Carnegie Mellon University
Department of Mechanical
24-352 Dynamic Systems and Control
Lab 4 - Motor
Part I. Introduction
In this lab, you will be measuring the
speed-dynamics of a DC motor. A schematic of the setup you will use is shown
below. You will measure the speed of the motor using a second, identical motor
connected to the first. The second motor acts as a generator, and is called a
tachometer. The tachometer's output is measured with the oscilloscope. The
signal to command the motor is produced by the function generator. Since the
function generator is not capable of powering the motor by itself, its signal
is first passed through an amplifier to boost the power of the signal.
The lab will consist of three sections:
- Identify Amplifier
- Relate output voltage of the amplifier to the
- Motor Step Response
- Look at the motor's step response and identify
the time constant and DC gain parameters.
- Motor Frequency Response
- Obtain the motor's response to sinusoidal inputs
of varying frequencies. Relate this to the step response.
- The amplifier is assumed to output a voltage which is
proportional to the input:
Vout = Ka * Vin
where Ka is the gain of the amplifier.
- Motor-Tach Model
- The motor and tach together is assumed to be a first
order system with a transfer function from voltage into the motor to voltage
out from the tach of the form:
|s + 1
where K is the DC (or steady-state)
Gain of the motor, obtained from the Final Value Theorem, and
is the Time Constant of the motor, obtained from the exponential form
of the step response.
Part II. Measurement
1. Identify Amplifier
Besides boosting the power of the signal from the function
generator, the amplifier multiplies the voltage by a constant. This part of
the lab involves identifying the value of this multiplicative constant. A
range of voltages will be inputted to the power supply, and the output will be
The amplifiers are not protected from improperly
connected power, so be sure that the power cables are connected properly
before turning on the power.
- Connect Power supply
The amplifier is powered with +/-20V from the dual power supply. This
requires three connections: +20V, GND, and -20V.
- Turn on power supply.
- Set the power supply tracking switch to Independent,
switch both sides to Volts.
- Set each side of the power supply to 20V by using
- Turn the supply off!
- Connect the negative terminal of the left side of
the power supply to the positive terminal of the right side with a
jumper wire (see picture), creating the GND signal from either of the
- Attach a BNC/banana adapter to the left side of
the supply, with the GND tab to the right. This gives +20V
- Attach a banana cable to the negative terminal of
the right side. This gives -20V.
- Connect Power to Amplifier
- Attach a BNC/banana adapter to the +V and GND
terminals of the amplifier with the GND tab to the right (See
- Connect this BNC/banana adapter to the BNC/banana
adapter on the power supply with a BNC cable.
- Plug the banana cable from the -20V on the power
supply to the -V terminal of the amplifier.
- Connect Signal Cables to Amplifier
- Attach a jumper wire to the GND terminal of the
amplifier. All devices must be grounded to the same level.
- Attach jumper wires to the IN and OUT terminals
of the amplifier.
- Attach the black clip of two BNC/pigtail clips to
the ground wire.
- Attach one red clip of the BNC/pigtail clips to
each of the jumpers on the IN and OUT terminals.
- Connect Function Generator and Multimeter
- Attach the IN BNC/pigtail-clip cable from the
amplifier to the output of the function generator.
- Attach the OUT BNC/pigtail-clip cable from the
amplifier to the multimeter using a BNC/banana adapter with the
GND tab to the bottom.
- Set The Multimeter and Function Generator
- Turn on the function generator and multimeter.
- Hold any of the function shape buttons on the
function generator for several seconds to set it to DC Voltage mode
(in order to apply constant voltages to the amplifier). Set the
voltage to zero.
- Set the multimeter to measure DC Voltage.
- Verify Power Connections
- Check the +20V, GND, and -20V connections to
verify they are correct. Do not turn on the power supply unless these
connections are correct, or damage to the amplifier will occur (trust
me - it WILL happen, including possible explosions).
- Turn on the power supply.
- Take Data
2. Motor Step Response
- Disconnect Multimeter
- Turn off power supply and multimeter.
- Disconnect and remove the BNC/pigtail cable which
connects the multimeter to the amplifier.
- Connect source and oscilloscope.
- Disconnect the BNC cable from output of function
generator and connect it to a BNC T-connector and then connect this
T-connector to the output of function generator.
- Connect the other side of the T-connector to
Channel 1 of the oscilloscope using a BNC cable.
