dc motor system
TRANSCRIPT
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DC Motor System K. Craig 1
DC Motor System
DC Motor SystemDC Motor
+
MOSFET Amplifier
+Magnetic Tachometer
+
Frequency-to-VoltageConverter
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DC Motor System K. Craig 2
Step Response of a Brushed DC Motor
System Overview
Components and Experimental Set-Up
Brushed DC Motor
Magnetic Tachometer
MOSFET Amplifier & Diode Frequency-to-Voltage Converter
Background: Elementary Approach to Permanent-Magnet DC
Motor Modeling
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DC Motor System Hardware Overview
Electro-Mechanical Electric MotorMagnetic
Tachometer
Computer LabVIEWComputer Control
(Used for Closed-Loop Control)
Electrical
Power Amplifier
Circuit
Frequency to
Voltage Converter
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DC Motor System K. Craig 4
Brushed DC Motor
Electro-MechanicalDC Electric Motor
+ -
Merkle-Korff Industries
Permanent Magnet DC Motor
Reversible Direction
8400 rpm @ 12V
Includes Magnetic Tachometer
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Elements of a
Brushed DC Motor
Animation
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A current-carrying wire in the
presence of a magnetic field
has a force induced on it
(basis of motor action).
A moving wire in the
presence of a magnetic field
has a voltage induced in it
(basis of generator action).
N = 1/2
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Electro-Mechanical
Magnetic Tachometer
Built into the Merkle-Korff Industries
Permanent Magnet DC Motor
+ -
Magnetic
Tachometer
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Sensor
Rotating Magnet
DC MotorArmature
Sensor Stationary
Winding
Variable-Reluctance
Sensor
Brushed DC Motor
& Speed Sensor
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Variable-Reluctance Sensor (VRS)
Completely self-powered, VRS (magnetic) sensors are simple,
rugged devices that do not require an external voltage source
for operation.
They are generally used to provide speed, timing or
synchronization data to a display (or control circuitry) in theform of a pulse train.
Common Applications include:
Engine RPM measurement on aircraft, automobiles, boats,
buses, trucks, and rail vehicles.
Motor RPM measurement on drills, grinders, lathes,
automatic screw machines, etc.
Process speed measurement on food, textile, woodworking,
paper, printing, tobacco and pharmaceutical industry
machinery.
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Motor speed measurement of electrical generating
equipment.
Speed measurement of pumps, blowers, mixers, exhaustand ventilating fans.
Flow measurement on turbine meters.
Motor RPM measurement on precision camera, taperecording, and motion picture equipment.
Wheel-slip measurement on automobiles, trucks, and
locomotives. MPH measurement on agricultural equipment.
Some of the unique characteristics that make the use of VRS
sensors valuable in the above applications include:
Self-powered operation.
Error-free conversion of actuator speed to output
frequency.
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Simple installation.
No moving parts. Useable over a wide speed range.
Adaptable to a wide variety of configurations.
These properties have led to wide-spread utilization in a
number of industries. As a result, VRS sensors have
become known by many use-related names such as:
Magnetic Pick-Ups, Speed Sensors, Motion Sensors, PulseGenerators, Variable-Reluctance Sensors, Frequency
Generators, Transducers, Magnetic Probes, Timing Probes,
Monopoles, and Pick-Offs.
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Principle of Operation
The output signal of a VRS sensor is an AC voltage thatvaries in amplitude and wave shape as the speed of the
monitored device changes, and is usually expressed in
peak-to-peak voltage (V P-P).
One complete waveform (cycle) occurs as each actuator
passes the sensing area (pole piece) of the sensor.
The most commonly used actuator is a metal gear, but alsoappropriate are bolt heads (cap screws are not
recommended), keys, keyways, magnets, holes in a metal
disc, and turbine blades.
In all cases, the target material must be a ferrous metal,
preferably unhardened.
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A permanent magnet is the heart of a VRS sensor and
establishes a fixed magnetic field.
An output signal is generated by changing the strength of
this field. This is caused by the approach and passing of a
ferrous metal target near the sensing area (pole piece).
