Motion control applications: observer based DC motor parameters estimation for novices

International Journal of Power Electronics and Drive System (IJPEDS)
Vol. 10, No. 1, March 2019, pp. 195~210
ISSN: 2088-8694, DOI: 10.11591/ijpeds.v10.i1.pp195-210  195
Journal homepage: http://iaescore.com/journals/index.php/IJPEDS
Motion control applications: observer based DC motor
parameters estimation for novices
Branesh M. Pillai, Jackrit Suthakorn
Department of Biomedical Engineering, Faculty of Engineering, Mahidol University, Thailand
Article Info ABSTRACT
Article history:
Received Jun 29, 2018
Revised Sep 17, 2018
Accepted Oct 3, 2018
Estimation of motor inertia and friction components is a complex and
challenging task in motion control applications where small size DC motors
(<100W) are used for precise control. It is essential to estimate the accurate
friction components and motor inertia, because the parameters provided by
the manufacturer are not always accurate. This research proposes a
Sensorless method of determining DC motor parameters, including moment
of inertia, torque coefficient and frictional components using the Disturbance
Observer (DOB) as a torque sensor. The constant velocity motion test and a
novel Reverse Motion Acceleration test were conducted to estimate frictional
components and moment of inertia of the motor. The validity of the proposed
novel method was verified by experimental results and compared with
conventional acceleration and deceleration motion tests. Experiments have
been carried out to show the effectiveness and viability of the estimated
parameters using a Reaction Torque Observer (RTOB) based friction
compensation method.
Keywords:
Advance motion control
DC motor parameter estimation
Disturbance observer
Friction compensation
Reverse motion acceleration
Sensorless sensor
Copyright © 2019 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Jackrit Suthakorn,
Center for Biomedical and Robotics Technology (BART LAB),
Department of Biomedical Engineering, Faculty of Engineering, Mahidol University,
999, Phuttamonthon Sai 4, Salaya, Nakorn Pathom, 73170, Thailand.
Email: jackrit.sut@mahidol.ac.th
1. INTRODUCTION
Motion control techniques have been significantly developed in recent decades. The first IEEE
International Workshop on Advanced Motion Control, held in 1990 emphasized the importance of physical
interpretation of motion control. Motion control systems play a vital role in many industrial automation
applications, such as position control, velocity control, acceleration control, force control etc. The
performance of industrial robotic application systems is mainly based on position and force control [1]. DC
servomotors are often used to achieve precise position and torque control. Moreover, in medical robotics
applications, DC servomotors are widely used due to its simple structure and outstanding control
performance at low cost [2].
DC servomotors used for control applications should incorporate accurate control methods to obtain
the desired responses. Controller parameters in such applications have to be tuned properly to obtain the
desired response of the system [3]. Tuning of controller parameters depends on the physical parameters of the
systems. Therefore, the identification of accurate physical parameters of systems is important. Armature
resistance Ra, armature inductance La and back emf constant Ke are considered to be fixed for a given DC
motor. Once a DC motor is in operation, the torque constant Kt may change due to magnetic effects. Motor
inertia J may change due to the addition or removal of loads to the rotary shaft [4].
DC motor friction compensation was a complex task and has been tried by many researchers.
However, no one has introduced an effective strategy for friction compensation of small size DC motors [5]-
[7]. There is no research available considering the four parameters (friction components (Tf and 𝐵𝜃 ),

