Closed orbit correction using singular value decomposition of the response matrix

A theory of global orbit correction using the technique of singular value decomposition (SVD) of the response matrix and simulation of its application to the Advanced Photon Source (APS) storage ring are presented. The response matrix relates beam motion at the beam position monitor (BPM) locations to changes in corrector magnet strengths. SVD reconfigures the BPMs and correctors into the same number of "transformed" BPMs (t-BPMs) and "transformed" correctors (t-correctors), each t-BPM being coupled to at most one t-corrector and vice versa with associated coupling strength which determines the efficiency of orbit correction. The coefficients of these linear transformations can be used to determine which BPMs and correctors are the most effective. Decoupling the weakly coupled pairs will enhance the overall correction efficiency at the expense of accuracy. The orbit errors at decoupled t-BPMs are conserved and the strengths of decoupled t-correctors can be adjusted appropriately to optimize the actual corrector strengths. This method allows for estimating the limitation on orbit correction with given sets of BPMs and correctors, as well as optimizing the corrector strengths without overloading the corrector magnet power supplies.<
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