The alternating presence and absence of ferrous metal (gear
tooth) varies the reluctance, or resistance of flow of the
magnetic field, which dynamically changes the magnetic
field strength.
This change in magnetic field strength induces a current
into a coil winding which is attached to the output
terminals.
If a standard gear is used as an actuator, this output signal
would resemble a sine wave if viewed on an oscilloscope.
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In the most general terms, the
purpose of the Power Amplifier
Circuit is to allow a Microcontroller
or a Signal Generator to turn themotor On and Off.
Later on we will use the Power
Amplifier Circuit to control the
speed of the Motor.
Electrical
Power Amplifier
Circuit
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The heart of the Power AmplifierCircuit is the MOSFET.
MOSFET stands forMetal Oxide
SemiconductorField EffectTransistor.
For the purpose of this course you
can think of it as a really fast
switch - about five nanoseconds to
turn On or Off.
Electrical
BS170
Small Signal MOSFET
Rated for500 mA
60 V
Power Amplifier
Circuit
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This is the Electrical Symbol for
the MOSFET we are using.
Electrical
The Pins correspond exactly to theactual Physical component.
Power Amplifier
Circuit
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d ON State
When a Voltage is applied to
Pin 2 (Gate), Current is
allowed to flow from the Drain
to the Source.
Electrical Power Amplifier
Circuit
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dOFF State
When Pin 2 (Gate) is tied toGround, Current does Not
flow from the Drain to the
Source.
Electrical Power Amplifier
Circuit
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Electrical
Power Amplifier
Circuit
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Complete Power AmplifierCircuit
Notice the Addition of a
Resistor and a Diode.
ElectricalPower Amplifier
Circuit
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1N4001 Diode
The diode in parallel with the
motor is used to help protect the
MOSFET from a voltage surge.
Take note of the Orientation of
the diode. The white side shouldbe pointing to the +5V side of the
motor. Reversing this will
destroy the MOSFET.
Power Amplifier
Circuit
Electrical
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An ideal diode has zero
resistance (short circuit)when forward biased
and infinite resistance
(open circuit) when
reverse biased.Switching between on
and off states requires
nanoseconds.
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5 k Resistor
This resistor is here to make surethat the input is either totally on
or totally off (i.e., not floating).
Power Amplifier
CircuitElectrical
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Electrical Power Amplifier
Circuit
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The purpose of the
Frequency-to-VoltageConverter
is to convert the frequency of
the sine wave outputted from
the magnetic tachometer intoan analog voltage.
Frequency to
Voltage Converter
Electrical
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MagneticTachometer
As the motor spins faster, the Sine Wave that the Magnetic Tachometer
generates will increase in Both Frequency and Magnitude.
Because the magnitude can be influenced by other factors, we shall
only use the frequency to determine the rotational velocity.
Electrical
Frequency to
Voltage Converter
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The Output of the Frequency-to-
Voltage Converteris an analog
voltage proportional to the speed
of the motor.
This fixed proportion is
determined by resistors in the
circuit.
Frequency to
Voltage ConverterElectrical
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Electrical Frequency to
Voltage Converter
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This is the Complete
Circuit for the Frequency-
to-Voltage Converter.
The Gains are set so thatthe circuit will output one
volt for every 67Hz.
(i.e., 1V @ 67Hz,4.5V @ 300Hz )
Frequency to
Voltage ConverterElectrical
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0.01 uF Ceramic Capacitor 1.0 uF Electrolyte Capacitor
Insure correct polarity -
black side is ground.
