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Parameters Identification of a Permanent Magnet DC Motor
Conference Paper · February 2010
DOI: 10.2316/P.2010.675-085
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Mohammed Said Salah
Mohamed Abdelati
University College of Applied Sciences
Istanbul Atlas University
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PARAMETERS IDENTIFICATION OF A PERMANENT MAGNET
DC MOTOR
Eng. Mohammed Salah
University College of Applied Sciences
Gaza, Palestine
email: mssalah@ucas.edu.ps
ABSTRACT
In this paper, driver circuits and parameters identification
of a permanent magnet dc motor are addressed. To identify the parameters of the motor, an experimental measurement of armature voltage, armature current and rotor speed
are performed using the NIDAQ USB-6008 data acquisition module. DAQ toolbox and Simulink in MATLAB are
used to acquire the test signals and perform analysis based
on the nonlinear least square method. The extracted motor parameters produced consistent simulation results with
experimental data. The proposed approach proved to be
simple, fast and accurate.
KEY WORDS
Parameters identification, NI DAQ, MATLAB, DC Motor.
1 Introduction
Direct current (DC) motors have been widely used in
many industrial applications such as electric vehicles, steel
rolling mills, electric cranes, and robotic manipulators due
to precise, wide, simple, and continuous control characteristics. Dc motors are preferred over ac motors because
of their lower cost and ease of controller implementation.
This comes as a result of their mathematical model which is
characterized by simplicity compared to other motor types.
Dynamic model identification has been a major topic of interest in control engineering, motivated by the new achievements in control systems theory and requirements of new
industrial and robotics applications.
System identification of dc motors is a topic of great
importance in control problems. Accurate mathematical
models and their parameters are essential when designing
controllers because they allow the designer to predict the
closed loop behavior of the plant. Errors in parameter values can lead to poor control and instability. Therefore, accuracy and adequacy of parameters identification are too
major modeling issues that always have to be dealt with.
Manufacturers usually run identification procedure for their
new products. On the other hand, researchers may apply
some identification experiments either to validate manufacture supplied parameters or to specify missing information.
Moreover, parameters might be subject to some time variations. In these cases, a mathematical model that is accurate
at the time of the manufacturing may not be accurate at a
Prof. Dr. Mohammed Abdelati
The Islamic University of Gaza
Gaza, Palestine
email: muhammet@iugaza.edu
later time. Also, a mathematical model is never a complete description of a given system; this is because a model
that represents a system on a specific operating point may
not represent the system as well as over different operating points. On broader sense, system identification is often
the only means of obtaining mathematical models of most
physical systems; this is because most systems are usually
so complex that, unlike dc motors, there is no easy way to
derive their models based on the physical laws.
There exists many methods and techniques for estimating unknown parameters. The conventional methods of
determining the parameters generally require a separate test
for each parameter. Such a procedure is time consuming
and leads to inaccuracy. Furthermore, the method cannot
be automated. To overcome some of the above difficulties, algorithms and techniques applied to acquiring signals
such as voltage response, current response and speed response to estimate parameters altogether. These methods
are divided into two categories: offline estimation and online estimation. Offline techniques use specific test inputs,
measure the corresponding output signals and then try to
establish the relation between them. Online techniques use
additional modules such as observers and Kalman filters to
recursively estimate parameters. Neural networks can be
used in either offline or online approaches.
Pasek’s method is one of the earliest techniques used
in parameters identification of dc motors [1, 2]. Pasek’s
method determines a high-performance dc motor’s mode
model type and all the model parameters based only on the
current response of the machine to a step input of armature voltage along with the steady state speed. But Pasek’s
method can introduce some instrumentation problems. The
technique requires an accurate reading of two points of
transient waveform, which can be difficult to do in presense of noise. Also Pasek’s method measures a few points
on the current time response curve making it very sensitive
to current commutation noise, which renders the method
inaccurate for low cost dc motors widely used in our industry. An alternative method to Pasek’s method is the frequency response method for determining the parameters of
high performance dc motors. This method has the following features :
1. All significant motor parameters are determined at
once in a dynamic and loaded condition.
Table 1. Specification of experimental dc motor.
