Download EE 4343 Lab#1 – Part 1

EE 4343 Lab#1 – Part 1
Identification of Static Motor Module Parameters
The goal of this lab is to determine values for the static parameters in the linear model of the DC motor
module (Figure 1). Static parameters are those parameters in the model, which can be determined by
steady-state measurements. The parameters to be determined are
Gear Reduction
Armature Resistance
N
Ra
Potentiometer Constant
K pot
Tachometer Constant
K tach
Back EMF Constant
Kb
Torque Constant
Kt
Power Amplifier Gain
A
Brake Constant
Bj

 V 
rev 
 V 

rpm 

N

m
oz  in

,
 A
A 
N  m oz  in
,

rpm rpm 

j  0,1,2
We will also find it useful to express the braking constant in a dimensionless form, which is shown
below.
Dimensionless Brake Constant C j 
Ra B j
KtKb
j  0,1,2
In every instance in which we have to take measurements to determine the value of a static parameter, we
will determine the value as the slope of a line. Due to nonlinearities in the physical motor module, some
of the measured characteristics will exhibit saturation or a deadband. In these cases, the value we will use
for the parameter is the slope of the linear part of the characteristic. You should also determine the
saturation and deadband limits in case we wish to construct a more detailed model in the future.
Two LabVIEW VIs (Virtual Instruments) are used in this lab. The "Static Test" VI is used to collect all
data. The "Linear Fit Stored Data" VI is used to perform linear least-squares fits on the collected data.
You can print the front panel of the Linear Fit VI in order to get a hard copy of your data.
Procedure:
1. Gear Reduction: The gear reduction (motor shaft revs per load shaft rev) can be determined by
counting teeth on the gears. Fortunately, the manual for the motor module tells us that the gear
reduction is 9, i.e. the load shaft rotates one revolution for every nine revolutions of the motor shaft.
2. Back EMF Constant: Since the tachogenerator and the motor on our DC motor module are identical
(within manufacturing tolerances), we will assume that they have the same back EMF and torque
constants. The back EMF constant is the ratio of the back EMF voltage generated to the angular
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velocity of the motor. The back EMF voltage is more accessible on the tachogenerator, so we will
measure it there and assume that the motor back EMF constant is the same. Refer to Figures 2 and 3
when making connections to the DC motor module.
a) Connect the data acquisition systems analog ground to the motor control module ground. This
connection should be made any time the data acquisition system is used.
b) Connect the Command Potentiometer to the amplifier input (Vin) of the motor drive input..
Connect the enable line to ground, this is labeled ‘E’ with a over-bar.
c) Lift the tachogenerator connector slightly in order to gain access to the armature connection (see
Figure 2.) Use a wire clip to connect the non-inverting lead of Analog Input Channel 0 (labeled
ACH0) to the V+ side of the armature. Connect the inverting lead (labeled ACH1) to motor
module ground. Note: The tachogenerator connector connects the tachogenerator’s armature to
the main circuit board. ACHO and ACH1 are part of the data acquisition system. Turn off the
power when making this connection. Before turning the power on make sure that the wire clip is
not shorting the V+ and 0V pins.
d) The brake should be in the off position. Vary the Command Potentiometer voltage manually.
For each voltage, type the resulting load shaft rpm's displayed on the motor module' digital
tachometer into the LabVIEW data acquisition VI, then click on the "Take Measurement" switch
to measure the tachogenerator voltage.
The data acquisition VI will record the load shaft velocity you typed in along with the measured
tachogenerator voltage. Notice that you will have to provide the minus sign on the velocity when the
tachogenerator voltage is negative, since the digital tachometer displays only the magnitude of the
velocity.
Calculate the back EMF constant. When calculating the back EMF constant, remember that it is the ratio
of back EMF voltage to motor shaft velocity, but the slope of the best-fit line for the data you collected
has units back EMF Volts per load shaft rpm.
3. Torque Constant: The torque constant of a DC motor is identical to the back EMF constant when
they are expressed in the same units.
Determine the torque constant in both Newton-meters per Amp and ounce-inches per Amp by performing
unit conversions on the back EMF constant.
4. Power Amplifier Gain: To measure the power amplifier gain:
a) Connect Analog Output Channel 0 (labeled DACH0OUT) of the data acquisition system to the
amplifier input (Vin) of the motor drive input.
