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Automatika
Journal for Control, Measurement, Electronics, Computing and
Communications
ISSN: (Print) (Online) Journal homepage: https://www.tandfonline.com/loi/taut20
A comparative study of DC servo motor parameter
estimation using various techniques
Ashna Batool, Noor ul Ain, Arslan Ahmed Amin, Muhammad Adnan &
Muhammad Hamza Shahbaz
To cite this article: Ashna Batool, Noor ul Ain, Arslan Ahmed Amin, Muhammad Adnan &
Muhammad Hamza Shahbaz (2022) A comparative study of DC servo motor parameter estimation
using various techniques, Automatika, 63:2, 303-312, DOI: 10.1080/00051144.2022.2036935
To link to this article: https://doi.org/10.1080/00051144.2022.2036935
© 2022 The Author(s). Published by Informa
UK Limited, trading as Taylor & Francis
Group.
Published online: 08 Feb 2022.
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AUTOMATIKA
2022, VOL. 63, NO. 2, 303–312
https://doi.org/10.1080/00051144.2022.2036935
A comparative study of DC servo motor parameter estimation using various
techniques
Ashna Batool, Noor ul Ain, Arslan Ahmed Amin , Muhammad Adnan and Muhammad Hamza Shahbaz
Department of Electrical Engineering, FAST National University of Computer and Emerging Sciences, Punjab, Pakistan
ABSTRACT
A lot of research is being carried out on the Direct Current (DC) servo motor systems due to their
excessive applications in various industrial sectors owing to their superior control performance.
Parameters of the DC servo motor systems to be used in the simulation software are usually
unknown or change with time and have to be determined accurately for obtaining the precise
simulation response. In this paper, three different estimation techniques for multi-domain DC
servo motor model parameters are discussed namely the Compare Coefficient Method, MAT-
LAB Parameter Estimation Toolbox, and System Identification Toolbox. The paper performs a
comparison of these methods to identify the one that gives the most accurate results. Experi-
mental data has been used for the comparison of the estimated response from the techniques.
The results show that the parameters obtained from the parameter estimation method give the
most accurate simulation results with the least error against the experimental results. The study
is significant for guiding researchers to prefer this method for estimation purposes of DC servo
motor simulation model parameters. The presented technique, i.e. parameter estimation tech-
nique, is relatively less complex and requires less computational cost as compared to other
techniques found in the literature.
ARTICLE HISTORY
Received 12 January 2021
Accepted 28 January 2022
KEYWORDS
DC servo motor; Parameter
estimation; Design
optimization toolbox;
Parameter estimation
toolbox; DC motor
first-principle model;
Comparing coefficient
method
1. Introduction
Direct Current (DC) motors are used in dierent
elds of consumer electronics, industries, and robotics.
Parameters of DC motor play an important role in
achieving high performance in simulation models.
Parameters vary with time due to the depreciation and
agingeectwhichreducesperformance,therefore,to
overcome this problem, motor parameters should be
updated and dierent techniques have been used for
this purpose [1]. Motion Control Techniques (MCT)
have been tremendously developed in the last decade.
In 1990, Advanced Motion Control based rst IEEE
International workshop was held, which highlighted
the physical examination of Motion Control (MC).
MC systems became dominant in velocity, position,
force, and acceleration control. Industrial robotic sys-
tems’ performance is measured by control of force and
position. DC servomotors are frequently used to attain
accurate torque and position control. Furthermore, due
to the low cost, outstanding control performance, and
simple structure, their usage is spreading in the robotics
eld [2,3].
DCServomotorshave beenprovedusefulforindus-
trial MC systems due to their good features of less
noise, energy eciency, low manufacturing cost, fast
response, torque to inertia ration, little volume, and
high accuracy [4–6]. In industries, servo motor systems
are extensively utilized as actuators [7], which include
permanent-magnet synchronous motor [8], direct cur-
rent brushless motor [8], and direct current brushed
motor [9]. Two types of actuators are used for vehi-
cle systems, rst one is used in electro-pneumatic sys-
tems or electro-hydraulic systems called solenoid valve
[10,11] while the second one is used in the electrome-
chanical system which is termed as direct current servo
motor systems or DC motor [12,13].