- Connect a Co-ax/pigtail cable to Channel 2 of the
- Connect motor and tach to amplifier and oscilloscope.
- Attach an alligator clip to the GND terminal on
- Attach the other end of the alligator clip to the
black lead from the motor and to the red lead from the tach.
- Attach the red lead from the motor to the OUT
terminal of the amplifier using a clip cable.
- Clip the black lead from Channel 2 on the
oscilloscope to the ground alligator clip near the motor. Clip the
corresponding red lead to the black lead coming from the tach.
- The entire setup is shown below:
- Set the function generator and oscilloscope.
- Select a square wave with peak-to-peak amplitude
100mV (this is actually 200mV.) and frequency 1Hz.
- Set the offset to 120mV (this is really a 240mV
offset). This offset is to ensure that the motor is always moving. If
the motor is allowed to stop, static friction will affect the
response. The step response will occur between a low speed and a high
speed, rather than from a stop.
- Setup oscilloscope.
Note: Do NOT use autoscale. It won't pick up low frequency signals
- Set the voltage scale for Channel 1 (the
input from the fnc. gen.) to 100mV/div.
- Set the time scale to 20ms/div.
- Set the horizontal delay to 80ms (this moves
the step to the left of the screen so that the entire step
response can be seen.)
- Set trigger by Channel 1, trigger mode
to Normal and set the trigger level at ~240mV
- Set the vertical position of trace 1 so the
step trace appears on the upper half of the screen.
- Set the voltage scale for Channel 2 (the tach
output) to 1V/div.
- Set the vertical offset so the origin of
trace 2 is near the bottom of the screen.
- Turn on power. The motor should spin, and you
should get a response similar to that shown below.
- The response will be very noisy, to get better
picture you can use Average display option of the scope with
256 Number of averages.
- Use the cursors to measure the difference in
voltage levels between the initial and final values of the step
response (Channel 2), record this value. Make sure that measurement
cursor's source is set to Channel 2.
- Print the resulting screen.
- After printing, switch back to Normal
display rather than Average display.
3. Motor Frequency Response
First, you will apply sinusoidal inputs to the motor,
adjusting the frequency manually, and measuring the output amplitude and
- Set the function generator and oscilloscope.
- Set the function generator to sinusoidal
- Set the frequency to 0.2Hz
- Set the time scale on the oscilloscope so that
one or two full periods of the sinusoid are on the screen.
- Use the cursors to measure the output amplitude.
- Use the time cursors to measure the phase shift
between a valley of the input sinusoid and the closest valley of the
output sinusoid. (Do not forget to set 360 degrees on the
oscilloscope for each frequency.)
- Output will appear as shown below and print
- Take the data to fill out the the following table
(just amplitude and delay), adjusting the input frequency and the time
scale on the oscilloscope as appropriate. Print the responses at 2Hz and
Did you print system responses at 0.2Hz, 2Hz and 20
This time, you will use the spectrum analyzer to
automatically apply a range of sinusoidal inputs to the motor. The magnitude
and phase will be computed automatically.
- Connect the spectrum analyzer.
- Turn off the power supply, oscilloscope, and
function generator, and turn on the spectrum analyzer.
- Disconnect the T-connector from output of
function generator and connect it directly to the Source of
- Detach the BNC cable from the Channel 1 of the
oscilloscope and attach it to Channel 1 of the spectrum analyzer. This
allows the spectrum analyzer to read its own output.
- Detach the BNC cable from the Channel 2 of the
oscilloscope and attach it to Channel 2 of the spectrum analyzer.
- Run automated frequency analysis.
- Press INST MODE button on MEASUREMENT
- Select SWEPT SINE by pressing F4.
- Press FREQ button on MEASUREMENT
- Press F3 to select START frequency
and set it to 0.2Hz.
- Press F4 to select STOP frequency
and set it to 100Hz.
- Set SWEEP to LIN (F6), UP (F7) and AUTO
- Select RESOLUTION SETUP by pressing F10.
- Set AUTO RESOLUTION to ON by pressing F4.
- Select MINIMUM RESOLUTION by pressing F6,
then set it to 101 pts/sweep (F1).
- Set MAX % CHANGE to 2.5% (F5).
- Press SOURCE button on MEASUREMENT
- Press F2 to set LEVEL, then enter
- Press SCALE button on DISPLAY menu.
- Set AUTOSCALE to ON by pressing F1.