 ISSN: 2088-8694
Int J Pow Elec & Dri Syst, Vol. 10, No. 1, March 2019 : 195 – 210
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mechanical parameter J and electrical parameter Kt) in a single experiment. In order to achieve accurate force
control based friction compensation, it is essential to identify the system parameters accurately and deal with
the non-linear friction components [8]. In this research, the authors propose a novel RTOB model based
friction compensation method using a PID controller. If the friction components and mechanical parameters
of the system are accurate, then the proposed friction compensation method will give the desired system
characteristics.
Frictional components also may vary with wear and tear effects [9], [10]. Usually motor
manufacturers may supply the parameters Kt and J. However, for smaller size DC motors (10-100W),
manufacturers’ given values for commercially available motors may not always be accurate. For precise
control applications, the accuracy of the motor parameters is very important [11]-[13]. Manufacturers do not
normally supply friction related parameters.The varying parametric value of DC motors can also be attributed
to the load connected with the motor [14]. The friction components present in a DC servo motor are static
friction, coulomb friction, viscous friction and Stribeck friction.
Generally, Stribeck friction is generated using fluid lubricants and the effect of this friction is
ignored in this research. Coulomb friction is independent of velocity and is assumed negligible for small size
DC motors. The static friction Tf is the force required in order to start the motion from a stand still. This
friction is also called as the breakaway friction. When the motor starts to rotate, viscous friction appears and
it increases with the increase of velocity. The estimation of accurate friction components (Tf and 𝐵𝜃) and the
mechanical parameters (Kt and J) lead to the desired system response [15]. In this paper, the estimation of
static friction, viscous friction, torque constant and motor inertia are discussed in detail.
Several methods of identification for DC motor parameters have been proposed using various
techniques. Many researchers have proposed methods of finding mechanical parameters of DC motors [16-
21]. For example, [16] the general system parameters identification is considered. The distribution-based
approach [17] is used to identify parameters from discrete time data. The fuzzy PID [18] is used to estimate
the loaded torque; the least-squares algorithm is implemented [19]-[21] to estimate system parameters.
However, none of them can be effectively used for small size DC motors. In [22], the importance of
estimation of parameters was emphasized, but there were no methods for estimating the motor inertia and the
frictional components. Although there are researches to estimate the viscous friction of DC motors used in
precise control applications such as position control, the torque coefficient and motor inertia were not taken
into consideration [23]-[26]. In [27], load model parameters were obtained using an evolutionary algorithm
but the friction coefficient of the motor was not considered.
Tuning the controller parameters for the desired system response can be achieved only with
accurately estimated physical parameters of the system. In motion control applications, the real time desired
system response is not achievable if controller tuning is done based only on the nominal motor parameters
without considering the physical parameter variations [28]. The algebraic identification method [29], [30] are
to estimate the parameters for a continuous time system. The recursive least square method [31] and the
inverse theory with conjugate gradient method [32] are used to determine system parameters.
In this research, the torque coefficient Kt was estimated using the conventional DC motor rotor stall
test. The friction components were identified by conducting the constant velocity motion test [33]. Here, the
disturbance observer (DOB) is used as a torque sensor. DOB identifies the total mechanical load and the
effect of system parameter change that is considered as the total disturbance of the motor [34], [35]. In order
to estimate the motor inertia, the authors propose a RTOB based novel Reverse Motion Acceleration test.
RTOB subtracts the identified parameters from the disturbance torque and hence outputs the reaction torque
applied to the system [36]-[39].
The estimated motor inertia using Reverse Motion Acceleration test was compared with
conventional acceleration and deceleration tests results. The results of these three tests were analyzed and
compared in section 3. The estimated parameters were validated by conducting a force control based friction
compensation test. Experiments where carried out to show the importance and validity of the all estimated
parameters using Reaction Torque Observer (RTOB) based friction compensation technique as explained in
section 4. The proposed inertia values were compared with the conventional test results using the same
friction compensator.

Int J Pow Elec & Dri Syst ISSN: 2088-8694 
Motion control applications: observer based DC motor parameters estimation for… (Branesh M. Pillai)
197
2. MODELING
2.1. DC motor modeling
Using Kirchhoff’s voltage law in circuit as shown in Figure 1.
Figure 1. Electrical model of a DC motor
(1)
And,


e
b K
e  (2)
a
t
m I
K
T  (3)
Motor torque is expressed as,
l
f
m T
B
T
dt
d
J
T 


 
 

(4)
Where, Ra - Armature resistance; La - Armature inductance; Ia - Armature current; Kt - Torque coefficient; J-
Moment of inertia of motor; Ke - Back emf constant; Va - Armature voltage; eb - Back emf; 𝜃 - Angular speed;
Tm - Motor torque; Ti- Load torque ; Tf-Static friction torque; B- Viscous friction coefficient. TL consists of
external applied torque and all the disturbance effects of the system as shown in Figure 2(a). (4) can be
rewritten as follows.
L
m T
T
J 


 (5)
L
a
t T
I
K
J 


 (6)
Where TL consists of inertia torque, external torque and torque due to Coulomb and viscous friction.

B
T
T
T f
l
L 

 (7)
The input to the motor is the reference current Ia and is controlled according to the PWM voltage
pulses [40], [41]. With the TL motor torque cannot be directly controlled using Ia. Therefore, for correct
functionality, TL must be compensated as shown in Figure 2(b). TL is referred to as ‘Disturbance Torque’ as
this torque disturbs the output torque. To measure this disturbance torque and compensate for it, the
‘Disturbance Observer’ is introduced [42] as shown in Figure 2(c).