Rated power
Rated speed
Armature rated voltage
Armature rated current
Field voltage
Field current
Magnetic break
200 W
1500 rpm
110 V
3A
2.5 V
1.3 A
24 V
2 System Architecture
Figure 1. General view of the experimental DC Motor
2. No nonelectrical measurements are required (such as
speed in Pasek’s method).
3. Results are averaged out to minimize errors caused by
noise.
The experimental platform is implemented as illustrated
in Figure 1. It is composed of the following components
shown in Figure 2:
1. Separately excited DC motor
2. Power supply unit
3. Field driver circuit
4. Sophisticated instrumentation is not necessary.
5. The approach is readily adaptable to automatic testing.
4. Armature driver circuit
5. NI-DAQ USB-6008
Frequency response method determines the parameters of high performance dc motors by treating a second order motor model as an electrical impedance (RLC circuit),
and by tuning the values of RLC circuit elements to match
the response of dc motor and by some relations the parameters of dc motor are calculated [3]. This method uses an ac
signal with specific frequency about 1kHz. Unfortunately,
this method is not suitable to the power drivers used in our
experimental platform. Sensitivity to noise is another reason that discouraged us to utilized this method.
The pseudo inverse technique is a method capable of
identifying an equivalent discrete transfer function of simple systems like motor, thermal system, mass damper systems etc with no zeros (only poles). This method assumes
a single input single output system and unable to find the
dc motor parameters and doesn’t fit our objective [4].
Nonlinear least square method is a general approach
in identification seeks to define an objective function that
would reach its minimum. The physical system to be investigated is described in terms of parameters, and then,
the objective function is minimized with respect to the parameters by an iterative procedure. At the minimum of the
objective function, the values of the parameters describe
the real structure of the physical system [5].
We will begin with system architecture illustration in
section 2, followed by a review of the dc motor modeling
in section 3. In section 4, computer interface is presented.
The identification procedure and experimental results are
shown in section 5. Conclusion is given finally in sections
6.
The DC motor is the backbone of our system. It is
used as a permanent magnet DC motor by applying a constant voltage to its field terminals. This motor has the nominal characteristics shown in Table 1.
The power supply unit consists of a traditional components which supply all necessary voltage levels. Separate voltage levels are required for the field driver unit and
for the armature driver unit. The first unit requires voltage supplies of +20VDC, +12VDC and +5VDC. On the
other hand, the second unit requires +110VDC, +24VDC
and +12VDC voltage levels.
A Pulse width modulation (PWM) signal at a frequency of 250Hz is used to adjust the magnitude of excitation voltage applied on the field terminals [6]. Reversing
the rotation direction of the motor is easily done by reversing the filed excitation. Therefore an additional relay is employed to facilitate user control of motor direction. Voltage
and current sensing components are added in the armature
driver circuit. Moreover, a 100nf capacitor is connected
across the motor armature in order to reduce electromagnetic interference (EMI). Both filed and armature driver circuits are featured by the ability to be controlled locally or
remotely via the data acquisition card. Two digital panel
meters are used to monitor the current and voltage of the
armature winding and a third one is used to monitor field
current.
NIDAQ USB-6008 from national instruments is used
for computer interface [7]. This is an affordable module
and will suited for our experiments.
20 VDC
12 VDC
5 VDC
220 VAC
- La +
- Ra +
+
ia
Field control
Field
Driver Unit
+
Direction
control
Power
Supply
if
+
V
E=Ke
Vf
110 VDC
24 VDC
12 VDC
Armature
Driver Unit
Armature
control
-
-
Motor
Tf
B
J
I
V
USB
NI DAQ
USB-6008
T=Kt ia
Optical encoder
Figure 3. Complete equivalent model for dc motor
Figure 2. Architecture of the system
Table 2. DC motor parameters.
3 DC Motor Model
We studied the modeling of dc motors for control applications [8], and we found that there are three different mathematical models of an armature controlled dc motor. These
models are:
1. Precise nonlinear model.
2. Piecewise linear model.
3. Second-order linear model.
A mathematical model for a physical device must often reflect a compromise. It must not attempt to mirror
the real device in such great detail that the model becomes
complex, on the other hand it should not be so simplified
that predictions and explanations based on it are either trivial or far from reality.
We preferred the second order linear model to other
models due to its simplicity. The main difficulty with the
nonlinear models is the requirement of numerical solution
and the use of this model in those applications of adaptive
and optimal control which require a digital computer. The
second-order linear model assumes the following for ease
of use:
1. The static friction is negligible and the frictional
torque can be considered directly proportional to angular velocity.