Dierent advanced techniques self-tuning con-
troller, model reference adaptive controller, sliding
mode controller (SMC), adaptive backstepping control,
fuzzy control, and genetic algorithm have been imple-
mented for the improvement of the system’s perfor-
mance [14–16]. The schematic diagram of the DC servo
motor is shown in Figure 1. Controller parameter tun-
ing depends upon system physical parameters. Hence,
recognition of system physical parameters accuracy is
essential. Some xed parameters (resistance of arma-
ture Ra, the inductance of armature La, and Ke back-
emf constant) are considered for DC motor. Because
of magnetic eects, the torque constant may change,
when the direct current motor is in operation mode.
Also with the removal of loads or additional loads to
therotaryshaft,inertiaJofmotorchanges[17].
This literature review shows that all the previ-
ously developed methods are built upon parameter
CONTACT Arslan Ahmed Amin arslan_engineer61@yahoo.com Department of Electrical Engineering, FAST National University of Computer and
Emerging Sciences, Chiniot Faisalabad Campus, Punjab 35400, Pakistan
© 2022 The Author(s). Published by Informa UK Limited, trading as Taylor& Francis Group.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted
use, distribution, and reproduction in any medium, provided the original work is properly cited.
304 A. BATOOL ET AL.
Figure 1. Schematic diagram of the DC servo motor [16].
knowledge of the accurate model. Still, because of
manufacturing discrepancy and dierent application
schemes disturbances, unknown parameters and back-
lashes surely occur in the DC motor servo systems.
Consequently, with previously mentioned uncertainties
it seems still tough to control DC motor servo systems.
It is noted that adaptive control can handle dierent
types of system uncertainties [18,19], which includes
parametric uncertainties [20–22], non-smooth non-
linear uncertainty [23–25], time-delay [26–28], and
disturbances that are not known [29,30]. A PID-type
feedback controller with adaptive gain parameters was
introduced for backlash nonlinearity, for position con-
trol [31]. In actuality, with the advancement and bet-
terment of manufacture highly precise actuators are
needed in vehicle applications when the backlashes and
gaps are very small. As a result of the above discus-
sion, we can say that the main uncertainties are dis-
turbances and unknown parameters, not backlashes. In
the future an indirect method of comparing coecients
canbeusedalsoonlineparameterestimationofDC
motorcanbedonewithouttheneedtohaveinforma-
tion about parameters in advance. Further, controller
parameters can be estimated from articial intelligent
techniques.Wheneverloadchangesoccur,thismethod
will improve the system response in real-time. Scien-
tists and Engineers of dierent elds and industries
have good knowledge about the advantages of mod-
elling dynamic systems. They can use test-data-based
methods or methods of rst-principles mathematics.
First-principles models give understanding about the
behaviour of the system, but at the same time reduce
accuracy. Data-driven models give good accuracy, but
they provide a limited understanding of system physics.
In this paper ve parameters (Ra, La, Km, J, and B) are
used for the model of the motor.
There has been a lot of studies done on parameter
estimation techniques in general. In [32], the authors
propose a new parameter estimation approach based on
the Dynamic Regressor Extension and Mixing (DREM)
method. When compared to gradient-based and least-
squares estimators, this method has been shown to
perform better. The DREM strategy’s performance has
been improved further in [33,34]. [35] describes how
signal injection techniques may be used to reduce the
complexity of parameter estimation-based observers.
This approach is used to create a sensorless controller
for magnetic levitation devices, and the ndings are
conrmed using numerical simulations. [36] describes
anewtechniqueforpartialstateidenticationofnon-
linear systems based on parameter identication. In
[37], an adaptive parameter estimation approach for
nonlinear systems with unknown time-varying param-
eters was introduced. The adaptive method estimates
parameters using input and output data and is val-
idated using gradient-based and least-squares tech-
niques. Furthermore, the method’s resilience is demon-
strated experimentally on a roto-magnet plant with
limited disturbance.
