TEAM 11 WINTER TERM PRESENTATION
DESIGN OF MAGNETIC LEVITATION
DEMONSTRATION APPARTUS
Fuyuan Lin,
Marlon McCombie,
Ajay Puppala
Xiaodong Wang
Supervisor: Dr. Robert Bauer
Dept. of Mechanical Engineering,
Dalhousie University
April 4, 2014
http://poisson.me.dal.ca/~dp_13_11
Presentation Overview
2
Project Description
Design Requirements
Product Architecture
Component Selection
Conceptual Design
1.
2.
3.
4.
5.
i.
ii.
Design Alternatives
Chassis Design
6.
Control System
i.
ii.
iii.
7.
8.
9.
10.
11.
Plant Subsystem
Circuit Design:
Amplifier & Driver
Controller
System Implementation
GUI
Budget
Assessing Requirements
Future Considerations
1. Project Description
3
 Design and build a magnetic levitating device
 To levitate an object magnetically
 Demonstrate different control theories taught in MECH
4900 Systems II course
Arduino (MCU) &
Circuitry for Levitation
Object Levitating
2. Design Requirements
4
 Demonstrative Requirements
 Levitate object magnetically
 Compare simulated and experimental position of the object
being levitated
 Lag, lead, lag-lead P, PI, and PID control
 User Requirements
 Graphical User Interface (GUI) to interact with device
 Plug ‘n Play
 Safe and Ergonomic
2. Design Requirements
5
 Visual Requirements
 Viewable from 15- 20 ft. (back of the classroom)
 Levitate the object at least 2-4 cm away from the coil
 Power Requirements
 Conventional 120 VAC input
 No potential electrical risk to the user
 Operating Budget $1,500
3. Product Architecture
6
General Schematic of demonstration device
4. Component Selection
7
Levitation
Object
Technique
Material
Shape
Motion
Permanent
Rectangular
Chrome Steel
Horizontal
Magnets
prism
Electromagnets
Electrodynamics
Superconductors
Regular Steel
Circular
disk
Neodymium Solid sphere
Composite
Hollow
sphere
Vertical
MCU
Sensor
Arduino
Hall Effect
LEGO
Mindstorm
NXT 2.0
Reflective
BeagleBoard
Optical
Proximity
Altera DE2 Photoelectric
Table shows selected components of the subsystem
Electromagnetic Levitation
8
 Strength of magnetic field generated by the coil
depends on the current supplied
 Control challenge:
 𝐹𝐸𝑙𝑒𝑐𝑡𝑟𝑜𝑚𝑎𝑔𝑛𝑒𝑡 ∝
𝑐𝑢𝑟𝑟𝑒𝑛𝑡 2
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 2
Electromagnetic Levitation
5.1. Design Alternatives
9
1.Single Electromagnet
with Hall Effect Sensor
2. Double
Electromagnet Design
3. Multiple Coil
Parallel Arrangement
5.2. Chassis Design
10
Design evolution of the chassis
Material
Aluminum 1060
Mass (kg)
3.95
ABS Plastic
1.50
Wood (Birch Ply)
1.20
Material options for the chassis
Cost
$235
$675
$126
6. Control System
11
Input
Desired
Position
+_
Error
Controller
Current
Unity Feedback System
Plant
Actual
Position
6.1. Plant Subsystem
12
Current
Levitation
Position
Change
Sensor
Breakdown of the Plant System
Voltage
Output
Electromagnet Design Requirements
13
Air Gap, X = 20 mm,
Object Mass = 20 g,
⟹ Fobject = 0.196 N
Coil Turnings, N = 1000
For pole D = 3 cm,
πD2
4
⟹ A=
=0.00071 m2
Permeability of free space,
μo = 4π × 10−7
Vs
Am
Electromagnet Selection
14
Height of the
electromagnet
Core Diameter
Cu wire gage
Coil Turnings
Field Strength
Design
Criteria
12 VDC Pneumatic
Solenoid
< 7 cm
3.65 cm
3 cm
Max. 22
(Dia. 0.645)
1000
2 cm
Dia. 0.65
0.0833 wb/𝑚2
~2000
-Satisfactory Test Results
-No heat issues
Assessment of 12 VDC Pneumatic Solenoid based on design requirements
6.1. Plant Subsystem
15
Current
Levitation
Position
Change
Sensor
Voltage
Output
Breakdown of the Plant System
Hall Effect Sensor
Sensor Component
16
 Hall Effect Sensor
 Analog position sensor
(Solid State Type – SS49 Series)
 Size: 30 x 4 x 2 mm
 Range of Detection: up to 4 cm
 Unit Cost: $2.50
Picture Courtesy of Honeywell.
