Contents

Lab 6 - Procedure

In this lab, you will measure the response of a DC motor to an applied voltage. Using this information, you will determine:

  1. The time constant \(\tau\) and the steady-state gain \(k\)

  2. Mechanical system parameters \(J\) and \(b\)

  3. The motor generator constant \(K_g\)

Task 0 - Getting Started

  1. Read through the information in the Background and Resources section to get an idea of the approach to making the measurements listed above.

  2. Have a look at your lab bench. There is a motor assembly with a button and a switch. Read the operating instructions on the handout to learn how to turn the motor on and select/deselect the in-line resistor. The resistance of the motor windings and the resistance of the external resistor are both marked on your motor assembly. The applied voltage from the power supply is 12 Volts.

  3. The output shaft of your motor is connected to a small DC motor that serves as a tachometer. The voltage it outputs will be recorded by LabView. There is no internal conversion to RPM or rad/s - it will be slightly different for each station, and you will determine the conversion coefficient.

Task 1 - Recording Data

  1. Plug in the motor and verify that the green light is lit.

  2. After starting the data collection VI, toggle the switch to “MW Only” and press and hold the start button. This will run the motor without the extra in-line resistor. When you see the output on the VI reach a steady state, release the button and switch to stop the motor, then save the data.

  3. Repeat step two with the extra resistor (i.e., the switch held in the other direction). Save the data.

  4. The nominal steady-state speed of the motor with an applied voltage of 12V is 2400RPM. Use this to determine the conversion coefficient of your tachometer.

NOTE: These data collection runs should only take a few seconds, and there should be no need to repeat them. Please avoid extended or repeated tests, as they are hard on the control circuitry.

Task 2 - Determining the Time Constant

NOTE: We are determining the time constant of the motor, i.e. without the in-line resistor. Use your “MW Only” Data for this task.

  1. By inspection, find the 63.2% response point and the corresponding estimate of the time constant.

  2. Using the central difference method, take the derivative of a point on your response curve. Use it to construct a tangent line to the curve, then find the intersection with the steady state response to estimate the time constant.

  3. Transform your data into the semi-log format shown in Figure 5 of the Background and Resources section, then perform a linear regression to estimate the time constant.

Task 3 - Determining System Parameters

  1. The Blocked Rotor Test to determine \(K_t\) has the potential to harm the motor and assembly. The manufacturer supplied torque constant is 0.0461 N-m/A. Use this value for the remaining calculations.

  2. As described in the Free Speed Test in the Background and Resources section, use your two recorded steady state \(\Omega\) values (corresponding to two different known resistances) and known system parameters \(K_t\) and \(e_i\) to determine the motor voltage constant \(K_g\) and damping coefficient \(b\). Don’t forget that you are adding the external resistor in series with the motor windings - the total resistance is their sum.

  3. Use your calculated time constant to determine the system rotational inetia \(J\), as described in the Transient Test. For this task, use the time constant calculated from linear regression. It is the most likely to be accurate.

Your Report

  • How reliable might the three methods for determining the time constant be, and why?

  • Is there anything you can say about the suitability of using a small DC motor as a tachometer?

  • How might measurement uncertainties present themselves in the calculation of system parameters?

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Lab 6 - Background and Resources