Optimal stochastic compensator for time-delayed active structural control systems subjected to random excitations

Abstract

Active feedback control systems confront with technical challenges when they are applied in civil engineering structures for vibration mitigation; one of which is the potential instability risk inherent in structure-control systems caused by insufficient compensation of time delay, especially in the scenario considering randomness associated with external excitations. To this end, this paper proposes an optimal stochastic compensator (OSC) to improve time-delayed active structural control systems subjected to random excitations. By extending the state vector, the OSC can be denoted as a linear combination between system state at the present time-step and control forces at the previous time-steps. According to the probabilistic criterion in function of reliability metrics of system state and control force, optimal cost-function weights of the OSC for good trade-off between control gain and control cost can be readily derived by introducing the framework of physically-based stochastic optimal (PSO) control. For verification purposes, randomly base-excited structures controlled by time-delayed active tendon systems, comprising single-degree-of-freedom, multi-degree-of-freedom and nonlinear oscillator systems, are investigated. The analysis and results reveal that the control performance is seriously degraded with increasing time delay; however, a rationally-designed OSC can be used to significantly improve control systems. Moreover, a definite relationship in cubic polynomial functions between optimal control cost-function weight of the OSC and time delay is obtained, by which the problem of time-varying delay compensation can be elegantly solved. In addition, the OSC has a good robustness, and can accommodate a larger effective time delay to linear systems than to nonlinear systems.