Design and Experiments of a Galloping-Based Wind Energy Harvester Using Quadruple Halbach Arrays

This study aims to develop a device for harvesting electrical energy from low-speed natural wind. Four linear Halbach arrays are adopted to design a high-performance galloping harvester with the advantage of high durability and efficiency at low-frequency vibrations. The results of magnetic field analysis reveal that there are optimal sizes of the main and transit magnets of the Halbach arrays and coil to obtain the maximum magnetic flux density normal to the coil. The experimental and simulation results show that the electrical external load resistance significantly affects the vibration amplitude and the galloping onset velocity of the harvester. The results also reveal that the performance of the original design using the quadruple Halbach array was lower than that of the existing harvester because of the heavy magnet mass embedded in the tip prism. The modified design, reducing mass, improved the performance by four times compared to the original design.

Nonlinear Feedback Control of the Inductrack System Based on a Transient Model

As a new strategy for magnetic levitation envisioned in the 1990s, the Inductrack system with Halbach arrays of permanent magnets has been intensively researched. The previous investigations discovered that an uncontrolled Inductrack system may be unstable even if the vehicle travels well below its operating speed and that instability can be persistent near and beyond the operating speed. It is therefore necessary to stabilize the system for safety and reliability. With strong nonlinearities and complicated electro-magneto-mechanical coupling, however, the transient response of such a dynamic system is difficult to predict with fidelity. Because of this, model-based feedback control of Inductrack systems has not been well addressed. In this paper, by taking advantage of a recently available 2-DOF transient model, a new feedback control method for Inductrack systems is proposed. In the control system development, active Halbach arrays are used as an actuator, and a feedback control law, which combines a properly tuned PID controller and a nonlinear force-current mapping function, is created. The proposed control law is validated in numerical examples, where the transient motion of an Inductrack vehicle traveling at constant speed is considered. As shown in the simulation, the control law efficiently stabilizes the Inductrack system in a wide range of the operating speed, and in the meantime, it renders a smooth system output (real-time levitation gap) with fast convergence to any prescribed reference input (desired levitation gap).

Transient Vibration and Feedback Control of an Inductrack Maglev System

As a new strategy for magnetic levitation envisioned in 1990s, the Inductrack system with permanent magnets (PMs) aligned in Halbach arrays has been intensively studied and applied in many projects. Due to the nonlinear, time-varying electro-magneto-mechanical coupling in such a system, the dynamic behaviors are complicated with transient responses, which in most cases can hardly be predicted with fidelity by a steady-state Inductrack model. Presented in this paper is a benchmark 2-DOF transient Inductrack model, which is derived from the first laws of nature, without any assumed steady-state quantities. It is shown that the dynamic response of the Inductrack dynamic system is governed by a set of nonlinear integro-differential equations. As demonstrated in numerical simulations with the transient model, unstable vibrations in the levitation direction occur when the traveling speed of the vehicle exceeds a threshold. To resolve this instability issue, feedback control is implemented in the Inductrack system. In the development, an assembly of Halbach arrays and active coils that are wound on the PMs is proposed to achieve a controllable source magnetic field. In this preliminary investigation, the proposed control system design process takes two main steps. First, a PID controller is set and tuned based on a simple lumped-mass dynamic system. Second, the nonlinear force-current correlation is obtained from a lookup table that is pre-calculated by steady-state truncation of the full transient Inductrack model. With the implemented feedback control algorithms, numerical examples display that the motion of the vehicle in levitation direction can be effectively stabilized at different traveling speeds. Although only a 2-DOF transient model is used here, the modeling technique and the controller design approach developed in this work are potentially applicable to more complicated models of Inductrack Maglev systems.