Semi-active damping with negative stiffness for multi-mode cable vibration mitigation: approximate collocated control solution

Abstract

This paper derives an approximate collocated control solution for the mitigation of multi-mode cable vibration by semi-active damping with negative stiffness based on the control force characteristics of clipped linear quadratic regulator (LQR). The control parameters are derived from optimal modal viscous damping and corrected in order to guarantee that both the equivalent viscous damping coefficient and the equivalent stiffness coefficient of the semi-active cable damper force are equal to their desired counterparts. The collocated control solution with corrected control parameters is numerically validated by free decay tests of the first four cable modes and combinations of these modes. The results of the single-harmonic tests demonstrate that the novel approach yields 1.86 times more cable damping than optimal modal viscous damping and 1.87 to 2.33 times more damping compared to a passive oil damper whose viscous damper coefficient is optimally tuned to the targeted mode range of the first four modes. The improvement in case of the multi-harmonic vibration tests, i.e. when modes 1 and 3 and modes 2 and 4 are vibrating at the same time, is between 1.55 and 3.81. The results also show that these improvements are obtained almost independent of the cable anti-node amplitude. Thus, the proposed approximate real-time applicable collocated semi-active control solution which can be realized by magnetorheological dampers represents a promising tool for the efficient mitigation of stay cable vibrations.

Multimode vibration control of stay cables using optimized negative stiffness damper

“…Results showed that a nonlinear damper could effectively suppress cable motion containing a wide range of modes and was, therefore, more advantageous than linear dampers in multimode vibration control. More recently, Weber and Distl introduced a semi‐active control scheme for multimode cable vibration mitigation. It is based on the approximate collocated solution of a clipped negative‐stiffness viscous damper optimized by the linear quadratic regulator (LQR) method and requires real‐time measurement of the damper stroke and force.…”

Development of a Self-Powered Magnetorheological Damper System for Cable Vibration Control

“…As expected, the damping coefficient almost remains a constant with the increase of the mode order of the cable for each circuit, while the negative stiffness increases with the increase of the mode order. However, the optimum negative stiffness for a stay cable does not depend on the mode number [36,37]. Hence, the DC generator with frequency-dependent negative stiffness may be better than viscous damping only, but is still suboptimal when compared with optimum viscous damping with negative stiffness for cable vibration control.…”

Adaptive Semiactive Cable Vibration Control: A Frequency Domain Perspective

“…Furthermore, the forcedisplacement trajectories exhibit the negative stiffness behavior provided by the self-sensing MR damper. The negative stiffness force yields the reduced local stiffness of the cable at the damper position, which augments the amplitude of the damper displacement to dissipate increased amount of vibrational energy due to the improved cable damping [25] and, hence, results in overall better control performance. control performs better than the optimal passive MR control, when is larger than 0.01, with 17.4%, 7.4%, 12.5%, and 22.2% further reductions of RMS cable displacement compared to the optimal passive case at the damper locations of 0.02 , 0.03 , 0.04 , and 0.05 , respectively.…”

“…However, the passive dampers may potentially lead to insufficient damping to other concerned modes without increasing the damper installation location that may undesirably affect the esthetics of the bridge [12,13], especially for very long cables. Alternative promising solution to cable vibration mitigation is semiactive control based on controllable magnetorheological (MR) dampers due to their real-time adjustable damping effect, fail-safe behavior, and superior energy dissipation over passive dampers [2,6,[14][15][16][17][18][19][20][21][22][23][24][25].…”

“…The optimal control methodology has been adopted in the semiactive cable damping system, based on either the linear quadratic regulator (LQR) control with available full state 2 Shock and Vibration feedback [24,25] or the linear quadratic Gaussian (LQG) control with state observation from noncollocated or collocated measurements [15][16][17][18][19][20][21]. The LQR or LQG control problem is usually treated from a time domain perspective by considering that the cable system model and its associated parameters are known.…”