Low Power Extended Range DC Motor
Controller
By
Jeffrey Ma
Sungjoon Cho
ECE 345 Senior Design Project
Spring 2004
TA: Joseph Mossoba
May 4, 2004
Project #47
ABSTRACT
The goal of this project is to design and implement a low power extended range DC motor speed
controller. The utilization of an electric DC motor with an effective speed control is very
extensive in today’s market and is used to run anything from an electric bicycle to a golf cart. A
buck-boost converter was designed for an input voltage range between 9-15V, and an output
range of 0-15V. The implementation of a speed control allowed the user to control the speed of
the motor and to provide speed regulation. The DC motor controller was designed for outputs up
to 250W. At the same time, the converter worked well for low power, thus making the range of
possible applications very broad.
ii
Table of Contents
Page
1.
Introduction ……………………………………………………………………………….1
1.1
1.2
1.3
2.
Design Procedure …………………………………………………………………………3
2.1
2.2
2.3
2.4
2.5
3.
Equipment …………..…………………………………………………………...10
Converter verification …………………………………………………………...11
Overcoming high current ………………………………………………………..14
Sensing verification……………………………………………………………...16
Speed Control verification ……………………………………………………....16
Cost Analysis …………………………………………………………………………....18
4.1
4.2
4.3
5.
Buck/Boost Converter ……………………………………………………………3
PWM and Gate Drive …………………………………………………………….5
Motor ……………………………………………………………………………..5
Speed Sensor ……………………………………………………………………..6
Speed Control …………………………………………………………………….8
Design Verification ……………………………………………………………………...10
3.1
3.2
3.3
3.4
3.5
4.
Specifications ……………………………………………………………………..1
Block Diagram ……………………………………………………………………1
Subprojects ……………………………………………………………………….2
Parts Cost ………………………………………………………………………..18
Labor Cost …………………………………………………………………….....18
Total Cost ………………………………………………………………………..18
Conclusions ……………………………………………………………………………...19
5.1
5.2
5.3
Successes ………………………………………………………………………...19
Uncertainties …………………………………………………………………….19
Future Development …………………………………………………………......19
References ……………………………………………………………………………………….20
iii
1.
INTRODUCTION
In today’s market, products with a wide range of use serve a great value. The development of a
DC motor controller with an extended range of output power will allow it to be utilized in a wide
variety of applications.
The DC motor controller proposed in this design will maintain speed control while having the
ability to output a very wide range of current and power.
1.1
Specifications
The prominent specification of this project is the voltage conversion. The input range was
designed for 9-15V, representing the inconsistencies of a 12V lead acid battery. The required
output range was 0-15V, thus warranting a buck-boost converter. In addition, the output power
was required to handle 250W continuously. Finally, a control circuit was implemented to control
the load motor speed through an outside reference, while keeping the speed constant through
feedback.
1.2
Block Diagram
The basic block diagram of the project is shown in Fig. 1.1.
Figure 1.1. Block Diagram for the Extended Range Motor Control Circuit.
The gate drive and converter both take power from a power supply. The gate drive produces a
duty cycle through PWM comparison, and feeds it to the gate of the MOSFET in the converter.
The converter output is then measured through a current sense resistor, whose reading is sent to
the control circuit. Within the control circuit, the converter output is compared to a user-defined
control reference through the use of operational amplifiers. The resulting error signal is then sent
back to the gate drive, which compares the error signal to the internal reference, in order to
adjust the duty ratio, and thus adjust the converter output.
1
1.3
Subprojects
Initially, the project was divided into two subprojects consisting of the gate drive/converter
aspect, and the motor control/feedback aspect. However, throughout the course of the project, it
was discovered that laboratory limitations restricted us from implementing a high power motor
control circuit, due to the lack of a high power motor. As a result, the project was split into two
different subprojects consisting of entirely separate circuits. One part consisted of high power
conversion, and the other dealt with low power motor control and feedback. However, the buckboost converter and gate drive were identical for both circuits, with the exception of the high
current interconnections and an inductor rated for higher current in the high power circuit. The
two separate circuits are shown below in Fig. 1.2, with the low powered circuit with motor
control built on the power board, shown on the left, and the high powered converter built on a
vector board, shown on the right.