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(a) (b)
(c) (d)
Figure 2. (a) Block diagram of DC motor (b) Block diagram of servomotor (c) Disturbance observer control
block (d) Reaction torque observer control block
2.2. Disturbance observer modeling
In (6) has two parameters, named motor inertia and torque constant. These two parameters may be
changed due to several properties. Inertia may be changed due to the mechanical configuration of the motion
system. The torque coefficient will vary according to the rotor position of the electric motor due to irregular
distribution of magnetic flux on the surface of the rotor [43], [44].
J
J
J n 

 (8)
t
tn
t K
K
K 

 (9)
Jn - Nominal motor inertia; J
 -Inertia variation; Ktn - Nominal torque coefficient; t
K
 -Variation of torque
coefficient. From (6)-(9) it can be determined that,


n
a
tn
dis J
I
K
T 
 (10)
In (10), the unknown value of Tdis is calculated using the known values at right hand side. From
(11), Tdis is calculated as follows.
a
t
f
l
dis I
K
J
B
T
T
T 





 
 

 (11)

199
Normally, disturbance torque consists of all internal torques, external torques, friction torques and
torques due to parameter variations, which must have compensated for to obtain the accurate output torque.
The estimated disturbance torque dis
T
ˆ is obtained from the velocity response and the torque current Ia. It is
estimated through a first-order low-pass filter as shown in Figure 2(c) where dis
G denotes the cut-off
frequency of the low-pass filter. The purpose of the low-pass filter is to filter out noise arising from
differentiation [45], [46].
2.3. Reaction torque observer modeling
The disturbance observer is used not only for disturbance compensation but also for reaction torque
estimation. The disturbance observer is able to estimate the reaction torque without using a torque sensor by
identifying the internal disturbance of the system [47]. When the motor is running with a load, the load
torque exerted on the motor due to the load is obtained from equation (12). As shown in Figure 2(d), all the
disturbance components are removed at the reaction torque observer; hence, the RTOB output is the
estimated load torque 𝑇 .
)
( a
t
f
dis
l I
K
J
B
T
T
T 





 
 

 (12)
3. DC MOTOR PARAMETER ESTIMATION METHODS
3.1. Experimental Setup
In the experiment, as shown in Figure 3, the system composed of l-DOF main motor, manufactured
by Maxon RE-max 29 and the motor specifications are listed in Table 1 and a motor driver SE-HB-40-1 with
driver IC (IRF 4905 S/L) along with a current sensor, which can carry a current of up to 40A peak load. The
current sensor installed in the system is to estimate the actual current of the main motor. The motor driver is
operated by the PWM signals generated by the processor. An encoder coupled with the main motor does
position sensing.
Table 1. DC Motor specifications
Parameter Value Units
Rated output 67.2 W
Rated/max torque 21.5/146 mNm
Encoder resolution 512 Pulse/rev
Figure 2. One DOF rotational manipulator

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3.2. Estimation of Torque Coefficient (Kt)
It is important to identify the exact Kt of DC motor, since the given value from manufacturers may
not be an exact representation of Kt for the loaded DC motor. The change of the torque coefficient is also
considered as a disturbance to the motor. The input power P of the DC motor can expressed in terms of
torque  and angular velocity.

 

P (13)
The power P also can be represented using armature voltage Va and armature current Ia.
a
a I
V
P  (14)
a
t I
K

 (15)
From (14) and (15) it can be shown as


t
a K
V  (16)
Hence, the angular velocity is directly proportional to the armature voltage, and the armature current
is an independent variable in this relationship. When the DC motor is running under no load conditions, the
Kt value does not vary. However, Kt may vary when the motor is loaded. The change of Kt of the loaded
motor was determined using the conventional rotor stall test. Figure 4 shows the setup used for a rotor stall
test [48]. This experiment was conducted to measure motor torques against a range of armature currents. In
this test, torque coefficient was obtained from the slope of the graph of Figure 8, by plotting the variation of
torque against the armature current. The torque coefficient Kt found using (15) from Figure 5(a) is 0.256
Nm/A.
Figure 3. Rotor stall test
3.3. Estimation of Friction Components
The authors propose use of Disturbance Observer (DOB) [1], [40] in a closed loop control system,
to estimate the disturbances torque to find the friction components. The disturbance observer identifies the
total mechanical load torque and the effects of system parameters as represented in equation (11). The
friction components were estimated by conducting a constant velocity motion test [48], [40], when the motor
is running at a constant velocity. The acceleration of the motor is zero and hence there is no effect on the
motor inertia J [48]. The torque coefficient was 0.0256 Nm/A form the previously discussed rotor stall test.
The test was conducted with no-load conditions and therefore the external torque is zero. The DOB output
given as,