ElectricalFrequency to
Voltage Converter
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Frequency to
Voltage Converter
Electrical
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DC Motor System Flow of Information
Electro-Mechanical
Electric MotorMagnetic
Tachometer
Electro-Mechanical
FrequencyDigital
Electrical Frequency to
Voltage ConverterPower Amplifier
Circuit
Computer AnalogDigitalLabVIEW
Computer Control
Digital
(For Closed-Loop Control)
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F to V Converter
2
3
4 5
1
7
8
60.01uF
100kOhm
1uF
10kOhm
Voltage OUTPUT
Magnetic Tachometer Connection (Yellow and Green)
VDD
15V
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Elementary Approach to Permanent-Magnet
DC Motor Modeling
b
F id B Bi
V v B d B v= =
= =
i
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Elements of a Simple DC
Motor
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Torque of a DC
Motor
( )nd
T 2F N iB sin dN iABNsin mBNsin2
= = = =
T N m B
=
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Schematic of a Brushed
DC Motor
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Modeling Assumptions
The copper armature windings in the motor are treated as a
resistance and inductance in series. The distributed
inductance and resistance is lumped into two characteristic
quantities, L and R.
The commutation of the motor is neglected. The system is
treated as a single electrical network which is continuously
energized.
The compliance of the shaft connecting the load to the motoris negligible. The shaft is treated as a rigid member.
Similarly, the coupling between the tachometer and motor is
also considered to be rigid. The total inertia J is a single lumped inertia, equal to the sum
of the inertias of the rotor, the tachometer, and the driven
load.
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There exists motion only about the axis of rotation of
the motor, i.e., a one-degree-of-freedom system.
The parameters of the system are constant, i.e., they do
not change over time.
The damping in the mechanical system is modeled as
viscous damping B, i.e., all stiction and dry friction are
neglected.
Neglect noise on either the sensor or command signal.
The amplifier dynamics are assumed to be fast relative
to the motor dynamics. The unit is modeled by its DC
gain, Kamp.
The tachometer dynamics are assumed to be fast
relative to the motor dynamics. The unit is modeled by
its DC gain, Ktach.
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Physical Modeling
For a permanent-
magnet DC motor,if= constant.
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Mathematical Modeling
The steps in mathematical modeling are as
follows:
Define System, System Boundary, System Inputs andOutputs
Define Through and Across Variables
Write Physical Relations for Each Element Write System Relations of Equilibrium and/or
Compatibility
Combine System Relations and Physical Relations toGenerate the Mathematical Model for the System
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m t m b bT K i V K = =
out m t m in b m b m
out t
in b
P T K i P V i K i
P K
P K
= = = =
=
out in
t b m
P P
K K K
=
=
LL R R B
J motor tachometer load
diV L V Ri T B
dt
T J J J J J J
= = =
= = + +
t b
3
t b
t b
K (oz in / A) 1.3524K (V / krpm)
K (Nm / A) 9.5493 10 K (V / krpm)
K (Nm / A) K (V s / rad)
=
=
=
Physical Relations
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System Relations + Equations of
Motionin R L bV V V V 0 =
m B JT T T 0 =
R L mi i i i= =
in b tdiV Ri L K 0 J B K i 0dt
= + =
t
in
b
KB0J J V
1i iK R LL L
= +
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Steady-State Conditions
in b
in b
t
t t b
in
ts in
in0
b
diV Ri L K 0
dt
TV R K 0K
K K K
T VR R
KT V
R
V
K
=
=
=
=
=
Stall Torque
No-Load Speed
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Transfer
Functions
in b t
diV Ri L K 0 J B K i 0
dt = + =
( ) ( )in b tV s (Ls R)I(s) K (s) 0 Js B (s) K I(s) 0 + = + =
( ) ( ) ( ) ( )
t t
2
in t b t b
t
2 t b
K K(s)
V (s) Js B Ls R K K JLs BL JR s BR K K K
JL
K KB R BR s sJ L JL JL
= =
+ + + + + + +
=
+ + + +
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Block Diagram
1
Ls R+
1
Js B+
bK
tK
mTiinV
+
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DC M t S t K C i 50
Simplification
in b tV Ri K 0 J B K i 0 = + =
( ) ( )tt t in b in b
t b tin
tin
motor m
tin m motor
motor
K1J B K i K V K V K
R R
K K KBVRJ J RJ
K1 1V
RJ
K1V since
RJ
+ = = =
+ + =
+ + =
+ = >>
m eJ L>>B R
= =