Coupling of Pointing Angles and Angular Rates in the GRACE Follow-On Laser Ranging Interferometer

2020 ◽  
Author(s):  
Henry Wegener ◽  
Vitali Müller ◽  
Malte Misfeldt ◽  
Laura Müller ◽  
Gerhard Heinzel
Keyword(s):  
Center Of Mass ◽  
Rate Of Change ◽  
Laser Ranging ◽  
Model Parameters ◽  
Combined Model ◽  
Yaw Rate ◽  
Coupling Parameters ◽  
Yaw Angle ◽  
Cross Track ◽  
Satellite Rotation

<p>The Laser Ranging Interferometer (LRI) of the GRACE Follow-On (GFO) mission has successfully shown its capability of continuously measuring the inter-satellite biased range with higher precision than the established microwave ranging system. The instrument behaviour is already well understood. For Fourier frequencies below 30 mHz, the largest error source of the LRI is the so-called tilt-to-length (TTL) coupling, which means that satellite pointing jitter couples into the measured range. We have modelled the TTL error and estimated the model parameters using satellite rotation maneuvers, the so-called center-of-mass calibration (CMCal) maneuvers.</p> <p>We report here that not only the pointing angles (roll, pitch, yaw) couple into the LRI range, but also the rate of change of one of the angles, namely the yaw angle of the main S/C. We give a theoretical model, which predicts this effect qualitatively and quantitatively. Based on a combined model for TTL and yaw rate coupling, we have re-analyzed the CMCal maneuvers, the results of which we present here.</p> <p>From the TTL coupling parameters, one can derive nadir and cross-track components of the center-of-mass (CM) positions with respect to the LRI reference point. These will also be shown here, and we can conclude that the LRI is capable of providing accurate tracking of CM movement over time.</p>

Comparison of Analytical and Empirical Models to Capture Variations in Off-Road Vehicle Dynamics

2005 ◽  
Author(s):  
Paul J. Pearson ◽  
David M. Bevly
Keyword(s):  
Empirical Data ◽  
Vehicle Dynamics ◽  
Experimental Validation ◽  
Inertial Sensors ◽  
Analytical Models ◽  
Control Algorithms ◽  
Model Parameters ◽  
Steering Control ◽  
Steering Angle ◽  
Yaw Rate

This paper develops two analytical models that describe the yaw dynamics of a farm tractor and can be used to design or improve steering control algorithms for the tractor. These models are verified against empirical data. The particular dynamics described are the motions from steering angle to yaw rate. A John Deere 8420 tractor, outfitted with inertial sensors and controlled through a PC-104 form factor computer, was used for experimental validation. Conditions including different implements at varying depths, as would normally be found on a farm, were tested. This paper presents the development of the analytical models, validates them against empirical data, and gives trends on how the model parameters change for different configurations.

scholarly journals Relations Between Celestial and Selenocentric Reference Frames

1981 ◽  
Vol 63 ◽  
pp. 268-280
Author(s):  
J. Kovalevsky
Keyword(s):  
Reference Frames ◽  
Center Of Mass ◽  
Great Accuracy ◽  
Laser Ranging ◽  
Lunar Laser Ranging ◽  
Geometric Means ◽  
The Earth ◽  
Lunar Laser ◽  
Unique System ◽  
Different Types

AbstractThe very great accuracy with which the motions of the Moon can now be monitored by laser ranging, differential VLBI and occultation observations, implies that the interpretation of the measurements is conditioned by the choice and the accurate knowledge of a selenocentric, a terrestrial and a celestial frames. Two different types of selenocentric reference frames can be envisioned. The present selenographic frames are discussed but the author proposes that one should introduce a system defined by a purely geometric means. Some consequences of such a choice are discussed. One feature of the future conventional terrestrial frame is very important for Earth-Moon dynamics. Its origin should coincide with the center of mass of the Earth as determined by lunar laser ranging. As far as the quasi-inertial reference systems are concerned, the liaisons between a purely lunar dynamical system, subject to some hardly modelable effects, and purely celestial systems are analysed. The reduction of observations made with various techniques implies the use of different systems, and several problems are stated that should be solved before a unique system for Earth-Moon dynamics might be used.

