Proceedings of the Technical University of Sofia

Abstract: A return to the operating set-point does not necessarily demonstrate that a cyber-physical system has rejected a disturbance. The output may recover while the disturbance is still active or only after the normal command path is restored. This study develops a trace-based assessment that separates these two situations. The empirical part of the study is based on an open KIOS cyber-physical sandbox dataset describing battery set-point manipulation. The record includes 205 observations collected over 1115 s. Four command-mismatch episodes are examined separately from the output error. Their behaviour is compared using tracking error, time spent within the tolerance band, recovery time, and the proposed Self-Regulation Index (SRI). With a 1% error tolerance, the SRI values during the active disturbance are 0.0070, 0.8558, 0.0134, and 0.4090 for the four episodes. The additive disturbance is corrected within one recorded update. The fixed-command case is more problematic: after the imposed command is removed, the deviation becomes 7.08 times larger than the highest error observed during the disturbance itself. In the held-command case, the system remains close to the operating point at first, but this changes once the legitimate reference starts to move. The results shows descriptivelly that disturbance rejection, recovery after restoration, and the ability to follow a changing reference should not be treated as the same property. The proposed measures describe what is observed in these traces, but they do not by themselves prove stability, autonomy, or resilience under other disturbances.