Jan Becker Høgsberg

Resonant Vibration Control of Three-Bladed Wind Turbine Rotors

Rotors with blades, as in wind turbines, are prone to vibrations due to the flexibility of the blades and the support. In the present paper a theory is developed for active control of a combined set of vibration modes in three-bladed rotors. The control systemconsists of identical collocated actuator-sensor pairs on each of theblades, and targets a set of three modes constituting a collective mode with identical motion of all the blades, and two independent whirling modes, in which a relative motion pattern moves forward or backward over the rotor. The natural frequency of the collective mode is typically lower than the frequency of the whirling modes due to support flexibility. The control signals from the blades are combined into amean signal, addressing the collective mode, and three components from which the mean signal has be subtracted, addressing the pair of whirling modes. The response of the actuators is tuned to provide resonant damping of the collective mode and the whirling modes by using the separate resonance characteristics of the collective and the whirlingmodes. In the calibration of the control parameters it is important to account for the added flexibility of the structure due to influence of other nonresonant modes. The efficiency of the method is demonstrated by application to a rotor with 42mblades, where the sensor/actuator system is implemented in the form of an axial extensible strut near the root of each blade. The load is provided by a simple but fully threedimensional correlated wind velocity field. It is shown by numerical simulations that the active damping system can provide a significant reduction in the response amplitude of the targeted modes, while applying control moments to the blades that are about 1 order of magnitude smaller than the moments from the external load.

Tuned resonant mass or inerter-based absorbers: unified calibration with quasi-dynamic flexibility and inertia correction

A common format is developed for a mass and an inerter-based resonant vibration absorber device, operating on the absolute motion and the relative motion at the location of the device, respectively. When using a resonant absorber a specific mode is targeted, but in the calibration of the device it may be important to include the effect of other non-resonant modes. The classic concept of a quasi-static correction term is here generalized to a quasi-dynamic correction with a background inertia term as well as a flexibility term. An explicit design procedure is developed, in which the background effects are included via a flexibility and an inertia coefficient, accounting for the effect of the non-resonant modes. The design procedure starts from a selected level of dynamic amplification and then determines the device parameters for an equivalent dynamic system, in which the background flexibility and inertia effects are introduced subsequently. The inclusion of background effect of the non-resonant modes leads to larger mass, stiffness and damping parameter of the device. Examples illustrate the relation between resonant absorbers based on a tuned mass or a tuned inerter element, and demonstrate the ability to attain balanced calibration of resonant absorbers also for higher modes.

Balanced calibration of resonant shunt circuits for piezoelectric vibration control

Shunting of piezoelectric transducers and suitable electric circuits constitutes an effective passive approach to resonant vibration damping of structures. Most common design concepts for resonant resistor-inductor (RL) shunt circuits rely on either maximization of the attainable modal damping or minimization of the frequency response amplitude. However, the former is suboptimal near resonance due to constructive interference of the two modes with identical frequency, and the latter results in reduced implemented damping. This article proposes an explicit pole placement–based design procedure for both series and parallel RL circuits. The procedure relies on equal modal damping and sufficient separation of the complex poles to avoid constructive interference of the two modes. By comparison with existing design procedures, it is demonstrated that the present calibration leads to a balanced compromise between large modal damping and effective response reduction with limited damping effort.

Equal modal damping design for a family of resonant vibration control formats

The principle of equal modal damping is used to give a unified presentation and calibration of resonant control of structures for different control formats, based on velocity, acceleration–position or position feedback. When introducing a resonant controller the original resonant mode splits into two, and if these are required to have the same modal damping ratio, the characteristic equation conforms to a two-parameter format. By selecting a suitable relative separation of the modal frequencies, the design problem defines a one-parameter family – determined, for example, in terms of the resulting modal damping ratio. While velocity feedback, and the associated acceleration–position formats, lead to near-equal resonant peak heights of the velocity in a frequency response diagram, position feedback leads to balanced acceleration peaks. It is demonstrated, how a simple additional time derivative term in the control coupling can change these properties into balanced position and velocity peaks, respectively. In particular this gives an improved control format based on measurement of structural displacement or deformation. In all cases the optimal calibration in terms of a root locus identification leads to a simple explicit pair of design formulae for controller frequency and damping ratio based on a simple two -degrees-of-freedom system. Unconditional stability is demonstrated for a general multi-degrees-of-freedom system with multiple controllers for the velocity and acceleration-velocity formats, while the position and extended position feedback format give a simple stability condition in terms of the gain factors and the structure flexibility matrix. The paper concludes with a simple design procedure based on the desired effective damping of a flexible structure with equal modal control in any of the discussed resonant formats.

