Transcript Control of magnetic levitation system

By
Marwan Karrar
Abbadi
Advisor
Dr. W. Anakwa
Date: April 22, 2004
Outline
• Introduction
– Problem definition
– Objectives
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Functional description
System Block diagram
System identification
Control algorithm
Software implementation
Hardware interface
Results and analysis
Conclusions
Recommendations and future work
Introduction
• What are Magnetic levitation systems?
Maglev. are devices that suspend ferromagnetic
materials with the aid of electromagnetism. It has wide
number of applications such as high-speed trains,
magnetic bearings and high-precision platforms.
• Problem definition
Maglev. systems based on electromagnetic attraction are
characterized by non-linear and unstable open-loop
dynamics which suggests the need of stabilizing
controllers.
Project objectives
• Obtain a good model for the magnetic levitation system,
maglev model 33-120 from Feedback Inc. Limited.
• Design and implement a microcontroller-based digital
controller to stabilize a 21 gram steel ball at a desired
vertical position. The overall system should track applied
reference input signals.
Functional description
• Inputs:
Set point (Constant 1.50 [V] ), corresponds to a
distance of 22.5mm between the ball and the
electromagnet.
Reference signal (±0.4 Vpp)
Internal disturbances such as power supply fluctuation.
• Output
Actual ball position
System block diagram
System identification
• Importance of modeling the system.
• There are two approaches to identify the plant:
a) Analytical model- Using differential
equations.
b) Practical model- Bode frequency
response data fitting.
To obtain a good model for the system, both models were
obtained for comparison.
System identification
• Analytical model
There are two sets of equations that
describe magnetic levitation
systems.
This is the general electrical circuit for
1) Electrical:
magnetic levitation systems.
δi
i δx
e  R  i  L  L0  x0 2
δt
x δt
Where
However, our maglev. System is
driven by an active coil driver that
adds further non-linearity since e is a
function of i.
e = Coil input voltage
R= Coil resistance
i = Coil current
L= Coil inductance
t = Time
L0= Nominal point inductance
x0= Nominal point pos.
System identification
2) Mechanical equation
Using Newton second
law of motion
Electromagnetic force
EF= C (i/x)2
i
F  GF  EF  m  g  C   
x
2
Where
F= Resultant force
m= Mass of the steel ball= 0.0021 Kg
g= gravitational acceleration = 9.82 m/s2
C= Magnetic plant constant
Gravitation force
GF = m*g
System identification
• The previous equation contained non-linear
elements, linearization is needed.
• Taylor series expansion is used to approximate
the equations near the operating point of
x0=22.5 mm from electromagnet.
• Operating region= 18  27 mm from
electromagnet.
• Magnetic plant constant, C= 1.477x10-4 N.m2.A-2
System identification
Coil Inductance vs Ball Distance
y = 0.001x2 - 0.0761x + 298.12
R2 = 0.9958
298.5
298
297.5
Coil Inductance (mH)
• Coil inductance L was
approximated as a
constant = 296.74mH.
Series
Poly. (
297
296.5
296
Y(x)= 450.3*x
[V/m]
Ball distance from the coil (mm)
39
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
• Sensor calibration
was performed.
1
295.5
System identification
• Combining the previous equations:
Gp(s)analytical 
0.0013
(s
29.14
 1)( s
29.14
 1)( s
70.15
 1)
System identification
• The analog controller of the manufacturer
was connected to the plant to obtain
frequency response data.
• The data was obtained at the nominal
operating point x=x0=22.5 mm
• The reference input frequency was swept
between 0 and 20 Hz.
System identification
• The practical model of
the plant is:
Gp(s) practical 
(s
30.5
1.60
 1)( s
30.5
 1)
System identification
• The practical model was used instead of
the analytical model, since the analytical
model did not account for the non-linearity
of the active coil driver.
• The high-frequency pole at -70.15 rad/s
was omitted in the practical model
approximation.
Controller algorithm
Software implementation
• The digital controller was implemented
using assembly language program on an
Intel-80515 microcontroller.
• The software code:
– Samples the error signal via the A/D.
– Computes the control signal.
– Sends the control signal to the plant via the
D/A.
Software implementation
Intializations
80515, Stack, Timer 0 interrrupt,
MAIN
Timer 0
- Sample A/D input
Call Controller
Produce via D/A
Update vairables
e(n), e(n-1), u(n-1)
Prepare E(n)
- Set sign bit if neg.
- Multiply by coefficient
Prepare U(n-1)
- Set sign bit if -ve.
- Multiply by coefficient
Multiplex operation 1
Multiplex operation 2
Prepare E(n-1)
- Set sign bit if -ve
- Multiply by coefficient
Hardware interface
• Hardware interface circuitry is needed to
level shift and scale the error to the scale
of the microcontroller A/D.
• Furthermore, the control signal generated
via the D/A must be readjusted back to the
full scale.
Hardware interface
2
E1(t) = 0 ~ -5V
Since using inverting op-amp
3
E2(t) = 0 ~ +5V
Ready to be
interfaced to the
EMAC
1
Error signal E(t) = ±5V