Fig. 1.2. Circuits for the two separate low power/high power subprojects
2
2. DESIGN PROCEDURE
2.1 The Buck-Boost Converter
Figure 2.1. Basic circuit design for the buck-boost converter
The primary concern in the design of this converter was the high current levels that would be
present with high power loads. The maximum dc current was calculated through the relation,
Imax = Pmax / V
(2.1)
Since the maximum power was specified to be 250W, which would be reached at the highest
output voltage of 15V, the maximum dc current was calculated to be 16.7A. However, with this
calculated current referring to the output current, the maximum possible current within the circuit
had to be compensated even more due to the loss that would inevitably be present in the
converter. As a result, we doubled the maximum input current to estimate the input current, and
thus rated the circuit for 33.4A.
Although this rating was likely a heavy overshoot of the actual input rating, at the levels of
current that we estimated, it was agreed upon that a safe overestimation would be much better
than the potentially dangerous consequences of underestimating. In addition, for the high power
circuit, efficiency was not a high priority, which made overestimating in design make even more
sense.
2.1.1 Switch Selection
With the current rating determined, the first step of the design was to determine the switches that
would be used. The fundamental concept of dc-dc conversion is the use of switching to change
the voltage from the input to the output. The MOSFET acts as the first switch, which is
controlled by the duty cycle supplied by the gate drive. When the square wave duty cycle is high,
the positive bias at the gate will cause current to freely flow from the drain terminal to the source
terminal. As a result, in this situation the MOSFET can be seen as a short circuit. Due to
Kirchoff’s laws, when the MOSFET is on, the diode must be off. Similarly, when the duty cycle
is low, the MOSFET becomes an open circuit, and the diode basically acts as a short circuit with
the exception of a small voltage drop.
3
The MOSFET used in this project is the IRFP044N, with ratings of VDSS = 55V, ID = 53A and
RDS(on) = 0.02Ω. This particular FET was chosen due to the high current rating, as well as for the
relatively low RDS(on). In addition, the TO-247 casing was chosen in order to attach large heatsinks. Although at first glance the 53A rating may seem to be too severe of an overshoot, the
rating is somewhat of a marketing trick, as the 53A rating pertains to an operating temperature of
25°C. Since it is nearly impossible to keep the temperature as low as 25°C at such high current
levels, the more realistic rating was the current rating at 100°C, which is 37A, and thus much
closer to our estimated maximum
The diode chosen is the MBR4045WT schottky rectifier, with ratings of IF(AV) = 40A, VR = 45V,
and VF = 0.56V. Like the FET, the TO-247 package was chosen for heat-sink purposes. Despite
the high ratings, the forward voltage drop is very low and leakage is moderate, thus making the
MBR4045WT a sensible choice.
2.1.2 Inductor Design
With the switches determined, the next step was the design of the storage components.
Switching causes the charging and discharging of the storage elements which essentially
determine the average output voltage. The inductor acts as current source when the FET is off
and the diode is on, and the output capacitor provides the voltage source to the output when the
FET is on and the diode is off.
The two considerations in determining the inductor value of a buck-boost converter circuit are
the maximum current ripple, and the avoidance of discontinuous mode. Because the current
ripple was not a large concern in the design of this convert, the inductor value was designed to
avoid discontinuous mode. Avoiding discontinuous mode is important in order to avoid the
resulting control and regulation problems. The general equation for the inductor is
V = L*Δi/Δt
(2.2)
Rearranging Eq. (2.2) to find the critical inductance required to keep the inductor current above
discontinuous mode yields
Lcrit ≥ Vin(D1T)/Imax
(2.3)
D1 refers to the duty ratio required to produce the maximum required 15V. D1 can be estimated
by the ideal buck-boost relationship given as
Vout/Vin = D1/(1-D1)
(2.4)
Thus, theoretically the maximum duty ratio will be needed when the input is 9V and the desired
output is 15V. Using Eq. 2.4
15V/9V = D1/(1-D1)
(2.5)
and solving D1 is found to be 0.625.
The only other unknown variable is Eq. 2.3 is T, which refers to the switching period. The
switching period is given by the relationship
T = 1/f
(2.6)
4
Thus, to determine the switching period, a switching frequency for the circuit had to be designed.
In selecting the switching frequency, two major tradeoffs were considered. As implied in Eq. 2.3,
a high switching frequency allows for the required inductance to be low. However, with
increasing frequency, higher switching losses result. Due to the high current aspect of our
converter, high switching losses were deemed to be unacceptable and a conservative frequency
of 35kHz was chosen.
Thus, using Eq. 2.6, we solve
T = 1 / 35000Hz
(2.7)
and find the switching period to be 28.6µs.
Having determined the worst case duty ratio, the switching period, and the maximum current, the
critical inductance was calculated using Eq. 2.3
Lcrit ≥ 15V(0.625)(28.6µs) / 16.7A
Lcrit ≥ 16.1uH
(2.8)
(2.9)
Thus, the inductor value was designed to be 25uH.