Optimal Yaw Regulation and Trajectory Control of Biorobotic AUV Using Mechanical Fins Based on CFD Parametrization

2005 ◽  
Vol 128 (4) ◽  
pp. 687-698 ◽  
Author(s):  
Mukund Narasimhan ◽  
Haibo Dong ◽  
Rajat Mittal ◽  
Sahjendra N. Singh
Keyword(s):  
Discrete Time ◽  
Center Of Mass ◽  
Immersed Boundary ◽  
Reference Trajectory ◽  
Control Input ◽  
Time Model ◽  
Pectoral Fins ◽  
Undersea Vehicle ◽  
Flapping Foils ◽  
Yaw Angle

This paper treats the question of control of a biorobotic autonomous undersea vehicle (BAUV) in the yaw plane using a biomimetic mechanism resembling the pectoral fins of fish. These fins are assumed to undergo a combined sway-yaw motion and the bias angle is treated as a control input, which is varied in time to accomplish the maneuver in the yaw-plane. The forces and moments produced by the flapping foil are parametrized using computational fluid dynamics. A finite-difference-based, Cartesian grid immersed boundary solver is used to simulate flow past the flapping foils. The periodic forces and moments are expanded as a Fourier series and a discrete-time model of the BAUV is developed for the purpose of control. An optimal control system for the set point control of the yaw angle and an inverse control law for the tracking of time-varying yaw angle trajectories are designed. Simulation results show that in the closed-loop system, the yaw angle follows commanded sinusoidal trajectories and the segments of the intersample yaw trajectory remain close to the discrete-time reference trajectory. It is also found that the fins suitably located near the center of mass of the vehicle provide better maneuverability.

A Nonlinear Oscillator Model to Generate Lateral Walking Force on a Rigid Flat Surface

2018 ◽  
Vol 18 (02) ◽  
pp. 1850020 ◽  
Author(s):  
Prakash Kumar ◽  
Anil Kumar ◽  
Silvano Erlicher
Keyword(s):  
Nonlinear Oscillator ◽  
Perturbation Technique ◽  
Center Of Mass ◽  
Reaction Force ◽  
Lateral Force ◽  
The Body ◽  
Model Parameters ◽  
Lateral Direction ◽  
Van Der Pol Oscillators ◽  
Walking Speeds

This study proposes a single degree of freedom nonlinear oscillator to model the lateral movement of the body center of mass of a pedestrian walking on a flat rigid surface. Experimentally recorded ground reaction force of a dozen of pedestrians in the lateral direction is used to develop the model. In detail, the hardening and softening effects are observed in the stiffness curve as well as higher odd harmonics are present in the frequency spectrum of the lateral force signals. The proposed oscillator is a modification of the Rayleigh and the Van der Pol oscillators with additional nonlinear softening and hardening terms. To obtain an approximation of the limit cycle of the oscillator and its stability, two methods are studied: the energy balance method and the Lindstedt–Poincare perturbation technique. The experimental force signals of pedestrians at four different walking speeds are used for the identification of the values of the model parameters. The results obtained from the proposed model show a good agreement with the experimental ones.

A Modeling of Fe-Ga Magnetostrictive Shunt Damper

2014 ◽  
Author(s):  
JinHyoeng Yoo
Keyword(s):  
Magnetic Flux ◽  
Permanent Magnet ◽  
Cantilever Beam ◽  
Mechanical Energy ◽  
Rate Of Change ◽  
Magnetic Flux Density ◽  
Pickup Coil ◽  
Model Parameters ◽  
Mass Load ◽  
Shunt Circuit

This study presents mechanical energy dissipation with a proof-of-concept prototype magnetostrictive (Fe-Ga alloy, galfenol) based shunt circuit using passive electrical components. Magneto strictive material can harvest electricity out of the structural vibrations based on the Villari effect using permanent magnet and pickup coil configuration. The device in this study consists of a polycrystalline galfenol strip bonded to a brass cantilever beam. Two brass pieces, each containing a permanent magnet, are used to mass load at the end of the beam and to provide a magnetic bias field through the galfenol strip. The voltage induced in an induction coil closely wound around the cantilever beam captures the time rate of change of magnetic flux within the galfenol strip as the beam vibrates. To dissipate the electrical voltage output from the pickup coil and/or to change the phase of eddy current from the magnetic flux density fluctuation, a shunt circuit is attached. The effective mechanical impedance for the magnetostrictive shunt circuit is derived in a model. The effectiveness of a series L-R and L-C shunt circuit is demonstrated theoretically and experimentally. The non-linear model parameters, which include the mechanical-magnetic coupling factors, α and αT, and the permeability of galfenol, β, are extracted from experimental measurement. The shunted magnetostrictive damping model of both resistive and capacitance shunt cases compare well with the experimental results.

