Relative Angular Velocity Research Articles

Robust control for a network of electric power generators

We solve the robust control problem for a network of electric power generators whose mathematical model is represented by a system of third order differential-algebraic equations with parameters that are not known a priori. In our solution, we assume that only relative angular velocities of generator rotors are available for observation. We obtain a control algorithm that ensures network synchronization with the necessary accuracy in both standard mode of operation and in emergencies related to abrupt changes in the transmission line resistance. Operation of the proposed scheme is demonstrated with a numerical example dealing with a network of three generators.

Distributed adaptive attitude tracking of multiple spacecraft with a leader of nonzero input

This paper considers the distributed attitude tracking problem of multiple spacecraft with a leader whose control input is possibly nonzero, bounded, and not available to any follower. Based on the relative attitudes and angular velocities of neighboring spacecraft, we design a distributed discontinuous adaptive controller to each follower to guarantee that the attitude errors between the followers and the leader converge to zero for any communication graph containing a directed spanning tree with the leader as the root. To tackle the chattering effect caused by the discontinuous controller, we further propose a distributed continuous adaptive controller, under which both the attitude tracking errors and the adaptive gains are ultimately bounded.

Immediate compensation for variations in self-generated Coriolis torques related to body dynamics and carried objects

We have previously shown that the Coriolis torques that result when an arm movement is performed during torso rotation do not affect movement trajectory. Our purpose in the present study was to examine whether torso motion-induced Coriolis and other interaction torques are counteracted during a turn and reach (T&R) movement when the effective mass of the hand is augmented, and whether the dominant arm has an advantage in coordinating intersegmental dynamics as predicted by the dynamic dominance hypothesis (Sainburg RL. Exp Brain Res 142: 241-258, 2002). Subjects made slow and fast T&R movements in the dark to just extinguished targets with either arm, while holding or not holding a 454-g object. Movement endpoints were equally accurate at both speeds, with either hand, and in both weight conditions, but subjects tended to angularly undershoot and produce more variable endpoints for targets requiring greater torso rotation. There were no changes in endpoint accuracy or trajectory deviation over repeated movements. The dominant right arm was more stable in its control of trajectory direction across targets, whereas the nondominant left arm had an improved ability to stop accurately on the target for higher levels of interaction torques. The trajectories to more eccentric targets were straighter when performed at higher speeds but slightly more deviated when subjects held the weight. Subjects did not slow their torso velocity or change the timing of the arm and torso velocities when holding the weight, although there was a slight decrease in their hand velocity relative to the torso. The delay between the onsets of torso and finger movements was almost twice as large for the right arm than the left, suggesting the right arm was better able to account for torso rotation in the arm movement. Holding the weight increased the peak Coriolis torque by 40% at the shoulder and 45% at the elbow and, for the most eccentric target, increased the peak net torque by 12% at the shoulder and 34% at the elbow. In accordance with Sainburg's dynamic dominance hypothesis, the right arm exhibited an advantage for coordinating intersegmental dynamics, showing a more stable finger velocity in relation to the torso across targets, decreasing error variability with movement speed, and more synchronized peaks of finger relative and torso angular velocities in conditions with greater joint torque requirements. The arm used had little effect on the movement path and the magnitude of the joint torques in any of the conditions. These results indicate that compensations for forthcoming Coriolis torque variations take into account the dynamic properties of the body and of external objects, as well as the planned velocities of the torso and arm.

Geometric Relations Between Rigid Bodies (Part 2): From Semantics to Software

Rigid bodies are essential primitives in the modeling of robotic devices, tasks, and perception. Basic geometric relations between rigid bodies include relative position, orientation, pose, linear velocity, angular velocity, twist, force, torque, and wrench. In Part 1 of this tutorial [3], we explicitly stated the semantics of all coordinate-invariant properties and operations, and, more importantly, all the choices that are made in coordinate representations of these geometric relations. This resulted in a set of concrete suggestions for standardizing terminology and notation.

