Lab 6 – Characterization of DC Motors
Updated Sp 2015, ADH
6.1 Introduction
In the earlier experiment, you designed and implemented the switch mode control and no
load measurement of DC-motor along with the current and speed measurement. In this
experiment, characterization of a DC-motor will be done, which will be helpful in designing
the closed loop control of DC-motor (a topic of future course – EMET 410).
6.2 Open loop control of DC-motor with load
We will use the same Simulink model used in the earlier experiment (to do the no load testing
of DC-motor). To save time, you will download this file, with updates, from Angel.
 Create a new folder Exp06 on your jump drive.
 Start Matlab and change the directory path to Exp06.
 Download (from Angel) the Simulink file EXP06.mdl and save it to your new folder.
 Open Simulink and EXP06.mdl.
To this model, appropriate blocks for controlling the active load (a DC-generator whose
electromagnetic torque will be varied) have already been added.
6.2.1 Adding a DC-load (LOAD) to the DC-motor (MOTOR)
To determine the DC-motor steady state characteristics, a second DC-motor will be axially
coupled to the motor under test (MUT). The second motor will be open-loop voltage
controlled, similar to the MUT.
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
The terminals of the load (DC-motor) should be connected to PHASE A2 and
PHASE B2 terminals on the power board. Set the Bus Voltage, Vd = 36 Volts on the
power supply. Connect a BNC cable for current measurement between CURA2 and
DSPACE interface connection ADCH6.
Connect the MUT (2nd DC motor) as in previous labs (including current measurement
connections to ADCH5 from CURA1)
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Fig. 6.1 Real-time Simulink model for motor and load control
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Ensure (or verify) a firm mechanical coupling between the motors.
Note that a second set of voltage-control blocks have been added in the Simulink
model and the respective duty-cycles have been added to the 2 and 3 inputs of
DS1104SL_DSP_PWM.
The load current (CURR. A2) is available in the Simulink model current measurement
blocks and through DS1104ADC_C6. The motor (MUT) current is available as in
previous labs.
Make sure the model looks similar to the one in Fig. 6.1 and is saved to your Exp06
folder.
Be sure to set Vd (36) and Ts (.0001) as global variables in Matlab.
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6.2.2 Creating the Control Desk Interface
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Build (CTRL+B) the Simulink model.
Once the real-time model is successfully built, open Control Desk.
Using the File menu, select "New" and create a Project +New Experiment (name it
something like lab6) and save it in the same working root as the real-time Simulink
model (Browse to the appropriate folder on your jump drive). Name the experiment
(something like exp 6-1). Select DS1104 R&D Controller Board for the platform.
Select the variable file (with .sdf file extension) that your Simulink code built (E.g. For
Simulink model named exp6.mdl, the variable file will be exp6.sdf). Select Finish.
At the new layout, drag two Slider Gain controls and two Plotters.
Drag and drop the V_motor and V_load variables to the Slider gains. Also add
Numeric Input blocks with the same variables. TIP: right click on the Input blocks and
change the Increment value to tenths of a unit for more precise control.
Assign one plotter to display I a and I L currents (Im and IL in Fig. 6.1--It may be easiest
to grab these signals from the output of their respective gain blocks) and one
plotter to display the speed ω m.
In order to record the numerical values of currents and speed, add three Displays to
the layout and assign them the speed and current variables. The control desk layout
should look similar to Fig. 6.2.
6.3 Steady-state characteristics of dc-motor drives
In this experiment, you will derive the characteristics of a DC-motor, using the second motor
as load. For a constant V_motor voltage, the load is varied using V_load. The MOTOR current
and speed are recorded in a table. A set of measurements is obtained for different supply
voltages. The characteristics will be drawn using Matlab. I.e. we will use plots in Matlab that
represent the characteristics.
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Fig. 6.2 Control-desk layout
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6.3.1 Theoretical background
The steady-state mechanical characteristics of a DC-motor are the dependency between the
electromagnetic torque (N-m) and the electrical speed (rad/s). Since the dependency is linear,
the characteristics will be straight lines for the entire voltage range 0 - V rated and is
independent of the load. The motor equations reflect this linearity:
(1)
Vmotor  RaIa  ke
(2)
Ta  kt Ia
From equation (1), one can obtain the steady-state motor characteristic:

Ra
Vmotor
    ke I a  ke  mI a  n
where m  
(3)
V
Ra
and n  motor .
ke

ke
The steady-state model for the load can be approximated with a friction-type model, where
the torque is proportional to the speed, and a constant friction torque is always present:

Ta  TL  B  Tfriction
(4)
where all terms in the right hand side are load related. For our setup, where the load is a
voltage controlled DC-machine, the load torque TL is, in fact, the electromagnetic torque

developed by the second DC-motor. The procedure to determine the parameter for the
steady-state model uses the current, voltage and speed measurements to obtain a linear
approximation for both equation (3) and (4). Once the slope and the interception point are
found, the parameters can be easily calculated.
6.3.2 Steady-state parameters determination
According to the theoretical description from section 6.3.1, the motors will be driven in
several steady-state operating points.
Estimation of ke :
 At the rated armature voltage supplying the MOTOR, control the LOAD
such that the MOTOR current becomes zero ( Ia = 0); measure the speed (ω rad/s).
See the next bullet for instructions. Substituting zero for Ia, equation (1) becomes:
V
ke  motor
(5)
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
Before doing performing this step, be sure to read the next bullet item first! To perform
the previous step, increase the V_motor slider gain to 35 V. Now adjust V_load voltage
 decrease the MOTOR current Im (same as Ia) until it
such that the active torque will
becomes zero.
IMPORTANT: With coupled motor shafts, we have to be careful of adjusting the
voltages in tandem. Otherwise, we will get faults (overcurrent). If Vload=0, then there
is equivalently a short circuit across the motor terminals (closed switch); this is a
heavy load! To keep currents low, slide Vmotor toward 35 V incrementally while
simultaneously moving Vload toward -35 V. Move each slider just a few volts at a time
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and watch the currents as you do this to keep them below 5A.
Record the values for speed, at Im = 0 (and V_motor = 35 V) and calculate ke as per
equation (5).
Drawing the torque-speed characteristics:
 Maintain the MOTOR voltage at constant levels {35; 21; 10; 3 V}. That is, use 35V,
THEN 21, etc. For each setting, adjust the LOAD voltage reference such that the
MOTOR current takes the following values at each voltage: {0; 1.0; 2.0; 3.0; 4.0; 5.0 A}.
Be sure to use the incremental adjustments described in the above important
note, and watch that current does not exceed about 5A!
 Record the speed (ωm), the LOAD current (IL) and LOAD voltage (V_load)
required to obtain the specified MOTOR currents. All current measurements will be
multiplied with ke to obtain the corresponding torque values as per equation (2).
 Record the measured data in TABLE 6.1.
 Draw the MOTOR and LOAD characteristics using the data acquired during the
measurement process. The bullet on the next page will provide guidance.
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Table 6.1: Steady-state Experimental Data
35
35
35
35
35
35
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For each of the 4 motor voltages, find the slope (m) and intercept (n) by plotting in
MATLAB:
o The slope and the intercept of the linearized characteristic could be determined by
plotting and finding the best fit (see previous lab, where you did the same thing for a
different data set). Do this for both the MOTOR and the LOAD (speed vs current).
Place speed on the y-axis and current on the x-axis. (use your judgment for how to
best organize and present these plots for the deliverables)
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Determine Ra and ke : Using the slope (m) and intercept (n) for each of the four plots (with
motor voltages 3,10,21,and 35), the machine parameters can be determined using the
following equations (based on eq. 3).
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ke 
Vmotor
n
Due to measurement errors, etc. you will likely get different value of ke for each voltage setting. To
average the results:

ke = average(ke values for each voltage setting)
Also, from Eq. 3, we can use the slope (m) to get the armature resistance. Again, use the average
value of the resistances obtained for each of the 4 voltage settings.
Ra  kem
Calculate values for Ra and ke by averaging the data in TABLE 6.2

