  Structural symmetries in the storage ring of synchrotrons are intentionally
created during the design phase of the magnetic lattices, but they are not
considered in the design of control algorithms that stabilize the beam of
accelerated particles. The choice of control algorithm, however, is limited by
the speed requirements of the synchrotron. Standard control algorithms for
synchrotrons are based on a singular value decomposition (SVD) of the orbit
response matrix. SVD controllers neither exploit the structural symmetries nor
exhibit any speed advantages. Based on the periodicity and the reflection
properties of the betatron function, we show that these structural symmetries
are inherited by the orbit response matrix. We show that the resulting
block-circulant and centrosymmetric properties of the matrix can be used for
different computationally efficient decompositions of the controller. We also
address the case of broken symmetry due to odd placements of magnets and
monitors. Our efficient decomposition could enable the use of more advanced
control techniques for synchrotrons, such as control algorithms that require
real-time optimization. These advanced control techniques could in turn
increase the quality of research in synchrotron light sources.