Design Refinement
17
Initial Design
Final Design
Addition of new Hall Effect Sensor to
differentiate Electromagnet signal
Sensor Testing
18
Sensor Circuit Design
19
Circuit for Differential Amplification of Sensor Ouput
6.1. Plant Subsystem
20
Current
Levitation
Voltage
Sensor
Position
Change Measurement Output
Sensor
Calibration
Actual
Position
2 Hall Effect Sensors
Position Sensor Calibration
21
Hall Effect Sensor Calibration
Sensor Voltage (V)
3.50
3.00
2.50
2.00
1.50
1.00
0.50
0.00
0
20
40
60
80
Actual Distance (mm)
100
120
6.3. Control System
22
Input
Desired
Position
+_
Error
Controller
Current
Unity Feedback System
Plant
Actual
Position
6.3. Controller Component
23
 Microcontroller - Arduino Mega 2560
 4 – Hardware serial ports for
communication with MATLAB
 Runs control algorithms
 Cost: $55
Picture Courtesy of Arduino
7. System Implementation
24
Receive Data
Levitation
Control
Serial
Communication
Arduino & Real Time
• Arduino uses feedback data from sensors to
manipulate position
MATLAB & Arduino
• Manipulation of control parameters
• Retrieval of feedback data
8. PID Controller
25
8. Budget
Materials
Unit
Cost
Amount
Arduino
Hall Effect Sensor
Potentiometer
Operation Amplifier
Power Supply Unit
Neodymium Magnet
USB Cable
Electromagnet
Other Parts
$55.09
$2.64
$27.40
$0.64
$77.42
$4.99
$6.00
$14.95
-
3
20
2
5
1
2
4
-
Wood (61 x 121 x 2.5 cm )
Acrylic glass
Aluminum sheet
Other Parts
$6.15
$13.99
$15.93
-
26
Cost
ELECTRONICS
$165.27
$42.78
$54.80
$3.20
$77.42
$4.99
$12.00
$38.97
$55.51
CHASSIS
Summary of Materials Cost
3
2
1
Sub Total
$18.45
$27.98
$15.93
$22.38
$564.09
8. Budget
27
Sub Total
$564.09
Total Shipping
$85.11
Total Taxes
$65.14
Contributions
-$150.00
Total
$564.34
Summary of Budget
9. Assessing Requirements
28
 Demonstrative Requirements
 Levitate object magnetically
~ Compare desired and measured controller variables
 Lag, lead, lag-lead compensation techniques
 P, PI, and PID control
 User Requirements
 Graphical User Interface (GUI) to interact with device
 Plug ‘n Play
 Safe and Ergonomic
9. Assessing Requirements
29
 Visual Requirements
 Viewable from 15- 20 ft. back of the classroom
 Levitate the object at least 2-4 cm away from the coil
 Power Requirements
 Conventional 120 VAC input
 No potential electrical risk to the user
 Operating Budget $1,500
10. Future Considerations
30
 Build more powerful electromagnet or add an extra
electromagnet to repel the levitated object – Might increase
the range of levitation.
 Implementation of lag, lead, and lag-lead compensator.
 Use different microcontroller capable of serial or other form
of communication without effecting the frequency of the
feedback signal.
 Use different interface instead of MATLAB for example
LabView
Acknowledgements
31
Dr.Y.J. Pan
Al-Mokhtar O. Mohamed
Post-Doctoral Position Mech. Dept.
Mechanical Dept. Professor
Jonathan MacDonald
Electrical Technician
Dr. Timothy Little
Angus MacPherson
Mechanical Technician
Electrical Dept. Professor
Reg Peters
Wood Workshop Technician
32
Thank You & Questions?
