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A Motor Feedback Demonstration Model for a
Control Systems Class
Andrew L. Wallner, Student Member, AES, Student Member, IEEE

performance from an operating device.
Abstract—In the educational context of control systems study,
it is useful to provide tangible models of discussed concepts. One
of the most typical applications of feedback control system theory
is that of tachometer-feedback motor speed control. A small scale
model can be implemented within a moderate budget using
readily available analog components. The design, construction,
operation, and performance of one such system are discussed
here.
I. INTRODUCTION
T
HE intent of this project is to investigate an application of
control system theory and to describe its implementation
in a small scale motor speed control system. The implemented
system is to be used as a model for individual experimentation
or classroom demonstration. The design of the system is openended to allow further study of control system theory and
development of the presented model design. Investigation into
the operation of the model design can provide a practical
example of electronic control circuitry and gives exposure to
factors involved in the realization of the abstracted system
concepts.
A. Open vs. Closed Loop Systems
If, in an open-loop system, a device is expected to produce
a particular output given a certain input, the system can
perform in an unsatisfactory way if an internal or external
force interrupts the device’s operation unbeknownst to the
controller. A closed loop system does a better job of
achieving the expected operation. It does so by informing the
controller of the device’s actual operation, and therefore
allows it to perform appropriate controlling actions to maintain
the expected performance.
INSTRUCTION
CONTROLLER
OPERATION
(a)
ADJUSTABLE
CONTROLLER
OPERATION
INSTRUCTION
VERIFICATION OF PERFORMANCE
(b)
Fig. 1. Block diagrams of control systems: (a) open-loop, (b) closed-loop.
In closed-loop systems, the process of performance
measurement and subsequent controller adjustment is itself an
adjustable process. This sub-process determines how the
controller responds to deviation reported by the fed-back
measurement, the performance verification signal. Usually,
the characteristics of this response are built or programmed
into the system before operation.
Fig. 1. a small motor/ flywheel assembly with an optical tachometer.
II. CONTROL THEORY
Even at the risk of being simplistic, it is important to
mention the overall goal of a control system. Figure 1 contains
diagrams of open and closed-loop control systems. The
purpose of a closed loop system, such as a tachometerfeedback motor control, is to maintain an expected
A. L. Wallner is an engineering student at Calvin College in Grand
Rapids, MI 49546 USA (e-mail: [email protected]).
B. Feedback Modes
Feedback can be positive or negative. Positive feedback is,
generally, unstable. It increases the effects of measured
deviation in a compounding way; as an operation deviates,
positive feedback will cause it to deviate more. This is what
happens when a microphone is turned up too far. The sound
of a lecturer’s voice is amplified so much that the sound
emanating from the public address system is picked up by the
microphone again and again, until the system reaches its
loudest possible volume. This happens at the first deviating
frequency, and then usually at harmonics of that tone, resulting
in the ringing sound that is for many people the definition of
feedback. Negative feedback promotes stability. As an
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operating process deviates, the feedback is used to decrease
the extent of the deviation. A good control system employing
negative feedback should be able to maintain an instructed
operation even when the operating process is affected by some
form of disturbance.
Feedback characteristics comprise the majority of control
system design [1]. The most basic form of feedback is linear.
Linear feedback applies a percentage of the system output,
inverted, to attenuate a portion of the system input and
compensate for the detected deviation. This arrangement
works well, but reduces the magnitude of the process output
since it is always held in check by the compensating signal.
Greater amounts of feedback yield more control, but at the
cost of reduced output.
C. P.I.D. Control
More sophisticated topologies apply a feedback signal that
is not just merely a proportion of the output. Such feedback
signals are generated based on the absolute magnitude,
(integrated) output, and also from the rate of change (the
derivative) of the output. By using combinations of these
signals, a system can be designed that recovers from
disturbances in almost any desired way. Using a combination
of proportional, integral, and derivative (PID) signals, it is
possible to control the three possible response errors: 1.)
overshoot, the over-correction in response to the detected
error, 2.) settling time, how quickly the output returns to the
expected value, 3.) steady state error, the difference between
the desired value and the actual, stabilized output. This also
allows the use of feedback without a reduction in output
magnitude. It is important to note two things: 1.) corrections
to the three error modes are not directly related to the three
PID parameters, and 2.) PID control can also be used to
regulate open loop systems, though without the benefit of
disturbance correction.
