Variational Integrators for Reduced Magnetohydrodynamics

Reduced magnetohydrodynamics is a simplified set of magnetohydrodynamics equations with applications to both fusion and astrophysical plasmas, possessing a noncanonical Hamiltonian structure and consequently a number of conserved functionals. We propose a new discretisation strategy for these equations based on a discrete variational principle applied to a formal Lagrangian. The resulting integrator preserves important quantities like the total energy, magnetic helicity and cross helicity exactly (up to machine precision). As the integrator is free of numerical resistivity, spurious reconnection along current sheets is absent in the ideal case. If effects of electron inertia are added, reconnection of magnetic field lines is allowed, although the resulting model still possesses a noncanonical Hamiltonian structure. After reviewing the conservation laws of the model equations, the adopted variational principle with the related conservation laws are described both at the continuous and discrete level. We verify the favourable properties of the variational integrator in particular with respect to the preservation of the invariants of the models under consideration and compare with results from the literature and those of a pseudo-spectral code.Comment: 35 page

Analysis of Current Ripples in Electromagnetic Actuators with Application to Inductance Estimation Techniques for Sensorless Monitoring

Techniques for estimating the plunger position have successfully proven to support operation and monitoring of electromagnetic actuators without the necessity of additional sensors. Sophisticated techniques in this field make use of an oversampled measurement of the rippled driving current in order to reconstruct the position. However, oversampling algorithms place high demands on AD converters and require significant computational effort which are not desirable in low-cost actuation systems. Moreover, such low-cost actuators are affected by eddy currents and parasitic capacitances, which influence the current ripple significantly. Therefore, in this work, those current ripples are modeled and analyzed extensively taking into account those effects. The Integrator-Based Direct Inductance Measurement (IDIM) technique, used for processing the current ripples, is presented and compared experimentally to an oversampling technique in terms of noise robustness and implementation effort. A practical use case scenario in terms of a sensorless end-position detection for a switching solenoid is discussed and evaluated. The obtained results prove that the IDIM technique outperforms oversampling algorithms under certain conditions in terms of noise robustness, thereby requiring less sampling and calculation effort. The IDIM technique is shown to provide a robust position estimation in low-cost applications as in the presented example involving a end-position detection

A Self-Sensing Method for Electromagnetic Actuators with Hysteresis Compensation

Self-Sensing techniques are a commonly used approach for electromagnetic actuators since they allow the removal of position sensors. Thus, costs, space requirements, and system complexity of actuation systems can be reduced. A widely used parameter for self-sensing is the position-dependent incremental inductance. Nevertheless, this parameter is strongly affected by electromagnetic hysteresis, which reduces the performance of self-sensing. This work focuses on the design of a hysteresis-compensated self-sensing algorithm with low computational effort. In particular, the Integrator-Based Direct Inductance Measurement (IDIM) technique is used for the resource-efficient estimation of the incremental inductance. Since the incremental inductance exhibits a hysteresis with butterfly characteristics, it first needs to be transformed into a B-H curve-like hysteresis. Then, a modified Prandtl–Ishlinskii (MPI) approach is used for modeling this hysteretic behavior. By using a lumped magnetic circuit model, the hysteresis of the iron core can be separated from the air gap, thus allowing a hysteresis-compensated estimation of the position. Experimental studies performed on an industrial switching actuator show a significant decrease in the estimation error when the hysteresis model is considered. The chosen MPI model has a low model order and therefore allows a computationally lightweight implementation. Therefore, it is proven that the presented approach increases the accuracy of self-sensing on electromagnetic actuators with remarkable hysteresis while offering low computational effort which is an important aspect for the implementation of the technique in cost-critical applications

Sensorless Pedalling Torque Estimation Based on Motor Load Torque Observation for Electrically Assisted Bicycles

The need for reducing the cost of and space in Electrically Assisted Bicycles (EABs) has led the research to the development of solutions able to sense the applied pedalling torque and to provide a suitable electrical assistance avoiding the installation of torque sensors. Among these approaches, this paper proposes a novel method for the estimation of the pedalling torque starting from an estimation of the motor load torque given by a Load Torque Observer (LTO) and evaluating the environmental disturbances that act on the vehicle longitudinal dynamics. Moreover, this work shows the robustness of this approach to rotor position estimation errors introduced when sensorless techniques are used to control the motor. Therefore, this method allows removing also position sensors leading to an additional cost and space reduction. After a mathematical description of the vehicle longitudinal dynamics, this work proposes a state observer capable of estimating the applied pedalling torque. The theory is validated by means of experimental results performed on a bicycle under different conditions and exploiting the Direct Flux Control (DFC) sensorless technique to obtain the rotor position information. Afterwards, the identification of the system parameters together with the tuning of the control system and of the LTO required for the validation of the proposed theory are thoroughly described. Finally, the capabilities of the state observer of estimating an applied pedalling torque and of recognizing the application of external disturbance torques to the motor is verified

Analysis and Exploitation of the Star-Point Voltage of Synchronous Machines for Sensorless Operation

