Design of sliding mode control for structural vibration system with time-varying transmission delays
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Design of sliding mode control for structural vibration system with time-varying transmission delays Dipesh Shah1
· Devesh Soni2
Received: 20 June 2020 / Revised: 31 August 2020 / Accepted: 17 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract 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. Keywords Sliding mode control · Transmission delays · MR damper · LNG tank · Lyapunov approach · Stability analysis
1 Introduction The schemes to control structural vibration against an earthquake can be viewed as passive, active, semi-active and hybrid control. For over three decades seismic isolation technology and passive control scheme has been recognized as one of the promising alternatives for protecting the structures (see e.g. [1–4] and references therein). The active and semi-active control methods have also found increasing applications in civil engineering structures. In [5], a hybrid control method and a combination of passive and semi-active control systems have received considerable attention due to their advantages. In hybrid system, base-isolation helps in reducing superstructure responses where the semi-active
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Dipesh Shah [email protected] Devesh Soni [email protected]
1
Department of Biological Engineering, Indian Institute of Technology, Gandhinagar, India
2
Department of Civil Engineering, Sardar Vallabhbhai Patel Institute of Technology, Vasad, India
control devices reduce the displacement at the isolation level. Several semi-active devices like magnetorheological (MR) dampers, electrorheological (ER) dampers, variable stiffness dampers, etc. have gained significant attention in recent years for the vibration control of structures. Amongst various semiactive con
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