D. Advanced Control Methods
It is the interdependence of the amount of each PID
parameter on system response that has given the task of tuning
PID controls the reputation of being more of an art than
science. For these reasons, automated means of adjusting PID
loops have become very popular. An extension of this
convenience has been the development of fuzzy logic controls
and neural-net controls. Both of these approaches seek to
optimize controller operation through examination of longterm trends. Fuzzy logic implements a guess-and-check
system for specific parameter controls with is defining
characteristic being the consideration of a parameter’s degree
of accuracy [2]. It keeps track of trends, and makes new
guesses if the trends are approaching an undesirable condition.
Neural nets are an extension of this idea. They differ in their
“learning” capability. Rather than merely iterating parameters,
neural nets can create new combinations of parameters to
evaluate [3].
For both of these technologies, system
commissioning is greatly simplified when compared to PID
loops, as it requires only “teaching” rather than precise
measurement and manual adjustment. Both of these can
respond to the situation and take action based on expected
results.
In the demonstration project presented here, only
proportional negative feedback is implemented. The practical
design has inherent elements of integral and derivative gain to
provide system stability, but does not have any user-adjustable
ID parameters.
However, the system is designed to
accommodate the future addition of ID circuitry. Both fuzzy
and neural controls require computer processors, so
implementation of such devices would distractingly increase
the model’s complexity.
III. SYSTEM CONCEPT
The basic design for the system was shown on a schematic
presented for analytical evaluation as an in-class example of a
linear-feedback control system. It consists of four major
functional blocks, the variable power supply, the motor and
load, the velocity measurement, and the regulation circuitry.
A. Operation of Example System
The system presented was a design that used a linear power
amplifier for power adjustment and a generator connected to
the motor output to produce a feedback signal.
power
disturbance
output
reference
+
T3
-
T1/T2
MOTOR
LOAD
(power adjustment)
POTENTIOMETER
GENERATOR
Fig. 1. Block diagram of a generator feedback motor speed control system.
The schematic also included a power rectification circuit to
allow the low voltage dc system to operate from a standard
240v ac mains. The power amplifier was a cascaded power
transistor pair controlled by a regulating signal transistor. The
signal transistor was in a common-emitter configuration and,
in response to the current produced by the generator, would
sink the power transistors’ reference current to ground, thus
implementing negative feedback.
B. Conceptual Motivation
It was desirable to assemble a similar circuit. Apparently,
such a demonstration system is available for purchase, but at a
prohibitive expense. The simplicity of the design suggested
that it should be easily reproduced in a moderately-equipped
electronics lab.
When components were searched for, it
proved to be less convenient to identically reproduce the
presented system. There were three factors that motivated the
decision to seek a different design: 1.) a suitably matched
motor / generator pair was not found, 2.) appropriate bi-polar
power transistors were not available in-house, and 3.) it was
desirable to demonstrate a system topology that better depicts
current trends in circuit design.
It was decided to design a system that uses pulse-width
modulation (PWM) to adjust the power delivered to the motor
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and a non-contact tachometer to measure the rotational speed
of the motor output. These decisions directly addressed the
motivating design factors in the following ways: 1.) a noncontact tachometer eliminates the need for a generator, 2.)
available power MOSFET transistors can be used, and 3.)
PWM is one of the most common methods of power
adjustment used in recent designs. This design approach also
reflects current trends in system development; specifically, the
growth in system complexity. The availability of inexpensive
modules permits systems of greater complexity, and offers
greater design flexibility and control.
IV. SYSTEM DESIGN
After consideration of the important characteristics of the
original example system, it was determined that any proposed
design must contain the following: 1.) a motor driven by a
variable power supply, 2.) a motor speed sensor, and 3.) a
(reference) – (feedback) controller input. The design must
also be able to be used in a classroom or laboratory setting
with commonly available test equipment. Based on these
requirements and the other motivating factors, the system
presented here was developed.
A. Overview
Figure 2 depicts the functional blocks of the system. These
correlate directly to the functions of the original example
system, with the exception of the reference adjustment, which
is an additional feature of the new design. As will be
discussed later, this new system is voltage controlled—a subtle
difference from the original current-controlled circuit.
power
reference
voltage
output
(speed)
+
PWM
adjustment
disturbance
MOTOR
LOAD
feedback
OPTICAL
TACHOMETER
adjustment
Fig. 2. Block diagram of an optical tachometer-feedback motor speed control
system with pulse-width modulator (PWM) power adjustment.