CASIMIR TORQUE ON TWO ROTATING PLATES

We investigate the torque on two rotating particles and two rotating plates due to the thermal fluctuation and vacuum fluctuation. A general formula has been developed including the temperature difference on each plate and vacuum, and the different angular velocity on each plate. We show that the Casimir torque in absorbing material occurs whenever there is a difference in temperature or a relative angular velocity between the plates and the vacuum.

Experimental manifestation of vortices and Rossby wave blocking at the MHD excitation of quasi-two-dimensional flows in a rotating cylindrical vessel

Experiments on the excitation of counterpropagating zonal flows by the magnetohydrodynamic (MHD) method in a rotating cylindrical vessel with a conic bottom have been performed. Flows appear in a conducting fluid layer in the field of ring magnets under the action of a radial electric field. The velocity fields have been reconstructed by the particle image velocimetry (PIV) method. In the fast rotation regimes with a thin fluid layer, where the Rossby-Obukhov scale does not exceed the characteristic sizes of the vessel, the system of perturbations appears with almost immobile blocked anticyclones in the outer part of the flow and rapidly moving cyclones in the main stream. The diagram of regimes is plotted in the variables of the relative angular velocities of the averaged zonal flow and transfer of vortices about the system rotation axis. Attention is focused on the results for the regions of the diagram with slow motion of vortices with respect to the rotating coordinate system near the parameters for stationary Rossby waves (blocking of circulation). The results are compared to the results previously obtained in similar experiments using the source-sink method.

Bifurcations of the relative equilibria of a gyrostat satellite for a special case of the alignment of its gyrostatic moment

The bifurcations of the equilibria of a gyrostat satellite with a centre of mass moving uniformly in a circular Kepler orbit around an attracting centre are investigated. It is assumed that the axis of rotation of a statically and dynamically balanced flywheel rotating at a constant relative angular velocity is fixed in the principal central plane of inertia of the gyrostat containing the axis of its mean moment of inertia and that it is not collinear with any principal central axis of inertia of the system. The problem is solved in a direct formulation, that is, the whole set of equilibria with respect to the orbital system of coordinates of the gyrostat satellite is determined using the given moments of inertia, the value of the gyroscopic moment and the direction cosines of the axis of rotation of the flywheel and the changes in this set are investigated as a function of the bifurcation parameter, that is, the magnitude of the gyrostatic moment of the system. A parametric analysis of the relative equilibria of the three possible classes of equilibria for a system in a circular orbit in a central Newtonian force field is carried out using computer algebra facilities.

Input-to-state stable cooperative attitude regulation of spacecraft formation flying

In this paper, the problem of cooperative attitude control under the concept of input-to-state stability for spacecraft formation flying is discussed in the presence of external disturbances. More specifically, the relative attitude quaternion and relative angular velocity are firstly introduced to describe the relative attitude motion between different formation agents. A novel proportional-derivative type controller is then developed including bounded cooperative attitude control term composed of relative quaternion and angular velocity. Associated Lyapunov stability analysis shows that the closed-loop system is proved to be semi-globally input-to-state stable from the generalized disturbance (i.e. cooperative attitude control term and external disturbance) to system states. Besides, the selecting constraint on control parameters is given in the sense of input-to-state stability as one of the main contributions of this paper. Numerical simulation results are also presented which not only highlight the ensuring closed-loop performance benefits from the control law derived here but also shows a rapid transient process and high accuracy.

