Download SuPER Cart DC Motor Model and Ultra

SuPER Cart DC Motor Model
And
Ultra-Capacitor Addition
Joseph Witts
DC Motor Model
DC Motor Testing
In order to develop a model of the entire SuPER cart for simulation purposes, a model of the DC
motor had to be developed. The first task was to contact the manufacture in order to obtain as
much information about the motor as possible. A Dayton 6MK98 12V ¼ hp motor was
purchased from Grainger. However, Dayton is not really a company but just a name that
Grainger places on motors they sell. The real manufacture is Leeson, and the Leeson part
number for the motor is 108949. The following parameters were obtained from Leeson. This
information was obtained over the phone, because Leeson will not give written parameter values
to the public. These values were used as a starting point for developing a model that matches the
DC motor.
Motor Resistance: 0.048Ω @ 25o C
Back EMF Constant: 6.64 V/kRPM
Motor Torque Constant: 0.56 lbs-in/A
Rotational Inertia: 3.12 lb*in2
Armature Inductance: 0.33mH
Stall Torque: 99 in-lbs @ 179A
In order to properly model the DC motor, experimental data was required to determine how the
motor reacted during start up conditions under load. So testing was conducted to determine how
much current the DC motor was drawing during start up. This was tricky because there was no
available equipment that could plot the current as a function of time. Since the test setup
included only the battery and DC motor, the battery’s voltage drop during the start up of the
motor was used to determine how much current the battery was supplying to the motor. This
was accomplished by first determining the internal resistance of the battery, and then using the
change in voltage of the battery to calculate the current supplied. The assumption that the
battery’s internal resistance remains constant during motor start up was made, so the accuracy of
the calculated data depends on how much the battery’s resistance changes.
To determine the internal resistance of the battery the open circuit voltage of the battery was
measured, and a shunt was placed in series with the motor to determine the current flowing in the
circuit (Schematic 1).
Internal
Resistance
+
Battery
11.75 V
Battery
Terminal
Voltage
DC Motor
Shunt
_
Schematic 1: Circuit used to determine the battery’s internal resistance
Next the motor was turned on with a 1.6 lbs-in load. The steady state battery terminal voltage
and shunt voltage was measured and the battery’s internal resistance was calculated as follows.
Open circuit battery voltage = Voc = 11.75 V
Steady state battery terminal voltage = Vss = 10.50 V
Shunt voltage = 15.5 mV
30 A
A
= 0.6
Shunt Ratio =
50mV
mV
A ⎞
⎛
Shunt current = I = ⎜ 0.6
⎟(15.5mV ) = 9.3 A
mV ⎠
⎝
Voc − Vss 11.75V − 10.5V
=
= 0.129Ω
Battery’s Internal Resistance = RBat =
I
9.3 A
Now that the battery’s internal resistance is known. The current supplied by the battery can be
calculated using the following formula:
I (t ) =
Voc − V (t )
RBat
Where V(t) values were taken from the oscilloscope trace of Plot 1. The voltage values and
calculated current values during the motor’s starting in-rush can be seen in Data Table 1.
Plot 1: Battery terminal voltage trace with DC motor loaded at 8 in-lbs
Time
(ms)
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
Voltage
(V)
11.750
6.906
6.844
7.094
7.313
7.438
7.531
7.656
7.781
7.875
8.031
8.094
8.156
8.250
8.313
8.375
8.469
8.563
8.594
8.625
8.688
8.688
8.719
Current
(A)
0.00
37.55
38.03
36.09
34.40
33.43
32.71
31.74
30.77
30.04
28.83
28.34
27.86
27.13
26.64
26.16
25.43
24.71
24.47
24.22
23.74
23.74
23.50
Time
(ms)
230
240
250
260
270
280
290
300
310
320
330
340
350
360
370
380
390
400
420
450
500
550
1000
Voltage
(V)
8.781
8.813
8.844
8.875
8.906
8.938
8.938
8.969
9.000
9.000
9.031
9.031
9.063
9.063
9.063
9.094
9.094
9.094
9.125
9.156
9.188
9.188
9.188
Current
(A)
23.02
22.77
22.53
22.29
22.05
21.80
21.80
21.56
21.32
21.32
21.08
21.08
20.83
20.83
20.83
20.59
20.59
20.59
20.35
20.11
19.86
19.86
19.86
Data Table 1: Measured battery terminal voltage obtained from oscilloscope and calculated current
DC Motor Modeling
A PSpice model (Schematic 2) of a permanent magnet DC motor was found at
http://www.ecircuitcenter.com/Circuits/dc_motor_model/DCmotor_model.htm where the author
modeled the mechanical side of the motor with an electrical equivalent. Mechanical torque was
represented by voltage, speed by current, and drag by a resistor.