The functionality of each of these blocks is realized largely
through the use of integrated circuits. This increase in system
complexity is the most noticeable compromise in comparison
to the original design. It is possible that the increased
complexity can detract from the transparency of the design,
that is, it may be less obvious how the system operates, but if
the system is examined as an assembly, it is obviously similar
to the original.
B. Power Supply
While the schematic of the original design had provision for
connection to ac line power, this design calls for connection to
a regulated dc supply. The control circuit is presently
configured for connection to +/- 15 volts and the motor supply
can be from the same source, or a separate dc supply with a
shared ground. With minimal modification, the motor drive
circuit could be isolated from the control circuitry, if it was to
be used with a different motor-supply combination. No overcurrent, over-voltage, or polarity protection devices are
incorporated in the design. It is expected that this system will
be operated in a laboratory setting connected to a protected
and regulated power source. The motor drive circuit is robust
and can withstand continuous operation.
C. Power Adjustment Circuit
The current amplifier stage of the original circuit is
replaced by a voltage-controlled PWM driver connected to a
MOSFET switch. The pulse width modulation varies the duty
cycle of a carrier signal to the MOSFET switch. The switch
delivers full-voltage power to the motor for a period of time
determined by the modulated carrier signal.
1) Pulse-Width Modulation
In a PWM system, if a carrier signal modulated to have a
100% duty cycle will trigger a MOSFET to connect the motor
to the supply voltage constantly. If the carrier is modulated to
50%, the switch will be closed for only half of the carrier
signal period and, as power is time dependant (power in Watts
= Joules / second), the motor will receive half as much power.
It follows, that the carrier frequency has no apparent effect on
the long-term power delivered to the motor, but is important in
speed regulation.
Consider a small dc motor with a low-inertia load that takes
1 second to reach full speed; it is connected to a PWM supply.
The carrier frequency is .01 Hz and the duty cycle is 50%.
The motor will run for 50 seconds, and be stationary for
another 50 seconds. It is true that the power delivered to the
motor is half of what it could have received in the 100 second
cycle, but the speed of the motor in operation was not
affected. Consider the same arrangement, but with a carrier
frequency of 100 Hz. In 0.05 sec. (half the carrier period), the
motor is nowhere near full operating speed. In the next 0.05
sec. (the “off” portion of the duty cycle), the motor slows
somewhat, but has enough inertia to keep turning. In the next
cycle, another pulse of power is delivered, but not enough for
the motor to reach full speed. Within a few cycles, the speed
will center about a certain value. If the frequency of the
carrier is high enough, its inverse, the period of consecutive
pulses will be short enough that the irregular power delivered
to the motor will not result in irregular motion. Because the
increments of power from one pulse to the next are small, they
do not overcome the inertia maintaining the motor’s speed.
For successful PWM speed regulation, the carrier frequency
should be as high a possible. Limitations on the upper limit of
carrier frequency include signal generation and conveyance,
but the most common limitation is inability of a motor coil to
pass a high frequency signal. When applied to a motor, high
frequency components that cannot make a complete circuit
constructively interfere within the coils and produce high
voltage transients that can damage insulation. This is called
reflected-wave phenomenon and is of concern to designers of
variable-frequency motor drives, a technology that employs a
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similar modulated switching technique.
The design presented here uses a carrier frequency of
1000Hz.
2) PWM implementation
For this system, a PWM controller is realized with three
main devices: 1.) the carrier frequency generator, 2.) the
voltage-to-duty-cycle modulator, and 3.) the power switching
unit.
The carrier generator is simply a multivibrator created
with a 555 timer IC. It produces a steady 1000Hz square
wave. The device used was a Texas Instruments NE555. A
schematic from the corresponding data sheet [5] is shown,
modified, in the left half of Fig. 3. The frequency and duty
cycle are a function of resistor and capacitor values; they are
calculated below in (1) and (2), respectively.
fc 
1.44
 1005Hz
( RA  2  RB )  CC
DC  1 
RB
 50.4%
R A  2  RB
(1)
(2)
Where: RA  1.1k, RB  68k, C  10nF
Fig. 3. Schematic of carrier signal generator (U1), a 555 timer configured for
astable (clock) operation, and the VC-PWM (U2), a 555 timer configured for
duty cycle modulation.
The voltage-to-duty-cycle modulator function is
accomplished with a second 555 timer. It varies the duty cycle
of its square wave output proportionately to the amplitude of
the voltage present at the modulation input. The frequency of
the cycles is that of the signal applied to the clock input from
the carrier generator. This circuit, also modified from the TI
data sheet, is shown in the right half of Fig. 3.
