SUMMARY Two control approaches for magnetorheological (MR) dampers on cables based on collocated control without state estimation are formulated, which generate amplitude and frequency independent cable damping: cycle energy control and controlled viscous damping (CVD). The force tracking is solved by the inverted Bingham model whose parameters are fitted as function of current and frequency. Cycle energy control and CVD are experimentally validated by hybrid simulations and free decay tests on stay cables of the Sutong Bridge, China, and the Eiland Bridge, the Netherlands. The implementation of CVD on the Russky Bridge, Russia, includes two novelties: the force tracking also takes the actual MR damper temperature into account to ensure precise force tracking for MR damper temperatures −40 to +60 °C and the decentralised real‐time control units with pulse width current modulation are installed next to each MR damper to avoid long direct current (DC) power lines with associated losses and thereby minimise power consumption. Copyright © 2014 John Wiley & Sons, Ltd.

The dissipated cycle energy of magnetorheological (MR) dampers operated at constant current results from controllable hysteretic damping and from almost current independent, small viscous damping. Thus, the emulation of Coulomb friction and linear viscous damping necessitates current modulation during one vibration cycle and therefore current drivers. To avoid this drawback, a cycle energy control (CEC) approach is presented which controls the hysteretic MR damper part such that the total MR damper energy equals the energy of optimal linear viscous damping by constant current during one cycle. The excited higher modes due to the hysteretic damping part are partially damped by the MR damper viscous part. Simulations show that CEC copes better with damper force dynamics and constraints than emulated linear viscous damping due to the slow control force dynamics of CEC which are given by cable amplitude dynamics. It is demonstrated that CEC of MR dampers with viscosity of approximately 4.65% of the optimal modal viscosity performs better than optimal linear viscous damping. The reason is that this damper viscosity represents an optimal compromise between maximum energy spillover to higher modes due to the controllable hysteretic part which produces more cable damping and maximum viscous damping of these higher modes. Damping tests on a cable with an MR damper validate the CEC approach.

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.

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Im Mai 2010 traten auf der Wolgograd‐Brücke windinduzierte Biegeschwingungen mit geschätzten Amplituden bis 40 cm auf. Seit November 2011 wird die Wolgograd‐Brücke durch adaptive Massendämpfer bedämpft, deren Frequenz und Dämpfung über geregelte MR‐Dämpfer in Echtzeit an die aktuelle Schwingfrequenz der Brücke angepasst sind. Im schlechtesten Fall bedämpft dieses Konzept die Brücke gleich stark wie passive Massendämpfer und in allen übrigen Fällen stärker. Diese Verbesserung ist mit ungefähr nur halb so viel Massendämpfermasse im Vergleich zu passiven Massendämpfern erreicht, was der Bauweise der Brücke entgegenkommt.Real‐time controlled tuned mass dampers for Wolgograd BridgeIn May 2010, the Wolgograd Bridge underwent wind‐induced bending vibrations with estimated amplitudes of up to 40 cm. Since November 2011, the Wolgograd Bridge is mitigated by adaptive tuned mass dampers whose frequency and damping are adjusted to the actual frequency of vibration in real‐time by controlled MR dampers. This concept mitigates the bridge in the worst case similarly to and in all other cases better than passive tuned mass dampers. This improvement is achieved by approximately half the mass damper mass compared to passive tuned mass dampers which is a desirable feature for the bridge construction type.