Practical Predefined-Time Sliding-Mode Adaptive Resilient Control for PMSM Cyber–Physical Systems

The permanent magnet synchronous motor (PMSM) is extensively utilized in the power drive systems of Cyber-Physical Systems (CPSs). In scenarios where control signals are subjected to malicious attacks within the network, ensuring that the PMSM achieves its designated speed within a specified timeframe serves as a critical metric for evaluating the efficacy of security control strategies in networked systems. To address practical challenges arising from updates to controlled objects at the physical layer and limitations of control layer algorithms-wherein convergence time for system trajectory tracking errors (TTEors) may extend indefinitely-we have developed a novel resilient control algorithm with predefined-time convergence (PreTC) tailored for uncertain PMSMs susceptible to cyber threats. Firstly, we introduce an innovative Lyapunov stability criterion characterized by an adjustable gain reaching law alongside PreTC. Following this, we design an SMS (SMS) that incorporates PreTC and employ an extreme learning machine (ELM) to facilitate real-time identification of both physical layer models and malicious cyber-attacks. A sliding-mode adaptive resilient controller devoid of explicit physical model information is proposed for CPSs, with Lyapunov stability theory substantiating the system's predefined-time (PDT) stability. This significantly enhances resilience against malicious cyber-attacks and other uncertainties. Finally, comparative simulations involving four distinct resilient control algorithms demonstrate that our proposed algorithm not only guarantees predetermined convergence times but also exhibits robust resistance to cyber-attacks, parameter perturbations, and external disturbances-notably achieving a motor speed tracking error accuracy of 0.008. These findings validate the superior robustness and effectiveness of our control algorithm against malicious cyber threats.