References
40
Arduino UNO webpage. http://arduino.cc/en/Main/arduinoBoardUno. Retrieved Mar. 30, 2014
ATmega238 datasheet. http://www.atmel.com/Images/doc8161.pdf. Retrieved Mar. 30, 2014
Honeywell SS49 datasheet. http://www.wellsve.com/sft503/Counterpoint3_1.pdf. Retrieved Mar. 30, 2014
"RobotShop : The World's Leading Robot Store." RobotShop. N.p., n.d. Sun. Mar. 30, 2014
“MathWorks MATLAB/Simulink website.” http://www.mathworks.com/products/simulink/. Retrieved
Mar. 30, 2014
Mikonikuv Blog, “Arduino Magnet Levitation – detailed description.”
http://mekonik.wordpress.com/2009/03/17/arduino-magnet-levitation/. Retrieved Nov. 20, 2013
Williams, Lance. "Electromagnetic Levitation Thesis." N.p., 2005. Web. 28 Oct. 2013.
Control System Question
System Model
𝑚𝑜 = 0.02 𝑘𝑔,
𝑥𝑜 = 0.02 𝑚,
𝑖𝑜 = 0.738 A
Ball Model:

Force Balance 𝐹𝑛𝑒𝑡 = 𝑚𝑎,
𝑚𝑥 = 𝑚𝑔 − 𝐹

𝑖2
𝐹(𝑖, 𝑥) = 𝐶 2
𝑥
 For change in position, 𝑥 = 𝑥 − 𝑥𝑜
𝑖2
Inverse Square Law!
𝑚𝑥 = 𝑚𝑔 − 𝐶 2
𝑥
2
2𝑖𝑜
2𝑖𝑜
𝑚𝑥 − 𝐶
𝑥
=
−𝐶
𝑖
3
2
𝑥
𝑥
𝑜
𝑜
2
Static equilibrium:
𝑚𝑔 = 𝐶
Magnetic Plant Constant:
𝑖𝑜
𝑥𝑜 2

𝑚𝑔𝑥𝑜 2
𝑁𝑚2
−4
⟹C=
= 1.441 × 10
𝐴2
𝑖𝑜 2
Linearization of electromagnetic force using Taylor
series approximation:
𝑖2
𝐶 2
𝑥
𝑖2
𝐶 2
𝑥
𝑖𝑜 2
=𝐶 2
𝑥𝑜
𝑖𝑜 2
=𝐶 2
𝑥𝑜
−𝐶
−𝐶
Electromagnetic Force
2𝑖𝑜 2
𝑥𝑜 3
2𝑖𝑜 2
𝑥𝑜 3
𝑥 − 𝑥𝑜 + 𝐶
𝑥−𝐶
2𝑖𝑜
𝑥𝑜 2
𝑖
2𝑖𝑜
𝑥𝑜 2
(𝑖 − 𝑖𝑜 )
Thus, the differential equation:
𝑥 − 3695 𝑥 = − 63 𝑖
2
⟹ 𝑠 𝑋 𝑠 − 26.59𝑋 𝑠 = −0.536 𝐼 𝑠
𝑋 𝑠
𝐼 𝑠
=
−0.536
𝑠 2 − 26.59
System Model
Electromagnet Model
Electromagnetic coil driving circuit
System Model
𝐿 = 87 mH,
𝑅 = 17.5 Ω
 Electromagnet Model
𝑑𝑖
− 𝑉𝑜𝑢𝑡 = 0
𝑑𝑡
𝑑 𝑉𝑜𝑢𝑡
𝑉𝑖𝑛 − 𝐿
− 𝑉𝑜𝑢𝑡 = 0
𝑑𝑡 𝑅
Laplace transform:
𝐿𝑠
𝑉𝑖𝑛 (𝑠) −
+ 1 𝑉𝑜𝑢𝑡 (𝑠) = 0
𝑅
Rearranging the equation
𝑉𝑜𝑢𝑡
1
=
𝐿
𝑉𝑖𝑛
𝑠+1
𝑅
Finally, ∵ 𝑉𝑜𝑢𝑡 = 𝐼 𝑅 :
𝑉𝑖𝑛 − 𝐿
Simplified Circuit
1
𝐼
0.057
𝑅
=
=
𝐿
𝑉𝑖𝑛
0.00497𝑠 + 1
𝑠+1
𝑅
Control Systems
Electromagnet
Voltage
Input
Plant
(Levitation)
Position
Change
Ball
Combination of Electromagnet & Ball Model
𝐼 𝑠
𝑋 𝑠
𝑋 𝑠
×
=
𝑉 𝑠
𝐼 𝑠
𝑉 𝑠
Thus, the uncompensated system
𝑋 𝑠
0.057
0.536
𝑂𝐿𝑇𝐹 =
=
0.00497𝑠 + 1 𝑠 2 − 26.59
𝑉 𝑠
Note: Negative controller gain is required