2. The brush voltage drop is negligible.
3. Armature reaction can be neglected.
4. The resistance and the inductance of the armature can
be regarded as constants.
Applying these assumptions, the block diagram of the
dc motor used in this study may be illustrated as shown in
Figure 3.
Consequently, the dynamics of the dc motor are expressed by the following equations:
V =R i +L
a a
di
+K !
dt
a
a
e
(1)
Parameter Definition
Ke
Back-EMF constant
K
t
Torque Constant
R
a
Terminal Resistance
L
a
Armature Inductance
J
B
Moment of inertia of
the rotor
Viscous (Damping)
Friction
Ki =J
t a
Comment
Dominate factor in
determining motor’s
steady state speed for
a given voltage
Determines motor’s
required current for a
given torque output
Determines
how
much power will
be dissipated in the
motor for a given
current level
Determines how fast
current to the motor
can be turned on
A measure of an object’s resistance to
changes in its rotation rate
A measure of dynamic friction
d!
+ B! + T
dt
f
(2)
Where V , ia , w, Tf are respectively, the the armature
voltage, the armature current, rotor angular speed and the
load torque. The specifications of the dc motor parameters
needed for identification are detailed in Table 2.
Transforming the system equations to Laplace domain the motor block diagram is concluded as shown in
Figure 4.
4 Computer Interface
In this section, our aim is to show how the system can be
interfaced to NI DAQ to acquire test signals and the method
is used for the identification process of dc motor parame-
Tf
V
+
1
Las+Ra
-
Ia
Kt
Tg
+
-
Table 3. NI DAQ inputs and outputs.
1
Js+B
1
s
Ke
Figure 4. The block diagram of dc motor
+110VDC
R10
120k
C1
D1
100nF
High side
voltage sensing
C2
R12
5.1k
Gate Driver
Circuit
Channel
Analog
0
(AI0)
Analog
1
(AI1)
Analog
2
(AI2)
Analog
0
(AO0)
Digital pin
P0.0
Digital pin
P0.1
Mode
Differential
input
Differential
input
Differential
input
Differential
output
Digital output
Digital output
Purpose
measuring voltage at
motor terminals
measuring
current
flowing in motor
count # of pluses
from optical encoder
controlling speed of
motor
controlling direction
of motor
controlling break of
motor
470nF
Q1
R13
IRF840 120k
R8
Low side
voltage sensing
15
Sensing Current
R9
0.2
C4
100nF
R14
5.1k
C3
470nF
Figure 5. Sensing circuit of the system
The specifications for connections to NI DAQ is summarized in Table 3.
In MATLAB, the Data Acquisition Toolbox (DAT) is
used to communicate with the DAQ module and to acquire
data from the sensing channels and sending necessary control signals. This toolbox is integrated with MATLAB and
well documented by Mathworks [10].
5 The Identification procedure and experimental results
ters. The voltage of the motor’s armature is measured using voltage dividers at both of the motor terminals to get
the difference between them. The capacitors are used as
low-pass filters in order to reject high frequency noise and
to deliver the average value of applied PWM signal.
Selecting 5.1K and 125K for the voltage divider
yield to a ratio of 0.0408 between the sensing terminals and
the armature voltage. Consequently, the differential voltage
at the DAQ input terminals will have a maximum value of
0:0408 110 = 4:488 and this is within the maximum
allowable input voltage (5V). The resultant resolution of
1105
the armature voltage is equal to 4:488
212 = 30mV and
this is more than enough for the precision level required in
our experiments [9].
The current flow in the motor is sensed as a voltage
signal across a (0:2 ) resistance connected in series with
the motor armature. The sensing circuit is shown in Figure 5.
Speed of dc motor is measured using optical encoder
(GP1A30R) which is mounted in the shaft of the motor.
