Identification of a Magnetic Levitation System

Transcription

KFUPM
SE 513 – Modeling & Systems Identification
Course Project
Identification of a Magnetic Levitation System
For
Prof. Doraiswami
By
Mohammad Shahab, Systems Engineering dept.
JUNE 2008
1
Maglev Trains
JR-Maglev MLX01 reached 581 km/h (Japan)
JUNE 2008
superconducting magnets which allow
for a larger gap, and repulsive-type
Electro-Dynamic Suspension (EDS).
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
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3
Research Experimentation
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4
Outline
1. System Dynamic Model
1.
2.
Nonlinear Model
Linearized Model
2. System in the LAB
1.
2.
Feedback® MAGLEV System
Control Loop
3. Experiment
1.
2.
3.
Hardware
Software
Data
4. Identification
1.
2.
3.
Models
Results
Analysis
5. Future Directions
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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 Control
Concepts", 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
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Free-Body Diagram
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Free-Body Diagram
Input: Voltage / Output: Ball Position
Total Inductance
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Coil Inductance
Operating Points
8
Free-Body Diagram
Assume no dynamics
Coil Resistance
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Input: Voltage
9
Nonlinear Model
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Linearization
For some Operating Points
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Transfer Function
So,
2nd order system
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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
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Closed-Loop System
Set-Point
disturbance
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+
Controller
V
x
MAGLEV
14
Controller
error
V
Lead/Lag Compensator
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Experiment
Identification OL
Set-Point
+
Controller
V
MAGLEV
Identification CL
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Experiment
d
NI USB-6008:
12 bit resolution,
Up to 10kHz sampling rate
Disturbance Generation
V
x
d
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2 PCs!!
Signals Acquisition
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Software
• Collected data Using:
– “VI Logger”
• Disturbance Generation:
– “LabVIEW”
•
•
•
•
• You can generate any kind
of signals as required:
Data-logging software
Scheduling features
Flexible adjustments
Choose sampling speed
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– Random Sequence,
– sinusoids,
– Etc
18
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
2
1.8
System
Output for
set-point 0
1.6
1.4
1.2
1
0.8
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
4
x 10
1.5
1.45
Output
Magnified
1.4
1.35
1.3
1.25
1.2
1.15
1
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1.05
1.1
1.15
1.2
1.25
4
x 10
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SYSTEM IDENTIFICATION
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Model Structure
• Recall
• Due to discretization
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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
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MAGLEV Identification
• Open-loop System Input: V, Output: x
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Results Plots
actual output and its estimate
Samples 2000-3000 showing
actual output
estimated output
1.8
outputs
1.6
1.4
Set-point = 0
1.2
1
0.8
2000
2100
2200
2300
2400
2500
2600
actual outputtime
and its estimate
2700
2800
-0.5
2900
3000
actual output
estimated output
-0.6
outputs
-0.7
Set-point = 1
-0.8
-0.9
-1
2100
2200
2300
2400
2500
2600
actual outputtime
and its estimate
2700
2800
2.5
2900
3000
actual output
estimated output
outputs
2
Set-point = -1
1.5
1
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2008
2200
2300
2400
2500
time
2600
2700
2800
2900
25
Results Analysis
• System 1 Poles:
 0.9932, 0.9057
• System 2 Poles:
• All poles proved to be near the
unit circle
 0.9968, 0.8401
• System 3 Poles:
 0.9958, 0.9148
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Identification Approach 2
• Here, lets make
=1
• To make poles exactly at the unit circle
Unknown parameters
• Y & A matrices will be different
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Results 2
• Tested for Set-Point 0,
• Poles
actual output and its estimate
actual output
estimated output
1.8
outputs
1.6
1.4
1.2
1
0.8
2000
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2100
2200
2300
2400
2500
time
2600
2700
2800
2900
3000
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Closed-Loop Identification
• Input: Disturbance, Output: x
• Poles
• Controller should be tuned!
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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
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Final Remarks
• Acknowledgement:
– Thanks for Prof. Doraiswami for constant advising
• Interesting Project!
– Included many concepts together: Modeling, Magnetic Fields, Opamps, Nonlinearities, Numerical Methods, LabVIEW, Discrete-time Analysis, and
of course Identification, etc.
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THANKS!
•Q & A
JUNE 2008
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Identification of a Magnetic Levitation System

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