# Active Tendon Control of Stay Cable by a Giant Magnetotrstive Actuator Considering Time-Delay
## 1 Introduction  
Cables are very important structural members of cable-stayed bridges. However, large vibration of the cables is easily excited due to their light weight and low inherent damping, under external excitations such as wind, wind-rain combined and vehicles loads. Large vibrations of cables mainly include vortex-induced vibrations [1, 2], wind-rain-induced vibrations [3, 4, 5, 6], parameter vibrations [7, 8], etc. Hence, the vibration control of cables is a key issue that needs to be solved urgently with more and more long-span cable-stayed bridges built. Three methods for cable vibration control, including passive control, semi-active control, and active control, were proposed based on different vibration mechanisms. Among those passive methods, one of the effective methods in aerodynamic strategies is increasing the roughness of the cable, which can prevent the cable from forming the upper rain water rivulet, and then suppress the wind-rain induced vibration of the cable [9, 10]. The other is the structural measures that can increase the natural frequency and enhance the inherent damping of the cable by providing a secondary cable between the cables [11]. In addition, several passive dampers were attached to cables near their anchorages in some cable-stayed bridges to suppress the cable vibrations, which can effectively improve the modal dampingof the cables [12; 13; 14; 15]. However, the passive damper can only be optimally adjusted to control a specific mode vibration of stay cables and may be ineffective in multi-mode vibration mitigation [14]. Therefore, developing semi-active control and active control methods of cables is more effective. Many new dampers for semi-active control of stay cables are developed and their properties are also studied, such as superelastic shape memory alloy (SMA) dampers [16], Magnetorheological (MR) dampers [17], and self-powered MR dampers [18]. With regard to active control for stay cables, the application of axial motion to control the lateral vibrations has been studied. [PERSON] et al. [19] proposed a modal control approach using the axial motion of the cable end induced by an actuator to suppress cable vibrations. [PERSON] et al. [20] conducted the research on the active control of the small sag cables under vertical sinusoidal oscillation by numerical simulation and experiments, discussing the influence of linear and nonlinear internal resonance on control. Then, [PERSON] and [PERSON] [21] developed a globally asymptotic stable control strategy based on the bi-linear control theory. Based on this strategy, an in-plane vibration control for stay cables applying piezoelectric actuators was investigated by [PERSON] and [PERSON] [22], and [PERSON] et al. [23] verified the feasibility of multi-mode active control of cable vibrations using piezoelectric actuator via numerical simulations and experiments. Recently, an active control method of stay cable vibration using a Giant magnetostrictive actuator (GMA) is proposed by [PERSON] et al. [24]. Although active control can effectively mitigate the vibration of the cable, it produces some problems in actual implementation. One of the most critical issues is the time-delay resulted from the control system. The time-delay mainly affects the control performance in two aspects. One is that the time-delay existed during the processing of signal transmissions, especially the time-delay caused by the wireless transmissions of sensor data and control commands when the wireless network is used for information transmission. The other one is the time-delay of signal processing and actuator response, especially response time from the actuator receiving the control signal to applying the control force on the cable. As explained, the performance of active vibration for cables cannot be guaranteed to be solid due to the time-delay of the control system.