Showing papers on "Angular velocity published in 2007"

Speed-Sensorless Estimation for Induction Motors Using Extended Kalman Filters

Abstract: In this paper, extended-Kalman-filter-based estimation algorithms that could be used in combination with the speed-sensorless field-oriented control and direct-torque control of induction motors (IMs) are developed and implemented experimentally. The algorithms are designed aiming minimum estimation error in both transient and steady state over a wide velocity range, including very low and persistent zero-speed operation. A major challenge at very low and zero speed is the lost coupling effect from the rotor to the stator, which makes the information on rotor variables unobservable on the stator side. As a solution to this problem, in this paper, the load torque and the rotor angular velocity are simultaneously estimated, with the velocity taken into consideration via the equation of motion and not as a constant parameter, which is commonly the case in most past studies. The estimation of load torque, on the other hand, is performed as a constant parameter to account for Coulomb and viscous friction at steady state to improve the estimation performance at very low and zero speed. The estimation algorithms developed based on the rotor and stator fluxes are experimentally tested under challenging variations and reversals of the velocity and load torque (step-type and varying linearly with velocity) over a wide velocity range and at zero speed. In all the scenarios, the current estimation error has remained within a very narrow error band, also yielding acceptable velocity estimation errors, which motivate the use of the developed estimation method in sensorless control of IMs over a wide velocity range and persistent zero-speed operation

Torque scaling in turbulent Taylor–Couette flow between independently rotating cylinders

Abstract: Turbulent Taylor–Couette flow with arbitrary rotation frequencies ω1, ω2 of the two coaxial cylinders with radii r1 < r2 is analysed theoretically. The current Jω of the angular velocity ω(x,t) = u(r,,z,t)/r across the cylinder gap and and the excess energy dissipation rate w due to the turbulent, convective fluctuations (the ‘wind’) are derived and their dependence on the control parameters analysed. The very close correspondence of Taylor–Couette flow with thermal Rayleigh–Benard convection is elaborated, using these basic quantities and the exact relations among them to calculate the torque as a function of the rotation frequencies and the radius ratio η = r1/r2 or the gap width d = r2 − r1 between the cylinders. A quantity σ corresponding to the Prandtl number in Rayleigh–Benard flow can be introduced, . In Taylor–Couette flow it characterizes the geometry, instead of material properties of the liquid as in Rayleigh–Benard flow. The analogue of the Rayleigh number is the Taylor number, defined as Ta (ω1 − ω2)2 times a specific geometrical factor. The experimental data show no pure power law, but the exponent α of the torque versus the rotation frequency ω1 depends on the driving frequency ω1. An explanation for the physical origin of the ω1-dependence of the measured local power-law exponents α(ω1) is put forward. Also, the dependence of the torque on the gap width η is discussed and, in particular its strong increase for η → 1.

Automatic generation of gouge-free and angular-velocity-compliant five-axis toolpath

Abstract: Existing works in automatic generation of interference-free five-axis surface machining toolpaths bear a serious drawback — in order to avoid the obstacles, the tool is often required to make drastic change in its orientation between neighboring contact points. Such a quick change in the tool’s orientation can never be made possible in reality due to the stringent physical limit on the speed and acceleration of the rotary motions of the machine tool. The usual ad hoc solution to this problem is to smooth the toolpath in the configuration space, which, however, is prone to special situations of failure and is not able to guarantee the absolute compliance with the given angular velocity limit. In this paper we present an approach to this problem by directly involving the angular velocity limit in the search process. The presented algorithm will automatically generate a five-axis toolpath that not only is interference-free but also guarantees the angular-velocity compliance. Delicate computation and manipulation of visibility maps and their derivative data ensure that the proposed algorithm is computationally feasible with acceptable computing time and memory requirement. Test examples are given to demonstrate the promising use of the proposed solution.