In the field of sensorless drive of synchronous machines (SMs), many techniques have been proposed that can be applied successfully in most applications. Nevertheless, these techniques rely on the measurement of the phase currents to extract the rotor position information. In the particular case of low-power machines, the application of such techniques is challenging due to the limited bandwidth of the available current sensors. An alternative is offered by those techniques that exploit the star-point voltage rather than phase currents. This work aims at providing a model of the dynamic behavior of the star-point voltage and presenting a technique for extracting the rotor electrical position needed for sensorless operation of SMs. Two different circuitries for measuring the star-point voltage are also presented and then compared. The presented mathematical analysis and the measurement methods are validated both numerically and experimentally on a test machine

Improvement of Position Estimation of PMSMs Using an Iterative Vector Decoupling Algorithm

This paper presents an improvement of sensorless techniques based on anisotropy for the estimation of the electrical angular position of synchronous machines by means of an iterative algorithm. The presented method reduces the effect of the fourth saliency harmonics on the measured signals avoiding the use of an observer or filter, thus, no additional dynamics are introduced on the system. Instead, a static algorithm based on iterative steps is proposed, minimizing the angular position error. The algorithm is presented and applied using the DFC (Direct Flux Control) technique but it is not limited to this choice. The advantages and limitations of this method are presented within this paper. The proof of the algorithm convergence is given. Simulations and experimental tests are performed in order to prove the effectiveness of the proposed algorithm

Super Twisting Sliding Mode Control with Compensated Current Controller Dynamics on Active Magnetic Bearings with Large Air Gap

Due to their unique properties, like no mechanical contact and therefore no wear and no lubrication needed, Active Magnetic Bearings (AMBs) have been a dynamic field of research in the past decades. The high non-linearities of AMBs generate many challenges for the control of the otherwise unstable system, thus they need to be addressed to deliver the performance that modern applications require. Integrating the current controller dynamics into the model of a position controller in a cascading control loop helps to improve the performance of the control loop compared to a plain current controlled schema. Further, this nested control loop guarantees the predefined current dynamics of the current controller, tuned according to an industrial criterion. The systems dynamics are modelled and the proposed controller is validated experimentally on a physical test bench. The experimental results show a performant position control with a nested and explicit current controller on an AMB, even with a large air gap and star-connected coils. The trajectory range of the rotor was reduced by 87% to ±20 µm, compared to a plain current-controlled model. The proposed control strategy lays the foundation for further research, especially concerning sensorless position estimation techniques since these usually have limited bandwidth and benefit from a predefined current dynamic

Design and Implementation of a Driving Strategy for Star-Connected Active Magnetic Bearings with Application to Sensorless Driving

For decades, sensorless position estimation methods gained lots of interest from the research community, especially in the field of electric drives and active magnetic bearings (AMBs). In particular, the direct flux control (DFC) technique promises unique advantages over other sensorless techniques, such as a higher bandwidth, but on the other hand, it requires the coils to be connected in a star topology. Until now, star-point connections are rarely found on active magnetic bearings. In consequence, there is no known publication about the application of the DFC to an AMB to this date. In order to apply the DFC to an AMB, a star-point driving approach for AMBs must be developed beforehand. A star-connected driving approach, capable of driving a four-phase AMB, is proposed and validated against traditional H-bridges in a simulation. Further, the strategy is tested in a physical application and generalised for 4∗n phases. In terms of current dynamics, the simulation results can be compared to the well-known full H-bridge driving. The experiments on the physical application show that the actual current in the coils follows a reference with satisfactory accuracy. Moreover, the inductance measurements of the coils show a strong dependency on the rotor’s position, which is crucial for sensorless operation. A star-point connection delivers a satisfying response behaviour in an AMB application, which makes sensorless techniques that require a star point, such as the DFC, applicable to active magnetic bearings

An Exact Solution to the Modified Winding Function for Eccentric Permanent Magnet Synchronous Machines

The Winding Function Approach has been used since 1965 to describe the inductance behavior of small air-gap electrical machines, and several works have contributed to its formulation in the presence of mechanical faults, such as eccentricity, leading to the Modified Winding Function Approach (MWFA). In order to use the MWFA, an integral over a full rotation period needs to be computed. Nevertheless, this typically requires the performance of numerical integration, and thus it is affected by integration error, requires relatively high computational effort and, at the same time, it does not easily allow for performance of the analysis of the inductance harmonics. In this work, an exact analytical solution to the MWFA equation is provided in a form that allows to highlight the harmonic content of the inductances. After a thorough mathematical derivation of the solution, a numerical investigation is proposed for verification purposes

A Secondary-Side Controlled Electric Vehicle Wireless Charger

In this paper, the design procedure of an electric vehicle (EV) wireless charger is presented. Unlike most of the systems available in the literature, the proposed charging system is regulated from the vehicle side. The on-board electrical circuit automatically adapts the resonant compensation to guarantee compatibility with the primary inverter characteristics and achieve high transmission efficiency without communication between sides. Moreover, the proposed control strategy, used to regulate the secondary full active rectifier (FAR), allows the supply of the the EV battery, maximizing the efficiency during the whole charging process