Design of sliding mode control for structural vibration system with time-varying transmission delays

This paper investigates the application of the robust control strategy for reducing structural vibrations using the hybrid protective system in the presence of network abnormalities. It focuses on the design of sliding mode control using a novel sliding variable and modified reaching law approach in the presence of time-varying transmission delay and matched uncertainties. The novel sliding variable is designed using compensated state information which nullifies the effect of time-varying or deterministic transmission delay and ensures finite-time convergence of state variables in the presence of system uncertainties. Further, the stability analysis of the proposed control algorithm with the closed-loop system in the presence of system uncertainties is also presented using the Lyapunov approach. The compound equation of motion of the hybrid protective structural system is formulated and solved in the time domain by the state-space approach. The simulation results are obtained for a typical massive storage structure equipped with a hybrid protective system under seismic excitation. To prove the efficacy of the proposed control algorithm, the results are compared with the power-rate reaching law and conventional delayed system. It is observed that the proposed control strategy is quite effective and robust in the presence of system uncertainties.