Rotor Coordinates Research Articles

Pilot-Wave Quantum Theory with a Single Bohm’s Trajectory

The representation of a quantum system as the spatial configuration of its constituents evolving in time as a trajectory under the action of the wave-function, is the main objective of the Bohm theory. However, its standard formulation is referred to the statistical ensemble of its possible trajectories. The statistical ensemble is introduced in order to establish the exact correspondence (the Born's rule) between the probability density on the spatial configurations and the quantum distribution, that is the squared modulus of the wave-function. In this work we explore the possibility of using the pilot wave theory at the level of a single Bohm's trajectory. The pilot wave theory allows a formally self-consistent representation of quantum systems as a single Bohm's trajectory, but in this case there is no room for the Born's rule at least in its standard form. We will show that a correspondence exists between the statistical distribution of configurations along the single Bohm's trajectory and the quantum distribution for a subsystem interacting with the environment in a multicomponent system. To this aim, we present the numerical results of the single Bohm's trajectory description of the model system of six confined rotors with random interactions. We find a rather close correspondence between the coordinate distribution of one rotor along its trajectory and the time averaged marginal quantum distribution for the same rotor. This might be considered as the counterpart of the standard Born's rule. Furthermore a strongly fluctuating behavior with a fast loss of correlation is found for the evolution of each rotor coordinate. This suggests that a Markov process might well approximate the evolution of the Bohm's coordinate of a single rotor and it is shown that the correspondence between coordinate distribution and quantum distribution of the rotor is exactly verified.

Fast Real-Time Constrained Predictive Current Control in Permanent Magnet Synchronous Machine-Based Automotive Traction Drives

The current control in permanent magnet synchronous machine (PMSM) drives is a challenging problem which has to deal with physical and real-time constraints. The goal of this paper is to provide a control solution that can deal effectively with these challenges. The objective is to adjust the stator voltages to obtain fast and monotonic transient current response while satisfying the existing constraints. To this end, using the PMSM model in the rotor coordinates, an explicit one-step ahead predictive control law which uses tools from Lyapunov theory is developed. First, a polytopic approximation of the quadratic constraints is used to reduce the complexity. Then, the optimization problem is reduced to a linear program. Furthermore, a piecewise affine explicit control law is obtained via multiparametric linear programming. As a consequence, the online computation of the control law is reduced to a point location problem yielding a fast control method suitable for real-time implementation. Second, the speed-dependent terms of the mathematical model are considered as disturbance. Then, a state and disturbance observer is designed using a quadratic Lyapunov function to guarantee asymptotic stability of the estimation error. Real-time results obtained in an industrial hardware-in-the-loop test-bench are reported and analyzed.

English

The principle of vector control of electrical drives is based on the control of both the magnitude and the phase of each phase current and voltage. For as long as this type of control considers the three phase system as three independent systems, the control will remain analog and thus present several drawbacks. With high computational power silicon devices, it has been possible to realize precise digital vector control algorithms. The most common is the Field Orientated Control, which demonstrates the capability of performing direct torque control of handling system limitations and of achieving higher power conversion efficiency. The new families of DSPs enable cost-effective design of intelligent controllers for brushless motors which can fulfill enhanced operations, consisting of fewer system components, lower system cost and increased performances. This algorithm maintains efficiency over a wide range of speeds for a 24V, 4000 rpm Permanent Magnet Synchronous Motor and takes into consideration torque changes with transient phases by controlling the flux directly from the rotor coordinates.

Langevin approach to the Porto system

M. Porto (Phys. Rev. E 63 (2001) 030102) suggested a system consisting of Coulomb interacting particles, forming a linear track and a rotor, and working as a molecular motor. Newton equations with damping for the rotor coordinate on the track x, with a prescribed time-dependence of the rotor angle Θ, indicated unidirectional motion of the rotor. Here, for the same system, the treatment was generalized to nonzero temperatures by including stochastic forces and treating both x and Θ via two coupled Langevin equations. Numerical results are reported for stochastic homogeneous distributions of impact events and Gaussian distributions of stochastic forces acting on both the variables. For specific values of parameters involved, the unidirectional motion of the rotor along the track is confirmed, but with a mechanism that is not necessarily the same as that one by Porto. In an additional weak homogeneous potential field U(x)=const.x acting against the motion, the unidirectional motion persists. Then the rotor accumulates potential energy at the cost of thermal stochastic forces from the bath.

Robust Control for a Class of Bilinear Systems with Application to Induction Motor

A robustness proof for a class of uncertain bilinear systems is given. The full order model of an induction motor is used as a demonstration example. Motor parameters are not assumed to be constant or well known. To eliminate the back and forth coordinate transformations between the rotor and stator coordinates, vector control is not used. The rotor flux is not measured but estimated. The speed and flux track arbitrary reference signals. The only requirement on the reference signals is that they are continuous so that their first derivatives are bounded.

Measurements of the Pressure and Velocity Distribution in Low-Speed Turbomachinery by Means of High-Frequency Pressure Transducers

The flow in a low-speed, single-state compressor with a very high blade loading has been measured using a two-probe arrangement. The measuring technique and data reduction procedure described have been especially adjusted for application in low-speed turbomachinery. Those machines show only small pressure fluctuations in the flow downstream of the rotor, for which specific requirements concerning the measuring technique have been taken into account. The probes used contain unsteady pressure transducers and simulate an unsteady multisensor pressure probe. This technique proves to be suitable for applications in low-speed turbomachinery. The measurements are based on phase-locked ensemble averages of multiple samples, where the data are acquired using a simple and convenient experimental setup. This allows the velocity and pressure distribution of the flow to be determined in rotor coordinates. The results show the flow field and the loss distribution of an aero-dynamically highly loaded rotor at design flow rate.

Navier-Stokes calculations of hovering rotor flowfields

Unsteady, thin-layer Navier-Stokes equations written in rotor coordinates are solved using a partially flux-split, implicit numerical algorithm to calculate the flowfields of a hovering rotor blade at subsonic and transonic conditions. Numerical results are in good agreement with experimental data for both nonlifting and lifting rectangular blades. For the lifting case, the rotor wake effects are modeled by applying a correction to the geometric angle of attack of the blades. Alternate methods of calculating the hovering rotor flowfields in blade-fixed mode that have the same circulation distribution as a hovering blade are explored. All of the results presented in this paper were computed on a Cray-2 supercomputer.

Measurements of the Flow From a High-Speed Compressor Rotor Using a Dual Probe Digital Sampling (DPDS) Technique

The flow from a high-speed rotor in a rotor-first arrangement has been measured using a “dual-probe, digital sampling (DPDS)” technique. The flow field was found to be steady in rotor coordinates (periodic in machine coordinates) outside the rotor wake, and three components of velocity and the pressure field were determined in this area. The wake regions were unsteady. In these regions the measurements based on ensemble averages of multiple samples did not follow the behavior established during calibration in steady uniform free-jet flow, except near the wake center. The broadening of the wake and three-dimensional effects in the flow field were measured at reduced throttle and increased speeds. The results serve to illustrate the potential of the measurement technique, on which the emphasis of the presentation is placed.

Basic relations for proposing mechanical neutron selectors

Relations are derived for calculating the physical parameters of mechanical neutron selectors. After transforming the equations of motion of the neutron into a system of rotor coordinates, an approximate equation of the trajectory of the neutron in the rotor is derived. From this equation there follows relations between the radius of the rotor, the rate of the revolutions, the geometric and effective width of the slit, the curvature of the slit and the maximum flight distance at which all the channels of the analyzer are still used. A relation is derived from the geometric conditions for an approximate estimate of the luminosity of the instrument. (auth)