Attitude cooperative control of spacecraft formation via output‐feedback

PurposeThe purpose of this paper is to propose a decentralized output feedback controller for cooperative attitude regulation of spacecraft formation in absence of angular velocity feedback.Design/methodology/approachThe nonlinear relative attitude dynamic and kinematic equations represented by relative quaternion and relative angular velocity, respectively, are considered in this paper. The lead filter is employed to synthesize virtual angular velocity signal so that the design of output feedback controller is achieved. Lyapunov method is adopted to prove the stability of closed‐loop system. Considering the external disturbance, the theory of L2‐gain disturbance attenuation is employed to improve the designed controller. Numerical simulations are carried out to verify the controllers proposed.FindingsIt is found that the closed‐loop system can be guaranteed asymptotically stable in absence of external disturbance. When disturbance is considered, as long as the sufficient condition proposed is satisfied, the improved controller can render system uniformly ultimately bounded stable.Practical implicationsThe proposed output feedback control scheme can be considered as a fall‐back alternative for the case that the angular velocity sensors fail, or seen as another option for the system without angular velocity sensors at all.Originality/valueUnlike most classical works in the field of output feedback which focus on centralized scheme and neglect the disturbance, the controller proposed in this paper is able to handle the output feedback control problem of multi‐agent formation in a decentralized fashion, so as to avoid the single failure point of a centralized scheme. Meanwhile, the capability of L2‐gain disturbance attenuation is also achieved simultaneously.

Study on Flow Field Intensification of Dynamic Pre-Cyclone Separators

Abstract Because of external driving, dynamic pre-cyclone separators have excellent operational performances in areas of pressure vary occasionally. In this work, a numerical model of the dynamic separator been built and the flow field is thoroughly studied. The distribution results of angular velocity show that an appropriate structure of pre-cyclone vanes is of great importance to get a relative uniform flow angular velocity field. A novel structure of pre-cyclone vanes under different separation requirements is developed and verified by a number of experiments.

Study on the Temperature Filed of Wet Dual Clutch Transmission during Starting Process

Based on the analysis of starting process of wet dual clutch transmission, dynamic rules for piston pressure and relative angular velocity of wet clutch were determined, According to the unsteady heat exchanging theory and the heat exchanging process of clutch engagement, a two dimensional heat conduction model of wet clutch was developed with reasonable initial conditions and boundary conditions. Matlab/PDE toolbox was used to solve the established model. The temperature distribution of friction pairs along the axial and radial direction were revealed in the Simulation results. Testing program had been designed, and real vehicle test was done to the temperature field on friction interface of wet dual clutch transmission in starting process. The test result indicated that the temperature field model and its solution were reliability, and it was instructive to optimize the design of wet clutch and its engaging control in starting process.

Overturning instability of a two‐rigid block system under ground excitation

AbstractThe rocking response of a freely standing two‐rigid block 2‐DOF system under ground excitation is comprehensively presented. The highly nonlinear governing equations of motion, properly established, under certain conditions may be linearised leading after integration to closed form solutions. The analysis is based on the assumption that friction at the interface between the two‐rigid blocks or the lower block and the ground is sufficient to prevent sliding. All possible configuration patterns exhibited by the two‐rigid block system during rocking motion are examined in detail. Attention is focused on the determination of the minimum amplitude ground acceleration among all patterns which leads the system to overturning instability. The effect of week damping is included in the analysis by reducing the relative angular velocity after impact. Conditions for overturning instability with or without impact, either between the two blocks or between the lower block and the ground, associated with an escaped motion in the phase‐plane portrait, are thoroughly discussed. It is found that for moderately large values of excitation frequencies overturning instability occurs after impact. Beyond these values overturning instability without impact prevails. In case of overturning instability without impact, surprisingly enough, it was also found that there are ranges of values of excitation frequencies in which a monolithic rigid block as a 1‐DOF system becomes more stable when divided into two equal rigid blocks, acting as a 2‐DOF system.

Stokes flow between eccentric rotating spheres with slip regime

The steady axisymmetric flow problem of a viscous fluid contained between two eccentric spheres that rotate about an axis joining their centers with different angular velocities is considered. A linear slip of Basset-type boundary condition at both surfaces of the spherical particle and the container is used. Under the Stokesian assumption, a general solution is constructed from the superposition of basic solutions in the spherical coordinate systems based on the inner solid particle and the spherical container. The boundary conditions on the particle’s surface and spherical container are satisfied by a collocation technique. Numerical results for the coupling coefficient acting on the particle are obtained with good convergence for various values of the ratio of particle-to-container radii, the relative distance between the centers of the particle and container, the slip coefficients and the relative angular velocity. In the limiting cases, the numerical values of the coupling coefficient for the solid sphere in concentric position with the container and when the particle is near the inner surface of the container are obtained, and the results are in good agreement with the available values in the literature. The variation of the coupling coefficient with respect the parameters considered are tabulated and displayed graphically.