Exact solution for the nonlinear pendulum

Abstract: This paper deals with the nonlinear oscillation of a simple pendulum and presents not only the exact formula for the period but also the exact expression of the angular displacement as a function of the time, the amplitude of oscillations and the angular frequency for small oscillations. This angular displacement is written in terms of the Jacobi elliptic function sn(u;m) using the following initial conditions: the initial angular displacement is different from zero while the initial angular velocity is zero. The angular displacements are plotted using Mathematica, an available symbolic computer program that allows us to plot easily the function obtained. As we will see, even for amplitudes as high as 0.75p (135o) it is possible to use the expression for the angular displacement, but considering the exact expression for the angular frequency w in terms of the complete elliptic integral of the first kind. We can conclude that for amplitudes lower than 135o the periodic motion exhibited by a simple pendulum is practically harmonic but its oscillations are not isochronous (the period is a function of the initial amplitude). We believe that present study may be a suitable and fruitful exercise for teaching and better understanding the behavior of the nonlinear pendulum in advanced undergraduate courses on classical mechanics.

Bumps and rings in a two-dimensional neural field: splitting and rotational instabilities

Abstract: In this paper we consider instabilities of localised solutions in planar neural field firing rate models of Wilson-Cowan or Amari type. Importantly we show that angular perturbations can destabilise spatially localised solutions. For a scalar model with Heaviside firing rate function we calculate symmetric one-bump and ring solutions explicitly and use an Evans function approach to predict the point of instability and the shapes of the dominant growing modes. Our predictions are shown to be in excellent agreement with direct numerical simulations. Moreover, beyond the instability our simulations demonstrate the emergence of multi-bump and labyrinthine patterns. With the addition of spike-frequency adaptation, numerical simulations of the resulting vector model show that it is possible for structures without rotational symmetry, and in particular multi-bumps, to undergo an instability to a rotating wave. We use a general argument, valid for smooth firing rate functions, to establish the conditions necessary to generate such a rotational instability. Numerical continuation of the rotating wave is used to quantify the emergent angular velocity as a bifurcation parameter is varied. Wave stability is found via the numerical evaluation of an associated eigenvalue problem.

The predictive start of hunting archer fish: a flexible and precise motor pattern performed with the kinematics of an escape C-start

Abstract: SUMMARY Once their shots have successfully dislodged aerial prey, hunting archer fish monitor the initial values of their prey9s ballistic motion and elicit an adapted rapid turning maneuver. This allows these fish to head straight towards the later point of catch with a speed matched to the distance to be covered. To make the catch despite severe competition the fish must quickly and yet precisely match their turn and take-off speed to the initial values of prey motion. However, the initial variables vary over broad ranges and can be determined only after prey is dislodged. Therefore, the underlying neuronal circuitry must be able to drive a maneuver that combines a high degree of precision and flexibility at top speed. To narrow down which neuronal substrate underlies the performance we characterized the kinematics of archer fish predictive starts using digital high-speed video. Strikingly, the predictive starts show all hallmarks of Mauthner-driven teleost C-type fast-starts, which have previously not been noted in feeding strikes and were not expected to provide the high angular accuracy required. The high demands on flexibility and precision of the predictive starts do not compromise their performance. On the contrary, archer fish predictive starts are among the fastest C-starts known so far among teleost fish, with peak linear speed beyond 20 body lengths s -1 , angular speed over 4500 deg. s -1 , maximum linear acceleration of up to 12 times gravitational acceleration and peak angular acceleration of more than 450 000 deg. s -2 . Moreover, they were not slower than archer fish escape C-starts, elicited in the same individuals. Rather, both escapes and predictive starts follow an identical temporal pattern and all kinematic variables of the two patterns overlap. This kinematic equivalence strongly suggests that archer fish recruit their C-start escape network of identified reticulospinal neurons, or elements of it, to drive their predictive starts. How the network drives such a rather complex behavior without compromising speed is a wide open question.

