Parameter Estimation of DC Motor Using Chaotic Initialized Particle
Swarm O
p
timization
Muhammad Ali Mughal
1
, Mansoor Khan
2
, Aamer Abbas Shah
3
and Aftab Ahmed Almani
3
1
School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China
2
School of Electrical Engineering, Sichuan University, Chengdu, China
3
School of Electrical Engineering, Shandong University, Jinan, China
1
engr_mughal@yahoo.com,
1
m.ali@buaa.edu.cn
Keywords: DC motor, parameter estimation, particle swarm optimization, PSO, chaotic.
Abstract: Parameter estimation plays an important role in system modelling and control. This paper presents a parameter
estimation strategy for separately excited DC motor using a chaotic initialized particle swarm optimization
algorithm. The parameter estimation problem is converted into an optimization problem using an objective
function. The presented strategy is significant in estimating the motor parameters accurately when compared
to standard particle swarm optimization portrayed by low mean square error between actual and estimated
speed.
1 INTRODUCTION
DC motors have wide applications ranging from
small home appliances to complex industrial control
systems for the reason that they are easy in modelling
and control. Sometimes precise parameters of a DC
motor are needed for analysis and design of control
system and optimization. The information given by
manufacturer may not be sufficient in this situation.
This scenario led to the application of numerical
techniques for the parameter estimation. In particular,
various techniques have been applied to parameter
estimation of electric motors such as least squares
(Cirrincione et al. 2003), equation error method
(Petrovas, Pitrenas & Savickiene 2017), inverse
problem method (Hadef & Mekideche 2009), Nelder-
Mead simplex method (Dub & Jalovecký 2010).
Recently, evolutionary algorithms have gained much
attention in parameter estimation problems (Mughal,
Ma & Xiao 2017). Many evolutionary algorithms
have been applied to parameter estimation of electric
machines in particular to DC motors. Bosco et al.
(Bosco et al. 2017) applied differential evolution
(DE) algorithm for parameter estimation and PI
control tuning of a permanent magnet DC motor.
(Puangdownreong 2017) applied flower pollination
algorithm to parameter estimation of a DC motor.
(Udomsuk et al. 2010) applied an adaptive tabu
search (ATS) algorithm to parameter estimation of a
separately excited DC motor. (Kumpanya, Thaiparnat
& Puangdownreong 2015) applied ATS and
intensified current search techniques to parameter
estimation of a brushless DC motor. Among various
evolutionary algorithms, Particle Swarm
Optimization is relatively prominent due to its simple
structure and ease in implementation (Zhang et al.
2015). PSO has found numerous applications in
solving engineering optimization problems;
(Mohammadi et al. 2014) used PSO for parameter
estimation of a three-phase induction motor. In this
paper, an improved PSO known as chaotic initialized
PSO (CIPSO) was applied to parameter estimation of
a separately excited DC motor. The accuracy of the
estimation was evaluated by the degree of agreement
between the actual motor speed response and the
estimated speed response and also by comparing the
results with standard PSO (SPSO).
2 MODELLING OF DC MOTOR
In this section a separately excited DC motor is
modelled as a transfer function (DC Motor Speed:
System Modeling n.d.) that relates the input voltage
(volts) and output rotational speed (rad/sec) as
expressed in (1):
(1)
Mughal, M., Khan, M., Shah, A. and Almani, A.
Parameter Estimation of DC Motor Using Chaotic Initialized Particle Swarm Optimization.
In 3rd International Conference on Electromechanical Control Technology and Transportation (ICECTT 2018), pages 391-395
ISBN: 978-989-758-312-4
Copyright © 2018 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
391
where is the transfer function, is the
rotational direction and is the input voltage. All
other parameters are defined in Table 1 with their
actual values and units.
Table 1: Actual parameter values with units.
Paramete
r
Value
Moment of inertia (
)
0.01 Kg.m
2
Viscous friction ()
0.1 N.m.s
Electromotive force constant ()
0.01 V/rad/sec
Torque constant ()
0.01 N.m/Amp.
Resistance ()
1 Ohm
Inductance ()
0.5 H
is the parameter vector to
be estimated by time-varying PSO
3 PARAMETER ESTIMATION
PROBLEM FORMULATION
The DC motor parameter estimation problem was
converted to an optimization problem by using an
objective function. A mean square error (MSE) is
used in this paper as objective function as expressed
in (2):
min
1
.
