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DCM - Introduction

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DCM - Introduction

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The diagram of the virtual laboratory test bench is shown in figure 1. 



Figure 1: Virtual Test Bench of the DCM Drive

The major elements in the test bench are:

  • The DC motor under test (MUT) with adjustable field voltage Vf.
  • A DC machine with adjustable field voltage and a variable load.
  • Command switches (K1) and (K2) allow connecting the MUT and DCM to the single-phase two-level inverter, while (K3) allows the connection (disconnection) of the variable load to (from) DCM.
  • A mechanical shaft coupling the DCM and MUT.
  • A protection system composed of fuses connected in series with the windings from both machines.
  • A single-phase two-level inverter as armature voltage to either the MUT or the DCM.

The different modules covered in this laboratory are discussed next.

DC Motor Parameters Identification

Determination of the back-emf Constant Ke

The back electromotive force (emf) that is generated in a DC motor is directly proportional to the speed ω of the motor [2].


To determine Ke, the MUT is driven at a certain speed by the DC machine running as a motor (see figure 2).
During this test, switch (K1) is closed, and the MUT armature voltage is open.


Figure 2: Open Circuit Test for the Determination of Ke

By varying the applied voltage, different switching pulses are generated to drive the inverter, which then applies different voltages to the DCM armature.
This leads to the DCM driving the MUT at different speeds that are recorded, while at the same time measuring the open circuit armature voltage Va.
The student can then plot the speeds and the measured Va values and find the slope of this line.
This slope corresponds to Ke as seen from equation (1) above.

Determination of the Armature Resistance Ra


To estimate the MUT armature resistance, a varying voltage is applied to its armature via the inverter.
The MUT drives the DCM running as a generator which is connected or not to a variable load resistance (see figure 3).
The armature voltage of the MUT can be written as:

Under the assumption of steady state, equation (2) is rewritten as:



Figure 3: Steady State Test for the Determination of Ra


From (3), Ra is obtained as:

With Ke known, one can determine Ra by measuring the armature voltage Va and current Ia of the MUT, and its speed ω (referred to as N in figure 3) for a random operating point.
For a more accurate result, the student can test many different operating points, and then take the average result as an estimation of the armature resistance.

Determination of the Armature Inductance La


Figure 4: Blocked Rotor Test for the Determination of La

To estimate the armature inductance, the motor under test must be held in a standstill, ω = 0 (locked rotor), as shown in figure 4.
Therefore, equation (2) above simplifies to:

At time  (right after a step voltage is applied), the instantaneous current is  so we can say from the voltage equation in (5) that:

From (6), one can determine the value of La by measuring Va during the block rotor test and the slope of the armature current right after the step voltage is applied.
It is important to mention that during the blocked rotor test, the applied voltage should not exceed 10% of the MUT nominal voltage.

Note

The parameters Ke, Ra, and La are defined as the electrical parameters of the brushed-DC motor under test.

Determination of the Friction Torque Tf and Friction Coefficient B


Figure 5: Identification of Friction Parameters

The equation for the electrical torque in steady state (constant speed) can be approximated by a friction-type model [2, 3]:

where  is the MUT electromagnetic torque [Nm] and  is the load torque applied on the shaft [Nm].
In a no-load test, there is no load torque  and the expression simplifies to:

To simulate the no-load test, the MUT drives the DCM running as a generator with switch K3 open (see figure 5 above).
The student can apply different voltage values and record the speed and armature current of the MUT.
With the armature current known, the electromagnetic torque can be calculated as:

Finally, plot the values of speed (x-axis) vs Te and find the slope of the line and the y-intercept.
The slope corresponds to the friction coefficient B, and the y-intercept to the friction torque Tf

Determination of the Moment of Inertia J


Figure 6: Identification of the Moment of Inertia

The equation for the electrical torque in transient state (acceleration or deceleration) is as follows: