DC Motor System

8/6/2019 DC Motor System

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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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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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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.


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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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

= =

DC Motor System

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