Schematic 2: DC motor model found online
After looking at the mechanical side of this model it became apparent that it can only be accurate
for one value of torque. Schematic 3 is a simplified version of the mechanical side of the model.
Once the motor reaches steady state operation the inertia can be ignored, so the speed is
determined by torque and viscous drag (R). If the value of R is determined from the steady state
values of Data Table 1, and the same value of R is used for rated torque the error is large as seen
below.
Inertia
1
2
R
Torque
Viscous
Drag
Schematic 3: Simplified mechanical side of the DC motor model
Using measured values from Data Table 1 to calculate R:
At steady state inertia does not need to be considered.
Torque = (Speed )(Viscous _ Drag )
R=
Torque
lb − in
8lb − in
=
= 7.944
Speed 1.007kRPM
kRPM
Using this value of R to calculate speed at rated torque:
Speed =
Torque
8.75lb − in
=
= 1.101kRPM
Viscous _ Drag 7.944 lb − in
kRPM
(
)
Error of the DC motor’s calculated speed using this value of R for rated speed:
⎛ 1.101 − 1.800 ⎞
Error = ⎜
⎟ × 100% = −38.8%
1.800
⎝
⎠
So this model of a DC motor is missing some component that can yield more reliable results. I
came across a document online for testing and modeling a DC motor at
http://www.mech.utah.edu/~me3200/labs/motorchar.pdf that showed there was another
component of drag that needs to be considered when modeling a motor. Coulomb drag, unlike
viscous drag, is not a function of speed and is constant. So the coulomb drag was modeled as a
DC voltage source opposing the applied torque voltage source of Schematic 4. To solve for the
appropriate value of viscous and coulomb drag two equations with two unknowns needed to be
developed. By using the steady state values in Data Table 1 and the motor’s rated values the two
equations were developed. Below are the calculations used to determine the values of coulomb
drag (X) and viscous drag (R) to be used in Schematic 4.
Coulomb Drag
Inertia
1
2
X
Torque
R
Viscous
Drag
Schematic 4: Variables used to determine both viscous and coulomb drag
At steady state inertia does not need to be considered.
Torque = X + (Speed )(R )
From measured values of Data Table 1
Torque = 8lb − in
Speed = 1.007kRPM
DC motor’s rated values
Torque = 8.75lb − in
Speed = 1.8kRPM
Equation 1
(8lb − in ) = X + (1.007 kRPM )(R )
Equation 2
(8.75lb − in ) = X + (1.8kRPM )(R )
Equation 3, solving for X in Equation 2
X = (8.75lb − in ) − (1.8kRPM )(R )
Substitute Equation 3 into Equation 1
(8lb − in ) = (8.75lb − in ) − (1.8kRPM )(R ) + (1.007kRPM )(R )
R=
(
0.75lb − in
= 0.9458 lb − in
kRPM
0.793kRPM
)
Substitute R into Equation 1 and solve for X
(8lb − in ) = X + (1.007kRPM )⎛⎜ 0.9458 lb − in ⎞⎟
X = 7.048lb − in
⎝
kRPM ⎠
Now that the values of viscous and coulomb drag have been determined, the rest of the DC
motor’s model parameters can be found. The DC motor model has an electrical side and a
mechanical side represented by electrical components. The electrical side uses an inductor to
represent the motor’s armature inductance, a resistor for the armature resistance, and a current
controlled voltage source to represent the back emf. The mechanical side uses a current
controlled voltage source to represent the applied torque, a DC source for coulomb drag, an
inductor for inertia, and a resistor for viscous drag. All of these parameters, except the two
drags, where solved by trial and error by comparing the simulations output to the data gathered
in Data Table 1. The manufactures supplied values were used for the initial motor parameters
and adjusted until the simulated current waveform Plot 5 represented the actual current
waveform Plot 4. See Schematic 5 for the final DC motor model circuit and parameters.
R_Battery
1
V_Battery
11.75V
L_Motor
0.7m
0.129
2
R_Motor
0.16
Back_EMF
Km=6.1
+
-
0
Torque
Kt=0.404
Coulomb_Drag
7.048
1
Inertia
1.2
+
-
0
0
2
Viscous_Drag
0.9458
Schematic 5: Final PSpice DC Motor Model
Notice that the magnitude of the armature inductance and resistance is noticeably greater than the
manufacturer’s values. This is because the testing setup measured the voltage across the
battery’s terminals not the direct input to the motor. So the resistance and inductance of the wire
going from the battery to the motor’s plug, and the 16 foot long cord for plugging in the motor,
are added to the armatures inductance and resistance. To improve this model the voltage needs
to be measured at the battery terminal and the input to the 16 foot long plug for the motor. This
way the wire connecting the battery to the plug can be modeled separately, so the final motor
model will represent only the motor and the 16 foot cord connected to the motor.