B
T
T f
dis 
 (17)

201
A PID based DOB incorporating a tuned velocity controller was used to obtain a better velocity
response with this constant velocity test [47]. The corresponding experimental parameter values were shown
in Table 2. The test was conducted with different constant velocities ranging from +5000rpm to -5000rpm.
Figure 5(b) and (c) show the velocity response and the observer output (disturbance torque). In this test, as
shown in equation (18), the DOB output consists of friction components and the change of inertia effect of
the system 

J
 . This 

J
 effect exists only within the acceleration period.

 

 J
B
T
T f
dis 


 (18)
For the estimation of friction components, only the linear velocity region was considered, and
acceleration is zero during the period.
Table 2. Experimental parameters
Parameter Value Units
Motor Inertia (Jn) 13.5 g cm2
Torque Coefficient (Kt) 0.256 Nm/A
KP Constant: PID 0.01
KI Constant: PID 10-4
KD Constant: PID 0.006
Cut-off frequency of low pass
filter (Gdis)
0.003 Hz
(a) (b)
(c) (d)
Figure 5. (a) Torque response against current (b) Velocity response of the constant velocity test (c)
Disturbance observer output for different velocities (d) Measured friction torque
Observer output is averaged from 10 seconds to 30 seconds from Figure 5(b). Averaged observer
output against the corresponding velocity is redrawn in Figure 5(d), for clockwise and anti clockwise

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directions. The anti clockwise direction shows a higher friction for the given DC motor. Static friction Tf is
averaged for both directions and can be calculated as shown in Figure 5(d). However, Tf for each direction is
also calculable. The calculated average static friction value Tf is 0.0375Nm. The viscous friction coefficient B
was mathematically identified by using a standard curve fitting model from Figure 5(b), and estimated using
both the standard linear regression method and the method of evaluation [49], and expressed in (19).

 
 0002573
.
0

B (19)
The validity of these estimated friction components is proven in the friction compensation section 4 (B).
3.4. Estimation of motor inertia (J)
In (11), the inertia of the motor J subjected to variations is described. This variation is also
considered as a disturbance of the DC motor. Identification and compensation of the change of inertia
improve the DC motor robustness in operation. However, both identifying and compensating the inertia
variations are important tasks. There are no straightforward methods for this [16-21]. To overcome this
barrier, in this research, the authors propose a RTOB based inertia calculation and compensation technique.
Estimation of motor inertia estimated in three different ways: conventional acceleration, deceleration motion
test and novel Reverse Motion Acceleration test.
3.4.1. Acceleration motion test
In this test, the DC motor is attached with a planetary gearhead of ratio 246:1 brought to its rated
speed from initial zero speed. As shown in Figure 6(a), the acceleration of the motor was calculated by
dividing the rated speed to the time taken to reach its rated speed.
on
Accelerati
on
Accelerati
J
Inertia
Motor
Torque
)
(  (kg-m2
) (20)
Direct calculation of the acceleration torque is not possible with the conventional method. In this
experiment, the authors used RTOB as the torque sensor. The acceleration torque is the output of the torque
sensor. The calculated motor inertia value from this test using equation (20) is 16.7 g cm2
.
3.4.2. Deceleration Motion Test
The power supply to the motor is disconnected when the motor is running at its rated speed. The
motor speed then reduces to zero from its steady speed as shown in Figure 6(b), the dynamic torque equation
for this test becomes (21).
0


 
 

 B
T
J f (21)
The time domain solution obtained for equation (21) is expressed as below with a calculable constant A.


)
/
( J
B
f
Ae
B
T
t 


 (22)
The calculated motor inertia in the deceleration motion test is 14.2 g cm2
.
3.4.3. Reverse motion acceleration test
This is a novel method introduced by the authors to estimate the motor inertia. Here, RTOB is used
as a torque sensor. The calculated values for motor parameters values (Kt, Tf and B) were used for this test. A
DOB based robust velocity controller was used to achieve accurate velocity responses. The test was
conducted by reversing the motor direction suddenly whereas it was running at steady state speed. The
controller governs the immediate change of the direction as shown in Figure 6(c), the motor acceleration to
the opposite direction starts at t1 and ends at t2. At t2, the motor approaches a steady state speed in the
opposite direction. This direction variation results in a variation of torque, and from these variations the
motor inertia is directly estimated.

