A model attitude control system for a CCD camera magnetic suspension system is studied in this paper. In a recent work, a position and attitude sensing method was proposed. From this result, model position and attitude of a magnetic suspension system can be detected by generating digital outputs. Based on this achievement, a control system design using nonlinear feedback techniques for magnetic suspended model attitude control is proposed

Hou, Ann-San

Lin, CHIN-E.

English

NASA Technical Reports Server

NONLINEAR FEEDBACK MODEL ATTITUDE CONTROL USING CCD
IN MAGNETIC SUSPENSION SYSTEM
CHIN E. LIN ANN-SAN HOU
INSTITUTE OF AERONAUTICS AND ASTRONAUTICS
CHENG KUNG UNIVERSITY
TAINAN, TAIWAN, CHINA
 0-57
//y/o
ABSTRACT
A model attitude control system for a magnetic suspension system using CCD camera is
studied in this paper. In a recent work, a position and attitude sensing method was proposed
using CCD [117 From this result, model position and attitude in a magnetic suspension system
can be detected by generating digital outputs. Based on this achievement, a control system
design using nonlinear feedback technique for magnetic suspended model attitude control is
proposed.
THE PROPOSED METHOD
In the CCD sensing system, positions of specified points on the model are detected, x, and x 2. The
pitch angle, 0, and its sec(0) are calculated by hardware circuit. Assuming that two magnetic
coils are used in such a system to levitate and control the magnetic suspended model in the test
area, the control circuit then generates voltage outputs for magnet coils to induce appropriate
currents. A studied magnetic suspension system as shown in Fig. 1 includes two controlled
magnets with a longitudinal model. The proposed system block diagram is shown in Fig. 2.
Referring to the magnetic suspended model in Fig. 1, the energy equations of the model are
described as:
the kinetic energy:
T = (2) [d, + )_2)/2]2 + (_4 m 12)0.2 (I)
the potential energy:
v : - [(X, + X2 )/21 m g (2)
n'!l'tiC=ll[q,H_ P.AqE mt.kNK ]'lOT FILMP_
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where x_ and x 2 are positions of the specified points on the model, O is the pitch angle of the
model, m is the model mass on the center of gravity, l is the effective distance between two
specified points on the model, and g is the gravitational acceleration, with a constraint equation of:
sin(0) = (X2 - X1) / l (3)
From the Lagrange equation, we have:
to get:
for variable xt; then
d c3)_,) (OL/5X_) F, + X
_( aC/ - =-
oo It'l
(n4) (Xl +)(2 ) - rag 2 = - FI + )v (4)
d(c3L / 0A_2) - (OL / aX2) = -F2 -
to get:
for variable x2; and
(4)(_t ++_2)- rag/2 =-F2 - X (5)
dcc3L / 0_) - (c3L / c_30) = 1 cos(0) X
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to get:
for variable 0 ,
represent the constraint forces.
Subtracting Eq. 4 from Eq. 5,
(ml 2/12)_ = Icos(0) X (6)
where FI and F 2 represent the magnetic forces to the model,
_. = (Ft - F2)/2
and substituting into Eq. 6, we get:
(ml 2/12)_ +[(V2 -F1)/Z]tcos(0) = 0
Summing Eq. 4 and Eq.5, we get:
(7)
_, and l cos(O)X
Using the
feedback signals be:
(_I OOm +)(2)/2 - mg =-(F! + F2) (8)
nonlinear feedback technology, let the relations of applied magnetic forces and
+ kl0 + k2_)) see(0) (9)
Fz + F, = Co - CI(XI + X2) - Cz(A;, +9_2) (10)
where _'s and Ci's are system constants.
Substitute Eq. 9 into Eq. 7 to get:
(ml 2/12)_ + (l/2)(-k0 + kl0 + k20) = 0
and Eq. 10 into Eq. 8 to get:
,o
(m/2) (XI + )_'2) + C1 (XI + X2) + C2 (X_ + )_2) = mg +Co
F2 -F! = (-ko
(11)
(12)
From Eq. 11 and Eq. 12, the external forces F,, F2, pitch angle O and model position at its center
of gravity (x_+x2)/2 can be steadily controlled to a stable condition.
Summing Eq 9 and Eq. 10, we get:
F, = [(-ko + kl0+k2(_ )sec(O)+Co-Cl(X, + X2)-C2(9_ +A;2)]/2 (13)
F2 = [-(-k0 + kl 0 + k2(_ ) sec(0) + Co - C1 (X1 + X2) - C2(.J_1 + X2)1/2 (14)
From a known magnetic force model of the relationship between magnetic force and coil current
in quadratic forms,
Fl=(M,+C(i,)i_)/P(Xl,yl) (15)
F2=(M2+C(i2)i_)/P(x2,y2) (16)
where M_ and M z are magnetic dipoles. P(x,y) 's are polynomial functions of x and y. C(/) is
constant dependent on control current i
The magnetic coil currents can be obtained as:
i, = [FiP(xl,yl)- M,I 'n
i2 = [F2P(x2,y2) - M211/2
The control
(17)
(18)
parameters of magnetic coil current can be calculated and controlled.
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In this paper, the control system which feedbacks position signals from CCD camera and then
generates appropriate output currents to the magnetic suspension system is designed and
implemented using hardware circuits. System description and experimental results are
demonstrated in a two coil magnetic suspension system.
SYSTEM IMPLEMENTATION