Thetechniquespresentedintheliteraturearemuch
complex and require huge computational cost mak-
ing these unattractive for common DC servo motor
parameter estimation purposes. The contributions of
the paper are summarized as: (1) the rst-principle
model of DC servo motor is developed and compar-
ing coecients method has been used to determine
the system parameters. (2) The parameter estimation
toolbox has been used to estimate the parameters and
validate the response of the system. (3) System identi-
cation toolbox has been used to estimate parameters.
(4) comparison of the three methods has been car-
ried out to select the best option for such applications.
Experimental data has been used for the comparison of
theestimatedresponsefromthetechniques.Theresults
show that the parameters obtained from the parameter
estimation method give the most accurate simulation
results with the least error against the experimental
results. The study is signicant for guiding researchers
to prefer this method for estimation purposes of DC
servo motor simulation model parameters. The study
is novel with respect to literature that no such com-
parative study was found justifying the superior per-
formance of parameter estimation toolbox method for
estimating the parameters of a DC servomotor.
The next sections are organized in the following way,
Section II discusses the research methodology, Section
III presents results with discussion and the comparison
of two methods. Section IV concludes the document.
2. Research methodology
A list of parameters with symbols used in the study for
estimation is shown in Table 1.
2.1. Modelling using comparing coecient
method
In this method, we estimate the parameters of a DC
servomotorusingtheDCservomotorsubsystem.The
model of DC motor is formulated with its mechani-
cal and electrical subsystems using Simscape Driveline
AUTOMATIKA 305
Figure 2. DC servo motor subsystem [38].
Tab le 1. List of parameters and symbols for DC servo motor.
Parameter Abbreviation Units
Moment of Inertia JmKg.m2
Back EMF constant KbVol t s /rad/sec
Tor qu e Con st a nt KtN.m/A
Frictional Constant BmN.m/rad/sec
Electric Resistance Ra
Electric Inductance LaH
Armature Current IaA
Angle of motor shaft θrad
Developed Torque TmN.m
Load Torque TlN.m
Back EMF EbVol t s
Armature Voltage EaVol t s
and Electrical line. Input voltage (V)isappliedtothe
motor and output measured is the motor shaft’s angular
position, θas shown in Figure 2.
Dynamic parameters of Servo motor can be esti-
mated using the following equations given below:
Ea(s)=RaIa(s)+LasIa(s)+Eb(s)(1)
Tm=KtIa(s)(2)
Tm=(Jms2+Dms)θ(s)(3)
Eb(s)=Kbsθ(s)(4)
2.2. Modelling using parameter estimation
technique
In this method, practical measurements from a real DC
servomotorarersttaken.Wethenneedtoidentify
and specify parameters to estimate, starting with some
initial guess. After feeding this data into the model,
parameter values are approximated using a suitable
approximation algorithm from Parameter Estimation
Toolbox in Simulink. Five parameters: Frictional con-
stant Bm,MomentofInertiaJm, Torque Constant Kt,
Inductance Laand Resistance Raof servo motor are
chosen and are loaded in the Parameter Estimation tool.
Practically, measured data is also loaded for validation
of the model. The next step is to plot both measured and
simulateddatatoseehowmuchitmatchescurrentDC
ServoMotor’sdata.Ifthesimulationdoesnotmatchthe
measured data, model parameters need to be estimated
again. The parameter estimation tool will continue to
iterate parameter values until estimation converges or
terminates. Plots of measured and simulated data can be
overlaid to show how successful is the estimation pro-
cess. After completion of parameter approximation, we
need to validate our results using other test data sets
that can be measured from the real DC servo motor.
The steps involved in the evaluation of the parame-
ter estimation of DC Servo Motor using the parameter
estimation toolbox are shown in Figure 3.
2.3. Modelling using system identication
technique
Another technique to estimate parameters for DC
Servo Motor is using System Identication Toolbox
if we have measured input and output data. In this
study, the estimation and validation input and output
data were obtained from MATLAB DC Servo Motor
Example [38].
3. Results and discussion
DC Servo Motor system is developed in Simulink
using the Simscape Driveline and Simscape Electrical
as shown in Figure 4which shows Simulink model
of DC Servo motor used for estimation of motor
parameters.