With the inductor value determined, the next step was to design the fabrication of the inductor.
Due to the high current aspect of the project, it was critical to minimize the number of turns of
the inductor in order to minimize the wire loss. As a result, the Micrometals model T300-26D
toroidal core was chosen for its high inductance/turn2 ratio of 160nH/turn2. Using this core, the
number of turns required to ensure a value of 25uH was found using the equation
N = (L/AL)1/2
with AL representing the inductance/turn2 ratio.
calculated to be 13 turns.
(2.10)
Thus, the required number of turns was
Due to the high levels of current passing through the inductor, along with the relatively long
length that the wires would be, it was important to make the windings of the inductor to be rated
properly. The thickest wires that were available in the lab at the time of inductor design were
14-gauge wires. However, referring to the AWG table, it was determined that 6-gauge wire
would be needed to safely handle the potential current flowing through the inductor [1]. As a
result, we decided to braid five 14-gauge wires in parallel to create a 6-gauge wire. This was
made possible because each wire in parallel decreases the gauge rating by two [2].
For the low power circuit, an inductor was created with the same core and the same number of
turns, but only one 14-gauge wire was used as the windings because of the significantly lower
current ratings.
The inductance of the high-power inductor was measured to be 30.8uH, while the low-power
inductor had a value of 28.7uH.
5
2.1.3 Capacitor Design
The primary purpose of the input and output capacitors is to reduce the voltage ripple caused by
switching. Equation 2.11 below gives the capacitance required to keep the voltage ripple below
a certain value [1].
C = Vout(1-D1)(T)2 / (8*L*ΔV)
(2.11)
Using our previously determined inductor value and a reasonable voltage ripple of 2.5%, we
calculated our capacitor value to be 49.7µF. Thus, we conservatively chose 100µF electrolytic
capacitors for both the input and the output. However, as it will be discussed in the later sections,
the chosen capacitors had many problems dealing with the heat, and therefore had to be replaced
with larger capacitors.
2.2 The Gate Drive
Initial design and testing was done using a gate drive run by the UC3843 PWM chip. However,
with implementation of the control circuit, it was discovered that the UC3843 had an internal
current source that pointed in the outward direction of the PWM Feedback input. As a result, the
output signal of the control circuit feeding the feedback input was partially negated. Thus, the
control circuit had no effect on the duty cycle, and an alternative was needed.
The alternative gate drive chip that was discovered was the TL494 PWM chip. The datasheet for
the TL494 also revealed a current source on the Feedback input node, but unlike the UC3843, the
current source was pointing inward. The TL494 gate drive chip and external circuit schematic is
shown below in Fig. 2.2.
Fig. 2.2. Schematic of the gate drive circuit
The duty cycle was initially designed for manual user control using the internal reference voltage
with a potentiometer. However, with the implementation of the control circuit, the control
circuit output was applied directly the Feedback PWM Comparator Input at pin 3. The output
was made usable for the gate of the MOSFET by including a pull-up scheme using VCC and two
250Ω resistors in parallel. Finally, the frequency was designed to be set by a potentiometer at
pin 6.
6
2.3
Motor
We first needed to find a motor in order to involve the variable speed aspect of our project and to
ensure that our control circuit was able to function properly. Although our original converter
circuit was designed for a maximum output current of about 20 amps, we were unable to obtain a
motor with a current rating that could handle that high of a current without spending hundreds of
dollars. As a result, we elected not to test the speed control for high power, but rather focus on
developing a functional control circuit. At the same time, we would build a converter that is
capable of outputting our desired current levels and implement the converter with the control
circuit only for low power.
The motor that we used was a Litton 4Z143 12/24 Volt permanent magnet DC motor. The motor
can handle up to 1/7 of an hp or about 100 W of power. We had the motor shaft coupled to that
of the same motor so we could load the motor and test the efficiency of our control circuit.
2.4
Speed Sensing
The speed sensing circuit basically has the task of determining and scaling the speed of the
motor. Since the speed of the motor is internal, it is not easily measured and cannot be
determined from just the terminal voltage of the motor. The permanent magnet DC motor also
contains an electrical resistance of the armature known as the armature resistance. So in order to
characterize the speed of the motor, we must take into account the voltage that is created by the
armature resistance of the motor. As a result, we characterize the speed, ω, by
kω = VT - RaI
(2.12)
To obtain the speed, we need to measure the terminal voltage of the motor and the output current
that is going through the armature. The armature resistance of the motor is known and can be
measured by connecting the terminals of the motor into an ohmmeter. We thus obtained a value
of Ra ≈ 1Ω.