The following plots below can be used to tell how well the model reflects the actual data by
comparing the actual waveform of the current and voltage during the motor’s in-rush stage to the
simulation. As you can see by comparing Plot 2 and Plot 3 the voltage sags are reasonably
similar, and the current spike of Plot 4 and Plot 5 are also very similar. There is still room for
improving the model by not lumping the impedance of the wire going from the battery to the
plug and the 16 foot cord with the DC motor’s armature inductance and resistance. Since this is
just the initial prototype phase of the project, and the wiring will likely change, further
refinement of the model was not conducted. Plots 6 and 7 were included to show how the
modeled DC motor’s applied torque and speed change as a function of time, and how the steady
state values are very close to those in Data Table 1.
Battery Terminal Voltage During DC Motor In-Rush
Mechanical Load = 8 in-lbs
12
11
Voltage (V)
10
9
8
7
6
0
100
200
300
400
500
600
700
0.6s
0.7s
800
900
1000
Time (ms)
Plot 2: Plot of the actual battery terminal voltage from Data Table 1
12V
10V
8V
6V
0s
0.1s
V(L_Motor:1)
0.2s
0.3s
0.4s
0.5s
Time
Plot 3: Modeled DC motor’s battery terminal voltage
0.8s
0.9s
1.0s
DC Motor In-Rush Current
Mechanical Load = 8 in-lbs
40
35
30
Current (A)
25
20
15
10
5
0
0
100
200
300
400
500
600
700
0.6s
0.7s
800
900
1000
Time (ms)
Plot 4: Plot of the actual motor in-rush current from Data Table 1
40A
30A
20A
10A
0A
0s
0.1s
I(R_Battery)
0.2s
0.3s
0.4s
0.5s
Time
Plot 5: Modeled DC motor’s in-rush current draw
0.8s
0.9s
1.0s
16V
12V
8V
4V
0V
0s
0.1s
V(Torque:3)
0.2s
0.3s
0.4s
0.5s
0.6s
0.7s
0.8s
0.9s
1.0s
Time
Plot 6: Modeled DC motor’s torque in lb-in
1.0A
0.5A
0A
0s
0.1s
I(Coulomb_Drag)
0.2s
0.3s
0.4s
0.5s
0.6s
0.7s
0.8s
0.9s
1.0s
Time
Plot 7: Modeled DC motor’s speed in kRPM
Next the model was used to compare simulated values to actual data found on the wiki (files
dc_motor and dc_motor_solar) and the motor’s rated values. As you can see from Data Table 2
the simulated values are reasonably close to the actual data. One discrepancy is with the
dc_motor file simulation where the simulated speed is 12% less than the actual data. I’m not
sure how the data was gathered for the dc_motor file, but if the recorded voltage is actually the
motor voltage instead of the battery voltage this could account for the larger error. If this is true
the simulation should have a slightly higher battery voltage, which will increase the simulated
torque and speed slightly and decrease the error. As far as the 20.4% error for the motor
operating at rated values, the error is likely due to the fact that the model has impedance of the
wire going from the battery to the plug and the 16 foot cord, lumped together with the motor’s
armature inductance and resistance. Even though the battery voltage is 14.45 V the actual
voltage at the input of the motor (manufacture’s rated voltage location) is lower. So the real
percent difference is lower than 20%, due to the voltage drop across the wire going from the
battery to the plug and 16 foot cord.
Condition
Battery Voltage (V)
Torque (lb-in)
Speed (rpm)
Motor Current (A)
Data Table 1
Simulation
Percent Difference
9.188
9.188
0.0%
8.00
7.98
-0.2%
1007
988
-1.9%
19.86
19.76
-0.5%
dc_motor_solar
Simulation
Percent Difference
12.2
12.2
0.0%
8.00
8.42
5.3%
1523
1453
-4.6%
20.16
20.85
3.4%
dc_motor
Simulation
Percent Difference
8.14
8.14
0.0%
8.00
7.83
-2.1%
939
826
-12.0%
19.80
19.38
-2.1%
8.75
8.75
0.0%
1800
1800
0.0%
21.00
21.66
3.1%
12
Motor Rating
14.45
Simulation
20.4%
Percent Difference
Data Table 2: Comparison of simulated and actual data
Ultra-Capacitor
In an attempt to extend the life of the battery the idea came about to use an ultra-capacitor for
energy storage for short term high energy demands, like the in-rush current associated with
starting the DC motor.