Apparatus and method for taking panoramic photograph

Abstract: An apparatus and a method for taking a panoramic photograph are provided. While a lens of the apparatus is rotated, an angular velocity sensor such as a gyroscope outputs an angular velocity and calculates therefrom a rotation angle of the lens. Accordingly, a user can capture sequential image segments for the panoramic photograph at suitable rotation angles. Since unintended rotations due to a user's hand trembling as well as user's intended rotations can be detected, it may be easy to align overlapped portions of adjacent images and thereby to obtain suitable images for panoramic photograph combination. Also, a user can be informed of a capturable section and a rotating direction by using the calculated angular velocity, so the apparatus may promote a user's convenience and without the need for a burdensome tripod.

Transmission Subspace Tracking for MIMO Systems With Low-Rate Feedback

Abstract: This paper describes a feedback algorithm for tracking the dominant subspaces of continuously time-varying channels in multiantenna communication systems. The nature of the problem is quantization of subspaces. It is well known that subspaces can be mathematically modeled as points in a Grassmann manifold. We model the variations between the dominant subspaces of channels at adjacent time instants to be along geodesics in the Grassmann manifold. Instead of quantizing the subspaces themselves, we propose to quantize the geodesic trajectory connecting two subspaces. More specifically, we quantize a key entity that characterizes a geodesic arc: the velocity matrix, which resembles angular speed in a one-dimensional complex space. Two techniques are proposed for quantizing the velocity matrix of the geodesic. In the first, a 1-bit feedback is utilized to indicate the preferred sign of a random velocity matrix of the geodesic. In the other, the velocity matrix is quantized using a Gaussian vector quantization codebook. Numerical results show that the performance of the proposed 1-bit feedback algorithm is better than a previously proposed Grassmannian subspace packing scheme at low-to-medium Doppler frequencies and better than a gradient sign feedback scheme at all Doppler frequencies. In our simulations, the Gaussian vector quantization algorithm is always better than the 1-bit feedback algorithm.

The Westward Drift and Geomagnetic Secular Change

Abstract: Summary Short-term fluctuations in the length of the day on the order of a decade are discussed in relation to fluctuations in westward drift of the outer part of the Earth’s core. Decreases in the Earth’s rotation rate noted near 1910 and 1965 are shown to be correlated with decreases in westward drift of the Earth’s magnetic eccentric dipole, which probably originates fairly deep within the Earth’s core. If the outer 200-km thickness of the core moves approximately as does the eccentric dipole field, the changes in angular momentum implied for this part can explain the observed changes in the length of the astronomical second, on the basis of conservation of angular momentum. Other estimates of westward drift in the core based on higher-degree harmonic terms give a lower westward drift, and also seem to show less precision in the estimates of flow in the core. These discrepancies are unexplained. Since quite early times it has been known that the Earth undergoes several small and little-understood motions additional to its motion about the Sun, the precessional motion, and the daily rotation (Munk & MacDonald 1960). Astronomical observations on the Moon and stars during the past century have shown that the Earth’s rotation is non-uniform (Brouwer 1952). Since the Earth’s total angular momentum changes very slowly during centuries of time, effects noted during only a few decades suggest that compensatory motions within the Earth’s interior would seem required when fluctuations in surface rotation are observed (Munk & Revelle 1952; Vestine 1952). The main possibility for such motions, which could yield internal angular momentum changes within decades, would seem to be in the Earth’s fluid metallic core. Accordingly it is of interest to estimate possible changes in the rotation of the core expected to compensate for fluctuations in angular momentum of the mantle indicated by changes in the length of day. Since the Earth’s field is thought to originate in a hydromagnetic core, the geomagnetic field lines may be firmly attached to the surface flow in the core. Therefore, field lines moving about on the Earth’s surface may show whether such compensatory motion in the core takes place. Previous work establishing such connection has unhappily been less certain than desired (Kalinen 1949; Vestine 1952; Smirnov 1965). Vestine (1952) showed that if the Earth’s eccentric dipole motion is monitored at five-year intervals since 1840, it undergoes a westward drift of about 0-30”/yr7 except for several five-year intervals centred near 1910, for which the westward drift is perceptibly reduced (to less than half), corresponding to an increase in the angular velocity of the core. This occurred at a time when the mantle and crust slowed down, so that the day became longer.