Although the armature resistance is not constant for the motor, it is approximated to 1 ohm as it
usually varies between 0.7 – 1.5 ohms. As the armature of the motor rotates with the shaft, so
does the resultant magnetic field that is within the permanent magnet DC motor, which affects
the resistance of the armature.
The terminal voltage can be easily measured, as it is the same as the output voltage of the
converter. This is taken by taking the voltage drop across the output load of the converter, and
connecting it to an opamp from the LF347 chip. It is then configured to act as a differential input
amplifier, as shown in Fig. 2.3. The output of this will give us a scaled version of the output
voltage. The actual scale of the output is determined by the gain of the differential amplifier,
which is determined by the value of the resistors. [3]
Vout = (1kΩ / 10 kΩ) * (-V+T + V-T) = -0.1VT
(2.13)
7
V+T
V1
V -T
-0.1 VT
Fig. 2.3. Sensing Terminal Voltage
Next, we need to measure the voltage loss from the armature resistance that is brought about by
the output current through the armature. There is no feasible way to directly measure this from
the motor. As a result, we measure the output current by placing a sense resistor before the load
whose purpose is to measure the current going into the load. For the sense resistor, we chose the
smallest resistance possible. This is because our converter was expected to generate very high
current, and we wanted to minimize the losses in the output by keeping the resistance as small as
possible. The smallest resistor that we could obtain was 0.02Ω. We know the value of the
armature resistance and we want our speed sensing circuit to scale the value of the sense resistor
multiplied by the output current so that it will eventually be proportional to the armature
resistance multiplied by the current. So we take the voltage drop across the sense resistor and
connect it to another differential op amp, as shown below in Fig. 2.4.
R-sense
R+sense
V2
4.7(RsenseI)
Fig. 2.4. Sensing Output Current
The result of this, along with the scaled version of the terminal voltage is then fed into an
additional op amp. The output of the additional operational amplifier would then be a scaled
version of the speed [3]. When we add the two signals from the two previous differential op
amps, we get
-0.1VT + 4.7RsenseI
= -0.1VT + 4.7(0.02)I
= -0.1(VT - 0.94I)
(2.14)
(2.15)
(2.16)
8
= -0.1(VT - RaI)
(2.17)
This value is then further scaled to whatever we want the final scaled speed to be and inverted
through the inverting terminal of the op amp, as shown in Fig. 2.5.
0.33(VT – RaI) = V
Fig. 2.5 Motor Speed Sensing
The final output of our speed sensing circuit is thus a scaled version of the motor speed. The
entire schematic of the speed sensing circuit is shown below in Fig. 2.6.
R7
R1
R5
U2
0 .0 2
1k
1 0k
OUT
+
OPAMP
1 0k
R8
1k
R9
R11
1 0k
3 3k
U3
-
0
R14
1 0k
OUT
4 .7 k
+
OPAMP
R2
U1
-
1k
OUT
R3
0
+
OPAMP
1k
R4
4 .7 k
0
Fig 2.6 Complete Speed Sensing Circuit
2.5
Speed Control
The speed control circuit implements an integrating op-amp, which takes in the scaled speed
signal along with a reference voltage that is taken from the PWM chip. The output of this opamp will be the integral with respect to time of the speed subtracted from the reference voltage,
multiplied by the gain, [3]
(1/(RC))∫(Vref – V) dt
(2.18)
9
V is negative as it is fed into the inverting terminal of the opamp. The difference between the
reference voltage and the speed is called the error. The error is basically the difference between
the actual speed of the motor and what we want the speed of the motor to be. The opamp will
integrate the error with respect to time, thus eliminating the steady state error. The outputs signal
of the integrating opamp will then feedback and control the duty cycle of the gate drive to
regulate the speed of the motor. The circuit for this process is shown below in Fig. 2.5. [1]
C1
2 .2 u
R13
U4
To duty cycle
-
V
1M
OUT
+
(1/R13C1)∫(Vref – V) dt
OPAMP
HI
5 50
Fig 2.5 Integrator Control
Vref
0
The reference voltage is taken from a 1 kΩ potentiometer that is connected between the +5V
reference output from the PWM chip and ground. The reference voltage can thus be adjusted by
the potentiometer. This implements the user adjustable speed control of our design as the motor
speed will change with different values of Vref. We are setting Vref to what we want the speed of
the motor to be.
