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After completing the following series of exercises, the student will understand the characterization and control of a DC motor.
Real-time simulation results are shown in the laboratory panel.

Parameters Identification

back-emf Constant

Open the model with the default settings.
Gradually apply a field voltage of 460 V for the DC machine.
Gradually apply a field voltage of 460 V for the DC motor under test.
Connect K1 as shown in figure 10.

Figure 10: DC Machine Armature Connected to the Inverter

Apply different voltage values and fill out table 10 below.

Applied Voltage (V)	Armature voltage of MUT (V)	Speed of MUT (rpm)
0
46
92
138
184
230
276
322
368
414
460

Table 10: Speed and Voltage Values for the Determination of Back-emf Constant

Plot the speed values (x-axis) vs armature voltage (y-axis).
- Show your graph.
- Find the slope of the plotted line.
- What is the value of the back-emf constant in V/rpm?
- What is the value of the back-emf constant in V.s/rad?
- Compare the estimated back-emf constant with the value of table 6.
  What do you observe?

Note

1 rad/s = 9.5493 rpm.

Armature Resistance

Disconnect K1, then set the applied voltage to 0 V.
Connect K2 as shown in figure 11.

Figure 11: MUT Armature Connected to the Inverter

Connect K3 as shown in figure 12.

Figure 12: Connection of the DCM Resistive Load

Apply different voltage values and fill out table 11.
The values of V_a, I_a, and N can be directly taken from the displays under the Tab “Parameters Identification Ra”.

Applied Voltage (V)	V_a (A)	I_a (A)	N (rpm)	R_a (Ω)
0
46
92
138
184
230
276
322
368
400
460

Table 11: Speed, Voltage, and Current Values for the Determination of R_a

From table 11, compute the average value of the armature resistance.
Compare the obtained result for armature resistance with the value of table 6.
How accurate is the estimation?
Explain.
Hint: Use equation (4) with the back-emf constant [V/rpm] found earlier to compute R_a.

Armature Inductance

Disconnect K3, then slowly decrease the applied voltage to 0 V.
Block the rotor as shown in figure 13.

Figure 13: Activation of Blocked Rotor Test

Apply a voltage source value of 40 V.
- What is the armature voltage of the DC machine?
- What is the armature voltage of the MUT?
Observe the waveform under the “Parameters Identification L_a” tab.
Use the zoom-in capability of the graph and the available cursors to measure two values of armature current at the linear part of the graph.
- Compute L_a using equation (6).
- Compare the obtained result of armature inductance to the value of table 6.
- How accurate is the estimation?
  Explain.

Friction Parameters

Decrease the applied voltage to 0 V.
Deactivate the “Block Rotor” button. If a fault occurs, click on the “Reset” button.
Go to the “Parameters Identification Tf & B” tab.
Fill out table 12 by varying the applied voltage.

Applied Voltage (V)	Speed (rad/s)	I_a (A)	T_em (N.m)
0
46
92
138
184
230
276
322
368
400
460

Table 12: Speed, Current, and Torque Values for Friction Parameters’ Determination

Based on table 12, plot the speed (x-axis) vs T_em (y-axis).
- Show your graph.
- Find the slope of the line and the y-intercept.
- What is the value of the friction torque T_f?
- What is the value of the friction coefficient B?
- Compare the obtained T_f to the total friction of table 9.
Based on table 12, plot the current (x-axis) vs T_em (y-axis).
- Show your graph.
- What is the slope of the line?
- Explain your result based on equation (9).

Moment of Inertia

Slowly decrease the applied voltage to 0 V.
Go to the “Parameters Identification J” tab.
Apply a voltage source value of 100 V.
- What is the armature current of the MUT?
  This value corresponds to i_a(0^-) in equation (12).
Increase the Trigger Level to 340 rpm, then activate the Apply Trigger for Acquisition, as presented in figure 14 below.

Figure 14: Activation of Trigger Level

Disconnect K2 and observe the waveform of the decreasing speed.
Use the zoom-in capability of the graph and the available cursors to measure two speed values at the very beginning of the decreasing slope.
- Compute the slope of the line.
- Compute the inertia using equation (12).
- Compare the obtained inertia with the value of table 9.

Current control

Deactivate the Apply Trigger for Acquisition
Bring the voltage source to 0 V, then connect K2.
Activate K3, the “Connect Load” button. Then reduce the load resistance to 15 ohms.
Go to “Current Control” tab and activate the current control as shown in figure 15.

Figure 15: Activation of Current Control

Apply a reference current of 10 A.
- Does the measured current follow the reference?
- What is the speed of the DC motor under test?
- What is the armature voltage of the MUT?
Increase the reference current to 15 A.
- Does the measured current follow the reference?
- What is the speed of the DC motor under test?
- What is the armature voltage of the MUT?
Increase the reference current to 20 A.
- Does the measured current follow the reference?
- What is the speed of the DC motor under test?
- What is the armature voltage of the MUT?
Increase the reference current to 25 A.
- Does the measured current follow the reference?
- What is the speed of the DC motor under test?
- What is the armature voltage of the MUT?
- How do the speed and voltage of the MUT change with increase of reference current?
  Explain your observation.

Note

Show results to support your answers regarding the measured current following the reference.

Speed control

Decrease the reference current to 0 A.
Go to the “Speed Control” tab and activate the speed control as shown in figure 16.

Figure 16: Activation of Speed Control

Apply a reference speed of 200 rpm.
- Does the measured speed follow the reference?
- Does the measured current follow the reference?
- What is the armature voltage of the MUT?
- What is the armature voltage of the DCM?
Increase the reference speed to 400 rpm.
- Does the measured speed follow the reference?
- Does the measured current follow the reference?
- What is the armature voltage of the MUT?
- What is the armature voltage of the DCM?
Increase the reference speed to 600 rpm.
- Does the measured speed follow the reference?
- Does the measured current follow the reference?
- What is the armature voltage of the MUT?
- What is the armature voltage of the DCM?
Increase the reference speed to 800 rpm.
- Does the measured speed follow the reference?
- Does the measured current follow the reference?
- What is the armature voltage of the MUT?
- What is the armature voltage of the DCM?
Increase the reference speed to 1000 rpm.
- Does the measured speed follow the reference?
- Does the measured current follow the reference?
- What is the armature voltage of the MUT?
- What is the armature voltage of the DCM?
- How do the armature voltages of the MUT and the DCM change with increase of reference speed? Explain your observation.

Note

Show results to support your answers regarding the measured current and speed values following the references.

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