Search results for: frictional oscillations

Authors: Sherif Keddis, Rafik Mitry, Norbert Schwesinger

Abstract:

Intelligent networking of devices has rapidly been gaining importance over the past years and with recent advances in the fields of microcontrollers, integrated circuits and wireless communication, low power applications have emerged, enabling this trend even more. Connected devices provide a much larger database thus enabling highly intelligent and accurate systems. Ensuring safe drinking water is one of the fields that require constant monitoring and can benefit from an increased accuracy. Monitoring is mainly achieved either through complex measures, such as collecting samples from the points of use, or through metering systems typically distant to the points of use which deliver less accurate assessments of the quality of water. Constant metering near the points of use is complicated due to their inaccessibility; e.g. buried water pipes, locked spaces, which makes system maintenance extremely difficult and often unviable. The research presented here attempts to overcome this challenge by providing these systems with enough energy through a flow harvester inside the pipe thus eliminating the maintenance requirements in terms of battery replacements or containment of leakage resulting from wiring such systems. The proposed flow harvester exploits the piezoelectric properties of polyvinylidene difluoride (PVDF) films to convert turbulence induced oscillations into electrical energy. It is intended to be used in standard water pipes with diameters between 0.5 and 1 inch. The working principle of the harvester uses a ring shaped bluff body inside the pipe to induce pressure fluctuations. Additionally the bluff body houses electronic components such as storage, circuitry and RF-unit. Placing the piezoelectric films downstream of that bluff body causes their oscillation which generates electrical charge. The PVDF-film is placed as a multilayered wrap fixed to the pipe wall leaving the top part to oscillate freely inside the flow. The warp, which allows for a larger active, consists of two layers of 30µm thick and 12mm wide PVDF layered alternately with two centered 6µm thick and 8mm wide aluminum foil electrodes. The length of the layers depends on the number of windings and is part of the investigation. Sealing the harvester against liquid penetration is achieved by wrapping it in a ring-shaped LDPE-film and welding the open ends. The fabrication of the PVDF-wraps is done by hand. After validating the working principle using a wind tunnel, experiments have been conducted in water, placing the harvester inside a 1 inch pipe at water velocities of 0.74m/s. To find a suitable placement of the wrap inside the pipe, two forms of fixation were compared regarding their power output. Further investigations regarding the number of windings required for efficient transduction were made. Best results were achieved using a wrap with 3 windings of the active layers which delivers a constant power output of 0.53µW at a 2.3MΩ load and an effective voltage of 1.1V. Considering the extremely low power requirements of sensor applications, these initial results are promising. For further investigations and optimization, machine designs are currently being developed to automate the fabrication and decrease tolerance of the prototypes.

Keywords: maintenance-free sensors, measurements at point of use, piezoelectric flow harvesting, universal micro generator, wireless metering systems

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Authors: Riccardo Fratini, Riccardo Santini, Jacopo Serafini, Massimo Gennaretti, Stefano Panzieri

Abstract:

This paper presents a nonlinear differential model, for a three-bladed horizontal axis wind turbine (HAWT) suited for control applications. It is based on a 8-dofs, lumped parameters structural dynamics coupled with a quasi-steady sectional aerodynamics. In particular, using the Euler-Lagrange Equation (Energetic Variation approach), the authors derive, and successively validate, such model. For the derivation of the aerodynamic model, the Greenbergs theory, an extension of the theory proposed by Theodorsen to the case of thin airfoils undergoing pulsating flows, is used. Specifically, in this work, the authors restricted that theory under the hypothesis of low perturbation reduced frequency k, which causes the lift deficiency function C(k) to be real and equal to 1. Furthermore, the expressions of the aerodynamic loads are obtained using the quasi-steady strip theory (Hodges and Ormiston), as a function of the chordwise and normal components of relative velocity between flow and airfoil Ut, Up, their derivatives, and section angular velocity ε˙. For the validation of the proposed model, the authors carried out open and closed-loop simulations of a 5 MW HAWT, characterized by radius R =61.5 m and by mean chord c = 3 m, with a nominal angular velocity Ωn = 1.266rad/sec. The first analysis performed is the steady state solution, where a uniform wind Vw = 11.4 m/s is considered and a collective pitch angle θ = 0.88◦ is imposed. During this step, the authors noticed that the proposed model is intrinsically periodic due to the effect of the wind and of the gravitational force. In order to reject this periodic trend in the model dynamics, the authors propose a collective repetitive control algorithm coupled with a PD controller. In particular, when the reference command to be tracked and/or the disturbance to be rejected are periodic signals with a fixed period, the repetitive control strategies can be applied due to their high precision, simple implementation and little performance dependency on system parameters. The functional scheme of a repetitive controller is quite simple and, given a periodic reference command, is composed of a control block Crc(s) usually added to an existing feedback control system. The control block contains and a free time-delay system eτs in a positive feedback loop, and a low-pass filter q(s). It should be noticed that, while the time delay term reduces the stability margin, on the other hand the low pass filter is added to ensure stability. It is worth noting that, in this work, the authors propose a phase shifting for the controller and the delay system has been modified as e^(−(T−γk)), where T is the period of the signal and γk is a phase shifting of k samples of the same periodic signal. It should be noticed that, the phase shifting technique is particularly useful in non-minimum phase systems, such as flexible structures. In fact, using the phase shifting, the iterative algorithm could reach the convergence also at high frequencies. Notice that, in our case study, the shifting of k samples depends both on the rotor angular velocity Ω and on the rotor azimuth angle Ψ: we refer to this controller as a spatial repetitive controller. The collective repetitive controller has also been coupled with a C(s) = PD(s), in order to dampen oscillations of the blades. The performance of the spatial repetitive controller is compared with an industrial PI controller. In particular, starting from wind speed velocity Vw = 11.4 m/s the controller is asked to maintain the nominal angular velocity Ωn = 1.266rad/s after an instantaneous increase of wind speed (Vw = 15 m/s). Then, a purely periodic external disturbance is introduced in order to stress the capabilities of the repetitive controller. The results of the simulations show that, contrary to a simple PI controller, the spatial repetitive-PD controller has the capability to reject both external disturbances and periodic trend in the model dynamics. Finally, the nominal value of the angular velocity is reached, in accordance with results obtained with commercial software for a turbine of the same type.

Keywords: wind turbines, aeroelasticity, repetitive control, periodic systems

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