Since the internal resistance of the battery and the battery’s open circuit voltage was known, a
PSpice simulation was run to determine what would happen if the uncharged ultra-capacitor was
placed across the battery (Schematic 6). It turns out that a large amount of current is drawn for a
significant amount of time due to the large capacitance of the ultra-capacitor (Plot 8).
R_Battery
0.129
ESR
0.019
V_Battery
12Vdc
Ultra_Cap
58
0
Schematic 6: Charging the ultra-capacitor without current limiting resistor
100A
50A
0A
0s
10s
20s
30s
40s
50s
60s
I(R_Battery)
Time
Plot 8: High ultra-capacitor charging current due to lack of current limiting resistor
To limit this charging current, a current limiting resistor needs to be added to the circuit. The
parameters that were used to determine the appropriate resistor value were physical resistor size,
power dissipation, and charging time. The larger the resistance, the smaller the resistors became
because they had to dissipate less power, but this also increased the charging time. Likewise, the
smaller the resistance, the larger the resistors become to dissipate a larger amount of power. To
narrow down the options a total charging time of 15 minutes was determined to be an acceptable
charging time, which equals five time constants. The required resistance value to yield this
charging time was calculated as follows:
(15 min )⎛⎜ 60 sec ⎞⎟
⎝ min ⎠ = 3.1Ω
5τ = 5 RC = 15 min ⇒ R =
(5)(58F )
Now that knowing a resistance of around 3Ω was needed to produce a charging time of 15
minutes, the power rating of the resistor could be calculated by using the nominal 12 volts of the
battery.
V 2 (12V )
=
= 48W
R
3Ω
2
P=
Using the calculated resistance and power rating, an Ohmite 270 series 3Ω 50W resistor was
determined to be a good choice. Ideally the PV array should charge the ultra-capacitor instead of
the battery. The problem with this is that the output of the DC-DC converter is usually between
13V and 14V. So the resistor needs to be able to handle the higher power dissipation due to the
higher output voltage of the converter. The resistor’s datasheet states the resistor can take an
overload of 10 times rated power for 5 seconds without damaging the resistor. A simulation was
conducted using a 14V source simulating the DC-DC convert (Schematic 7), plotting the
charging current and resistor power dissipation as a function of time (Plot 9). From the
simulation one can conclude that the resistor can handle the increased power dissipation, since
the maximum power is only 1.3 times the rated value and decays to the rated value in about 20
seconds.
R_Charging
3
ESR
0.019
V_Conv erter
14Vdc
Ultra_Cap
58
0
Schematic 7: Charging the ultra-capacitor with PV array using current limiting resistor
80
60
40
20
0
0s
50s
W(R_Charging)
100s
150s
I(R_Charging)
200s
250s
300s
350s
400s
450s
500s
Time
Plot 9: Charging current and power dissipated by the 3Ω current limiting resistor
Operating Mode PCB
Once the ultra-capacitor is charged to the same voltage as the battery, there is no need for the
current limiting resistor. So a circuit needed to be developed that could switch a current limiting
resistor in and out of the system. Since we are still in the prototype phase of the project we
might have to remove the ultra-capacitor at some point, so there should be a provision to safely
discharge the capacitor. So the circuit will have three different modes of operation called
normal, charging, and discharging, and will be known as the operating mode PCB (Schematic 8).
In normal mode power will come from the battery and pass through the board to the charged
capacitor and the load bus (Schematic 9). During the charging mode a 3Ω resistor will be placed
in series with the battery and capacitor to limit the initial charging current of the uncharged ultracapacitor (Schematic 10). When in the discharge mode the ultra-capacitor will be isolated from
the battery and connect to ground through a 3Ω resistor (Schematic 11). Power MOSFETs will
be used to act as the switches on the operating mode PCB. The switching of the circuit will be
controlled by the computer, so the board must be able to interface with the NiDAQ’s.
S2
S3
S1
Charging Resistor
To Load Bus
S0
Battery
DC to DC
Converter
Ultra
Capacitor
Discharging
Resistor
0
Schematic 8: Simplified version of the operating mode PCB
S2
S3
S1
Charging Resistor
To Load Bus
S0
Battery
DC to DC
Converter
Ultra
Capacitor
Discharging
Resistor
0
Schematic 9: Operating mode PCB in normal mode
S2
S3
S1
Charging Resistor
To Load Bus
S0
Battery
DC to DC
Converter
Ultra
Capacitor
Discharging
Resistor
0
Schematic 10: Operating mode PCB in charging mode
S2
S3
S1
Charging Resistor
To Load Bus
S0
Battery
DC to DC
Converter
Ultra
Capacitor
Discharging
Resistor
0
Schematic 11: Operating mode PCB in discharge mode
The actual circuit is obviously more complicated than the simplified versions above, and was
constructed on a six by eight inch board. Schematics 12 and 13 show the component
connections on the PCB, while the rest of this section explains how components were selected.
