Semi-active control of vortex-induced vibration in long stay cable based on adaptive compensation sliding mode control

Abstract

With the increase in cable length, previous studies have shown that long stay cables experience high-mode vortex-induced vibration (VIV) frequently at the normal wind velocities, which are prone to fatigue damage on the anchorage end of the cable. Compared to the limitations posed by passive dampers in multi-mode vibration control, the semi-active magnetorheological (MR) dampers operated by intelligent controllers exhibit superior performance for long stay cables. This paper establishes a time-domain model to solve the VIV response based on the vibration equation of the cable and the coupling equation of the modified wake oscillator. A novel semi-active control strategy is proposed based on the adaptive compensation sliding mode control (ACSMC), which integrates both simple adaptive control (SAC) and sliding mode control (SMC). It dynamically adjusts parameters in real time according to the varying vibration response and then employs a semi-active MR damper to mitigate the VIV responses of long cables. An inverse model of MR damper is developed through the real-time force tracking method. The model determines the command current of MR damper using data from configured displacement and velocity sensors, along with the optimal control force. Finally, the control efficiency and robustness of the proposed control strategy are assessed taking a 454.1 m long stay cable as a numerical simulation. The responses of single-mode and multi-mode VIV are calculated to compare with the optimal passive control and semi-active control based on linear quadratic regulator (LQR). The results demonstrate that the ACSMC-based semi-active control strategy outperforms both the optimal passive control and LQR-based semi-active control. Moreover, the measurement noise of sensors in the control feedback loop, the abrupt change of structure parameters and load conditions have a negligible impact on control performance. The ACSMC-based semi-active control strategy nearly reaches the level of direct active control with minimal feedback requirements, demonstrating its potential in multi-mode vibration control. The strategy proposed can provide reliable support and reference for the semi-active control of long cables.