3) Power Switching
The final stage of the PWM is simply a high-speed switch
used to toggle the motor’s connection to the power source. Its
major component is a MOSFET transistor.
For this
application, an International Rectifier IRF130 was used. Many
other power MOSFETs would be equally suitable devices, and
possibly less over-qualified. The `130 is rated at 14A and up
to 100V, so no heat-sink was required for this design. Since
all MOSFETS are susceptible to damage caused by reversebias voltages, a diode is connected between the drain and
source of the transistor to divert transient over-voltages to the
power source and parallel buffer capacitor. The circuit is
shown in Fig. 4.
Fig. 4. Schematic of MOSFET power switch circuit with motor.
D. Motor Assembly
The motor selected is a permanent magnet dc motor. It is a
high-quality rotary actuator that has published performance
characteristics. This sophistication is not mandatory for the
design’s operation, but can be useful for comparison of a
theoretical analysis with empirical testing. The model chosen
is from the Canon Precision FN30S series [6]. The load
connected to the motor is a simple flywheel. The wheel is a
solid aluminum cylinder measured to have a 25.4cm diameter,
a 12.7mm length, and a 4mm, axially concentric hole. It also
has a threaded hole that accommodates a #4-40 x ¼” sockethead set-screw in perpendicular orientation to the concentric
hole. The end of the wheel that is not directed toward the
motor has two finishes. One half of its surface area is a semicircle of the smooth, bare aluminum. The other half is covered
with a non-reflective finish. This gives the optical tachometer
a target for counting revolutions.
E. Optical Tachometer
The optical tachometer provides a way of detecting rotation
of the flywheel without damping its mechanical energy. It
counts rotations by sensing light reflected off of the wheel’s
end. It is comprised of four major components: 1.) the photodetector, 2.) the pulse shaper, 3.) the frequency-to-voltage
converter, and 4.) the output buffer.
1) Photo-detector
The photo-detector is a diffuse light-reflection sensor. For
its operation, a red LED is used to illuminate the target to be
sensed. Light reflecting off the target is detected by a photodiode oriented symmetrically to the incident angle of the LED.
The photodiode, which appeared to be a somewhat standard
(though unmarked), component worked suitably to detect the
red wavelengths. For maximum sensitivity, the diode is used
in an unbiased “photovoltaic mode” [7]. This arrangement
works by sensing the voltage produced by photons “pushing”
electrons across the diode’s p-n junction. This highly sensitive
configuration has inherent signal bandwidth limitations, but
the charge-carrier propagation time does not limit performance
in the present application.
The voltage produce by the incident red light is on the order
of 0.01-0.1mV. This voltage is amplified by an LF366 JFET
input operational amplifier. The JFET input preamp presents a
high impedance load and a minimally interfering bias current
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to the delicate signal produced by the photodiode. As
diagrammed in Fig. 5., it was determined that using a 10 mega
ohm feedback resistor produces output voltages near 0V
when the diode was subjected to ambient light and about 2V
when exposed to moderate amounts of red light.
Fig. 5. Schematic of photo-detector and preamp.
2) Pulse shaper
The output of the photo-detector preamp provides a
somewhat inconsistent analog waveform. A pulse shaper is
used to create square digital pulses. This function is
accomplished with an LM193 voltage comparator. The
comparator is set to produce full-voltage pulses when the
preamp’s output increases above a threshold slightly higher
that the noise floor. A limited amount of hysteresis is
incorporated to reduce false triggering.
3) Frequency-to-voltage converter
The frequency of the digital pulses produced by the photodetector and pulse shaper is translated into a voltage by an LM
331. The voltage/frequency relationship is a function of
resistor and capacitor values. This relationship is shown in (3)
and a schematic, modified from the `331 datasheet, is in Fig. 6.
Fig. 6. Schematic of frequency to voltage converter.
Vout  f in  2.09V 
RL
 ( Rt Ct )
RS
(3)
4) Output buffer
The output buffer is simply a voltage follower that isolates
the output of the frequency to voltage converter from the input
impedance of the device to which it is connected. This is
necessary to allow the feedback signal to be attenuated with a
potentiometer. The feedback voltage can be adjusted without
altering the relationship presented in (3), above. The voltage
follower is realized with an LM301 op-amp.
It is also useful to note that the buffered voltage level can
be used as a stimulus to almost any circuit. It leaves provision
for the insertion of advanced control circuitry into the
feedback loop.