Since Vref is expected to be a fairly small value as it is taken between 0V to 5V, it was definitely
necessary to scale down the speed, VT - RaI. We want the scaled speed to be within range of
Vref so that the error is a reasonable amount. If the error were too great, then it would take a
very long time to integrate the error, which would cause instability of the control. Since the
output current is expected to be fairly small for the motor, we expect the maximum VT - RaI to
be close to 10V. We set the gain of the additional amplifier of the speed sensing circuit so that
we would get 0.33(VT - RaI), which we expect to be within a reasonable range of Vref.
The resistor and the capacitor at the inverting terminal of the opamp determine the gain of the
integrator. We set the gain to be relatively low because when the gain at the integrator is too
high, the control will integrate the error at an alarming rate and the integrator will never stabilize.
The output of the control would jump from a low voltage to a high voltage while error is being
integrated and the motor speed will not stabilize as the speed will constantly be shifting. So it is
better for the speed control circuit to keep the gain at a low level, as shown below in Eq. 2.19.
Gain = 1/(RC) = 0.4545
(2.19)
10
3. DESIGN VERIFICATION
3.1 Equipment
Due to the high power aspect of this project, the laboratory equipment often provided hurdles for
us to overcome, and in some cases set complete roadblocks.
3.1.1 Power Supplies
The gate drive and control circuit supply used throughout the project was the Tektronix PS503
Dual Power Supply. Although the supply of the gate drive and control circuit were supposed to
be the same as the supply to the converter, we used a separate supply for the sake of consistency.
However, the input was adjusted accordingly whenever the input to the converter was adjusted.
At low power levels the Kenwood Regulated DC Power Supply was used for the converter.
However, this power supply had a 10A current limit, which only provided up to output ranges of
approximately 100W.
In order to reach higher output power levels, the Xantrex XHR 40-25 DC Power Supply was
obtained. As indicated in the model number, this supply was rated for 40V and 25A. However,
the particular Xantrex Supply we received had a faulty display which gave no indication of how
much voltage and current was actually being supplied. As a result, the input of the power supply
had to be taken through a Valhalla Digital Power Analyzer, and then to the converter in order to
know how much power was being inputted into our converter. However, the wattmeter had a
current limit of 20A, so for input current above 20A, the wattmeter was used only to read the
input voltage, and the input current was estimated by taking the oscilloscope mean of the input,
measured by a current probe.
Due to loss, the input power was significantly higher than output power. The maximum output
power was 225W, due to load limitations that will be discussed in the next section. Therefore, in
the ideal case with no loss, a 225W output would require a 225W input. Using the relation given
by Eq. 2.1, a 9V input would result in a current of
225W / 9V = 25A
(3.1)
Since the input current for ideal conditions is the current limit of the power supply, it is obvious
that the current limit will be reached long before the maximum output power is reached. As a
result, the limitations of the power supply prevented us from reaching maximum output power
levels for low input voltages. However, for input voltages of approximately 14V and above, the
225W output was able to be reached.
3.1.2 Programmable Electronic Load
The HP6060B DC Electronic Load was used as the load for all testing except the motor control
testing. The programmable load proved to be a crucial tool throughout the course of the project.
Not only did it provide convenient load variation, it also gave automatic displays of the output
current and voltage, as well as the output power. In addition the current control mode allowed us
to easily set the current limit of the Xantrex power supply. However, the programmable load
11
came with one limitation, in that the resistance could not be set below 1Ω. With the highest
output voltage specification being 15V, the highest output power attainable was limited to
P = V2/R
(3.2)
2
P = (15V) / 1Ω = 225W
(3.3)
3.1.3 Motor
We initially tested the motor by itself by connecting its terminals to a DC power supply and
loaded a 1.5 Ω resistance to the couple. We calculated the efficiency of the motor and
determined that the motor was incredibly inefficient for low power. The motor had average
power losses of about 40 W. The motor efficiency is shown in Fig. 3.1.
Efficiency v s. Pin
0.7
Efficiency
0.6
0.5
RLOAD = 1.5Ω
0.4
0.3
0.2
0.1
0
0
50
100
150
Pin (W )
Figure 3.1 Motor Efficiency
In addition, we examined the speed of the motor in relation to the terminal voltage. As we
expected, the speed of the motor was almost directly proportional to the terminal voltage of the
motor, as shown in Fig. 3.2.
Vt vs. Speed
Speed(rpm)
2000
1500
1000
speed
500
0
1
2
3
4
5
6
7
8
9
10 11 12 13
Terminal Voltage (V)
Figure 3.2 Vt vs. speed
3.2 Converter Verification
With a working converter in place, the next step was to test and verify to determine how close
the converter was working to its theoretical ideal
3.2.1 Duty Ratio vs. Output Voltage
The ideal buck-boost converter output voltage can be found using Eq. 2.4. However, this
equation fails to consider the significant sources of loss that is present throughout the converter.