The Taylor–Couette motor: spontaneous flows of active polar fluids between two coaxial cylinders

We study the dynamics of active polar fluids in a Taylor–Couette geometry where the fluid is confined between two rotating coaxial cylinders. This system can spontaneously generate flow fields and thereby set the two cylinders into relative rotation either by spontaneous symmetry breaking or via asymmetric boundary conditions on the polarization field at the cylinder surfaces. In the presence of an externally applied torque, the system can act as a rotatory motor and perform mechanical work. The relation between the relative angular velocity of the cylinders and the externally applied torque exhibits rich behaviors such as dynamic instabilities and the coexistence of multiple stable steady states for certain ranges of parameter values and boundary conditions.

Suspensions with a tunable effective viscosity: a numerical study

AbstractIn this paper, we conduct a numerical investigation of sheared suspensions of non-colloidal spherical particles on which a torque is applied. Particles are mono-dispersed and neutrally buoyant. Since the torque modifies particle rotation, we show that it can indeed strongly change the effective viscosity of semi-dilute or even more concentrated suspensions. We perform our calculations up to a volume fraction of 28 %. And we compare our results to data obtained at 40 % by Yeo and Maxey (Phys. Rev.E, vol. 81, 2010, p. 62501) with a totally different numerical method. Depending on the torque orientation, one can increase (decrease) the rotation of the particles. This results in a strong enhancement (reduction) of the effective shear viscosity of the suspension. We construct a dimensionless number$\Theta $which represents the average relative angular velocity of the particles divided by the vorticity of the fluid generated by the shear flow. We show that the contribution of the particles to the effective viscosity can be suppressed for a given and unique value of$\Theta $independently of the volume fraction. In addition, we obtain a universal behaviour (i.e. independent of the volume fraction) when we plot the relative effective viscosity divided by the relative effective viscosity without torque as a function of$\Theta $. Finally, we show that a modified Faxén law can be equivalently established for large concentrations.

425 乗り心地解析を可能とする新しい人体モデルの開発

This paper presents theoretical investigation concerning modeling of a human body, seat, steering wheel and pedals system. We have developed a new model of human body that the evaluation of ride comfort is able to estimate. The model of human body consists of six parts: the head, body, thigh, shin, upper arm and fore arm. Each part of the human body is composed with the same fundamental element which is called as a dumbbell model. The dumbbell model is the one that two mass is connected with a flexible bar that has the coefficient of spring, dumper, and plasticity. The movement of the dumbbell mode is considered in the vertical and horizontal direction and rotational movement at the point of center. Each part of the dumbbell model has different parameters and is connected to compose human body. Connected point of each part is considered the friction moment that depends on displacement, relative angle, and relative angular velocity. The functional model is applied in modeling. The analytical result is compared with the measurement result and it agreed extremely well. Some results are presented in the form of parametric graphs. It is shown that the model of human body that has newly developed is able to apply to evaluate the ride comfort.

敏捷小卫星对地凝视姿态跟踪控制

The attitude tracking control of staring imaging of an agile small satellite driven by Double-Gimbaled Control Moment Gyroscopes(DGCMG) was investigated.Firstly,an actuator configuration scheme was developed according to the characteristics of agile satellite and the staring imaging mission requirements.Then,the orbit information was used to compute the relative attitude angle and attitude angular velocity of a staring imaging target with respect to the satellite body reference frame,and the proper control law and steering law were introduced to avoid the singularity of Control Moment Gyroscope(CMG).Finally,based on the SY-3 satellite attitude and orbit control simulation platform,the agile small satellite closed-loop control simulation system was established by taking the mission requirements and the actuator adjustments into account and the proposed design scheme and control method were verified in a mathematical simulation.Obtained results show that the presented solution is effective for staring imaging attitude maneuver control of the agile small satellite and the least gimbal angle rate of DGCMG is the most important factor to determinate attitude tracking precision.