Hybrid viscous damper with filtered integral force feedback control

In hybrid damper systems active control devices are usually introduced to enhance the performance of otherwise passive dampers. In the present paper a hybrid damper concept is comprised of a passive viscous damper placed in series with an active actuator and a force sensor. The actuator motion is controlled by a filtered integral force feedback strategy, where the main feature is the filter, which is designed to render a damper force that in a phase-plane representation operates in front of the corresponding damper velocity. It is demonstrated that in the specific parameter regime where the damper force leads velocity the control is stable and yields a significant improvement in damping performance compared to the pure viscous damper.

Efficient Mooring Line Fatigue Analysis Using a Hybrid Method Time Domain Simulation Scheme

Dynamic analyses of mooring line systems are computationally expensive. Over the last decades an extensive variety of methods to reduce this computational cost have been suggested. One method that has shown promising preliminary results is a hybrid method which combines finite element analysis and artificial neural networks (ANN). The present study presents a novel strategy for selecting, arranging and normalizing training data for an ANN. With this approach one ANN can be trained to perform high speed dynamic response prediction for all fatigue relevant sea states and cover both wave frequency motion and slow drift motion. The method is tested on a mooring line system of a floating offshore platform. After training a full fatigue analysis is carried out. The results show that the ANN with high precision provides top tension force histories two orders of magnitude faster than a full dynamic analysis.Copyright

Comparison of Neural Network Error Measures for Simulation of Slender Marine Structures

Training of an artificial neural network (ANN) adjusts the internal weights of the network in order to minimize a predefined error measure. This error measure is given by an error function. Several different error functions are suggested in the literature. However, the far most common measure for regression is the mean square error. This paper looks into the possibility of improving the performance of neural networks by selecting or defining error functions that are tailor-made for a specific objective. A neural network trained to simulate tension forces in an anchor chain on a floating offshore platform is designed and tested. The purpose of setting up the network is to reduce calculation time in a fatigue life analysis. Therefore, the networks trained on different error functions are compared with respect to accuracy of rain flow counts of stress cycles over a number of time series simulations. It is shown that adjusting the error function to perform significantly better on a specific problem is possible. On the other hand. it is also shown that weighted error functions actually can impair the performance of an ANN.

Characterization of clay-modified thermoset polymers under various environmental conditions for the use in high-voltage power pylons

The effect of nanoclay on various material properties like damping and strength of typical thermoset polymers, such as epoxy and vinyl ester, was investigated. Different environmental conditions typical for high-voltage transmission pylons made of composite materials were taken into account. Resin samples were prepared with various clay weight fractions ranging from 0% to 3%. Scanning electron microscopy, transmission electron microscopy, X-ray diffraction and rheological analysis were used to study the morphology and the structure of the nanocomposites. For all nanoclay-modified thermoset polymers, the morphology was found to be of exfoliated structure mainly. Static, uniaxial tensile tests showed that the addition of nanoclay to thermoset polymers led to a beneficial effect on the stiffness, whereas the tensile strength and ductility significantly decreased. When exposed to different environmental conditions, nanoclay was found to have a positive influence on the dynamic properties, analysed by a dynamic mechanical thermal analysis. The addition of nanoclay to the thermoset resin led to an increase of the damping properties by up to 28% for vinyl ester and up to 6% for epoxy at −20°C. The dielectric properties were evaluated by electrical breakdown strength tests resulting in 11% better insulating behaviour for nanoclay-modified vinyl ester.

Resonant passive–active vibration absorber with integrated force feedback control

A general format of a two-terminal vibration absorber is constructed by placing a passive unit in series with a hybrid unit, composed of an active actuator in parallel with a second passive element. The displacement of the active actuator is controlled by an integrated feedback control with the difference in force between the two passive elements as input. This format allows passive and active contributions to be combined arbitrarily within the hybrid unit, which results in a versatile absorber format with guaranteed closed-loop stability. This is demonstrated for resonant absorbers with inertia realized passively by a mechanical inerter or actively by the integrated force feedback. Accurate calibration formulae are presented for two particular absorber configurations and the performance is subsequently demonstrated with respect to both equal modal damping and effective response reduction.

Explicit solution format for complex-valued natural frequency of beam with R-shunted piezoelectric laminate transducer

Analysis and design of resistive shunt circuits for piezoelectric damping of beam structures is often based on a representation in terms of the single target vibration mode of the beam, neglecting spill-over effects from the out-of-bandwidth or residual vibration modes. In this article, a solution format is derived for the complex-valued natural frequency of the beam with a shunted piezoelectric laminate transducer, where the influence from the residual modes is taken into account by a quasi-static representation. This explicit solution format contains system parameters that directly represent the authority of the transducer and the spill-over from residual modes, and it recovers the short- and open-circuit frequencies as limit solutions. Furthermore, the frequency solution format provides the basis for design expressions for the optimal resistance and the corresponding attainable damping of the beam. The accuracy of the explicit frequency solution format is verified by comparison with numerical results. It is found that the complex-valued natural frequency of the first vibration mode of a beam with a piezoelectric laminate transducer shunted to a resistance is estimated with sufficient accuracy for engineering design purposes.