Inertial Stability Research Articles

Application of position and inertial-rate control to a 2-DOF gyroscopic platform

This paper presents a control application for the inertial stabilization of a gyroscopic platform with two degrees of freedom (2-DOF). The purposes of this application are, first, to control the angular positions of the platform in the absence of inertial disturbances and second, to control velocities measured in an inertial frame, while rejecting the disturbances associated with moving components. With regard to the first objective, a switching-control strategy is proposed in order to reduce the effects of friction as the main source of undesirable non-linear behaviors. Regarding the inertial-rate control, a master–slave control structure is suggested to achieve the desired specifications. Simulation and experimental results are presented, showing the performance attained on a real platform.

Rapid Development of the Tropical Cyclone Warm Core

Abstract This paper presents a simple theoretical argument to isolate the conditions under which a tropical cyclone can rapidly develop a warm-core thermal structure and subsequently approach a steady state. The theoretical argument is based on the balanced vortex model and, in particular, on the associated transverse circulation equation and the geopotential tendency equation. These second-order partial differential equations contain the diabatic forcing and three spatially varying coefficients: the static stability A, the baroclinity B, and the inertial stability C. Thus, the transverse circulation and the temperature tendency in a tropical vortex depend not only on the diabatic forcing but also on the spatial distributions of A, B, and C. Experience shows that the large radial variations of C are typically the most important effect. Under certain simplifying assumptions as to the vertical structure of the diabatic forcing and the spatial variability of A, B, and C, the transverse circulation equation and the geopotential tendency equation can be solved via separation of variables. The resulting radial structure equations retain the dynamically important radial variation of C and can be solved in terms of Green’s functions. These analytical solutions show that the vortex response to a delta function in the diabatic heating depends critically on whether the heating occurs in the low-inertial-stability region outside the radius of maximum wind or in the high-inertial-stability region inside the radius of maximum wind. This result suggests that rapid intensification is favored for storms that have at least some of the eyewall convection inside the radius of maximum wind. The development of an eye partially removes diabatic heating from the high-inertial-stability region of the storm center; however, rapid intensification may continue if the eyewall heating continues to become more efficient. As the warm core matures and static stability increases over the inner core, conditions there become less favorable for deep upright convection and the storm tends to approach a steady state.

Crush dynamics of square honeycomb thin rubber wall

Previous experimental study has proven that rubber honeycomb claddings with thin rubber core can be used to attenuate the water blast wave impinged onto ship hull. As a theoretical extension, the dynamic crush behavior of the square honeycomb core made by thin rubber wall is investigated in this paper. As the dynamic effects play a significant role in the behavior of core, several distinct dynamic effects are analyzed including inertial resistance, nonlinear elasticity, inertial stabilization of webs against buckling, and material viscosity. The influences of the initial imperfection shape and amplitude are discussed too. These effects are illustrated and quantified with the aid of detailed numerical calculations. Some preliminary attempts are also made on the theoretical prediction on the stress wave transmission process.

Modern tasks of inertial stabilization for data-measuring system

Modern tasks of inertial stabilization for data-measuring system

Estimating Maximum Surface Winds from Hurricane Reconnaissance Measurements

Abstract Radial profiles of surface winds measured by the Stepped Frequency Microwave Radiometer (SFMR) are compared to radial profiles of flight-level winds to determine the slant ratio of the maximum surface wind speed to the maximum flight-level wind speed, for flight altitude ranges of 2–4 km. The radius of maximum surface wind is found on average to be 0.875 of the radius of the maximum flight-level wind, and very few cases have a surface wind maximum at greater radius than the flight-level maximum. The mean slant reduction factor is 0.84 with a standard deviation of 0.09 and varies with storm-relative azimuth from a maximum of 0.89 on the left side of the storm to a minimum of 0.79 on the right side. Larger slant reduction factors are found in small storms with large values of inertial stability and small values of relative angular momentum at the flight-level radius of maximum wind, which is consistent with Kepert’s recent boundary layer theories. The global positioning system (GPS) dropwindsonde-based reduction factors that are assessed using this new dataset have a high bias and substantially larger RMS errors than the new technique. A new regression model for the slant reduction factor based upon SFMR data is presented, and used to make retrospective estimates of maximum surface wind speeds for significant Atlantic basin storms, including Hurricanes Allen (1980), Gilbert (1988), Hugo (1989), Andrew (1992), and Mitch (1998).

