Closed orbit feedback (COFB) systems at synchrotrons used for the global orbit correction rely on the pseudoinversion of the orbit response matrix (ORM). A mismatch between the model ORM used in the controller and the actual machine ORM can affect the performance of the feedback system. In this paper, the typical sources of such model mismatch such as acceleration ramp ORM variation, intensity-dependent tune shift and beta beating are considered in comprehensive simulation studies. Their effect on the performance and the stability margins are investigated for both the slow and fast regimes of a COFB system operation. The spectral radius stability condition is utilized instead of the small gain theorem to arrive at the theoretical limits of COFB stability. Comparisons with simulations for SIS18 of GSI and experiments at the cooler synchrotron (COSY) in the Forschungzentrum Jülich (FZJ) are presented.

中文翻译：

---

空间模型不匹配的封闭轨道反馈系统的性能

用于全球轨道校正的同步加速器上的封闭轨道反馈（COFB）系统依赖于轨道响应矩阵（ORM）的伪求逆。控制器中使用的模型ORM与实际机器ORM之间的不匹配会影响反馈系统的性能。在本文中，在全面的模拟研究中考虑了这种模型失配的典型来源，例如加速度斜坡ORM变化，强度相关的音调偏移和β拍动。对于COFB系统运行的慢速和快速状态，都研究了它们对性能和稳定性裕度的影响。利用光谱半径稳定性条件代替小增益定理来达到COFB稳定性的理论极限。