Self-similar adiabatic flow headed by a magnetogasdynamic cylindrical shock wave in a rotating non-ideal gas

Abstract: Similarity solutions are obtained for one-dimensional adiabatic flow behind a magnetogasdynamic cylindrical shock wave propagating in a rotating non-ideal gas in presence of an azimuthal magnetic field. The density of the medium ahead of the shock is assumed to be constant. In order to obtain the similarity solutions the angular velocity of the ambient medium is assumed to be obeying a power law and to be decreasing as the distance from the axis increases. It is found that the similarity solutions exist, in both the cases, when the initial magnetic field is constant or obeying a power law. The effects of an increase in the value of the index for variation of angular velocity of the ambient medium, in the value of the parameter of the non-idealness of the gas and in the strength of the initial magnetic field are obtained.

On the behavior of the porous rotating disk electrode

Abstract: The behavior of the current from a porous rotating disk electrode (PRDE) as a function of the rotation rate, electrode geometry, and porosity at large overpotentials is studied experimentally. The current shows a much richer behavior than the flat RDE, including a sigmoidal dependence on the rotation rate. At low rotation rates, the measured current is qualitatively similar to that of an RDE, with the current increasing with the square of the rotation rate. However, at a critical rotation rate, which we term the lower critical rotation rate and which depends on the radius, the thickness, and the porosity of the porous disk, the current increases much more rapidly than predicted by the Levich theory. At a larger, upper critical rotation rate, the current increases more slowly and then approaches a plateau. The plateau value greatly exceeds that predicted by Levich and is about 20 times greater than that for a flat electrode. The results are explained in terms of the angular velocity dependence of the ratio of the effective electrochemical reaction time to the residence time of the fluid in the porous disk. A theory is presented that collapses the data onto a universal curve.

Source seeking with a nonholonomic unicycle without position measurements and with tuning of angular velocity part I: Stability analysis

Abstract: We consider the problem of seeking the source of a scalar signal using an autonomous vehicle modeled as the nonholonomic unicycle. The vehicle does not have the capability of sensing its position or the position of the source but is capable of sensing the scalar signal originating from the source. The signal field is assumed to decay away from the position of the source but the vehicle does not have the knowledge of the functional form of the field. We employ extremum seeking to steer the vehicle to the source. Our control strategy keeps the forward velocity at a constant value and tunes the angular velocity, a setting suitable for most autonomous vehicles, including aerial ones. Because of the constant forward velocity constraint, after it has converged near the source, the vehicle exhibits extremely interesting and complex motions. Using averaging theory, we prove local exponential convergence to an "orbit-like" attractor around the source. We also present a thorough analysis of non-local behaviors and attractors that the vehicle can exhibit near the source.

On-line rigid object recognition and pose estimation based on inertial parameters

Abstract: This paper proposes an object recognition and gripping pose estimation approach based on on-line estimation of the complete set of inertial parameters, i.e. the mass, the coordinates of the center of mass, and the elements of the inertia matrix, of an object gripped by or attached to a manipulator. A multi-sensor fusion approach combining 6D force/torque, 6D acceleration, 3D angular velocity, and joint angle data to estimate these parameters is presented. In order to facilitate practical implementation, approaches to handling force/torque sensor offsets and to compensating the forces/torques caused by the distal mounting plate of the force/torque sensor and the gripper are incorporated. Regarding the joint angle signals, preprocessing steps to derive the angular velocity, linear acceleration and angular acceleration vector w.r.t. the sensor frame are addressed. The estimation of the complete set of inertial parameters employing the recursive instrumental variables (RIV) method is discussed. The extraction of features that are invariant w.r.t. translation and rotation, i.e. the mass and the principal moments of inertia, as well as a recognition approach based on the Kullback-Leibler divergence are presented. Experimental results show very low errors in the estimates of the inertial parameters, good pose estimation accuracy, and the viability of the recognition approach.