- Turn on power supply.
- Press yellow START button on MEASUREMENT
Motor will begin to oscillate back and forth. The frequency will
gradually increase (it spends more time at lower frequencies). The
whole process takes several minutes. Wait until the analysis is
- Press DISP FORMAT button on DISPLAY
- Select BODE DIAGRAM by pressing F9.
When the analysis is complete, the spectrum analyzer's screen will
look like the following picture.
- Print this screen. To print, press PLOT/PRINT
button on SYSTEM menu, then press F10 for MORE SETUP
and F2 to select DEVICE IS PRNT, then F10 for RETURN.
Finally press F1 to START PLOT/PRNT.
- Repeat the analysis between frequencies of 1Hz
and 1000Hz. Without changing any other variable in the spectrum
Press FREQ button on MEASUREMENT menu.
Press F3 to select START frequency and set it to 1Hz.
Press F4 to select STOP frequency and set it to 1000Hz.
Press yellow START button.
Press DISP FORMAT button on DISPLAY menu.
Select BODE DIAGRAM by pressing F9.
- Print this screen too.
- Finally, turn off the power supply first and then
the spectrum analyzer.
Part III. Lab Report
Your lab write-up should include the following information.
Be sure to justify all of your comments. Present your answers in the order of
- Amplifier Identification
- Plot the output of the amplifier vs. the input.
Draw a straight line representing only the linear portion of
- From both the slope of this line and from an
average of the data points, calculate the amplifier's gain Ka.
- Describe and explain the behavior at large
positive and negative voltages. How might this affect a control system
using this amplifier?
- Motor step response
- Even though the motor was moving between two non-zero
speeds, we can shift the datum so that the low speed input and output are
both considered zero, and the difference between the low and high
speeds is the size of the response.
- For the given transfer function of the motor with a
step input of the magnitude used in lab, calculate the following in terms
of K, Ka and .
Remember that the input voltage gets multiplied by the amplifier gain
before it is applied to the motor. (Note: In part a, all of your
answers should be in terms of system constants, no numerical values are
accepted here, you will calculate numerical values in part b)
- The final value of the output.
- The time it takes to reach 95% of the final
- The initial slope of the graph after the step.
- The location where the initial slope line
intersects the final value line.
- Using these results, compute K from the final
value, and from both the
95% settling time and the initial slope/final value intersection. How do
the two estimates of
compare? Which do you think is more accurate, and why?
- Write the transfer function of the
motor-plus-amplifier system substituting in the numbers you obtained. Also
write down its Amplitude and Phase Angle expressions in terms of
(Recall Lab#2 Calculations).
- Motor frequency response
- Compute the remaining entries of the data table.
Magnitude in dB is 20 times the log (base 10) of (output
- Generate a pair of Bode plots for this system.
- Using the manual data, plot Magnitude (dB)
vs. frequency (Hz), and Phase Angle (degree) vs. frequency (Hz),
with frequency on a log scale.
- Also prepare the same plots, that is
Magnitude (dB) vs. frequency (Hz) and Phase Angle (degree) vs.
frequency (Hz) using the transfer function Amplitude and Phase
expressions obtained in the Question 2c. Frequency span should
be from 0.2 Hz to 100Hz and frequency axis should be on a log
scale. Keep in mind,
is in radians/sec and you need to substitute 2*Pi*f
in place of
before plotting where f is frequency in Hz.
- Compare the frequency response plots
obtained from numerical plotting of transfer function, from the
manual experiment, and from the automated experiment both
qualitatively and quantitatively. How closely do they match? Are
there any extra features in the experimental plots? If so,
explain why there may be extra features.
- Describe what is happening at higher
frequencies. How might these high-frequency artifacts effect a
- Estimate the motor's DC gain, K, from the
experimental bode plots (do this for both manual and automatic plots.)
- The magnitude (dB) at low frequencies is
equal to 20*log(K*Ka). from this, calculate K.
- Compare this to the step response result.
- Estimate the time constant,
from the experimental bode plots. (Do this for both manual and
- Fit a -20dB/decade sloped line to the
downward-sloping portion of the magnitude plot. Mark a
horizontal line at the magnitude where the low frequency
magnitude lies. The frequency where these two lines cross is
called the break frequency. What is this frequency?
- Compute the time constant as the reciprocal
of the break frequency (in rad/s).
- How does this compare to the step response