scholarly journals EPQ model for imperfect production processes with rework and random preventive machine time for deteriorating items and trended demand

2015 ◽  
Vol 25 (3) ◽  
pp. 425-443 ◽  
Author(s):  
Nita Shah ◽  
Dushyantkumar Patel ◽  
Digeshkumar Shah
Keyword(s):  
Rate Of Change ◽  
Model Parameters ◽  
Deterioration Rate ◽  
Economic Production ◽  
Decision Variables ◽  
Maintenance Time ◽  
Demand Rate ◽  
Epq Model ◽  
Production Quantity ◽  
Critical Model

Economic production quantity (EPQ) model has been analyzed for trended demand, and units in inventory are subject to constant rate. The system allows rework of imperfect units, and preventive maintenance time is random. A search method is used to study the model. The proposed methodology is validated by a numerical example. The sensitivity analysis is carried out to determine the critical model parameters. It is observed that the rate of change of demand, and the deterioration rate have a significant impact on the decision variables and the total cost of an inventory system. The model is highly sensitive to the production and demand rate.

scholarly journals Performance and wake characteristics of a tidal turbine under yaw

2018 ◽  
Vol 1 (1 (Aug)) ◽  
pp. 41-50 ◽  
Author(s):  
P. Modali ◽  
N. S. Kolekar ◽  
A. Banerjee
Keyword(s):  
Center Of Mass ◽  
Three Dimensional ◽  
Turbine Rotor ◽  
Power Coefficient ◽  
Speed Ratio ◽  
Thrust Coefficient ◽  
Tip Vortices ◽  
Downstream Distance ◽  
Tidal Turbine ◽  
Yaw Angle

In tidal streams and rivers, the flow of water can be at yaw to the turbine rotor plane causing performance degradation and a skewed downstream wake. The current study aims to quantify the performance variation and associated wake behavior caused by a tidal turbine operating in a yawed inflow environment. A three-dimensional computational fluid dynamics study was carried out using multiple reference frame approach using κ-ω SST turbulence model with curvature correction. The computations were validated by comparison with experimental results on a 1:20 scale prototype for a 0° yaw case performed in a laboratory flume. The simulations were performed using a three-bladed, constant chord, untwisted tidal turbine operating at uniform inflow. Yaw effects were observed for angles ranging from 5° to 15°. An increase in yaw over this range caused a power coefficient deficit of 26% and a thrust coefficient deficit of about 8% at a tip speed ratio of 5 that corresponds to the maximum power coefficient for the tested turbine. In addition, wake propagation was studied up to a downstream distance of ten rotor radius, and skewness in the wake, proportional to yaw angle was observed. At higher yaw angles, the flow around the turbine rotor was found to cushion the tip vortices, accelerating the interaction between the tip vortices and the skewed wake, thereby facilitating a faster wake recovery. The center of the wake was tracked using a center of mass technique. The center of wake analysis was used to better quantify the deviation of the wake with increasing yaw angle. It was observed that with an increase in yaw angle, the recovery distance moved closer to the rotor plane. The wake was noticed to meander around the turbine centerline with increasing downstream distance and slightly deviate towards the free surface above the turbine centerline, magnitude of which varied depending on yaw.