Anti-shake apparatus

Abstract: An anti-shake apparatus of a photographing apparatus comprises a hand-shake quantity detector and a controller. The hand-shake quantity detector has a first detector having an angular velocity sensor and has a second detector having an angular displacement sensor. The controller performs an anti-shake operation based on a first angular signal from the first detector and a second angular signal from the second detector.

Unsteady magnetohydrodynamic non-newtonian flow due to non-coaxial rotations of disk and a fluid at infinity

Abstract: An analysis is carried out to study the flow generated in a semi-infinite expanse of an incompressible second-grade fluid bounded by a porous oscillating disk. The flow is due to non-coaxial rotations of a disk and a fluid at infinity. The fluid is electrically conducting in the presence of a uniform transverse magnetic field. The solutions of the developed flow are obtained for the cases when the angular velocity is greater than, smaller than, or equal to the frequency of oscillation. The velocity field is found analytically by a Laplace transform technique. It is found that for uniform suction and blowing at the disk, shear oscillations are confined to the Ekman-Hartmann layer near the disk for all values of the frequencies.

Stochastic optimization of bipedal walking using gyro feedback and phase resetting

Abstract: We present a method to optimize the walking pattern of a humanoid robot for forward speed using suitable metaheuristics Our starting point is a hand-tuned open-loop gait that we enhance with two feedback control mechanisms First, we employ a P-controller that regulates the foot angle in order to reduce angular velocity of the robot's body Second, we introduce a phase resetting mechanism that starts the next step at the moment of foot contact Using a physics-based simulation, we demonstrate that such feedback control is essential for achieving fast and robust locomotion

Axisymmetric Stagnation—Point Flow and Heat Transfer of a Viscous Fluid on a Rotating Cylinder With Time-Dependent Angular Velocity and Uniform Transpiration

Abstract: The unsteady viscous flow and heat transfer in the vicinity of an axisymmetric stagnation point of an infinite rotating circular cylinder with transpiration U 0 are investigated when the angular velocity and wall temperature or wall heat flux all vary arbitrarily with time. The free stream is steady and with a strain rate of Γ. An exact solution of the Navier-Stokes equations and energy equation is derived in this problem. A reduction of these equations is obtained by the use of appropriate transformations for the most general case when the transpiration rate is also time-dependent but results are presented only for uniform values of this quantity. The general self-similar solution is obtained when the angular velocity of the cylinder and its wall temperature or its wall heat flux vary as specified time-dependent functions. In particular, the cylinder may rotate with constant speed, with exponentially increasing/decreasing angular velocity, with harmonically varying rotation speed, or with accelerating/decelerating oscillatory angular speed. For self-similar flow, the surface temperature or its surface heat flux must have the same types of behavior as the cylinder motion. For completeness, sample semi-similar solutions of the unsteady Navier-Stokes equations have been obtained numerically using a finite-difference scheme. Some of these solutions are presented for special cases when the time-dependent rotation velocity of the cylinder is, for example, a step-function. All the solutions above are presented for Reynolds numbers, Re=Γa 2 /2v ranging from 0.1 to 1000 for different values of Prandtl number and for selected values of dimensionless transpiration rate, S=U 0 /Γa, where a is cylinder radius and v is kinematic viscosity of the fluid. Dimensionless shear stresses corresponding to all the cases increase with the increase of Reynolds number and suction rate. The maximum value of the shear stress increases with increasing oscillation frequency and amplitude. An interesting result is obtained in which a cylinder rotating with certain exponential angular velocity function and at particular value of Reynolds number is azimuthally stress-free. Heat transfer is independent of cylinder rotation and its coefficient increases with the increasing suction rate, Reynolds number, and Prandtl number. Interesting means of cooling and heating processes of cylinder surface are obtained using different rates of transpiration.