.
(2)
where is the objective function is the number
of speed data samples, is the index term whereas
.
and
.
represent the actual and estimated
speed, respectively. The purpose of the optimization
algorithm is to optimize (minimize) this error and
output the corresponding parameters. Figure 1 shows
the block diagram of the DC motor parameter
estimation.
Figure 1: DC motor parameter estimation block diagram.
4 CHAOTIC INITIALIZED PSO
Particle Swarm Optimization is a well-known
evolutionary algorithm which takes its inspiration
from food search behaviour of bird flocks. A swarm
of particles (initial solutions) is initialized randomly
with normal distribution. Each particle in the swarm
is evaluated against an objective function like the one
expressed in (2); best solution of each particle called
the personal best and best solution among all the
particles called the global best is retrieved. The
velocity of each particle is updated using (3) and
position is updated using (4)
⋯
(3)
where is the velocity, is the particle vector,
is the inertia weight,
is the personal acceleration
coefficient,.is the
social acceleration coefficient,
is the personal best, is the global best,
and
are the random numbers distributed
between 0 and 1.
(4)
The and are updated using
following (5) and (6).
,i
f
,i
f
(5)
,i
f
max
(6)
4.1 Chaotic Initialization
Chaos can be termed as bounded nonlinear system; it
is generated by iterating some deterministic equation
with an element of regularity (Tian 2017). In this
paper a tent chaotic map is utilized for initialization
of the swarm. The tent map is expressed by (7)
2
,
∈
0,0.5
2
1
,
∈
0.5,1
(6)
where
is the chaotic amplitude, is the iteration
counter and
∈
0,1
. Figure 2 shows the chaotic
variables generated for 50 iterations between 0 and 1.
ICECTT 2018 - 3rd International Conference on Electromechanical Control Technology and Transportation
392
Figure 2: Chaotic variables generated for 50 iterations.
Following is the pseudo code for chaotic tent map
generation
1. Begin
2. Randomly initialize chaotic
variables
3. while(maximum iterations)
Update the variables by (6)
4. End while
5. Normalize the chaotic variables
into the problem search space
6. End
Algorithm 1: Pseudo code for tent map generation.
.
1. Begin
2. Initialize position of particles using the chaotic map (6)
{X
i
|i = 1, 2, …, N};
3. Calculate the objective value of X
i
;
4. while (number of iterations)
5. for i = 1 to the number of particles
find pBest
find gBest
6. for d = 1 to number particle dimensions
Update the velocity of particles by (3)
Update the position of particles by (4)
7. end
8. end
9. Next generation until stopping criterion
10. end
11. End
Algorithm 2: Pseudo code for the CIPSO.
Figure 3: Convergence curve for CIPSO.
Parameter Estimation of DC Motor Using Chaotic Initialized Particle Swarm Optimization
393
Figure 4: Actual and estimated speed response
5 COMPUTATIONAL RESULTS
AND DISCUSSION
5.1 Algorithm Parameter Settings
Table 2 displays the parameter settings for the CIPSO
and SPSO. The CIPSO was initialized with chaotic
tent map based particles whereas the SPSO was
initialized with random numbers scaled in problem
range.
Table 2: Algorithm parameter settings.
Parameters Settin
g
Swarm size 30
Number of iterations 50
0.9
2
2
5.2 Computational Results
A unit-step signal was applied to the transfer function
model of the DC motor to record the speed response
(termed as actual speed) for a time period of 5
seconds. The CIPSO was then applied to minimize
the difference between the actual speed response and
the estimated speed by using (2). The parameters
estimated by CIPSO were compared with the standard
PSO (SPSO) and the actual parameters of the DC
motor. Table 3 tabulates the estimation results
obtained by the algorithms with the actual motor
parameters. It can be observed from Table 3 that the
CIPSO has outperformed the SPSO in terms of less
MSE values and accuracy in estimating the motor
parameters. CIPSO has achieved a MSE value of
1.399E-12 which is far less than the MSE achieved
by SPSO. The parameters estimated by CIPSO are in
close proximity with the actual motor parameters.
Figure 3 shows the convergence of the CIPSO. It is
clear from Figure 3 that the CIPSO converged to a
stable value in less than 15 iterations. Figure 4 plots
the actual speed response and the speed response
estimated by CIPSO; it can be seen that the speed
response estimated by CIPSO tracks the actual speed
response with high accuracy and close proximity
Table 3: Actual and estimated parameters with MSE.