How Do Outer Spiral Rainbands Affect Tropical Cyclone Structure and Intensity?*

Abstract A long-standing issue on how outer spiral rainbands affect the structure and intensity of tropical cyclones is studied through a series of numerical experiments using the cloud-resolving tropical cyclone model TCM4. Because diabatic heating due to phase changes is the main driving force of outer spiral rainbands, their effect on the tropical cyclone structure and intensity is evaluated by artificially modifying the heating and cooling rate due to cloud microphysical processes in the model. The view proposed here is that the effect of diabatic heating in outer spiral rainbands on the storm structure and intensity results mainly from hydrostatic adjustment; that is, heating (cooling) of an atmospheric column decreases (increases) the surface pressure underneath the column. The change in surface pressure due to heating in the outer spiral rainbands is significant on the inward side of the rainbands where the inertial stability is generally high. Outside the rainbands in the far field, where the inertial stability is low and internal atmospheric heating is mostly lost to gravity wave radiation and little is left to warm the atmospheric column and lower the local surface pressure, the change in surface pressure is relatively small. This strong radially dependent response reduces the horizontal pressure gradient across the radius of maximum wind and thus the storm intensity in terms of the maximum low-level tangential wind while increasing the inner-core size of the storm. The numerical results show that cooling in the outer spiral rainbands maintains both the intensity of a tropical cyclone and the compactness of its inner core, whereas heating in the outer spiral rainbands decreases the intensity but increases the size of a tropical cyclone. Overall, the presence of strong outer spiral rainbands limits the intensity of a tropical cyclone. Because heating or cooling in the outer spiral rainbands depends strongly on the relative humidity in the near-core environment, the results have implications for the formation of the annular hurricane structure, the development of concentric eyewalls, and the size change in tropical cyclones.

Humanoid robot Lola: Design and walking control

In this paper we present the humanoid robot LOLA, its mechatronic hardware design, simulation and real-time walking control. The goal of the LOLA-project is to build a machine capable of stable, autonomous, fast and human-like walking. LOLA is characterized by a redundant kinematic configuration with 7-DoF legs, an extremely lightweight design, joint actuators with brushless motors and an electronics architecture using decentralized joint control. Special emphasis was put on an improved mass distribution of the legs to achieve good dynamic performance. Trajectory generation and control aim at faster, more flexible and robust walking. Center of mass trajectories are calculated in real-time from footstep locations using quadratic programming and spline collocation methods. Stabilizing control uses hybrid position/force control in task space with an inner joint position control loop. Inertial stabilization is achieved by modifying the contact force trajectories.

Intermittent layering in the Atlantic equatorial deep jets

Equatorial observations in the Atlantic show three distinct vertical scales: quasi-barotropic eastward Extra-Equatorial Jets (EEJ), Equatorial Deep Jets (EDJ) of scale 500-800 m, and a smaller scale signal (50-100 m) of thin layers of well-mixed tracer fields. In the combined system of jets, westward EDJ correspond to zero-Potential Vorticity (PV) inside of which most of the thin well-mixed layers are found. Because of its correlation with zero-PV niches, the formation of layers is interpreted as due to inertial instability. The latter encompasses inertial barotropic instability due to meridional shear (either steady or parametric), baroclinic symmetric instability due to sloping isopycnals and vertical velocity shear, and effective-beta inertial instability due to the curvature of a westward jet at the equator. In very high resolution numerical simulations, where equatorial deep jets of 500-800 m vertical scale are produced, density layering is observed with a characteristic depth of mixing of about 50 m. A statistical analysis reveals that the well-mixed layers are located in zones of marginal inertial stability, mainly due to the vertical shear of zonal velocity and curvature of westward jets and therefore points toward a baroclinic symmetric instability mechanism and an effective-beta inertial instability.

