO based was producing good results
compared to conventional controler, PI. It clearly shows that
this method was improve the dynamic performance of the
PMSM controller. For further reccomendation, the hybrid
multilayer perceptron (HMLP) will be tested to analyze the
performance of speed and position estimation for PMSM
sensorless method versus existing method.
ACKNOWLEDGEMENT
This paper was funded by the Fundamental Research Grant
Scheme (FRGS) (FRGS/1/2015/TK04/UITM/02/12) from the
Ministry of Education (MOE) Malaysia and Faculty of
Electrical Engineering Universiti Teknologi MARA,
Malaysia.
REFERENCES
[1] K. Jinsong, Z. Xiangyun, W. Ying, and H. Dabing, “Study of
position sensorless control of PMSM based on MRAS,” Proc. IEEE
Int. Conf. Ind. Technol., no. 3, pp. 3–6, 2009.
[2] M. S. Mahammadsoaib and M. P. Sajid, “Vector controlled PMSM
drive using SVPWM technique - A MATLAB / simulink
implementation,” Int. Conf. Electr. Electron. Signals, Commun.
Optim. EESCO 2015, no. January 2015, 2015.
[3] P. Tiwari, “Analysis of Sensorless Permanent Synchronous Motor
Using PI and Adaptive Control Scheme,” vol. 4, no. 4, pp. 1193–
1198, 2015.
[4] E. M. Fernandes, a. C. Oliveira, M. a. Vitorino, E. C. Dos Santos,
and W. R. N. Santos, “Speed sensorless PMSM motor drive system
based on four-switch three-phase converter,” Proceedings, IECON
2014 - 40th Annu. Conf. IEEE Ind. Electron. Soc., pp. 902–906,
2014.
[5] Z. Q. Zhu and L. M. Gong, “Investigation of effectiveness of
sensorless operation in carrier-signal-injection-based sensorless-
control methods,” IEEE Trans. Ind. Electron., vol. 58, no. 8, pp.
3431–3439, 2011.
[6] A. Mishra, V. Mahajan, P. Agarwal, and S. P. Srivastava, “MRAS
based estimation of speed in sensorless PMSM drive,” 2012 IEEE
5th Power India Conf. PICONF 2012, 2012.
[7] F. Cupertino, a. Guagnano, a. Altomare, and G. Pellegrino,
“Position estimation delays in signal injection-based sensorless
PMSM drives,” 3rd IEEE Int. Symp. Sensorless Control Electr.
Drives, SLED 2012, pp. 1–6, 2012.
[8] G. Wu and X. Xiao, “Speed controller of servo system based on
MRAS Method,” Proc. IEEE Int. Conf. Ind. Technol., 2009.
[9] P. Vaclavek and P. Blaha, “Synchronous Machine Drive
Observability Analysis and Sensorless Control Design,” 2008 Ieee
2Nd Int. Power Energy Conf. Pecon, Vols 1-3, no. PECon 08, pp.
265–270, 2008.
[10] H. M. Kojabadi and M. Ghribi, “MRAS-based adaptive speed
estimator in PMSM drives,” Int. Work. Adv. Motion Control. AMC,
vol. 2006, no. 1, pp. 569–572, 2006.
[11] W. Gao and Z. Guo, “Speed sensorless control of PMSM using
model reference adaptive system and RBFN,” J. Networks, vol. 8,
no. 1, pp. 213–220, 2013.
[12] M. Dursun, A. F. Boz, M. Kale, and M. Karabacak, “Sensorless
Speed Control of Permanent Magnet Synchronous Motor With
Hybrid Speed Controller Using Model Reference Adaptive,” vol. 3,
no. 1, pp. 24–37, 2014.
[13] S. Mishra, R. Prusty, and P. K. Hota, “Analysis of Levenberg-
Marquardt and Scaled Conjugate gradient training algorithms for
artificial neural network based LS and MMSE estimated channel
equalizers,” Proc. - 2015 Int. Conf. Man Mach. Interfacing, MAMI
2015, no. Lm, 2016.
[14] A. Zabidi, L. Y. Khuan, W. Mansor, I. M. Yassin, and R. Sahak,
“Classification of infant cries with asphyxia using multilayer
perceptron neural network,” 2010 2nd Int. Conf. Comput. Eng. Appl.
ICCEA 2010, vol. 1, pp. 204–208, 2010.
[15] W. F. Tarmizi, I. Elamvazuthi, N. Perumal, K. Nurhanim, M. K. A.
A. Khan, S. Parasuraman, and a. V. Nandedkar, “A Particle Swarm
Optimization-PID controller of a DC Servomotor for Multi-
Fingered Robot Hand,” 2016 2nd IEEE Int. Symp. Robot. Manuf.
Autom. ROMA 2016, pp. 1–6, 2017.
[16] M. Elbuluk, “A sliding mode observer for sensorless control of
permanent magnet synchronous motors,” Conf. Rec. 2001 IEEE Ind.
Appl. Conf. 36th IAS Annu. Meet. (Cat. No.01CH37248), vol. 2, no.
C, pp. 1273–1278, 2001.
2017 7th IEEE International Conference on Control System, Computing and Engineering (ICCSCE 2017), 24–26 November 2017, Penang, Malaysia
371