To obtain a more realistic theoretical output voltage, we analyzed the converter under two
12
different conditions. First, the Kirchoff relations were analyzed with the FET on. The circuit for
this situation is shown below in Fig. 3.3
Fig. 3.3 Buck-Boost Converter with FET On
Fig. 3.3shows the buck-boost circuit, with the FET replaced by its RDS(on), an ESR in series with
the inductor, and the diode replaced by an open circuit. KVL analysis of this circuit gives
VLon = Vin – IL(RL + RDS)
(3.4)
While KCL analysis produces
ICon = VC / Rout
(3.5)
The second set of equations is produced by analyzing the buck-boost circuit with the FET off and
the diode on, as shown below in Fig. 3.4
Fig. 3.4 Buck-Boost Converter with FET off
The circuit in Fig. 3.4shows the circuit with the FET as an open circuit, thus eliminating the
input side from the analysis. In addition, the ESR of the inductor is once again present, along
with a forward voltage drop of the diode. Through KVL analysis, we obtain
VLoff = -IL - VC - VD
(3.6)
ICoff = IL - VC / Rout
(3.7)
With KCL analysis producing
From the charging and discharging properties of the storage elements, we obtain the relations
DVLon + (1-D)VLoff = 0
(3.8)
DICon + (1-D)ICoff = 0
(3.9)
Thus, by plugging in Eq. 3.4-3.7 into Eq. 3.8 and Eq. 3.9, and solving for IL and VC, we obtain
the expressions
IL = [DVin + (1-D)VD] / [D(RL + RDS) + RL(1-D) + Rout(1-D)2]
(3.10)
13
VC = (1-D)Rout * [DVin + (1-D)VD] / [D(RL + RDS) + RL(1-D) + Rout(1-D)2]
(3.11)
With RL, RDS, and VD known, VC, which is equal to Vout, can be expressed in terms of D and
Rout. Thus, following testing, data plots were generated as shown in Fig.3.5 and Fig 3.6. Fig.
3.5 shows theoretical and test values of the output voltage vs. the duty ratio for an output
resistance of 2.5Ω, and Fig. 3.6 shows the relationship for an output resistance of 5Ω.
Rout = 2.5 ohms
25
Voltage (V)
20
15
10
5
0
0
0.2
0.4
0.6
0.8
Duty
Fig. 3.5. Vout vs. D1 for Rout = 2.5Ω
Rout = 5 ohm s
25
Vout (V)
20
15
10
5
0
0
0.2
0.4
0.6
0.8
Duty
Fig. 3.6. Vout vs. D1 for Rout = 5Ω
As the graphs show, the actual voltage, shown by the blue plot deviates from the theoretical
voltage, shown by the pink plot as the duty cycle increases. This can be blamed on the sources
of loss that are unaccounted for, such as wire loss, which significantly affects the circuit,
especially for high levels of current that would accompany the high duty ratio.
3.2.2 Efficiency
Efficiency was simply calculated by the equation
Efficiency = Pout / Pin
(3.12)
The efficiency vs. duty ratio plots for output resistances of 2.5Ω and 5Ω are shown below in Fig.
3.7.
14
Efficiency
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Rout = 2.5 ohms
Rout = 1 ohm
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Duty
Fig. 3.7. Efficiency vs. Duty Ratio
The shape of the two curves is correct, as the efficiency increases with the duty ratio. However,
it is evident that the efficiency is decent at best, with the highest efficiency failing to reach 80%.
This is due to the fact that the converter was not designed for high efficiency, but instead
designed for high power and high current capabilities. Thus, many of the components sacrificed
loss for high current ratings, and in most cases additional loss was sacrificed for the sake of
safety.
3.3 Overcoming High Current
A shortcoming of the initial design was the extended complications of high current. As
mentioned in section 3.1.1, the high current led to difficulties and limitations of the power supply.
Another task that we faced in order for verification to take place, was the component
interconnections. The power board had a limit of 10A, so the high power converter was created
separately on a vector board. Within the vector board each component was connected by 12gauge wire. Although 12-gauge wire didn’t provide the necessary current ratings, because of the
short distances between the components, we decided that 12-gauge wire would be enough. Fig.
3.8 shows the back of the vector board and how the components of the converter were
interconnected.