6
C11
1u
8
C2+
C2-
3
C13
0.1u
C14
10u
5
Vout
4
2
C1-
OUT
R4
51k
U8
MAX1822
2
4
6
8
BATTERY
10
12
Output
SN7406N Inv eter
Input
Output
Input
Output
Input
Output
Input
Output
Output
Input
Input
1
3
S2
5
S1
9
11
LOAD VOLTAGE
S0
GND
13
1
2
3
4
5
6
7
C15
1u
14
7
IN
Vcc
C10
1u
GND
C1+
LM2937ET-5.0
GND
1
C12
1u
Vcc
U7
GND
C9
10u
U6
1
3
2
C8
0.1u
OUT
GND
IN
2
1
GND
U5 LM2937ET-8.0
BATTERY
Switch S3
IRF2804
R7
1k
Header f rom NiDAQ
MAIN LINE
Schematic 12: First half of the operating mode PCB
8
C2-
2
5
R1
51k
R2
51k
R3
51k
7
Vout
U4
MAX622
1
3
5
MAIN LINE
9
Switch S2
IRF2804
R9
1k
C16
1u
Switch S1
IRF540
R8
1k
Charging
3
C18
1u
Switch S0
IRF540
Discharge
3
11
13
Input
Output
Input
Output
Input
Output
Input
Output
Output
Input
Output
2
S2
4
S1
6
3
U17
+
OS2
OUT
2
LM741
-
OS1
5
6
1
S0
8
10
12
7
C17
1u
Output
MM74C90X Buf f er
V+
C2+
C4
10u
LOAD VOLTAGE
C1-
4
2
3
V-
C6
1u
OUT
4
6
IN
C3
0.1u
14
7
C5
1u
C7
1u
LM2937ET-3.3
Vcc
GND
C1+
U2
1
GND
1
3
Vcc
U3
GND
C2
10u
OUT
GND
IN
C1
0.1u
2
1
MAIN LINE
GND
U1 LM2937ET-8.0
R10
1k
R6
R5
51k
51k
ULTRA-CAPACITOR AND LOAD BUS
Schematic 13: Second half of the operating mode PCB
MOSFET Selection
An IRF2804S power MOSFET was selected for switches S2 and S3, which are connected to the
high current traces of the operating mode PCB. These MOSFET need to be rated for at least
30A continuous, with low on resistance to make the voltage drop across the MOSFETs as small
as possible. The MOSFETs have a continuous drain current rating of 75A, and an on resistance
of 2.5mΩ, so the voltage drop across each MOSFET will be 70mV at 30A. A D2pak package
was used in order to increase the surface area that will carry the high current. The drain terminal
on this package has a large flat surface that gets soldered directly to the board, which should also
help to dissipate heat.
The selection of switches S0 an S1 was not as critical as switches S2 and S3, since the will not
have high current flowing through them. They also do not need a low on resistance, since they
are only being used to charge and discharge the ultra-capacitor. An IRF540PBF power
MOSFET rated for 28A and an on resistance of 77mΩ was selected. Since only a small amount
of current will flow through these MOSFETs, a TO-220 was used to save board space.
Gate Driver Selection
Since the source terminal of the MOSFETs used for switches S1, S2, and S3 will be around 12 V
when the switches are on, the gate voltage must be higher than 12V to turn the MOSFETs on. A
Maxim MAX622 high-side power supply was selected to generate a gate voltage above 12V.
The output voltage of the MAX622 is 11V higher than MAX622 supply voltage.
Voltage Regulators
The maximum gate to source voltage of the MOSFETs is 20V. If the MAX622 was supplied by
the battery the output voltage would be the battery voltage plus 11V, which could be as high as
25V if the battery is being charged and the DC-DC converter is outputting 14V. This would
cause the gate to source junction to breakdown if the source of the MOSFETs were ever
grounded during a fault, or in the case of switch S0 connected to ground through the discharging
resistor to discharge the ultra-capacitor. So an 8V regulator was selected for the MAX622’s Vcc
to limit the voltage output to 19V.
It turns out that even though the NiDAQ’s are supposed to output 5V for a high signal, they
realistically can output as low as 2V according to Eran Tal’s thesis. So a 3.3V regulator was
used for the buffer’s Vcc, to work with the NiDAQ’s low VOH. However the inverter has a 5V
regulator for Vcc, which has a VIH minimum of 2V, so it is compatible with the NiDAQ’s.
Buffer/Inverter Selection
The control signals will comes out of the NiDAQs and to the inputs of either a buffer or inverter.
A MM74C906 open drain buffer was used, so that when the input is high the output is floating.
