identification of a magnetic levitation system1- p. s. shiakolas, r. s. van schenck, d....

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

JUNE 2008 7

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

JUNE 2008 10

Linearization

For some Operating Points

JUNE 2008 11

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

JUNE 2008 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)

JUNE 2008 19

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

JUNE 2008 24

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

JUNE 2008 25

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

JUNE 2008 26

Identification Approach 2

• Here, lets make

• To make poles exactly at the unit circle

• Y & A matrices will be different

= 1

Unknown parameters

JUNE 2008 27

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.

JUNE 2008 31

THANKS!

•Q & A

JUNE 2008 32