203
The RTOB output of Reverse motion acceleration test dis
T
ˆ consists of only the change of motor
inertia. The known disturbance components were eliminated in the inner loop of the RTOB as explained in
Figure 2(d).


J
Tdis 

ˆ (23)
From (8), dis
T
ˆ in (23) is expressed as


)
(
ˆ
n
dis J
J
T 
 (24)
(a) (b)
(c) (d)
Figure 4. (a) Velocity & acceleration response of acceleration motion test (b) Velocity response of
deceleration motion test (c) Velocity response of reverse motion acceleration test (d) Inertia response of
reverse motion acceleration test
By integrating (24) for the time interval t1 to t2, the above expression can be rewritten as follows:
 


2
1
)]
(
)
(
)[
(
ˆ
1
2
t
t
n
dis t
t
J
J
dt
T 
 
 (25)
Motor inertia J can be calculated from the right hand side known parameters of (26).




2
1
ˆ
)]
(
)
(
[
1
1
2
t
t
dis
n dt
T
t
t
J
J

 

(26)
From (26) and Figure 6(d) the calculated motor inertia is 19.1 g cm2
.
4. EXPERIMENTS AND RESULTS
A novel approach, RTOB based friction compensation model is introduced in this research to
evaluate the estimated frictional and inertail values. The block diagram of the proposed system is shown in
Figure 7. In order to achieve the accurate inertial value, this research derived the innovative (26). The

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204
significance of this equation is that it compensates for (24) value between that of the manufacturer and
actual inertia.
Figure 5. RTOB based friction compensation model
4.1. Stability Analysis
Friction sometimes causes reduced tracking performance in control systems when it is
uncompensated. This section analyzes the stability of the system when the friction is compensated. The
simplified transfer function (27) between the input Tdis and output is derived from Figure 7. The
experimental values used for the MATLAB simulations are listed in Table 3. The stability of the system is
analyzed using root locus plot for (27) shown in Figure 8. The transfer function gain K is changed from 1 to
10000, resulting in stable characteristics of the system. This illustrates that the friction compensated system is
stable. The effects of the parameter change were analyzed for the friction compensated system to measure the
stability [50].
))
(
)
(
)(
(
)
(
)
))(
(
(
2
2
2
I
d
p
dis
t
tn
dis
f
dis
tn
t
I
d
p
dis
tn
dis
f
dis K
K
s
sK
BG
K
K
G
s
Js
B
T
G
s
sK
K
K
K
s
sK
G
s
YK
G
T
T 












(27)
Where, Y is the current sensor output gain.
The system parameters J, B and Tf were assumed to be changed by with respect to their nominal
values. The subscript n is used to denote the nominal values.
J
J
J n 

 (28)
B
B
B n 

 (29)
f
fn
f T
T
T 

 (30)
The system frequency response is analyzed using bode plot tool in MATLAB to identify the effect
of parameter change. Figure 8 (a) & (b) shows the root locus plot and bode plot of inertia change respectively
and arrows indicate that the responses vary with J
 . When J
 element increases, the conjugate roots move
along imaginary axes, but the system remains stable. The effect of J
 is negligible for low frequencies and
is significant for higher frequencies (practical frequencies) [33]. Therefore, the estimation of an accurate J is
important for a stable system.
In Figure 8 (c) & (d), there is no substantial effect on stability and frequency responses when
changing B
 element. It is evident that the effect is significant only for low frequencies. Figure 8 (e) and (f)
show the responses corresponding to f
T
 element. The analysis of the effect of parameter change validates
that selecting the correct J and f
T values are vital for a stable system, and hence the friction compensated
system’s stability depends on them.