And a SN7406 open collector inverter was used, so that when the input is low the output is
floating. The outputs are connect to the MAX622’s output by a 51kΩ resistor. When the
inverter or buffer’s output is low the MOSFETs are turned off, and when the outputs are floating
the MOSFET’s gate voltage will be 19V turning them on.
In an effort to make the PCB more reliable it needed to be determined if there are any conditions
that could cause the NiDAQ’s to function strangely, and turn on a switch that should be off. It
turns out there are two conditions. When the computer is initially turned on the NiDAQ’s output
a high signal, which remains high until the program controlling the circuit switching is executed.
If all the gates are driven by buffers connected to the NiDAQ, then all the MOSFETS turn on.
Which means the battery will be connected to ground through a 3Ω resistor. So the idea of using
inverters instead of a buffer to control the switching came up, but this yield a new problem. If
the NiDAQs loose power their output is low, which will cause the inverters (powered by the
battery) to output high turning all the switches on. So an extra switch (S3) was added to the
board to eliminate the problem of turning on switches when they should be off. The board is set
up so that the gate on switch S3 is connected to the NiDAQs through an inverter, and the control
circuitry is powered directly by the battery. Whereas the gate on switch S0, S1, and S2 is
connected to the NiDAQs through a buffer and the control circuitry is powered up only when
switch S3 is on. This way when the NiDAQs are initially turned on and all outputs are high
switch S3 is turned off, which de-energizes the control circuitry of switch S0, S1, and S2 turning
them off. If the NiDAQs loose power and all outputs go low switch S0, S1, and S2 turn off,
while switch S3 turns on.
The best solution for this problem would be to purchase new NiDAQs that output low when
initially energized, which means the board can function properly by only using buffers to
interface with the NiDAQs. This way the cost and size of the board can be reduced by
eliminating a number of components that will no longer be needed, such as switch S3 and all of
its control circuitry.
Operating Mode PCB Testing
Once the operating mode PCB was constructed it needed to be tested before being installed on
the SuPER cart. Since there are no power supplies that can supply 30A, the DC source from the
AC machines lab was used. Data Table 3 shows voltage drop across switches S2 and S3 and the
calculated MOSFET on resistance at different current values.
I (A)
5
10
15
20
22
25
28
30
S2 (mV)
13.3
22.6
32.5
49.5
53.7
59.6
66.7
72.4
S3 (mV)
8.3
19.1
25.0
41.2
45.9
50.6
55.9
59.9
Rds on S3 (mΩ)
1.7
1.9
1.7
2.1
2.1
2.0
2.0
2.0
Rds on S2 (mΩ)
2.7
2.3
2.2
2.5
2.4
2.4
2.4
2.4
Data Table 3: MOSFET on resistance of switch S2 and S3
Plot 10 shows the voltage drop across each as a function of current. The slope of the trend line
represents the average on resistance, and this value could be used to describe the MOSFETs
resistance for simulation purposes.
Voltage Drop Across MOSFETS
80
S3
S2
70
y = 2.4199x - 0.5978
Voltage Drop (mV)
60
50
40
y = 2.1147x - 2.7353
30
20
10
0
0
5
10
15
20
25
30
35
Current (A)
Plot 10: Voltage drop across switch S2 and S3
DC Motor Model with Ultra-Capacitor Simulation
Although there is no data to prove how well the simulation compares to actual results, the circuit
(Schematic 14) was simulated to get an idea of how the circuit might behave when the DC motor
is started with the ultra-capacitor connected. The in-rush DC motor current peaks at about 62A,
with the battery suppling about 8A and the ultra-capacitor supplying about 54A. By looking at
Plot 13 the DC motor’s torque reaches steady state in about 0.5 seconds. However, according to
Plot 15 the speed doesn’t reach steady state until 35 seconds after start up which seems rather
long. If the circuit does behave like the simulation, then the battery is definitely not suppling a
large amount of current during motor start up. The bulk of the current is coming from the ultracapacitor.