Fig. 3.8. Interconnections of Converter Components
The most significant problem that occurred during testing was the overheating of circuit
components at high current levels, which led to the explosion of several capacitors. As a result,
the 100µF input capacitor rated for 85°C was replaced by a 470µF capacitor rated for 105°C. In
15
addition, the new capacitor had a significantly larger casing. The output capacitor was replaced
by two 220µF in parallel to split the current flowing through each capacitor into two, and thus
significantly reducing the heat. Although the capacitor values were much larger than what the
circuit was designed for, it was necessary measure to safely keep the circuit in tact. Following
the replacement of the capacitors, the input capacitor temperature was taken with respect to
increasing current. These measurements are shown by the blue plot in Fig. 3.9.
Another component which caused concern regarding temperature was the FET. In our circuit, it
was obvious that the FET would take more current than the diode, because the highest levels of
current were present in the circuit when the duty ratio was high. Thus, for these high levels of
current, the FET would be on for the greatest period of time. As a result, two heat sinks were
placed back to back on the FET in addition to the cooling fan cooling the entire circuit. The
temperature of the FET was also measured, and is shown as the pink plot in Fig. 3.9.
70
Temperature (C)
60
50
40
30
T Cap
T FET
20
10
0
0
5
10
Current (A)
15
20
25
Fig. 3.9. Component Temperatures vs. Input Current
As shown in the plots, the temperatures of the two major components of concern were kept well
below their maximum ratings. This is credited to good design adjustment as the temperatures
were significantly higher prior to the adjustments. Thus, with all adjustments made, the final
buck-boost converter schematic is shown below in Fig. 3.10.
Fig. 3.10. Finalized Schematic of Buck
16
3.4
Sensing Verification:
Before we were able to test the control of the circuit, we needed to make sure that all of the other
opamps in use were doing what was expected. The values of each output signal of each of the
speed sensing circuit op-amps were measured to ensure that all of the scaled voltages are what
we expected it to be in theory. This was done by running the converter through a DC power
supply while disabling the control. The op-amps were powered by the dual power supply. The
duty cycle was being directly controlled by a potentiometer in the gate drive so it was possible
for us to control the voltage through the circuit. We measured the output voltage through a
voltmeter, and the voltage through the sense resistor and the outputs of each of the op-amps
through an oscilloscope. The measured results were:
VT = 6.8 V, I = 2.12 A
V1 = -0.7 V
V2 = 0.256 V
V = 1.48 V
Theoretically: VT = 6.8 V, I = 2.12 A
V1 = -0.68 V ≈ -0.7V
V2 = (4.7)(0.02 Ω)(2.12A) = 0.2 V ≈ 0.256V
V3 = 0.33(6.8 – (1 Ω)(2.12A)) = 1.54 V
≈ 1.48V
So although the measured values are not exactly the same as what they are theoretically
supposed to be, they were very close, which means that the circuit will be able to sense the speed
of the motor.
3.5
Speed Control Verification:
We next wanted to make sure that the integral controller was operating properly. We tested the
controller without the feedback by monitoring the control output through an oscilloscope. The
Vref input of the control op-amp was connected to the PWM and controlled through a
potentiometer. When the control was turned on, the output of the controller would rise until it hit
12V, which would be the integrator peak. This shows that the controller was integrating the
error until the error was obsolete and the control was set on the integrator peak. This shows that
the integral controller was functioning properly.
We finally implemented the control circuit with the rest of the circuit and connected the output of
the integral control to the duty cycle pin of the PWM in the gate drive. The motor controller
functioned properly as the speed of the motor could be adjusted by changing V ref with a
potentiometer. In addition, the speed of the motor was able to regulate itself properly as
applying a resistance to the motor shaft would cause the terminal voltage of the motor to
increase. This is due to the motor controller compensating for the disturbance to the motor and
maintaining a fairly constant speed. The integral controller was providing a somewhat steady
maintenance of the desired control variable, the speed of the motor. To show the functionality of
17
the controller, we used a function generator to run Vref and measured the Vref signal and the Vout,
which is also the terminal voltage of the motor. As the Vref pulse changes with the function
generator, it is evident that there is a change in Vout. This indicates that the motor speed, which
is directly proportional to Vout, can be controlled by the user.
Although the controller is functional, it is unable to output the voltage range of 0 -15V as was
expected. The motor would hit its current limit before the output voltage, Vout, could reach 15V.
Below is the range of functionality for values of Vref and Vout:
Vref: 0 – 2.95 V
Vout: 0 – 9.86 V
Integrator Peak: 9.86 V
Fig. 3.11. Vref vs. Vout
Fig. 3.11 shows that although the controller is functional, it is not very stable. It shows that
when Vref changes, Vout does not change very smoothly as the voltage will overshoot the voltage
that at which it will stabilize. In addition, the output voltage will take some time to stabilize. In
Fig. 3.11, the recovery time is 3.0s, so it would take the integrator 3.5 s to stabilize when Vref is
adjusted.
