Analytical Series-PID controller design with Smith Predictor approach for analyzing and mitigating the Time Delay Cyber Attack (TDCA)

For a cyber-physical system
$(CPS_{m})$
, communication and control channels are the most crucial part, which is used for enhancing efficiency and providing a better response to the physical systems. However, these channels are also responsible for the vulnerability of cyber attacks and can create severe problems for physical systems. Among the different kinds of cyber attacks, this paper focuses on a particular cyber attack, i.e., a time delay cyber attack (TDCA), which can destabilize or disrupt the system. To handle such a problem, this article proposed a joint method consisting of (i) a Series Proportional Integral Derivative (series-PID) controller and (ii) Smith Predictor approach. The proposed method provides better performance and stable response, verified by an illustrative example. A comparative analysis has been done through simulation work, and performance criteria are based on the integral square error
$(ISE_{e})$
, integral absolute error
$(IAE_{e})$
, and total variations
$(TV_{q})$
.