![](bg4.png)
(a) (b)
Figure 5: Mode 4, 126.23 Hz (a). Mode 10, 261.77 Hz (b).
5 CONTROL DESIGN
Consider the linear time-invariant system given by
the following state equations,
Where
,
and
represent
the state, input and output respectively of the ith
local control station. A, B
i
and C
i
are real, constant
matrices. The results of the modal analysis are used
to determine the matrices A, B
i
and C
i
that will
describe the dynamics of the PPA structure.
For decentralized control, it is necessary to
determine n local feedback control laws that will
dynamically compensate for (1) in order to stabilize
the control loop, generating the following feedback
controllers:
where
and
are the ith
subcontroller and local external input and F
i
, G
i
, H
i
,
and K
i
are real, constant matrices. The standard two-
block mixed-sensitivity H-infinity technique,
(Morales et al., 1999), will be applied to accomplish
a pointing accuracy of 2 arc seconds to the final
reduced and validated state-space model.
6 CONCLUSIONS
An FEA model of an actuated laser platform used
for pointing control of a segmented telescope testbed
is developed. Modal analysis is performed on the
FEA model which calculates the natural frequencies,
mode shapes, degrees of freedom, and eigenvalues
of the structure. Further research is to be undertaken
to define which nodes are desirable and which nodes
are unnecessary in order to be able to perform
Guyan Reduction to reduce the size of the model for
practical implementation. The process described
here streamlines the process of modeling a
motorized platform from mechanical model (CAD,
SolidWorks, etc) to a preliminary, albeit enormous,
state-space model for the implementation of
controllers.
REFERENCES
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Performance Modeling and Decentralization of A
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H. Boussalis, 1994. “Decentralization of Large
Spaceborne Telescopes”, Proc. 1994 SPIE Symposium
on Astronomical Telescopes, Hawaii.
H. Boussalis, M. Mirmirani, A. Chassiakos, K. Rad, 1996.
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Large Segmented Space Reflector”, Control and
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K. Lim, 2011. “Modelling and Overlapping Decentralized
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