Table 6.2 Calculation of Electrical
Steady State Parameters
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Determination of the friction model parameters
For determining the friction parameters, the MOTOR will be run under no-load conditions as done
in the previous experiment. Since the MOTOR has to overcome only friction ( TL =0 ), the
electromagnetic torque ( T m  k e I a ) will follow the linear friction model (see equation (4)) in
steady-state. Fill in the TABLE 6.3 using the motor voltage values indicated below. For these tests,
the load generator current should be zero so that TL =0 (you can either adjust load current to zero,
or simply disconnect
 the generator terminal). Linearize the dependency of Ta(ω) by determining
the coefficients (m, n) depicted in equation (4) (Use the same procedure as for drawing the torque
speed characteristics earlier). Think carefully about which variable should be plotted on which
axis.
• Determine B and Tfriction : Using equation (4), the friction parameters will be
B = m; Tfriction = n; Fill in the Table 6.4 provided.
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Table 6.3 Steady State Friction Model Characteristic
Ia
Ke I a
20
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Table 6.4 Calculation of Mechanical Steady State Parameters
6.4 Dynamics of DC-motor
In this section the dynamic characteristics of the DC-motor will be derived. The dynamics can be
divided into electrical and mechanical dynamics. By independently studying both transients, two
motor parameters can be determined: armature inductance (La) and moment of inertia (J). For
this section the same Simulink model and dSPACE layout as in earlier section will be used. To
analyze the dynamics of a DC-motor some theoretical background will be presented, then using
the already determined steady-state parameters, the experiment steps will be described. The
setup consists of two DC-motors, axially coupled and supplied from two converters. One motor is
current controlled, such that it will act as an active load. This motor will be named as LOAD. The
second motor (MUT) is open-loop voltage controlled. This motor will be named as MOTOR. In this
experiment two parameters need to be determined: La - armature inductance [H] and J -moment
of inertia [ kg −m2 ].
6.4.1 Dynamic Model Characteristics
There are several ways to determine the inductance and the inertia. All methods involve the
dynamic analysis of the machines in transient operation. The dynamic equations of a dc-motor
are:
Vmotor  Ra I a  ke   La

dI a
dt
T m  T L T friction  B  J
d
dt
(6)
(7)
The system of two first order differential equations shows that the DC-motor is a second order
system. The two statevariables (differentiated quantities) --- armature current (Ia) and angular
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speed(ω ) --- are not independent. Therefore, the inductance (La) and the moment of inertia (J)
would both contribute to the variation of each of the two state variables. It is convenient to
“isolate” the state variables described in equations (6) and (7), thus only a first-order differential
equation has to be solved for each variable. Two sets of experiments are then required to
determine La and J, while keeping the speed and the current zero respectively.
Inductance Determination:
To estimate the armature inductance, the motor must be held a standstill (ω = 0). If the rotor is
blocked and a step voltage is then applied to the armature terminals, the current increases
exponentially in time and equation (6) becomes:
Solving equation (8) for current,

where  a 
La
.
Ra
Vmotor  Ra I a  La
dia
dt
(8)
t

Vmotor 
a
Ia 
1 e
Ra 





(9)

The current increases exponentially to the final value equal to
Vmotor
. The slope of this
Ra
 exponential curve (obtained by taking the derivative with respect to time of eq. 9), measured at t
= 0, is dependent on the value of inductance La as given below:
dI a
dt

t 0
Vmotor Ra 0 Vmotor

e 
Ra L a
La
(10)
A graphical determination of the slope, at a given voltage, would lead to the determination of the
motor inductance La .That is, the initial slope of the current versus time curve, where a step
change in the voltage is applied must be equal to the applied motor voltage divided by the
inductance.
Determination of Inertia
 d

The motor is brought to a no-load steady-state J
 0 speed ω0 , by disconnecting the load
 dt

(TL =0) . At the point just prior to disconnecting the load ( t  0 ),
Tm T friction  B0

where Tm  kt I a (0 ) and Ia (0 )  MOTOR current
 at steady-state no-load speed (just before
disconnecting the load).



 make electrical torque (Tm) equal to zero in the mechanical dynamics equation (7), a
To

complete shutdown of the motor supply is required. At (t = 0− ) the whole system is shutdown.
This implies that the electromagnetic torques in the MOTOR (Tm ) becomes zero. The dynamic
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equation will be:
0  Tfriction  B  J
d
dt
(11)
At (t = 0+ ) i.e. just after shutting down the system, equation (11) can be written as

Thus,

0  Tfriction  B  J

d
dt

(12)

kt Ia 0
 Tfriction  B 0
J

d 
d 
 
 
 dt t0 
 dt t0 
(13)
d 
By knowing 0 , 
Ia (0 ) , and graphically determining the slope   of the speed curve at (t =
 dt t0 
+
0 ) , the system inertia J can be calculated using equation (13).