R_Battery
1
0.129
L_Motor
0.7m
ESR
0.019
V_Battery
11.75
2
R_Motor
0.16
Back_EMF
Km=6.1
Ultra-Cap
58
+
-
0
Coulomb_Drag
7.048
1
Torque
Kt=0.404
Inertia
1.2
+
-
0
2
0
Viscous_Drag
0.9458
Schematic 14: DC motor simulation with ultra-capacitor
80
60
40
20
0
0s
5s
I(R_Battery)
10s
I(ESR)
15s
20s
25s
I(L_Motor)
V(Ultra-Cap:+)
30s
35s
40s
45s
50s
Time
Plot 11: Ultra-capacitor voltage and battery, ultra-capacitor, and DC motor current at steady state
55s
60s
80A
60A
40A
20A
0A
0s
0.1s
I(R_Battery)
0.2s
0.3s
I(ESR)
I(L_Motor)
0.4s
0.5s
0.6s
0.7s
0.8s
0.9s
1.0s
0.6s
0.7s
0.8s
0.9s
1.0s
Time
Plot 12: Battery, ultra-capacitor, and DC motor current during in-rush
30V
20V
10V
0V
0s
0.1s
V(Torque:3)
0.2s
0.3s
0.4s
0.5s
Time
Plot 13: Modeled DC motor’s torque in lb-in with ultra-capacitor
1.5A
1.0A
0.5A
0A
0s
0.1s
I(Coulomb_Drag)
0.2s
0.3s
0.4s
0.5s
0.6s
0.7s
0.8s
0.9s
1.0s
Time
Plot 14: Modeled DC motor’s peak speed in kRPM with ultra-capacitor
1.5A
1.0A
0.5A
0A
0s
10s
I(Coulomb_Drag)
20s
30s
Time
Plot 15: Modeled DC motor’s steady state speed in kRPM with ultra-capacitor
40s
50s
60s
Parts List
R1
R2
R3
R4
R5
R6
R7
R8
R9
R10
Description
51kΩ
51kΩ
51kΩ
51kΩ
51kΩ
51kΩ
1kΩ
1kΩ
1kΩ
1kΩ
Part #
MCRC1/4G513JT-RH
MCRC1/4G513JT-RH
MCRC1/4G513JT-RH
MCRC1/4G513JT-RH
MCRC1/4G513JT-RH
MCRC1/4G513JT-RH
MCRC1/4G102JT-RH
MCRC1/4G102JT-RH
MCRC1/4G102JT-RH
MCRC1/4G102JT-RH
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
C11
C12
C13
C14
C15
C16
C17
C18
Description
0.1μF
10 μF
0.1 μF
10 μF
1 μF
1 μF
1 μF
0.1 μF
10 μF
1 μF
1 μF
1 μF
0.1 μF
10 μF
1 μF
1 μF
1 μF
1 μF
Part #
KME50VBR10M5X11LL
106CKH100M
KME50VBR10M5X11LL
106CKH100M
105CKH050M
105CKH050M
105CKH050M
KME50VBR10M5X11LL
106CKH100M
105CKH050M
105CKH050M
105CKH050M
KME50VBR10M5X11LL
106CKH100M
105CKH050M
105CKH050M
105CKH050M
105CKH050M
X1
X2
X3
X4
X5
X6
X7
Description
15 amp terminal
15 amp terminal
15 amp terminal
15 amp terminal
30 amp terminal
30 amp terminal
30 amp terminal
Part #
7690
7690
7690
7690
8196
8196
8196
Newark Part #
73K0336
73K0336
73K0336
73K0336
73K0336
73K0336
72K6178
72K6178
72K6178
72K6178
Total
Price
0.128
0.128
0.128
0.128
0.128
0.128
0.128
0.128
0.128
0.128
1.28
Newark Part #
91F3293
69K7898
91F3293
69K7898
69K7895
69K7895
69K7895
91F3293
69K7898
69K7895
69K7895
69K7895
91F3293
69K7898
69K7895
69K7895
69K7895
69K7895
Total
Mouser Part #
534-7690
534-7690
534-7690
534-7690
534-8196
534-8196
534-8196
Total
Price
0.143
0.106
0.143
0.106
0.038
0.038
0.038
0.143
0.106
0.038
0.038
0.038
0.143
0.106
0.038
0.038
0.038
0.038
1.38
Price
0.46
0.46
0.46
0.46
1.24
1.24
1.24
5.56
U1
U2
U3
U4
U5
U6
U7
U8
U9
U10
U15
U16
U17
Description
8V Regulator
3.3V Regulator
High-Side Power Supply
Buffer
8V Regulator
5V Regulator
High-Side Power Supply
Inverter
MOSFET
MOSFET
MOSFET
MOSFET
Op Amp
Part #
LM2937ET-8.0
LM2937ET-3.3
MAX622
MM74C906N
LM2937ET-8.0
LM2937ET-5.0
MAX1822
SN7406N
IRF540PBF
IRF540PBF
IRF2804SPBF
IRF2804SPBF
LM741
Newark Part #
07B6337
41K4552
58K1928
07B6337
41K4553
08F7825
63J7322
63J7322
73K8240
73K8240
78K6012
Total
Description
3 ohm 50W
Crimp Connector
6 terminal housing
6 terminal header
Part #
L50J3R0E
3-350980-1
640250-6
640445-6
Newark Part #
64K5014
52K4327
Mouser Part #
571-6402506
571-6404456
Price
2.62
2.49
0
2.58
2.62
2.62
0
1.05
1.00
1.00
3.55
3.55
0.296
23.38
Quantity
2
6
1
1
Price
8.61
0.061
0.17
0.18
Total
Total
17.22
0.366
0.17
0.18
17.94
How to Operate the SuPER Cart
SuPER Prototype Operation
Modified 6/11/07 J. Witts
1)
2)
3)
4)
5)
6)
7)
8)
9)
Ensure that all breakers are open.