A class of exact solutions to the force-free, axisymetric, stationary magnetosphere of a Kerr black hole

Abstract: We analyze the constraint equation giving allowed solutions describing fields and currents in a force-free magnetosphere around a rotating black hole. Utilizing the divergence properties of the energy and angular-momentum fluxes, for physically allowed solutions with nonzero energy and angular momentum extraction, we conclude that poloidal surfaces are independent of the radial coordinate for large values of r. Imposing this requirement and the Znajek regularity condition, we explicitly derive all possible exact solutions admitted by the constraint equation for r independent poloidal surfaces which are given in terms of the electromagnetic angular velocity function \({\Omega = 1/a \sin^2 \theta}\) , where a is the angular momentum per unit mass of the black hole. Further, we show that for the class of solutions we have developed there is no electromagnetic extraction of energy.

Fall detecting apparatus and method, and emergency aid system and method using the same

Abstract: Provided are a fall detecting apparatus and method and an emergency aid system and method using the same. The fall detecting apparatus includes a storing unit configured to store fall data vectors; an angular velocity measuring unit configured to measure an angular velocity value; an acceleration measuring unit configured to measure an acceleration value; an acceleration extracting unit configured to extract a kinetic acceleration value and a gravitational acceleration value by filtering the acceleration value measured by the acceleration measuring unit; and a fall determining unit configured to convert the angular velocity value, which is measured by the angular velocity measuring unit, and the kinetic acceleration value and the gravitational acceleration value, which are extracted by the acceleration extracting unit, into a fall data vector, and determine a use's fall by comparing the converted fall data vector with the fall data vector stored in the storing unit.

Attitude Tracking With Adaptive Rejection of Rate Gyro Disturbances

Abstract: The classical attitude control problem for a rigid body is revisited under the assumption that measurements of the angular rates obtained by means of rate gyros are corrupted by harmonic disturbances, a setup of importance in several aerospace applications. This note extends previous methods developed to compensate bias in angular rate measurements by accounting for a more general class of disturbances, and by allowing uncertainty in the inertial parameters. By resorting to adaptive observers designed on the basis of the internal model principle, it is shown how converging estimates of the angular velocity can be used effectively in a passivity-based controller yielding global convergence within the chosen parametrization of the group of rotations. Since a persistence of excitation condition is not required for the convergence of the state estimates, only an upper bound on the number of distinct harmonic components of the disturbance is needed for the applicability of the method.

Optimal sequencing of rotation angles for five-axis machining

Abstract: In this paper, we propose two new algorithms to correct the trajectories of the tool tip of a five-axis milling machine by adjusting the rotation angles in such a way that the kinematics error is reduced. The first algorithm is based on the shortest-path optimization with regards to feasible rotations of the inverse kinematics. The cost function is represented in terms of the total angle variation. We show that such an optimization increases the accuracy of machining and is the most appropriate in the case of a rough cut. The shortest-path procedure applies to either the entire set of trajectories or to only the most inappropriate undercuts inside the workpiece. In the latter case, the algorithm generates an interesting family of solutions characterized by smaller undercuts obtained at the expense of increased overcuts. The second algorithm also exploits the idea of the minimization of the angle variation. It is based on the uniform distribution of the cutter contact points with regards to the rotation angles. The method inserts additional tool positions by numerically finding a grid of points distributed uniformly in the angular space. We prove that the proposed algorithm in the neighborhood of stationary points requires 3-4 times fewer additional points than the conventional scheme. Also, if a maximum angular speed has been exceeded, the controller detects this event and reduces the angular speed. Our correction algorithms minimize the total angle variation, thus, reduc- ing the probability of such an event. Finally, the efficiency of the two algorithms has been verified by a five-axis machine MAHO600E at the CIM Lab of the Asian Institute of Technology of Thailand and HERMLE UWF920H at the CIM Lab of the Kasetsart University of Thailand.