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6.4.2 Simulink model for dynamic parameter determination
The model presented in section 6.3 will be used for this section. However, one additional block
has to be inserted, such that a step command in voltage is possible (that is, the power supply
shutdown required is feasible via control desk).
Both, electrical and mechanical dynamic parameters require either a positive (from 0 to Vmotor) or
a negative (from 0 to Vmotor ) step change in supply voltage. The Vmotor = 0 condition implies also
that the motors have no armature current (Ia=0). To achieve open-circuit of the motors armature
winding (Ia=0) while Va = 0, the converters need to be shutdown. This operation is possible by
using the SHUTDOWN signal on the drives board. The SHUTDOWN signals are controlled by the
digital I/O channels 11 and 12. When IO11/12 is 0 (OFF state) the switching signals are inhibited
and the switches are opened. Setting IO11/12 to 1 (ON state) and resetting (IO10) resumes the
regular operation of the converters.
The IO10/11/12 digital channels will be added as slave bit out blocks for our model from the
slave library (of the RTI 1104 Simulink Library Browser). In addition two constant blocks and two
Boolean conversion blocks should be added with SD1 and SD2 using the same signal. The model
should like the one shown in Fig. 6.3.
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Fig. 6.3 Simulink model for dynamic parameter characterization
6.4.3 dSPACE Experiment Layout for dynamic model determination
 A new experiment will be created in the same directory containing the Step1_04.mdl
file.
 Copy the Layout from the previous experiment and rename it.
 Add 2 CheckButtons controls to the Layout.
 Link all variables from the model with the controls in the Layout, as in earlier section.
 Link Reset and SD to the CheckButtons control (drag them onto the layout).
The layout of the experiment is shown in Fig. 6.4.
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Fig. 6.4 Control Desk Layout for Dynamic Parameter Characterization
6.4.4 Dynamical parameters determination
Inductance determination
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Using the blocking device, block the rotors firmly.
Uncheck and then recheck the SD control. This button works as a switch to connect and
disconnect the machines from the power supply.
Set the V_motor to a low value (around 3 V) and uncheck Reset to give a step input
voltage. The current should increase exponentially (as shown in Fig. 6.6) and reach a
constant steady state value.
To save the current response, open View/Control bars/Capture Settings Window. Drag
the Reset signal from the Tool Window into the gray box situated below the Level Delay set boxes. Check the box called On/Off, check the edge direction, and set the
Level value to 0.5.
Now, you will observe that every time you uncheck the Reset control in the layout, the
plot area will display the current and it will stop when it reaches the maximum
measurement time. Set the Length to 0.2 (see Fig.6.5). This will set the data capture
time as 0.2s which is large enough to observe the whole transient process in current.
Check and uncheck SD and Reset to make some measurements. The current waveform
will look similar to the one shown in Fig. 6.6. After you are satisfied with the data
displayed go to the Capture Settings Window and press the SAVE button. The dialog
box will ask you to name the .mat file that will contain the graphic data in all plot areas.
Plot the .mat file by using MATLAB command “plot” (refer to help by typing help plot
in the command window, if required); determine the inductance value as explained in
section 6.4.1.
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Inertia determination
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In the Capture Settings Window two modifications must be made: Increase the display
length to 2 seconds and change the Trigger Signal to SD.
Check the SD control and increase the voltage on the MOTOR to 36 V. Make sure that
the LOAD terminals are disconnected from the Power-Electronics-Drive-Board.
Record the speed ω0 and armature current Im = Ia (0 ) value at this operating point.
Uncheck the Shutdown button. This will initiate the display process and, after two
seconds, the speed plot will stop and a decreasing exponential curve will be obtained
(see Fig. 6.7).

Press again the SAVE button in the Capture Settings Window and store the data in
another .mat file. Plot the .mat file using MATLAB command “plot”. Calculate the value
of J as explained in section 6.4.1.
Fig. 6.5 Capture Settings
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Fig. 6.6 Current Waveform (Note: Y-axis is current in amps, x-axis is time in seconds)
Fig 6.7 Speed Waveform (Note: y-axis is angular velocity in rad/s, x-axis is time in seconds)
6.5 Deliverables
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Each individual must submit the following:
• Complete and submit all the tables.
• Provide all the machine parameters which you obtained using the above procedures. Show your
calculations, and provide all evidence (data, plots, etc.) to support your calculations.
-If you did not gather data for the dynamic tests used to determining J or La, you need to
use the Figures 6.7 (assume V-motor = 36 volts) and Figure 6.8 to calculate these
parameters. Study the theory carefully to help you in solving for these two parameters;
Hint examine closely Equations 10 and 13. For Equation 13, data from your Table 6.4 may
be helpful.
• Provide all the graphs you obtained while finding the machine parameters. Use your judgment
for how to best organize and present the graphs.
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