Insert the hub cables into the laptop USB ports, followed by the NI DAQ device cables.
Then insert the PIC cable into the open laptop port. The mouse cable should be inserted
into the hub.
Power on the laptop (at this point running on its internal battery) and at the GRUB
window choose the latest version of Red Hat.
Login using root:super1.
Open a shell and change directories (cd) to /home/super1/pvpro/src to control the PV
and main switch board.
Close PV, converter and battery circuits by flipping the breakers marked PV, BATT
and BUS. The PV array will start charging the battery even though no programs are
running, because the NiDAQ’s default output is high (turning MOSFET switches on).
Execute the software with the command ./contAcquireNChan .
Open a new shell and change directories (cd) to /home/super1/cap/src to control the
ultra-capacitor board.
Execute the software with the command ./cap .
10) If the ultra-capacitor is not needed leave the breaker labeled CAP open, enter n to
operate the capacitor board in normal operation, and skip to step 14. If the capacitor is
needed proceed to step 11.
11) Check the capacitor voltage with a voltmeter. If the capacitor voltage is within 2 V of
the battery terminal voltage, run the capacitor board in normal mode. If the capacitor
voltage is not, run the capacitor board in charging mode. Once the capacitor voltage is
within 2 V of the battery terminal voltage, change the operating mode from charging to
normal. Follow prompt and enter correct mode of operation.
‘c’ to charge the capacitor (used if capacitor is not at battery voltage)
‘n’ for normal operation (used to operate the cart without any resistors)
12) Once the capacitor board is operating in the correct mode determined from step 11,
close the breaker labeled CAP. Once the capacitor is at the same voltage as the battery
node and the operating mode is set to normal, the SuPER cart is ready to operate
13) Close the breakers as desired to power indicated loads.
14) To turn the system off, open all circuit breakers connected to the load bus.
15) While in the shell for the ultra-capacitor board type
‘o’ to turn all switches off (used to turn all capacitor board switches off) then
‘q’ to quit (used to exit program)
16) Now go to the shell running the PV software and use ‘q’ to quit.
17) Shut everything down by opening all circuits at the breakers.
Note: If the ultra-capacitor has to be physically taken off the cart it must be discharged first.
Follow the instructions below to safely disconnect the ultra-capacitor.
1) Follow steps 1 through 4 listed above.
2) Close the breaker labeled BATT.
3) Follow steps 8 through 9 to run the ultra-capacitor board software. Set the board to run in
discharge mode by entering d.
4) Close the breaker labeled CAP.
5) When capacitor is fully discharged (use voltmeter to ensure 0 V) turn off the system
following step 15 listed above. The capacitor can now be safely removed.
Circuit Breaker Rearrangement
In order to connect the capacitor to the SuPER cart, some of the circuit breakers needed to be
moved. The 2 amp circuit breaker labeled BUS, that powers the sensors and control elements,
had to be removed from the load bus. When the ultra-capacitor is charging it pulls the bus
voltage down to zero volts, then slowly rises to the battery’s voltage. When the voltage is pulled
down to zero, none of the control circuitry can be used. This means the PV array cannot be used
to charge the ultra-capacitor, only the battery will be able to charge the ultra-capacitor. So by
moving the BUS circuit breaker off the load bus and powering it off the battery, the PV array can
now be used to charge the ultra-capacitor.
A 6 amp circuit breaker was selected to protect the capacitor. The breaker size was selected
based on looking at the simulated capacitor current during start up (plot 12), and compared to the
circuit breaker curve of plot 16. Since the circuit breaker curve is based on constant current
during a fault, the breaker should not operate for the decaying transient of the DC motor’s inrush current. The ultra-capacitors circuit breaker could not be directly connected to the load bus,
since the circuit breakers can only interrupt faults in one direction. The construction of the
circuit breaker only allows mounting in one direction, so it had to be installed adjacent to the
load bus. See Schematic 15 for actual breaker locations. The circuit breaker was connected this
way to interrupt fault current supplied by the ultra-capacitor if the load bus, or any point
connected to the load bus, was faulted to ground.
Plot 16: CBI circuit breaker curve
Schematic 15: Gavin Baskin’s SuPER schematic