The Effect of Time Delay on the Stability Control of Trailers

2020 ◽  
Author(s):  
Hanna Zs. Horvath ◽  
Denes Takacs
Keyword(s):  
Time Delay ◽  
Control Algorithm ◽  
Lateral Displacement ◽  
Stability Control ◽  
Vertical Position ◽  
Control Torque ◽  
Yaw Rate ◽  
The Stability ◽  
Yaw Angle ◽  
Theoretical Results

Abstract The instability of the car-trailer systems very often leads to the snaking and/or rocking motions of trailers. In order to reduce the safety risk of these unwanted vibrations, stability control can be applied. In this paper, we use a spatial trailer model to analyze the effect of a possible control algorithm, which actuates by means of braking. For the sake of simplicity, the dynamics of the towing vehicle is modeled by the lateral displacement of the tow hitch that is supported laterally by a spring and damper. The longitudinal speed of the vehicle is kept constant. The effect of the braking forces are emulated in our study via a control torque, which is proportional to the yaw angle and the yaw rate. The time delay of the controller is also considered. Linear stability charts are constructed in the plane of the different system parameters. Linearly stable and unstable parameter domains are identified both for the vertical position of the center of gravity and the control gains. Numerical simulations are used to validate the theoretical results.

GDP Dynamics as a Superposition of N. D. Kondratieff Technological Waves

2020 ◽  
pp. 7-22
Author(s):  
Petr F. Andrukovich
Keyword(s):  
Mathematical Models ◽  
Economic Activity ◽  
Rate Of Change ◽  
Long Waves ◽  
Wave Period ◽  
Entire Period ◽  
Model Parameters ◽  
Specific Data ◽  
Proposed Model ◽  
Periodic Fluctuations

A review of publications on the theory of long waves by Kondratieff–Schumpeter has shown that one of the imperfect elements of this theory in the case of modeling on their basis of GDP dynamics is the correlation of the dynamics of these waves with the dynamics of the observed values of GDP. The point is that the mathematical models currently used to describe periodic fluctuations in economic activity under this theory have a horizontal trend, and when moving to describe the growing (or declining) dynamics of GDP, it is necessary to include an exogenous trend that is not related to this theory in any way. This situation violates its integrity and often serves as one of the arguments against the adequacy of this theory to real economic processes. This article proposes a model of GDP dynamics based on the superposition of long Kondratieff waves and does not require the inclusion of exogenous trend. In this model, in addition to the generally accepted parameters of long waves, namely, the beginning and length of the wave period, two new parameters arise: the magnitude of its amplitude and the rate of change of this amplitude. These parameters allow you to configure the GDP model to describe the dynamics of the GDP of different countries, taking into account their real differences in the size of GDP. The problems of verification of the parameters of the proposed model arising in connection with the multi-extremality of the function describing this model are considered. Verification of the parameters of this model on specific data is carried out on the values of US GDP for the period from 1790 to 2018. The results of testing the model showed that the superposition of long Kondratieff–Schumpeter waves well describe the dynamics of US GDP over the entire period, and the model parameters are quite consistent with their generally recognized values.

Laser Ranging Interferometer on GRACE Follow-On: Current Status

2020 ◽  
Author(s):  
Vitali Müller ◽  
Keyword(s):  
Center Of Mass ◽  
Current Status ◽  
Laser Ranging ◽  
The Novel ◽  
Low Frequencies ◽  
Phase Measurements ◽  
Grace Satellites ◽  
Gravity Signal ◽  
The One

<p>The GRACE Follow-On satellites were launched on 22<sup>nd</sup> May 2018 to continue the measurement of Earth’s gravity field from the GRACE satellites (2002-2017). A few weeks later, an inter-satellite laser link was established with the novel Laser Ranging Interferometer (LRI), which offers an additional measurement of the inter-satellite range next to the one provided by the conventional microwave ranging instrument. The LRI is the first optical interferometer in space between orbiters, which has demonstrated to measure distance variations with a noise below 1 nm/rtHz at Fourier frequencies around 1 Hz, well below the requirement of 80 nm/rtHz.</p><p>In this talk, we provide an overview on the LRI and present the current status and results regarding the characterization of the instrument. We will address the scale factor, which is needed to convert the phase measurements to a displacement, and the removal of phase jumps that are correlated to attitude thruster activations. Moreover, the results comprise the coupling of attitude variations into the measured range, which is determined by means of the center-of-mass calibration maneuvers. This coupling is expected to be one of the major error sources at low frequencies, however, it is not directly apparent due to the large gravity signal.</p><p>We conclude with some learned lessons and potential modifications of the interferometry for future geodetic missions.</p>

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