Felix Weber

Frequency and damping adaptation of a TMD with controlled MR damper

This paper describes the new concept of a semi-active tuned mass damper with magnetorheological damper (MR-STMD). The real-time controlled MR damper force emulates controlled damping and a superimposed controllable stiffness force to augment or diminish the force of the passive spring stiffness which enables us to control the MR-STMD natural frequency. Both the damping and natural frequency are tuned according to Den Hartog’s formulae to the actual dominant frequency of the main structure irrespective of whether it is a resonance or a forced frequency. The MR-STMD is experimentally validated on the Empa bridge with a 15.6 m main span for different added masses to shift its resonance frequency 12.2% andC10.4% away from its nominal value. The experimental results are compared to those obtained when the MR-STMD is operated as a passive TMD that is precisely tuned to the nominal bridge. The comparison shows that the MR-STMD outperforms the TMD both in the tuned and all de-tuned cases by up to 63%. Simulations of the MR-STMD concept point out that the proposed semi-active control algorithm is most suitable for MR-STMDs due to the small amount of clipped active forces. A sensitivity analysis demonstrates that the real MR-STMD could be even more powerful if the force tracking errors in the MR damper force due to the current driver and MR fluid dynamics and remanent magnetization effects could be further reduced. The MR-STMD under consideration represents the prototype of the 12 MR-STMDs that have been running on the Volgograd Bridge since late fall 2011. (Some figures may appear in colour only in the online journal)

An adaptive tuned mass damper based on the emulation of positive and negative stiffness with an MR damper

This paper presents a new adaptive tuned mass damper (TMD) whose stiffness and damping can be tuned in real-time to changing frequencies of a target structure. The adaptive TMD consists of a tuned mass, a tuned passive spring and a magnetorheological (MR) damper. The MR damper is used to emulate controlled friction?viscous damping and controlled stiffness. The controlled positive or negative stiffness emulated by the MR damper works in parallel to the stiffness of the passive TMD spring. The resulting overall TMD stiffness can therefore be varied around the passive spring stiffness using the MR damper. Both the emulated stiffness and friction?viscous damping in the MR damper are controlled such that the resulting overall TMD stiffness and damping are adjusted according to Den Hartogs formulae. Simulations demonstrate that the adaptive TMD with a controlled MR damper provides the same reduction of steady state vibration amplitudes in the target structure as a passive TMD if the target structure vibrates at the nominal frequency. However, if the target structure vibrates at different frequencies, e.g.?due to changed service loads, the adaptive TMD with a controlled MR damper outperforms the passive TMD by up to several 100% depending on the frequency change.

Clipped viscous damping with negative stiffness for semi-active cable damping

This paper investigates numerically and experimentally clipped viscous damping with negative stiffness for semi-active cable damping. From simulations it is concluded that unclipped and clipped viscous damping with negative stiffness is equivalent to unclipped and clipped LQR. It is shown that optimized unclipped viscous damping with negative stiffness generates critical cable damping by an anti-node at the actuator position. The resulting curvature at the actuator position is larger than the curvature close to the anchors due to the disturbance forces which may lead to premature cable fatigue at the actuator position. Optimized clipped viscous damping with negative stiffness does not show this drawback, can be implemented using a semi-active damper and produces twice as much cable damping as optimal viscous damping. Close to the optimal tuning, it leads to approximately the same control force as optimal semi-active friction damping with negative stiffness, which explains the superior cable damping. The superior damping results from the negative stiffness that increases the damper motion. Clipped viscous damping with negative stiffness is validated on a strand cable with a magneto-rheological damper. The measured cable damping is twice that achieved by emulated viscous damping, which confirms the numerical results. A tuning rule for clipped viscous damping with negative stiffness of real cables with flexural rigidity is given.

Bouc–Wen model-based real-time force tracking scheme for MR dampers

A Bouc–Wen model-based control scheme is presented which allows tracking the desired control force in real-time with magnetorheological (MR) dampers without feedback from a force sensor. The control scheme estimates the MR damper force by parallel computing of several Bouc–Wen models with different constant currents as inputs and for the actual MR damper displacement and velocity, respectively. Based on the estimated forces and the desired control force the MR damper current is determined by a piecewise linear interpolation scheme. The model-based feed-forward control scheme is numerically and experimentally validated. If the desired control force is not constrained by the pre-yield region, residual force at 0 A and force at maximum current, the very small force tracking error ≤0.0015 in the simulation is caused by the control-oriented simplification of the linear interpolation scheme. The tests reveal that the real-time control scheme is numerically stable and the force tracking error of ≤0.078 represents an acceptable accuracy.