205
(a) (b)
(c) (d)
(e) (f)
Figure 6. (a) The effect of changing J (b) Frequency characteristics (change of J) (c) The effect of changing B
(d) Frequency characteristics (change of B) (e) The effect of changing Tf (f) Frequency characteristics
(change of Tf)

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Table 3. Experimental parameters for stability analysis
Parameter Symbol Value Units
Nominal Motor inertia n
J 13.5 g cm2
Actual Motor inertia J 13.5 g cm2
Nominal Torque
coefficient tn
K 0.0256 Nm/A
Actual Torque
coefficient t
K 0.0256 Nm/A
Proportional constant p
K 0.001 -
Integral constant i
K 0.0001 -
Derivative constant d
K 0.00001 -
Cut-off frequency of
low pass filter dis
G 1.00 - 200.0 Hz
Viscous friction
coefficient B 0.0002573 -
Static friction f
T 0.0375 Nm
Current feedback gain Y 0.01 Hz
4.2. Practical Results
Initially, in the experiment, one-DOF motion control test was carried out for Figure 7. The external
torque was commanded by applying a constant torque input signal as a disturbance signal Tdis for 5 seconds
and the module was rotated without the friction compensation. The rotor rotates for 5 seconds and then stops.
The velocity response of these rotations, reference torque applied, and disturbance torque as RTOB output is
shown in Figure 9 (a), (b) and (c). In ideal systems the RTOB output must be zero if the commanded torque
Tcmd is zero and in real world systems this can be achieved only with accurate system parameters and friction
components. In the proposed system model, the system parameters and friction components were estimated
as discussed in previous sections.
For the torque response of the system, it is eveident from Figure 9 (d) that the disturbance torque
variation of the system is almost zero when the friction is compensated. This response proves that the
proposed method performs competently when the estimated values are close to actual system parameters.
Friction compensation was tested with three different motor inertia values, which were calculated in three
distinct experiments as estimated in section 3. The authors proposed reverse motion acceleration test is
conducted to find the accurate motor inertia. The result of this test is significantly different from the
conventional test results. In this paper, friction compensation is represented in the form of a velocity response
when a constant external torque is applied to the system externally by applying constant torque input signal
as disturbance signal Tdis as shown in Figure 10 (a).
The velocity response graphs for the same external torque with different inertia values are shown in
Figure 10 (b)-(d). Three cases were analyzed using the estimated inertia values with respect to estimated
frictional values. A velocity response in Figure 10 (d) shows the robust velocity response compared to the
previous results in Figure 10 (b) and (c). It is evident from Figure 10 that the friction compensation model
showed the outstanding performance when the motor inertia is 19.1 g cm2
. This value is different from the
manufacturer’s given value of 13.5 g cm2
. The manufacturer provided value did not yield the desired system
response for the small DC motor used in this research. These tests were carried out assuming the system is
linear. For the next phase, authors will extend this research towards MU-LapaRobot (Minimally Invasive
Surgical Robot) robust control [51]. The system response can be further improved by introducing nonlinear
control techniques, especially adaptive fuzzy hierarchical sliding mode control for a class of MIMO
nonlinear time-delay systems with input saturation.

207
(a) (b)
(c) (d)
Figure 7. (a) Velocity response without friction compensation (b) Input torque externally commanded (c)
RTOB response without friction compensation (d) RTOB response when friction compensated with
estimated value
(a) (b)

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208
(c) (d)
Figure 8. (a) Input torque externally commanded (b) Velocity response when friction compensated with
J=16.7 g cm2
(c) Velocity response when friction compensated with J=14.2 g cm2
(d) Velocity response when
friction compensated with J=19.1 g cm2
5. CONCLUSION
In this paper, we proposed a novel friction compensation method and motor inertia estimation
method to be used specially for small DC motors. Throughout this research, Sensorless torque sensors are
used; where DOB is used as the disturbance torque sensor, and RTOB as the external torque sensor. The
torque coefficient calculated in the rotor stall test is 0.256 Nm/A. The friction components are estimated by
conducting the DOB based constant velocity test. The estimated static friction is 0.0375Nm.and viscous
friction coefficient is 0.0002573. The motor was inertia calculated using three tests; acceleration motion test,
deceleration motion test and reverse motion acceleration test. Three different inertia values resulted from
these tests and they are separately used for the three friction compensation cases. Friction compensation tests
are carried out using the estimated system parameters and these three inertia values are tested with the
friction compensator. The proposed method of estimating the motor inertia shows better results. The validity
of the proposed friction compensation method and the effect of parameters were verified experimentally.
ACKNOWLEDGEMENTS
Authors would like to express their gratitude to Health Systems Research Institute of Thailand
(HSRI), Grant No. 57-025, Dr.A.M.Harsha S Abeykoon, University of Moratuwa, Sri Lanka for his kind
Analytical and Technical support, and also Sakol Nakdhamabhorn, Korn Borvorntanajanya, Chawaphol
Direkwatana, Syed Saqib Hussain Shah and BART LAB Researchers for their kind support.
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