Magnetic Levitation System Onemli

MechatronicsMagnetic Levitation System

K. Craig1

MechatronicsMagnetic Levitation System

Dynamic System Investigation

Kevin CraigRensselaer Polytechnic Institute

MechatronicsMagnetic Levitation System

K. Craig2

Electromagnet

Infrared LED

Phototransistor

Levitated Ball

Magnetic Levitation System A Genuine Mechatronic System

MechatronicsMagnetic Levitation System

K. Craig3

Overall Objective• The objective of this exercise is to build and test

a one-degree-of-freedom magnetic levitation device, i.e., a device to keep a ferromagnetic object suspended, without contact, beneath an electromagnet, and perform a complete dynamic system investigation.

• By measuring the location of the object using a non-contact sensor, and adjusting the current in the electromagnet based on this measurement, the levitated object can be maintained at a predetermined location.

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Dynamic System Investigation

PhysicalSystem

ExperimentalAnalysis Comparison Mathematical

Analysis

MathematicalModel

PhysicalModel

DesignChanges

ParameterIdentification

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• This system is both inherently nonlinear and open-loop unstable.

• Steps for a Dynamic System Investigation– Physical System Description– Physical Modeling (Truth Model vs. Design Model)– Model Parameter Identification– Mathematical Modeling– Dynamic System Behavior Prediction– Experiments to Validate Analytical Model– Feedback Control System Design and Implementation– Testing to Evaluate System Performance– Determine Design Improvements

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Required Background

• Electromechanics: Elementary Electromagnet• Linearization of Nonlinear Physical Effects• Electronic Components

– Resistor, Capacitor, Inductor– Electrical Impedance & Analogies – Potentiometer and Voltage Divider– Op-Amp Basics + Buffer, Summer, Difference, Inverting– Active Lead / Lag Controller– Diode and Light-Emitting Diode (LED)– Transistor: npn BJT, pnp BJT, Phototransistor

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Physical System Description

• The Magnetic Levitation System consists of the following subsystems:– Electromagnet Actuator mounted in a stand– Ball-position Sensor: Infrared LED and

Phototransistor, positioned in the stand– Analog Circuitry on a breadboard

• Lead Controller (analog implementation)• Current Amplifier• Assorted op-amps, resistors, capacitors, potentiometers, and

diodes for controller implementation, sensor adjustment, buffering, gain adjustment, summing, and inverting.

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• Required Power Supplies include:– ± 15 volts for op-amps– + 15 volts for electromagnet and phototransistor– + 15 volts for command and bias voltage generation– + 5 volts for infrared LED– Current requirements: 300 mA maximum

• Microcontroller for Digital Control Implementation– Blue Earth Micro 485

• Microprocessor: Intel 8051 - 12 MHz• Digital I/O: 27 bi-directional TTL-compatible pins• Analog Inputs: 4 12-bit, 0-5 V, A/D converter channels• Serial Communication: RS 232• 128K battery-backed RAM; 32K ROM

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Electromagnet

Infrared LED

PhototransistorVsensor = 5.44 VAt Equilibrium

Levitated Ballm = 0.008 kg

r = 0.0062 m = 0.24 in

Magnetic Levitation System A Genuine Mechatronic System

Equilibrium Conditionsx0 = 0.003 mi0 = 0.222 A

+x

i

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• Electromagnet Actuator– Current flowing through the coil windings of the

electromagnet generates a magnetic field.– The ferromagnetic core of the electromagnet provides

a low-reluctance path in the which the magnetic field is concentrated.

– The magnetic field induces an attractive force on the ferromagnetic ball.

f x i C ix

( , ) = FHIK

2

Electromagnetic ForceProportional to the square

of the currentand

Inversely proportional to the square of the gap distance

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Core Windings

1.4"

1.5"

2.6"

0.25"

– The electromagnet uses a ¼ - inch steel bolt as the core with approximately 3000 turns of 26-gauge magnet wire wound around it.

– The resistance of the electromagnet at room temperature is approximately 32 Ω.

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InfraredLED

+15V

Phototransistor

+5V

+

-

Unity GainBuffer Op-Amp

Vsensor62 Ω

1 KΩ

200 KΩ

Emitter Detector

Ball-Position SensorLED Blocked: Vsensor = 0 V

LED Unblocked: Vsensor = 10 VEquilibrium Position: Vsensor ≈ 5.40 VKsensor ≈ 4 V/mm Range ± 1mm

iemitter = 15 mA

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• Ball-Position Sensor– The sensor consists of an infrared diode (emitter) and

a phototransistor (detector) which are placed facing each other across the gap where the ball is levitated.

– Infrared light is emitted from the diode and sensed at the base of the phototransistor which then allows a proportional amount of current to flow from the transistor collector to the transistor emitter.

– When the path between the emitter and detector is completely blocked, no current flows.

– When no object is placed between the emitter and detector, a maximum amount of current flows.

– The current flowing through the transistor is converted to a voltage potential across a resistor.

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– The voltage across the resistor, Vsensor, is sent through a unity-gain, follower op-amp to buffer the signal and avoid any circuit loading effects.

