identification of a magnetic levitation system1- p. s. shiakolas, r. s. van schenck, d....
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Identification of a Magnetic Levitation System
By
Mohammad Shahab, Systems Engineering dept.
KFUPMSE 513 – Modeling & Systems Identification
Course Project
For Prof. Doraiswami
JUNE 2008 1
Maglev Trains
JR-Maglev MLX01 reached 581 km/h (Japan)superconducting magnets which allowfor a larger gap, and repulsive-typeElectro-Dynamic Suspension (EDS).
JUNE 2008 2
Magnetic Bearings
-support moving machinery without physical contact- advantages include very low and predictable friction, ability to run without lubrication and in a vacuum- industrial machines such as compressors, turbines, pumps, motors and generators
JUNE 2008 3
Research Experimentation
JUNE 2008 4
Outline1. System Dynamic Model
1. Nonlinear Model2. Linearized Model
2. System in the LAB1. Feedback® MAGLEV System2. Control Loop
3. Experiment1. Hardware2. Software3. Data
4. Identification1. Models2. Results3. Analysis
5. Future DirectionsJUNE 2008 5
System Model
References for Model:
1- P. S. Shiakolas, R. S. Van Schenck, D. Piyabongkarn, and I. Frangeskou, "Magnetic Levitation Hardware in the Loop and MATLAB Based Experiments for Reinforcement of Neural Network ControlConcepts", IEEE Transactions on Education, 2004
2- A. Bittar and R. M. Sales, “H2 and H, control applied to an electromagnetically levitated vehicle”, IEEE International Conference on Control Applications, Connecticut, USA, 1997
JUNE 2008 6
Free-Body Diagram
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Free-Body Diagram
Input: Voltage / Output: Ball Position
Total Inductance Operating Points
Coil InductanceJUNE 2008 8
Free-Body Diagram
Input: Voltage / Output: Ball Position
Assume no dynamics
Coil Resistance Input: Voltage
JUNE 2008 9
Nonlinear Model
Input: Voltage / Output: Ball Position
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Linearization
For some Operating Points
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Transfer Function
So,
2nd order system
JUNE 2008 12
MAGLEV in Lab
• In closed-loop
• Photosensor (IR) for position– Sensor = 2.5V -> furthest from magnet
– Sensor = -2.5 -> closest to magnet
• Set-point manually changed
• Analog Controller onboard
JUNE 2008 13
Closed-Loop System
Controller MAGLEV+V xdisturbance
Set-Point
JUNE 2008 14
Controller
errorV
Lead/Lag Compensator
JUNE 2008 15
Experiment
Controller MAGLEV+V
Set-Point
Identification OL
Identification CL
JUNE 2008 16
Experiment
2 PCs!!
Disturbance Generation
Signals Acquisition
d
V
x
d
NI USB-6008:12 bit resolution,Up to 10kHz sampling rate
JUNE 2008 17
Software
• Collected data Using:
– “VI Logger”
• Data-logging software
• Scheduling features
• Flexible adjustments
• Choose sampling speed
• Disturbance Generation:
– “LabVIEW”
• You can generate any kindof signals as required:
– Random Sequence,
– sinusoids,
– Etc
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Data• Three set-points:
– 0, 1, -1
• Sampling rate:
– 1kHz, i.e. 1000 samples per second
• Disturbance = Random Sequence with small amplitude
• Data Collected for:
– Disturbance (d)
– System Output (x)
– Control Input (V)
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Data• Data(0) = 3 × 41431 samples
• Data(1) = 3 × 41309 samples
• Data(-1) = 3 × 39257 samples
• Sampling Period = 1ms
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
x 104
0.8
1
1.2
1.4
1.6
1.8
2
1 1.05 1.1 1.15 1.2 1.25
x 104
1.15
1.2
1.25
1.3
1.35
1.4
1.45
1.5
System Output for set-point 0
Output Magnified
JUNE 2008 20
SYSTEM IDENTIFICATION
JUNE 2008 21
Model Structure
• Recall
• Due to discretization
JUNE 2008 22
Other Information
• As hardware sampling period is 1ms
– we can artificially enlarge the sampling period by ‘skipping’ samples
• Convenient speeds 1~10ms
• It is expected to have:
– Poles around unit circle
JUNE 2008 23
MAGLEV Identification
• Open-loop System Input: V, Output: x
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2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 3000
0.8
1
1.2
1.4
1.6
1.8
time
outp
uts
actual output and its estimate
actual output
estimated output
2100 2200 2300 2400 2500 2600 2700 2800 2900 3000
-1
-0.9
-0.8
-0.7
-0.6
-0.5
time
outp
uts
actual output and its estimate
actual output
estimated output
2100 2200 2300 2400 2500 2600 2700 2800 2900
1
1.5
2
2.5
time
outp
uts
actual output and its estimate
actual output
estimated output
Results Plots
Set-point = 0
Set-point = 1
Set-point = -1
Samples 2000-3000 showing
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Results Analysis
• System 1 Poles:
0.9932, 0.9057
• System 2 Poles:
0.9968, 0.8401
• System 3 Poles:
0.9958, 0.9148
• All poles proved to be near the unit circle
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Identification Approach 2
• Here, lets make
• To make poles exactly at the unit circle
• Y & A matrices will be different
= 1
Unknown parameters
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Results 2
• Tested for Set-Point 0,
• Poles
2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 3000
0.8
1
1.2
1.4
1.6
1.8
time
outp
uts
actual output and its estimate
actual output
estimated output
JUNE 2008 28
Closed-Loop Identification
• Input: Disturbance, Output: x
• Poles
• Controller should be tuned!
JUNE 2008 29
Future Directions• Horizontal Motion Dynamics
– Maybe need of another sensor
– Or, observable model –> Horizontal motion can be estimated
• Going to Continuous-time Analysis:
– Study effect of discretization
• Improve Controller Design
– More stable design
JUNE 2008 30
Final Remarks
• Acknowledgement:
– Thanks for Prof. Doraiswami for constant advising
• Interesting Project!
– Included many concepts together: Modeling, Magnetic Fields, Op-
amps, Nonlinearities, Numerical Methods, LabVIEW, Discrete-time Analysis, and
of course Identification, etc.
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THANKS!
•Q & A
JUNE 2008 32