Precise stiffness and damping emulation with MR dampers and its application to semi-active tuned mass dampers of Wolgograd Bridge

This paper investigates precise stiffness and damping emulation with MR dampers when clipping and a residual MR damper force constrain the desired control force. It is shown that these force constraints lead to smaller equivalent stiffness and greater equivalent damping of the constrained MR damper force than desired. Compensation methods for precise stiffness and damping emulations are derived for harmonic excitation of the MR damper. The numerical validation of both compensation methods confirms their efficacy. The precise stiffness emulation approach is experimentally validated with the MR damper based semi-active tuned mass damper (MR-STMD) concept of the Wolgograd Bridge . The experimental results reveal that the precise stiffness emulation approach enhances the efficiency of the MR-STMD significantly when the MR-STMD is operated at reduced desired damping, where the impact of control force constraints becomes significant.

Optimal semi-active damping of cables: evolutionary algorithms and closed-form solutions

This paper presents a solution to the problem of cable vibration mitigation using a semi-active damping device. The optimal control of such a device is investigated with an evolutionary algorithm. A fitness function for the algorithm is defined, as the total energy removed from the cable by the damper in a numerical simulation. The initial and end conditions of the optimization are defined such that the solution is optimal for a single mode of vibration. The solution produced by the evolutionary algorithm is shown to outperform other popular semi-active control strategies for the given conditions, removing as much as 2.0 and 1.2 times more energy than the optimal linear viscous damper and clipped linear quadratic regulator controller, respectively. It is furthermore shown that the solution can be given as a simple control law parametrized with a single parameter. The performance of the control law derived is assessed by means of numerical simulation with a free vibration decay test. Due to the multiple modes of vibrations induced by the nonlinear damper in this test, the control law performance is slightly decreased compared to the aforementioned efficiency.

Cycle energy control of magnetorheological dampers on cables

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.

Modeling of a disc-type magnetorheological damper

Disc-type magnetorheological (MR) dampers are controllable semi-active actuators. The MR fluid within these devices is operated in shear mode, instead of the more frequently encountered flow mode. The present paper develops a model for this controllable device based on the measured behavior of an MR fluid sample deformed in a rheometer under operating conditions similar to those found within the damper. It is observed that for these conditions the behavior of the MR fluid is governed by friction. To capture the stick-slip motion of the MR fluid, the damper model is based on the popular LuGre friction model with additional parameters to account for the geometry of the fluid body. The model also includes the response dynamics due to the aggregation and radial migration of particles in the MR fluid body. These dynamics are separated into three first-order elements with time constants in the order of milliseconds, seconds and minutes. The model is validated with measurements on a cable–damper setup subjected to modal excitations.

Dynamic characteristics of controlled MR-STMDs of Wolgograd Bridge

This paper describes the dynamic characteristics of an adaptive tuned mass damper concept that is based on a real-time semi-actively controlled MR damper (MR-STMD) and is installed in the Wolgograd Bridge. The measurements and simulations of the prototype MR-STMD on the 15.6 m Empa bridge at different disturbing force levels demonstrate that the MR-STMD can cope with the nonlinear effect by which the resonance frequency and damping ratio of the Empa bridge depend on the amplitude and thereby on the excitation level. Whereas the efficiency of the MR-STMD is hardly affected by the aforementioned nonlinear effects, the passive TMD shows strong de-tuning. The tests for fast changes in frequency and amplitude of the disturbing force show that the response of the Empa bridge with the MR-STMD is smaller both during steady state and transient conditions than with a passive TMD, and the relative motion amplitudes in the MR-STMD are smaller or equal to those in the passive TMD. The force tracking accuracies of the prototype MR-STMD and of the Wolgograd MR-STMD are shown to be accurate, which generates precise frequency tuning of the MR-STMD in real-time and thereby explains the achievements described above. The test results indicate that the real-time controlled MR-STMD is an efficient and robust tool for the mitigation of structural vibrations. (Some figures may appear in colour only in the online journal)

Measured linear–quadratic–Gaussian controlled damping

This paper investigates experimentally the characteristics of LQG control for controlled vibration mitigation. The control algorithm is implemented in LabVIEW RT. The controller performance is measured at a test set-up consisting of a vibrating taut cable with MR damper. Measurements of the closed-loop system clearly point out that LQG control enables damping vibrations with respect to their intensity and frequency. When the cable is excited at constant frequency, the desired control force is dissipative and proportional to the vibration velocity at the damper position. Thus, for the system under consideration, LQG control ends up in the desired viscosity. With increasing frequency of the cable excitation, the desired viscosity decreases. The desired viscosities for the first four cable modes depend on the pole locations of the observer and regulator. The nearer they are located, the higher are the desired viscosities. Therefore, a design parameter describing precisely the distance between observer and regulator poles is introduced. Based on this design parameter, the paper proposes a systematic method of LQG controller design for practical applications.