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.
MechatronicsMagnetic Levitation System
K. Craig4
Dynamic System Investigation
PhysicalSystem
ExperimentalAnalysis Comparison Mathematical
Analysis
MathematicalModel
PhysicalModel
DesignChanges
ParameterIdentification
MechatronicsMagnetic Levitation System
K. Craig5
• 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
MechatronicsMagnetic Levitation System
K. Craig6
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
MechatronicsMagnetic Levitation System
K. Craig7
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.
MechatronicsMagnetic Levitation System
K. Craig8
• 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
MechatronicsMagnetic Levitation System
K. Craig9
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
MechatronicsMagnetic Levitation System
K. Craig10
• 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
MechatronicsMagnetic Levitation System
K. Craig11
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.
MechatronicsMagnetic Levitation System
K. Craig12
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
MechatronicsMagnetic Levitation System
K. Craig13
• 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.
MechatronicsMagnetic Levitation System
K. Craig14
– 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.
MechatronicsMagnetic Levitation System
K. Craig15
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
MechatronicsMagnetic Levitation System
K. Craig16
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
MechatronicsMagnetic Levitation System
K. Craig17
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
MechatronicsMagnetic Levitation System
K. Craig18
+
-
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
MechatronicsMagnetic Levitation System
K. Craig19
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
MechatronicsMagnetic Levitation System
K. Craig20
+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
=
MechatronicsMagnetic Levitation System
K. Craig21
+-
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
MechatronicsMagnetic Levitation System
K. Craig22
( ) ( )( )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
MechatronicsMagnetic Levitation System
K. Craig23
• 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