The disk of optical encoder has 120 slits. The collected
pulses from the optical encoder at specific time window
of 10ms at analog input of DAQ is used to calculate the
rotational speed of dc motor in rpm using the relation in
equ. ( 3)
60
#
of ounting pulses
Speed(rpm) =
(3)
10ms #ofslits
The nonlinear least-square method, which is built in
Simulink, is utilized to find motor parameters. The basis of
this method is to approximate the model by a linear one and
to refine the parameters by successive iterations. Simulink
Parameter Estimation consists of a number of well-defined
steps:
1. Set up the problem.
2. Specify which model parameters to estimate.
3. Import and prepare the experimental data for parameter estimation (or preprocess).
4. View the estimation progress.
5. Validate the estimation results based on plots of measured versus. simulated data and residuals.
A user interface which is illustrated in Figure 6 is designed to carry all necessary user interactions such as acquiring data, parameters identification and parameters validation. Moreover, it allows user control of speed and direction of the motor.
The resultant parameters are summarized in Table 4
for three identification trials. It is noticeable that Ke and
Kt are equal (in metric (SI) units) as justified in the literature [11].
Main
Parameters Identification of
a Permanent Magnet DC Motor
Armature voltage
Parameters
Trajectories of Estimated Parameters
Armature current
B
Motor speed
J
Parameters Iden.
Ke
Validation
La
B
Acquiring Data
J
Kt
Ra
Speed control
0.02
0.01
0
0.1
0.05
Figure 6. User interface
0
2
1
0
2
1
0
1
0.5
0
20
10
0
Ke
Change Dir.
Kt
Stop motor
La
Start motor
Parameter Values
Exit
Table 4. Summary of parameter estimation results
1 case
st
B (Nms)
0.041202
2
J (kg:m )
0.057419
K (V=rad=s) 1.8350
K (N:m=A) 1.8350
L (H )
0.104190
R( )
3.04840
e
t
a
a
2
case 3rd case
0.043926 0.0428167
0.044042 0.03188
1.8074
1.8674
1.8074
1.8674
0.1044227 0.104305
3.04325
3.045653
Ra
Parameters
nd
0
5
10
15
20
25
30
35
40
45
50
Iterations
Figure 7. Trajectories of estimated parameters
The trajectories of estimated parameters versus number of iterations are illustrated in Figure 7.
As the parameter values improve, the simulation
curves gets closer to the experimental data curves. In order to validate the model, the speed and current of the motor are acquired and plotted for 10 sec’s. These curves are
compared to simulated ones in Figures 8 and 9.
Current response
10
Actual current response
Estimated current reponse
9
8
7
I (s)
s + 0:7176
=
V (s) 0:1042s2 + 3:123s + 60:83
a
W (s)
31:96
=
2
V (s) 0:1042s + 3:123s + 60:83
6
Amp
Using a MATLAB code, the transfer functions for
current to voltage and speed to voltage are derived and the
result is shown below:
5
4
3
(4)
2
1
0
(5)
6 Conclusion and future work
This paper has investigated the issues involved in applying
different methods in parameters identification of DC motor models. These issues have been considered both theoretically and experimentally. The experimental work was
0
2
4
6
8
10
sec
Figure 8. Current response for the actual and estimated
models
Speed response rpm
problem methodology ”. Turk J Elec Eng and Comp
Sci, vol. 17, No.2, 2009.
2000
Actual speed response
Estimated speed reponse
1800
[5] Adrian V. Bos, Parmaeter Estimation for Scientists
and Engineers, First Edition, Wiley, Inc., 2007.
1600
1400
[6] Muhammad H. Rashid, Power Electronics Handbook,
Second Edition, Academic press, Inc., 2007.
rpm
1200
1000
[7] NI
USB-6008,
National
Instruments
Corporation,
Inc.
URL:http://sine.ni.com/nips/cds/view/p/lang/en/nid/14604.
800
600
400
200
0
0
2
4
6
8
10
sec
Figure 9. Speed response for the actual and estimated models
performed on a DC motor with an optical encoder as a position feedback device. All necessary drivers and sensor circuits are implemented to constitute a compact experimental
platform. Computer interface is based on a low-cost data
acquisition module from National Instruments. A MATLAB program, based on the Simulink Parameter Estimation toolbox, is created to call the nonlinear least-square algorithm and estimate the motor parameters. The estimated
parameters are used to generate simulation curves for current and speed step responses. These curves are found to be
in agreement with actual curves within the precision level
of our experiment. In a future work we plan to build an educational platform that can be used in undergraduate control
labs. The model is expected to carry identification for various DC type motors. Moreover students will be able to
experiment different control types, speed and position control of these motors.
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View publication stats
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