In an attempt to stabilize the integral controller, we tried changing the gain of the integrator.
When the gain was increased, the motor would never stabilize as it would go from a high speed
to a low speed constantly. When the gain was decreased, the recovery time for the integrator to
stabilize increased, as shown below in the results below, as well as in Fig. 3.12.
Gain = 1/(RC) = 0.2127
Vref: 0 – 2.45 V
Vout: 0 – 7.68V
Recovery time = 3.5 s
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Fig. 3.12 Vref vs. Vout (gain = 0.2127)
The deviation at the moment the error is produced causes the voltage to overshoot, which would
likely cause the motor to reach its current limit before it could stabilize at higher voltages.
Due to the inability of the controller to stabilize at higher power, the efficiency of the controller
is not applicable. The motor is too inefficient for lower power to determine an increase in the
efficiency with the motor controller.
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4. COST ANALYSIS
4.1
Parts Cost
Table 4.1 – Parts List
Part#
TL494
UC3843
LF347
IRFP044
MBR4045
12FR020
Quantity
Cost
2
$0.34
2
$3.80
2
$3.00
3
$5.20
3
$5.76
2
$3.12
2
$0.18
1
$0.09
1
$0.09
1
$0.06
2
$0.16
3
$3.27
20
$0.20
1
$4.56
Total:
$29.83
*note that these component cost calculations were done for the high power circuit as well as the
low power motor control circuit, and thus the cost of one circuit will be approximately half of the
total cost estimated above.
4.2
Part Name
PWM
PWM
Quad OpAmp
Power MOSFET
Schottky Rectifer Diode
0.02 Ω sense resistor
220uF Capacitor
470uF Capacitor
100uF Capacitor
0.047uF Capacitor
2.2uF Capacitor
Potentiometer
Resistors
Vector Board
Unit Price
$0.17
$1.90
$1.50
$2.60
$1.92
$1.56
$0.09
$0.09
$0.09
$0.06
$0.08
$1.09
$0.01
$4.56
Labor Cost
Dream Salary: $35 / hour
Labor Cost = ($30.00/hr * 100 total hrs/person * 2 people * 2.5)
= $15,000
4.3
Total Cost
Parts + Labor = Total Cost
$29.83 + $15,000 =
$15,029.83
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5. CONCLUSIONS
5.1
Successes
The goals and specifications that were set prior to the start of this project were met fully, or to a
high degree. The specified voltage conversion was fulfilled with the use of a buck-boost
converter, and the power specifications were met to the most possible extent. In addition, we
were able to successfully implement a speed controller that provides user speed control as well
as speed regulation. Although the motor control was not tested for high power, this was due to
the limitations of supplies. However, knowing that the converter was operational at high power,
it is safe to assume that with a properly rated motor the control would safely work at high power
as well.
5.2
Uncertainties
The main uncertainty involved with our motor controller is the stability of the speed control.
The integral controller, although a very effective controller in that it has the ability to return the
speed back to the exact set point following a disturbance, is very difficult to stabilize. The
integrator responds relatively slowly to an error signal, which creates a deviation the moment the
error is produced. In addition, the inefficiencies of the converter and the overall circuit were not
really taken into account.
5.3
Future Development
For future development, it may be more beneficial to implement additional control aspects, other
than just an integral control. For example, the use of a PID control method could stabilize the
control circuit and make it much more reliable.
In addition, it would be necessary to improve the efficiency of the buck-boost converter. With
more time, thorough experiments could have been performed in order to test and select
components that would just barely meet the requirements, but instead would have tradeoffs such
as less loss. However, due to our time constraints, we simply overestimated the ratings in order
to guarantee safe operation.
Furthermore it could be possible to reduce the distortion and increase stability so that a real leadacid battery could be used as the current source. Although our project didn’t reach the level of
being able to test with a real battery, since the project was intended for motor control, it would
have been ideal to get the system running with a power supply intended for actual motors.
21
References
[1] Krein, Philip T., Elements of Power Electronics New York: Oxford University Press, Inc.,
1998.
[2] J. Mossoba, “Inductor Design Process,” Class notes for ECE 345, Department of Electrical
and Computer Engineering, University of Illinois at Urbana-Champaign, Spring 2004.
[3] Sedra and Smith, Microelectronic Circuits, New York: Oxford University Press, Inc., 1998
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