– Vsensor is proportional to the vertical position of the ball with respect to its operating point; this is compared to the voltage corresponding to the desired ball position.

– The emitter potentiometer allows for changes in the current flowing through the infrared LED which affects the light intensity, beam width, and sensor gain.

– The transistor potentiometer adjusts the phototransistor current-to-voltage conversion sensitivity and allows adjustment of the sensor’s voltage range; a 0 - 10 volt range allows for maximum sensor sensitivity without saturation of the downstream buffer op-amp.

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From Equilibrium:As i ↑, x↓, & Vsensor ↓As i ↓, x ↑, & Vsensor ↑

+-

Vdesired

Σ Gc(s)Controller Σ

Vbias

+

+Current

AmplifierG(s)

Magnet + Ball

H(s)Sensor

Vactual X

i

Magnetic Levitation System Block Diagram

Linear Feedback Control Systemto Levitate Steel Ball

about an Equilibrium Position Corresponding to Equilibrium Gap x0

and Equilibrium Current i0

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Command and Error SignalGeneration

From Equilibrium:As i ↑, x↓, & Vsensor ↓As i ↓, x ↑, & Vsensor ↑

+

-Vsensor

Vcommand

-Verror

DifferenceOp-Amp

+

-

Unity GainBuffer Op-Amp

Vcommand

+15V

10 KΩ

100 KΩ

100 KΩ

100 KΩ

100 KΩ

VoltageDivider

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ActiveLead Controller

control 2 1 1 4 4

error 1 2 2 3 3

V R R C s 1 R R 0.01s 1V R R C s 1 R R 0.001s 1

+ + = − − = − + +

Vcontrol

-Verror

Lead Controller

+

-

InvertingOp-Amp

-

+

1R 100 K= Ω

1C 0.1 F= µ

2R 100 K= Ω

2C 0.01 F= µ

51 KΩ 1.6 KΩ

3R 1.6 K= Ω

4R 50 K= Ω

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+

-

Vbias

Vcontrol

Vbias +

Vcontrol

SummingOp-Amp

+

-

Vbias withUnity Gain

Buffer Op-Amp

Vbias

+15V

Unity GainInvertingOp-Amp

-

+

10 KΩ

10 KΩ

10 KΩ

10 KΩ

5.1 KΩ

10 KΩ

10 KΩ

5.1 KΩ

VoltageDivider

Vbias Generation & Summation with Vcontrol

Vbias = 1.77 VAt Equilibrium

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R1

+

-

Vcontrol+

Vbias +-

npn BJTTransistor

pnp BJTTransistor

R2

R3

Electro-Magnet

+Vsupply

diode

( ) 2em control bias

1 3

Ri V VR R

= +

iem

1

2

3

R 1000 R 510 R 17.8 (20W)

= Ω= Ω= Ω 0

0

i 0.222 Ax 3.0 mm=

=

Current Amplifier

Rem = 32 Ω

Vsupply = 15 V

supplysat

em 3

Vi

R R=

+

> 9.65 V

> 9.65 V

< 9.93 mA

< 9.93 V

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+x

i

mg

f x i C ix

( , ) = FHIK

2

Electromagnet

Ball (mass m)

Magnetic Levitation SystemControl System Design

Linearization:

2 2 2

2 2 3 2

i i 2 i 2 i ˆˆC C C x C ix x x x

≈ − +

Equation of Motion:

2

2

imx mg Cx

= −

2 2

2 3 2

i 2 i 2 i ˆˆ ˆmx mg C C x C ix x x

= − + −

At Equilibrium:2

3 2

2 i 2 i ˆˆ ˆmx C x C ix x

= −

2

2

img Cx

=

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+-

Vdesired

Σ Gc(s)Controller Σ

Vbias

+

+Current

AmplifierG(s)

Magnet + Ball

H(s)Sensor

Vactual X

i

2

2

img Cx

=

m 0.008g 9.81x 0.003i 0.222

====

C 1.4332E 5= −

2

3 2

2 i 2 i ˆˆ ˆmx C x C ix x

= −

ˆx 6540x 88iˆ ˆ= −

( )2

x 88ˆˆ s 6540i

−=

−

Kamp = 0.0287 A/V

Ksensor ≈ 4 V/mm

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( ) ( )( )2

88 0.0287 3000s 6540−

Open-LoopTransfer Function

4

3

R 0.01s 1 0.01s 14R 0.001s 1 0.001s 1 + + = + +

Controller

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• Digital Implementation of Controller– The analog controller has a high bandwidth needed to

compensate for inherent instability and nonlinearities.– Digital controllers have an advantage in that the control system

is implemented in software rather than in hardware, and is therefore much easier to modify.

– However, a controller implemented digitally has the disadvantages of quantization and limited sampling rate, which can adversely affect system performance.

-Verror ScalingCircuit0 – 5 V

12-bit A/D

DigitalController

Gc(z)

8-bit D/ADAC 08

MicrocontrollerWith

A/D Converter

Scale &Offset

CircuitryTs

ToBuffer Op-Amp