Nonlinear Optimal-Based Vibration Control of a Wind Turbine Tower Using Hybrid vs. Magnetorheological Tuned Vibration Absorber

This paper presents an implementation of a nonlinear optimal-based wind turbine tower vibration control method. An NREL 5.0 MW tower-nacelle model equipped with a hybrid tuned vibration absorber (HTVA) is analysed against the model equipped with a magnetorheological TVA (MRTVA). For control purposes, a 3 kN active actuator in parallel with a passive TVA is used in the HTVA system, while an MR damper is built in the MRTVA instead of a viscous damper, as in a standard TVA. All actuator force constraints are embedded in the implemented nonlinear control techniques. By employing the Pontryagin maximum principle, the nonlinear optimal HTVA control proposition was derived along with its simplified revisions to avoid a high computational load during real-time control. The advantage of HTVA over MRTVA in vibration attenuation is evident within the first tower bending frequency neighbourhood, with HTVA also requiring less working space. Using the appropriate optimisation fields enabled an 8-fold reduction of HTVA energy demand along with a (further) 29% reduction of its working space while maintaining a significant advantage of HTVA over the passive TVA. The obtained results are encouraging for the assumed mass ratio and actuator force limitations, proving the effectiveness and validity of the proposed approaches.

Studies on the damping mechanism of shape memory alloy-spring tuned vibration absorber attached to a multi-degree-of-freedom structure

To mitigate the adverse structural responses, an improved version of the traditional tuned vibration absorber has been proposed based on the shape memory alloy spring, referred as the shape memory alloy-spring tuned vibration absorber. The finite element numerical models of the multi-degree-of-freedom structure (e.g., transmission tower) and shape memory alloy-spring tuned vibration absorber are developed by using the commercial software ANSYS, and the nonlinear behavior of the shape memory alloy spring is validated based on a previous experimental study. The damping mechanism of the shape memory alloy-spring tuned vibration absorber attached to a multi-degree-of-freedom structure under seismic excitations is investigated, and the nonlinear hysteretic behavior of the shape memory alloy spring is also discussed. The results show that the proposed damper has a two-stage damping mechanism, and its control performance is remarkable. Because the coupled system response is sensitive to the amplitude level, the optimal configuration of the shape memory alloy-spring tuned vibration absorber can be obtained by parametric analysis. Particularly, because of the nonlinear target energy transfer and transient resonance capture mechanism, the shape memory alloy-spring tuned vibration absorber exhibits stable control ability under different seismic waves, indicating a good stability in vibration control of a multi-degree-of-freedom system.

Dynamic Balance of the Head in a Flexible Legged Robot for Efficient Biped Locomotion

In the biped robotics domain, head oscillations may be extremely harmful, especially if the robot is teleoperated, since vibrations strongly reduce the operator’s spatial awareness. In particular, undesired head oscillations occur in under-actuated robots, where springs and passive mechanisms are used to achieve a human-like motion. This paper proposes an approach to reduce the vibrations of a biped robot’s head; the proposed solution does not affect the dynamic locomotion properties, on which specific control logic could have been already tuned. The approach is tested on Rollo, a flexible-biped-wheeled robot, whose head vibrates throughout the robot locomotion. The two requirements, i.e., head vibration reduction and unchanged Rollo locomotion properties, are traduced in constraints to the robot possible modifications. Based on a 1D finite element model of the robot, tuned on experimental modal analysis, the undesired vibration causes are detected, and a solution for their reduction is proposed. Rollo’s head vibration amplitude is attenuated using a tuned vibration absorber, which achieves impressive performance in the robot. An archetype of the proposed vibration absorber is tailored designed on Rollo, without invasive changes to the robot structure. The proposed approach solves a significant problem in the biped robotic research community. The approach used to reduce the Rollo head oscillations may be utilized in other biped robot machines with or without flexible legs.

A Friction-Enhanced Tuned Ring Damper for Bladed Disks

This paper introduces a new type of damper for turbomachinery blisks. The major pitfalls of the damper concepts currently employed are two: the low level of relative motion that is available at the damper attachment location, and the inability to control the preload at the frictional interface. To address these issues, the proposed damper is designed as a tuned vibration absorber (TVA), which allows energy transfer from the blades to the damper provided that the natural frequency of the damper is close to that of the host structure. Thanks to the enhanced energy transfer, the damper can experience increased relative motion. Frictional contacts are then included to dissipate the energy transferred to the damper. The damper structure must be stiff enough to withstand centrifugal loading without affecting the preload too much. However, it also must be compliant to make sure that its natural frequencies can match the ones of the host structure. For this reason, the proposed damper involves a complex geometry that is stiff in the radial direction and softer in the circumferential direction, which is the direction of the relative motion. A model of the damper is created to damp the vibration of a realistic blisk. The effectiveness of the damper is investigated using high fidelity finite element (FE) models. The frequency response of the system is obtained to analyze the effectiveness of the proposed design. Preliminary results show the potential of this technology for structures with such low damping.

Analysis of a piecewise linear aeroelastic system with and without tuned vibration absorber

The dynamics of a two-degrees-of-freedom (pitch–plunge) aeroelastic system is investigated. The aerodynamic force is modeled as a piecewise linear function of the effective angle of attack. Conditions for admissible (existing) and virtual equilibria are determined. The stability and bifurcations of equilibria are analyzed. We find saddle-node, border collision and rapid bifurcations. The analysis shows that the pitch–plunge model with a simple piecewise linear approximation of the aerodynamic force can reproduce the transition from divergence to the complex aeroelastic phenomenon of stall flutter. A linear tuned vibration absorber is applied to increase stall flutter wind speed and eliminate limit cycle oscillations. The effect of the absorber parameters on the stability of equilibria is investigated using the Liénard–Chipart criterion. We find that with the vibration absorber the onset of the rapid bifurcation can be shifted to higher wind speed or the oscillations can be eliminated altogether.

A nonlinear optimization shooting method for bifurcation tracking of nonlinear systems

A continuation method for bifurcation tracking is presented based on the proposed optimization problem formulation which is designed to locate the bifurcation periodic solution. The bifurcation detection problem is formulated as a constrained optimization problem. The nonlinear constraints of the optimization problem are imposed on the shooting function and bifurcation conditions derived from the Floquet theory whereas the objective function associated with the pseudo-arclength correlation equation is devised to solution continuation. The proposed optimization formulation is integrated with the prediction–correction strategy to achieve bifurcation tracking. Two numerical examples about the Jeffcott rotor and the nonlinear tuned vibration absorber are illustrated to validate the effectiveness of the proposed methodology. Numerical results have demonstrated that the proposed method offers a convenient scheme to follow bifurcation periodic solution.