F. Controller
The controller delivers the duty cycle instruction signal to
the PWM motor drive. It synthesizes this signal from a
reference signal and the feedback loop. All three signals are
dc voltages and it is required that the feedback signal be
subtracted from the reference signal, so this function is
realized with a direct-coupled unity-gain difference amplifier.
Another LM 301 op-amp is used for this purpose. The
reference signal is the voltage that corresponds to the desired
motor speed. This voltage is obtained from the positive
voltage supply with a potentiometer voltage divider. The
feedback signal is also adjustable with a similar mechanism.
The reference voltage selected with the potentiometer is
applied to the non-inverting input of the difference amp and
the selected feedback signal is applied to the inverting input.
The output to the PWM drive is then the (reference) –
(feedback) signal.
V. ANALYSIS
A. Calculations
As documented, many calculations were performed in the
development of the circuit design for this system. In addition
to the critical calculations shown, other component values
were determined with quick calculations and estimations. As
will be discussed, it is advisable that this entire system be reanalyzed and some component values be reselected for optimal
performance.
B. Simulations
There are three major ways that this design can be
simulated. Each examines a different level of abstracted
operation. They are the: 1.) detailed electrical, 2.) detailed
functional, and 3.) abstract functional.
1) Detailed electrical
First, the electrical characteristics can be examined.
Depending on whether the motor load is represented
dynamically, this simulation approach would have the most
parameters and be the most complex. It would likely yield
detail about many parameters that are not of interest. This
virtual model would require a powerful simulation tool, such
as OrCAD PSpice®. The student evaluation version of the
software does not support all the devices used in the design,
nor does it allow simulation of the quantity of components
involved. However, the program is mentioned here because its
companion program Capture® was used as a CAD tool for the
schematic layout.
2) Detailed functional
An approach that would yield similar detail regarding the
operation of the system, would entail creating a detailed model
of the functional blocks that the circuit components instantiate.
This approach was taken using Simulink® for MATLAB®
from The MathWorks, Inc. and is introduced as follows:
First, a basic open-loop PWM / motor model is created.
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This model is tested against known parameters, if available.
Second, a model of the tachometer is created. Third, a
feedback loop is connected and examined.
In development of this project a PWM / motor model was
created and two Simulink models of the Canon FN30S were
implemented. The basic PWM / motor model is shown in Fig.
7. One of the motor models used the format of a known
working model from Carnegie Mellon University [9], shown in
Fig. 8. The other was developed based on a topology from
White [10] and is shown in Fig. 9. The two models were used
to investigate the role of the motor model parameters in
simulation. White’s model uses a motor velocity constant,
which, is what is provided with the Canon motor data. The
CMU model uses a mechanical damping ratio. This ratio was
tentatively calculated for the FN30S using (4). Neither of
these models effectively reproduced the data found in the
published specifications.
It appears, however, that the
discrepancy lies in the numbers, not the structure of the model.
Further investigation should reveal coherent results.
 mech  starting _ torque  mech _ const
Fig. 7. Basic PWM motor simulation.
(4)
3) Abstract functional
It is recommended that, for purposes of investigation into
feedback control mechanism, the most basic simulation be
developed. This transparent approach ignores the individual
mechanisms of the functional blocks, such as the PWM
instantiation of the speed controller. If interest lies only in
system behavior, there is no need to observe the inner
workings of the system.
C. Financial
Economic considerations are becoming a vital part of
almost all aspects of engineering design. While financial
matters ought not interfere with the technical quality of
engineering matters, they are often motivating factors when
determining a design’s feasibility or success. Often, after the
questions, “could it work?” and “is it physically possible?” are
asked, comes the question “what is the cost?” Since one of the
motivations of this project was to minimize expense, the cost
of development is considered here.
Since the design procedure is intended for education, time
and effort is not explicitly quantified. It should be noted that
this design is developed with the intent that it can be
reproduced by undergraduate engineering students within the
context of a control systems class. With such consideration, it
is believed that subsequent similar projects will pose
challenges intellectually, and not necessarily temporally.
The design of this system is based on components available
in a college electronics lab. All the parts are readily available,
so the cost of materials (already depreciated) is zero.
Admittedly, there is a positive list price associated with the
developed prototype, but a quick estimate would suggest that,
to replicate the design from recently purchased components,
would cost less than $20.
The itemization of development, component purchase,
assembly, and maintenance costs is a task recommended to be
done before and during progression of the prototype through
its stages of revision.
VI. TESTING
Fig. 8. DC motor model using back-emf.