306 A. BATOOL ET AL.
Figure 3. Shows steps involved in parameter estimation of DC
servo motor.
3.1. Parameter estimation using comparing
coecient method
Before starting the estimation process, we need to know
system equations that physically represent DC Servo
Motor. The dynamic parameters of the Servo motor can
be estimated using the Equations (1) to (4). By taking
Laplace Transform of all the above equations and after
simplifying, the following transfer function is obtained:
G(s)=θ(s)
Ea(s)=Kt−1
s[(Ra+sL
a)((Jm+Dm)+Kt2]
(5)
Expanding denominator we get,
G(s)=θ(s)
Ea(s)=Kt
(JmLa)s3+(RaJm+DmLa)s2
+(DmRa+Kt2)s
(6)
After nding Values of K,Tp1and Tp2,wecannd
numerical values of motor parameters by evaluat-
ing Equation (6) and process model transfer function
Equation (8).
G(s)=θ(s)
Ea(s)=Kt−1
(JmLa)s3+(RaJm+Dm La)s2
+(DmRa+Kt2)s
(7)
P(s)=K
s(1+Tp1s)(1+Tp2s)(8)
P(s)=K
Tp1Tp2s3+(Tp1+Tp2)s2+s(9)
Evaluating coecients of (6) and (8), we get
Tp1Tp2=JmLa(10)
RaJm+Dm La=Tp1+Tp2(11)
1=DmRa+Kt2(12)
The value of Rais assumed to nd other parameters by
solving and putting values in other equations. We get
the following values:
Jm=9.027e −3
Kt=4.943e −3(N.m/A)
Dm=0.518 (N.m/rad/sec)
Ra=1.93
La=2.348e −3H
Theestimatedvaluesareabout90%closertotheactual
measurements.
3.2. Parameter estimation using parameter
estimation toolbox
Estimation of the Motor parameter is done using the
Parameter Estimation toolbox. Pre-loaded data from
Figure 4. Shows the Simulink model of DC servo motor [38].
AUTOMATIKA 307
Tab le 2. Shows the initial values of these parameters.
Parameter Initial parameter values Units
Jm5.7e-7 Kg.m2
Kt0.0134 N.m/A
Dm0.008 N.m/rad/sec
Ra1.9
La6.5e-5 H
the practical experiment is already available in this
project. Experimental data can also be loaded from
MATLAB variables, MAT les, Excel, or comma-
separated-value les. The next task is to select parame-
ters that are planned to be estimated for the DC Servo
motor. Five Parameters are chosen Frictional constant
Bm,MomentofInertiaJm, Torque Constant Kt, Induc-
tance Laand Resistance Ra.Wesettheinitialvalues
of these parameters, as mentioned in the datasheet of
DC Servo Motor. The range of these parameters from
zero to innity is also dened. The initial values of these
parameters are shown in Table 2.
We plot the model response of the experimental data
along with the simulated data. It is found that the sim-
ulation data does not match with practically measured
data, showing that model parameters need to be tuned
as shown in Figure 5.
Next,weaddaplotofParameterTrajectory,which
shows how parameter values change during the esti-
mation process. Estimation is done based on a cost
function. For this experiment, the cost function of Sum
SquaredErrorisselected.Next,theEstimationpro-
cess is started, it keeps iterating parameter values
until estimation converges and stops. Once the process
terminates, we obtain the estimation progress report
featuring the iteration number and values from the cost
Tab le 3. Estimation progress report.
Iteration F- Count Estimation data
0 11 35.0694
1 22 11.0708
2 33 3.1677
3 44 1.0813
4 55 0.6050
5 66 0.5462
function. The convergence steps of the algorithm are
shown in Table 3.
The cost function minimization plot is shown in
Figure 6to show the progress of the algorithm after each
iteration till convergence.
The parameter trajectory plot for various parame-
ters to be estimated is shown in Figure 7to show the
progress to approach their nal values.
The model t plot of the estimated data with mea-
sured data is shown in Figure 8which shows the accu-
racy of the technique after few iterations.