For the implementation of the proposed method, the block diagram shown in
Figure 2 is designed and fabricated into hardware circuits. In the design process, the output
data of the position and attitude are generated as shown in Figure 3. The input data of Figure 3
are generated from the proposed CCD measurement system [1]. The detailed block diagram of
the real time control system for position and attitude control of the suspended model through
CCD is designed as shown in Figure 4. Before applying the control method to the proposed
system as shown in Figure 1, system model and parameters should be obtained. The system
parameter measurement is carried out via magnetic field and force measurement from different
locations within the control range of the two-pole levitation system. Assume that x denotes
the vertical suspending distance from the pole, and y denotes the horizontal shift distance between
two poles. The parameter measurement process sets the locations ofy at 0 ram, 8 mm, and
16 mm for magnetic coil currents of 1.0 A to 5.0 A with 0.5 A each step. The magnetic force in
g is measured and plotted on to figures similar to Figure 5. By a curve fitting process, the
constant C with respect to coil current i is measured to get Figure 6. Via the described
procedures, the polynomial function P(x,y) as defined previously can be fitted into a figure as
shown in Figure 7 with respect to different values of y. The data of P(x,y) is used to substitute
into Eqs. 15 and 16 to calculate the required magnetic force from each electromagnet pole. In
the implementation, the applied power supply voltage V,,_ and V,:2 should be determined. From
circuit designs, the relationship of voltage to current is fixed: Vcj = i_/2, and V,,2 = i2/2,
respectively. In the control concept, a ROM-mapping method is used. The basic idea of
ROM-mapping is to memorize all possible positions and attitude control data into the read-only
memory (ROM) . The corresponding control data of power voltage will be searched from the
ROM, and sent out as control commands.
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PRELIMINARY RESULTS
In this study, the magnetic suspended model control is accomplished by CCD cameras.
From the position and attitude sensing [1], two CCD's are proposed for six degrees of
freedom measurements, such as Zc, Xc, and 0t,;tch for CCD#1, and Yc,0roll, 0y_ for CCD#2
The control approach can also follow the previous resuIts. =Some control results will be
demonstrated in the conference. More details will be prepared on a revised version of the paper,
and will be published in the conference proceedings. In this paper, the control system which
feedbacks position signals from CCD camera and then generates appropriate output currents to
the magnetic suspension system is designed and implemented using hardware circuits. System
description and experimental results are demonstrated in a two coil magnetic suspension system.
ACKNOWLEDGEMENT
This work is supported by the National Science Council, Taiwan, ROC, under contract
number: NSC82-0424-E006-040.
REFERENCES
[1] C. E. Lin, A. S. Hou, "A Real Time Position and Attitude Sensing Using CCD in
Magnetic Suspension System Application", IEEE Instrumentation and Measurement Technology
Conference, May 18-20, 1993, Irvine, California, USA.
[2] C. E. Lin, H. L. Jou, "Force Model Identification for Magnetic Suspension System via
Magnetic Field Measurement", IEEE Transaction on Instrumentation and Measurement, June
1993, accepted.
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12
[__ideo Out
Fig. 1. The proposed experimental system using two electromagnet poles.
Real-time
Signal Processing
C1rcult
Control
Circuit
V___V tO I l" I1Convertor
V== -IiV t° I ___ _Convertor
Fig. 2. The block diagram of real time position and attitude control from
CCD measurement.
580
I 1 11 I
Fig. 3.
<D> 8751
The designed circuit in block diagrams to generate 0 ,sec 0
and (X1 +X2/2).
CO
+
(x,y) (x,y)
.I-
f M
Fig. 4. The designed circuit in block diagrams to implement
control algorithm.
581
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11.3
t}.2
0.1
]0 2,0 30 40 50 60 70 80 01 1_ 2 2,5 3
x.axis(mm) i CAmp)
3.5 4 4.5
,0A
4, A
y I _/ll
I0 20 30 40 50 60 70
x-zxi:(m=)
10 21) 30 40 50 60 70 80
x-axis(ram)
M,
Fig. 6. Curve fitting result of constant C.
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30
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I0 20 30 40 $0 60 70 14)
x-_m(m=)
Fig. 7. The polynomial of P(x,y) obtained from
results of Fig. 5.
Fig. 5. Magnetic force measurement with respect to
different coil currents.
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Nonlinear feedback model attitude control using CCD in magnetic suspension system

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