Parameters
MSE
Actual 0.01 0.1 0.01 1 0.5
CIPSO 0.0102 0.1 0.0101 1.007 0.503 1.399E-16
SPSO 0.0110 0.104 0.014 1.0901 0.508 2.080E-12
ICECTT 2018 - 3rd International Conference on Electromechanical Control Technology and Transportation
394
6 CONCLUSIONS
A chaotic initialized particle swarm optimization
(CIPSO) algorithm was applied to parameter
estimation of a DC motor. The DC motor was
modelled using transfer function. Five parameters of
the DC motor namely moment of inertia, viscous
friction, electromotive force constant, resistance and
inductance were estimated optimally using the
CIPSO. The initial population swarm was generated
by using a chaotic tent map. The estimated parameters
were compared with the actual parameters and the
parameters estimated by the standard PSO. The
CIPSO was accurate in estimating the parameters
with less mean square error, comparatively.
REFERENCES
Bosco, M.C., Guedes, J.J., Castoldi, M.F., Goedtel, A.,
Ravazzi, E., Francisco, L. & Buzachero, S. 2017,
'Estimation of Parameters and Tuning of a Speed PI
of Permanent Magnet DC Motor Using Differential
Evolution', Electric Machines and Drives
Conference (IEMDC).
Cirrincione, M., Pucci, M., Cirrincione, G. & Capolino,
G.A. 2003, 'A new experimental application of least-
squares techniques for the estimation of the
induction motor parameters', IEEE Transactions on
Industry Applications, vol. 39, no. 5, pp. 1247–56.
DC Motor Speed: System Modeling n.d., viewed 1
December 2017,
<http://ctms.engin.umich.edu/CTMS/index.php?exa
mple=MotorSpeed§ion=SystemModeling>.
Dub, M. & Jalovecký, R. 2010, 'DC motor experimental
parameter identification using the Nelder-Mead
simplex method', Proceedings of EPE-PEMC 2010 -
14th International Power Electronics and Motion
Control Conference, pp. 9–11.
Hadef, M. & Mekideche, M.R. 2009, 'Inverse problem
methodology for parameter identification of a
separately excited DC motor', Journal of Electrical
Engineering and Technology, vol. 4, no. 3, pp. 365–
9.
Kumpanya, D., Thaiparnat, S. & Puangdownreong, D.
2015, 'Parameter Identification of BLDC Motor
Model Via Metaheuristic Optimization Techniques',
Procedia Manufacturing, vol. 4, no. Iess, pp. 322–7.
Mohammadi, H.R., Akhavan, A., Mohammadi, H.R. &
Akhavan, A. 2014, 'Parameter Estimation of Three-
Phase Induction Motor Using Hybrid of Genetic
Algorithm and Particle Swarm Optimization',
Journal of Engineering, vol. 2014, pp. 1–6.
Mughal, M.A., Ma, Q. & Xiao, C. 2017, 'Photovoltaic cell
parameter estimation using hybrid particle swarm
optimization and simulated annealing', Energies,
vol. 10, no. 8, pp. 1–14.
Petrovas, A., Pitrenas, A. & Savickiene, Z. 2017, 'DC motor
parameter identification using equation error
method', Electrical Engineering, no. 1, pp. 1–9.
Puangdownreong, D. 2017, Application of Flower
Pollination Algorithm to Parameter Identification of
DC Motor Model, no. March, pp. 8–10.
Tian, D. 2017, 'Particle Swarm Optimization with Chaos-
based Initialization for Numerical Optimization
Particle Swarm Optimization with Chaos-based
Initialization for Numerical', Intelligent Automation
& Soft Computing, vol. 8587, no. March, pp. 1–12.
Udomsuk, S., Areerak, K.-L., Areerak, K.-N. & Srikaew,
A. 2010, 'Parameters identification of separately
excited DC motor using adaptive tabu search
technique', 2010 International Conference on
Advances in Energy Engineering, no. 2, pp. 48–51.
Zhang, Y., Wang, S., Ji, G., Zhang, Y., Wang, S. & Ji, G.
2015, 'A Comprehensive Survey on Particle Swarm
Optimization Algorithm and Its Applications',
Mathematical Problems in Engineering, vol. 2015,
pp. 1–38.
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