The feedback control of intra-bunch instabilities driven by electron-clouds or strong head-tail coupling (transverse mode coupled instabilities TMCI) requires bandwidth sufficient to sense the vertical position and apply correction fields to multiple sections of a nanosecond-scale bunch. These requirements impose challenges and limits in the design and implementation of the feedback control channel. This paper presents different models for the feedback subsystems: receiver, processing channel, amplifier and kicker, that take into account their frequency response and limits. These models are included in reduced mathematical models of the bunch dynamics and multi-particle simulation codes (WARP / C-MAD / HEADTAIL) to evaluate the impact of the subsystem limitations in the bunch stabilization and emittance improvement. With this realistic model of the hardware, it is possible to analyze and design the feedback system. This research is crucial to evaluate the boundary in the performance of the feedback control system due to technological limitations. Additionally, these models define the impact of parameter variations or mismatching and the effect of spurious perturbation and noise in the performance of the feedback system.



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