b) Use a wire clip to connect the non-inverting lead of Analog Input Channel 0 (ACH0) to the V+
side of the motors armature. You may need to lift the motor connector slightly in order to gain
access to the armature connection, but the motor must remain connected to the amplifier in order
to provide a load while you are measuring the amplifier gain. Note: The motor connector
connects the motor’s armature to the main circuit board. Turn off the power when making this
connection. Before turning the power on make sure that the wire clip is not shorting the V+ and
0V pins.
c) Connect the inverting lead of Analog Input Channel 0 (ACH7) to motor module ground.
d) Use the LabVIEW data acquisition VI to vary the amplifier input voltage and measure the
amplifier output voltage.
Calculate the power amplifier gain constant. The slope of the amplifier voltage transfer characteristic is
the amplifier gain. It should be positive.
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5. Armature Resistance: In order to properly measure the armature resistance of a DC motor, you
must lock the rotor, apply an armature voltage, and measure the armature current. A standard
Ohmmeter will not usually give a correct measurement because it does not use enough test current.
For the small DC motor on our motor module, however, the armature resistance measured by a
standard Ohmmeter has been found to be reliable. Remove the armature connector from the main
board for this step. The lab TA will give values to the students if no ohmmeters are available.
6. Tachometer Constant: The tachometer constant is simply the gain of an inverting operational
amplifier circuit. In order not to have minus signs running amok in our transfer functions, we will
extract the minus sign from the tachometer constant and place it instead on the block diagram.
Hence, our tachometer constant K tach will be positive.
a) To measure the tachometer constant, use a wire clip to connect Analog Output Channel 0
(DACH0OUT) to the V+ side of the tachogenerator’s armature. The tachogenerator connector
should be removed from the main circuit board.
b) Connect the non-inverting Analog Input (ACH0) to the output voltage of the tachogenerator
circuit on the motor module. Use the LabVIEW data acquisition VI to measure the voltage
transfer characteristic.
Calculate the tachometer constant. The slope of the characteristic is Ktach .
7. Brake Constant: We can determine the brake constant by applying a voltage to the amplifier input
and measuring the steady-state tachometer voltage. If we apply the final value theorem to the Laplace
transform of the tachometer voltage for a step input of magnitude Vin , we find that the steady-state
tachometer voltage versus amplifier input voltage characteristic predicted by our linear model is
Vtach ss 
AK tach
V ,
1 C j in
where C j is the dimensionless form of the brake constant. (If you are just now taking the controls
course, you probably won't be able to verify this fact for yourself for another couple of weeks. If you
have already completed the controls course, you should derive this result yourself.)
a) Connect Analog Output Channel 0 (DACH0OUT) of the data acquisition system to the input of
the power amplifier on the motor module.
b) Connect the non-inverting Analog Input Channel 0 (ACH0) to the tachogenerator circuit output
voltage. Use the LabVIEW data acquisition VI to measure the steady-state tachometer voltage
characteristic.
Calculate the dimensionless brake constant and the brake constant for the brake in the ‘off position’ (C 0)
and for the brake in position C1 . You do not need to calculate the brake constant for position C2.
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EE 4343 Lab #1 – Part 2
Identification of Effective Motor Inertia
The goal of this section is to determine the value of the effective motor inertia J in the linear model of
the DC motor module.
Two LabVIEW VIs (Virtual Instruments) are used in this lab. The "Step Response" VI is used to collect
all data. The "Analyze Stored Step Response" VI is used to identify the time constant of the step
response. You can print the front panel of the analysis VI in order to get a hard copy of your data.
Procedure:
The mechanical time constant of the motor module can be determined from either the tachometer or the
potentiometer step response. We will use the tachometer response because it has one less pole than the
potentiometer response. Measure the tachometer step response for a large (4V - 5V) step and a medium
(2V - 2.5V) step input with the brake in the off position, C0 and for position C1. Use the analysis VI to
calculate the final value and the time constant of each step response.
The tachometer voltage response to a step input is
Vtach (t)  K(1 e
 t/ 
)
where the final value and the time constant are given by
K
AVstep
K b (1 CB j )
,