A successful estimation should not match only the
experimental data set but also other test data, which is
collected from a practical experiment. The Validation
data set is pre-loaded for this experiment. It is observed
from simulation results that the model plot response
of the test dataset accurately matches with the simu-
lated data. The results obtained from this method are
about 99% closer to the actual measurements proving
its greater accuracy.
3.3. Parameter estimation using system
identication toolbox
We obtain two measured data sets for estimation and
validation. min and mout are measured input and
Figure 5. Shows the difference between model plot response of measured and simulated data.
308 A. BATOOL ET AL.
Figure 6. Cost function used for estimation process.
output that will be used for estimation and vin and
vout are measured input and output that will be used
for validation of the model. The next step is to con-
vert input and output data in MATLAB workspace to
iddata variable. This can be done by using the following
Figure 7. Parameter trajectory plot of DC servo motor.
command:
data =iddata(output, input, Ts)
where Ts is a sampling time that is 0.005s.
Figure 8. Model plot response of simulated data.
AUTOMATIKA 309
Figure 9. Measured input and output data plot, used for estimation.
Figure 10. Measured input and output data plot, used for validation.
Two iddata objects; mdata and vdata are set. These
two variables are added to the system identication
toolbox for the estimation of the model. We modify
mdataobjectandselectinputandoutputvaluesfrom
0to2swithTs =0.005 s.
The following steps are repeated for vdata and vdatae
is obtained with validation input and outputs ranging
from 0 to 2 s. The plots of input and output signals for
the estimation and validation are shown in Figures 9
and 10.
Next, we select a process model that will depict the
dynamicsofourDCServoMotorwhichistworeal
poles-based system with an integrator in series to esti-
mate gain and poles values. The values of K,Tp1and
Tp2are estimated. The plots of the process model with
estimationandvalidationdataareshowninFigures11
and 12.Itisseenfromtheresultsthatbothvalidation
and estimation data map each other accurately up to
96%.
3.4. Comparison of presented techniques
The paper presented a comparison of the three pop-
ular methods for estimating the parameters of the
DC servo motor system. The conventional method
using the comparing coecient method is an easy
one but lacks accuracy in terms of achieving experi-
mental results. The second method using the param-
eter estimation toolbox provided the highest accuracy.
The third method was the system identication tech-
niquethatprovidedanaccurateresponselessthan
the parameter estimation toolbox. Therefore, the rec-
ommended method from this study is the parameter
estimation toolbox (Table 4).The parameter estimation
310 A. BATOOL ET AL.
Figure 11. Process model P2 fits estimation data up to 96%.
Figure 12. Process model P2 fits validation data up to 94%.
Tab le 4. Comparison of the parameter estimation techniques.
Technique Accuracy
Comparing Coefficient Method 90%
Parameter Estimation Toolbox 99%
System Identification Toolbox 94-96%
technique is also relatively less complex and requires
lesscomputationalcostascomparedtoothertech-
niques found in the literature mentioned earlier.
4. Conclusion
This paper presented three estimation techniques for
multi-domain DC servo motor model parameters
namely the Compare Coecient Method, MATLAB
Parameter Estimation Toolbox, and System Identication
Toolbox. The paper also performed a comparison of
these methods to identify the one that gives the most
accurate results. The results showed that the parame-
ters obtained from the parameter estimation method
give the most accurate simulation results with the least
error against the experimental results. The study is sig-
nicant for guiding researchers to prefer this method
for estimation purposes of DC servo motor simulation
model parameters.
Future directions may include the inclusion of dif-
ferent parameters other than these for better results.
Advanced neural network or fuzzy-based or combina-
tion of these estimation methods may also be tested
for performance comparison in future studies with
experimental verication like Hardware-in-the Loop
technique.
AUTOMATIKA 311
Acknowledgements
The authors would like to thank to colleagues for suggestions
toimprovethepaperquality.
Disclosure statement
No potential conict of interest was reported by the author(s).
Funding
The author(s) received no nancial support for the research,
authorship, and/or publication of this article.
ORCID
Arslan Ahmed Amin http://orcid.org/0000-0001-8035-
595X
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