Stokes flow between two confocal rotating spheroids with slip

The steady axisymmetric flow problem of a viscous fluid confined between two confocal spheroids that are rotating about their axis of revolution with different angular velocities is considered. A linear slip, of Basset type, boundary condition on both surfaces of the spheroidal particle and the container is used. Under the Stokesian assumption, a general solution is constructed from the superposition of basic solutions in prolate and oblate spheroidal coordinates. The boundary conditions on the particle’s surface and spheroidal container are satisfied by a collocation technique. The torque exerted on the spheroidal particle by the fluid is evaluated with good convergence for various values of the slip parameters, the relative angular velocity and aspect ratios of the spheroids. The limiting case of no-slip is in good agreement with the available values in the literature.

Impact-induced vibration in complex flexible multi-body systems: numerical and experimental investigation of press machines

This article is concerned with the numerical and experimental investigations of impact-induced vibrations in highly non-linear complex multibody system applications. In order to accurately model the impact response of such complex systems, a computational procedure based on the integration of finite element and multibody system algorithms is used. This procedure, which employs the finite element floating frame of reference formulation, allows for defining arbitrary joint constraint and forcing functions, for accurately capturing the coupling between the rigid body motion and the elastic deformation, and for modeling the impact forces between rigid and flexible bodies in the multibody system model. The system equations of motion are developed using the augmented Lagrangian formulation that allows for the use of sparse matrix techniques. The algorithm used in this study ensures that the kinematic constraint equations are satisfied at the position, velocity, and acceleration levels. The impact-induced vibration of a highly non-linear press machine is numerically and experimentally examined in this study. In order to accurately model the dynamic behavior of such a press machine, it is necessary to model the transfer feeder elastic deformations resulting from the impulsive impact forces. The deformations of the transfer press system as well as those of its frame are modeled in this investigation using the floating frame of reference formulation that allows for effectively reducing the number of degrees of freedom by filtering out very high-frequency modes of vibration using component mode synthesis techniques. The formulations of several relative angle and angular velocity kinematic constraints that are required to model this multibody system are developed in order to model transfer feeder complex rotational components. The numerical results obtained using the three-dimensional multibody system transfer press model developed in this study are validated using experimental results.

Geologically current motion of 56 plates relative to the no-net-rotation reference frame

NNR-MORVEL56, which is a set of angular velocities of 56 plates relative to the unique reference frame in which there is no net rotation of the lithosphere, is determined. The relative angular velocities of 25 plates constitute the MORVEL set of geologically current relative plate angular velocities; the relative angular velocities of the other 31 plates are adapted from Bird (2003). NNR-MORVEL, a set of angular velocities of the 25 MORVEL plates relative to the no-net rotation reference frame, is also determined. Incorporating the 31 plates from Bird (2003), which constitute 2.8% of Earth's surface, changes the angular velocities of the MORVEL plates in the no-net-rotation frame only insignificantly, but provides a more complete description of globally distributed deformation and strain rate. NNR-MORVEL56 differs significantly from, and improves upon, NNR-NUVEL1A, our prior set of angular velocities of the plates relative to the no-net-rotation reference frame, partly due to differences in angular velocity at two essential links of the MORVEL plate circuit, Antarctica-Pacific and Nubia-Antarctica, and partly due to differences in the angular velocities of the Philippine Sea, Nazca, and Cocos plates relative to the Pacific plate. For example, the NNR-MORVEL56 Pacific angular velocity differs from the NNR-NUVEL1A angular velocity by a vector of length 0.039 ± 0.011° a−1 (95% confidence limits), resulting in a root-mean-square difference in velocity of 2.8 mm a−1. All 56 plates in NNR-MORVEL56 move significantly relative to the no-net-rotation reference frame with rotation rates ranging from 0.107° a−1 to 51.569° a−1.