m
1  CBj
.
Cv is a conversion constant, if Kb is expressed in terms of Radians and seconds Cv is not needed.  m is
the motor time constant and CB j is the dimensionless brake constant for the brake in position j . In terms
of the model parameters, they are given by
m 
JR a
,
K t K bC v
CB j 
R a Bj
.
KtKb
Values were determined in part 1 for all of the above parameters except the motor inertia J . The step
response analysis VI was used in this lab to determine values for K and  . Hence, you can calculate
values for  m and J for each step response. Note that these values should ideally be the same for each
step response you measure.
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Lab Report for Part 1:
Prepare a table of the motor model parameters you identified. Be sure to identify the motor module you
were working with. Give some thought as to how many of the figures in each parameter are significant.
As a rule, only the least significant digit you report should be substantially uncertain.



Include a copy of the graph from the linear regression VI for each parameter you measured.
Show your calculations for the cases when you had to derive the parameter value from the slope of
the graph.
Your report should also include values for the output saturation voltage of the power amplifier and for
the static friction torque on the motor shaft. Show how the static friction torque can be calculated
from the steady-state tachometer voltage characteristics you measured in part 8.
Lab Report for Part 2:
Your lab report should include a table showing Vstep , K ,  ,  m , and J for each step response you
measured.
 Compare the measured final value with the final value calculated from the parameter values you
identified in part 1 of this Lab . If they are significantly different, try to explain why.
 Average the values for  m and J from each trial (omitting any values that appear to be out of
line) to arrive at your best estimate for those parameters.
 Also estimate the uncertainty (standard error) of  m and J .

Now that you have identified all of the parameters in the model, draw a block diagram of the motor
model.
 Include the amplifier saturation and the static friction in your block diagram.
 Use the parameter symbols in the diagram and give the values of the parameters beside the
diagram.
 Be sure to identify the motor module you were working with.

Derive the following transfer functions from figure 1. m/Vin and Vtach/Vin
 Use the assumption that the model is a linear system (no deadband or static friction). These
transfer functions will be needed in later labs.
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TL
Vin
Va
A
+
1
Ra

TB
1
N
Bj
Tm -
Ia
Kt
-
+

1
J
m
1
s
m
1
s
m
1
N
L
Vpot
Kpot
Vtach
Kb
A - Power amplifier voltage gain
Bj - Brake constant (j= 0,1,2)
J - Total inertia of all moving parts
Kb - Back EMF constant of motor
Kpot - Potentiometer constant
Kt - Torque constant of motor
Ktach - Tachometer constant
N - Gear reduction ratio
Ra - Armature resistance of motor
-Ktach
Va - Applied motor armature voltage
Vpot - Potentiometer output voltage
Vtach - Tachometer output voltage
Ia - Motor armature current
m - Motor acceleration
m - Motor velocity
m - Motor position
L - Position of load shaft
Figure 1. Model of Analog DC motor control module
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TB - Braking torque
TL - External load torque
Tm - Motor torque
5V
0V
+12V
-12V
Motor Drive Input
Vin
E
0V
tachogenerator Output
V+
0V
Vout
0V
Armature
connections*
(Motor)
Potentiometer Output
Vout
OV
0V
V+
Gray Coded
Disk
Armature
connections *
(tachogenerator)
Slotted Disk
*Note that the armature connections are marked 0V and V+. On some motor modules the
polarity of the pins may be different. Verify the polarity of these pins during step 2 of
experiment 1.
Figure 2. Motor Module
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Description
ACHO non-inverting analog input
ACH1 inverting analog input.
ACH1 and ACHO are inputs to a differential amplifier that is part of the computer data
acquisition system. For this lab course ACH1 will always be connected to ground.
Measurement range is –5 to +5 volts.
DAC0OUT Analog output
Output range is –5 to +5 volts
AGND Analog ground.
AGND needs to be connected to the motor module ground whenever measurements are
taken or the analog output is used.
Figure 3. Data Acquisition Board I/O Wiring Block
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