Fig. 9. DC motor model using velocity constant.
A prototype of the system was assembled and tested. It
performed very well. The test assembly is shown in Fig. 10.
The most significant test performed was the verification of the
PWM duty cycle increase in response to decreased tachometer
frequency.
After setting a less-than-full power speed
reference and increasing feedback the amount just until the
speed decreased, the duty cycle of the signal delivered to the
motor would increase as the tachometer frequency decreased.
Thus, if the flywheel was slowed by applied friction, the power
to the motor was increased to compensate and maintain the
expected speed.
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ACKNOWLEDGMENT
The author gratefully acknowledges the contributions of the
following persons to this project: B. Bouma, C. Holwerda, M.
E. Husson, J. Lester, K. Palmer, P. F. Ribeiro, and D.
Ryskamp.
REFERENCES
[1]
Fig. 10. Prototype assembly showing system on breadboard, regulated power
supply, and oscilloscopes.
VII. CONCLUDING REMARKS
The design, construction, and testing of a small scale motor
speed control system provides an excellent method of
investigating control system theory and its practical
application. The development of a pulse-width modulated
switching motor drive presents many power-systems issues for
the designer to consider. The development of a highsensitivity optical detector is a good exercise in analog design
and touches on concepts relative to control systems such as
frequency response, bandwidth, gain and phase margins, and
compensation to promote stability. The testing of the
assembled system provides undeniable validity to the abstract
concepts considered. Furthermore, this project is a selfevident study of feasibility, demonstrating the opportunity to
wisely use available resources. It is also, hopefully, an
impetus for future, similar applications and projects. The
design presented here, is not complete by any measure, but is a
starting point for ongoing development.
APPENDIX
A. Comments for further development.
There are a few known issues regarding circuit
performance. These are being investigated and will be
documented later. A schematic of the prototype circuit is
available.
B. Availability of prototype
The prototype will be left available for inspection and testing
at Calvin College.
R. C. Dorf, R. H. Bishop, Modern Control Systems, ed. 9. Upper
Saddle River, New Jersey: Prentice Hall, 2001, p. 553.
[2] Steven D. Kaehler, “Fuzzy Logic – An Introduction” (2004, Dec).
[online].
Available:
http://www.seattlerobotics.org/encoder/mar98/fuz/fl_part1.html
[3] H. T. Nguyen, N. R. Prasad, C. L. Walker, E. A. Walker, A First Course
in Fuzzy and Neural Controls, Boca Raton: Chapman & Hall/ CRC,
2003, p.168, 86
[4] P. Avoke, presentation on neural networks, Calvin College ENGR 315.
(2004, Dec 8). (unpublished presentation)
[5] (Data sheet) NE555 Precision Timers, Publication SLFS022E, Texas
Instruments, (2004, March) [online] Available: http://www.ti.com
[6] (data sheet) DC motor catalog 2003(English), Canon Precision, Inc.,
[online] Available: http://www.canon-prec.co.jp/english/e.pdf
[7] Designing Photodiode Amplifier Circuits with OPA128, Burr - Brown,
Tucson, AZ, Application Bulletin AB-077, Jan. 1994. [online]
Available: http://www.ti.com
[8] (Datasheet) LM231A/LM231/LM331A/LM331 Precision Voltage-toFrequency
Converters,
Publication
DS005680,
National
Semiconductor,
(1999,
June)
[online]
Available:
http://www.national.com
[9] Control Tutorials for MATLAB® and Simulink®, Addison-Wesley
Publishing
Company,
Inc.,
1998
[online]
Available:
http://www.library.cmu.edu/ctms/ctms/index.htm
[10] Dr. J. R. White, “Dynamic Model of a Permanent Magnet DC Motor”
(Spring
1997),
UMass-Lowell,
[online]
Available:
http://www.profjrwhite.com/
system_dynamics/sdyn/s6/s6fanal/s6fanal.html
Andrew L. Wallner was born in Milwaukee, WI in
1981 and has ties to Chattanooga, TN and
Sheboygan, WI. He studied at the University of
Wisconsin, Sheboygan and Lakeshore Technical
College, in Manitowoc, WI. He is currently a
student at Calvin College pursuing a Bachelor of
Science in Engineering degree with a concentration
in electrical engineering in May 2005.
His employment experience included work at a
tool and equipment company, Quasius Equipment,
Calvin College Technical Services, and an engineering internship at Red
Arrow Products. His fields of interest include audio processing, and analog
electronics.
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