A Hurricane Boundary Layer and Wind Field Model for Use in Engineering Applications

Abstract This article examines the radial dependence of the height of the maximum wind speed in a hurricane, which is found to lower with increasing inertial stability (which in turn depends on increasing wind speed and decreasing radius) near the eyewall. The leveling off, or limiting value, of the marine drag coefficient in high winds is also examined. The drag coefficient, given similar wind speeds, is smaller for smaller-radii storms; enhanced sea spray by short or breaking waves is speculated as a cause. A fitting technique of dropsonde wind profiles is used to model the shape of the vertical profile of mean horizontal wind speeds in the hurricane boundary layer, using only the magnitude and radius of the “gradient” wind. The method slightly underestimates the surface winds in small but intense storms, but errors are less than 5% near the surface. The fit is then applied to a slab layer hurricane wind field model, and combined with a boundary layer transition model to estimate surface winds over both marine and land surfaces.

Investigation of motion sickness and inertial stability on a moving couch for intra-fraction motion compensation

Investigation of motion sickness and inertial stability on a moving couch for intra-fraction motion compensation

Investigation of motion sickness and inertial stability on a moving couch for intra-fraction motion compensation

Background. Respiration-induced tumor motion compensation using a treatment couch requires moving the patient at non-trivial speeds. The purpose of this work was to investigate motion sickness and stability of the patient's external surface due to a moving couch with respiration-comparable velocities and accelerations. Material and methods. A couch was designed to move with a peak-peak displacement of 5 cm and 1 cm in the S-I and A-P directions, respectively, and a period of 3.6 s. Fifty patients completed a 16-question motion sickness assessment questionnaire (MSAQ) prior to, during, and after the study. Seven optical reflectors affixed to the abdomen of each patient were monitored by infrared cameras. The relationship between reflector positions under stationary and moving conditions was evaluated to assess the stability of the patient's external surface. Results and discussion. Among the 4800 responses, 95% were 1 (no discomfort) of 9, and there were no scores of 6 or higher. Mild discomfort (scores of 4–5) was similar during couch motion and before couch motion (p = 0.39). Mild discomfort was less common after couch motion (p = 0.039) than before or during couch movement. There was a near 1:1 correspondence between marker-pair regression coefficients and phase offset values during couch-stationary and couch-moving conditions. Our results show that patients do not suffer motion sickness or external surface instability on a moving couch.

Body rate decoupling using haltere mid-stroke measurements for inertial flight stabilization in Diptera

Halteres, the modified rear wings of Diptera, have long been recognized as sensory organs necessary for basic flight stability. These organs, which act as vibrating structure gyroscopes, are known to sense strains proportional to Coriolis accelerations. While compensatory responses have been demonstrated that indicate the ability of insects to distinguish all components of the body rate vector, the specific mechanism by which the halteres are able to decouple the body rates has not been clearly understood. The research documented in this report describes a potential mechanism, using averaged strain and strain rate at the center of the haltere stroke, to decouple the inertial rate components. Through dynamic simulation of a nonlinear model of the haltere 3-dimensional trajectory, this straightforward method was demonstrated to provide an accurate means of generating signals that are proportional to three orthogonal body rate components. Errors associated with residual nonlinearity and rate-coupling were quantified for a bilaterally reconstructed body rate vector over a full range of pitch and yaw rates and two roll rate conditions. Models that are compatible with insect physiology are proposed for performing necessary signal averaging and bilateral processing.

The piecewise constant symmetric potential vorticity vortex in geophysical flows

The concept of piecewise constant symmetric vortex in the context of three-dimensional baroclinic balanced geophysical flows is explored. The pressure gradients generated by horizontal cylinders and spherical balls of uniform potential vorticity (PV), or uniform material invariants, are obtained either analytically or numerically, in the general case of Boussinesq andf-plane dynamics as well as under the quasi-geostrophic and semigeostrophic dynamical approximations. Based on the order of magnitude of the different terms in the PV inversion equation, approximated PV equations are deduced. In some of these cases, radial solutions are possible and the interior and exterior solutions are found analytically. In the case of non-radial dependence, exterior solutions can be found numerically. Linear, and upper and lower bound approximations to the full PV inversion equations, and their respective solutions, are also included. However, the general solution for the pressure gradient in the vortex exterior does not have spherical symmetry and remains as an important theoretical challenge. It is suggested that, in order to maintain everywhere the inertial and static stability of the balanced geophysical flows, small balls of finite radius, rather than PV singularities, could become, specially in numerical applications, useful mathematical objects.

Synchronization of the signal posturographic to optic-kinetic stimulus for the diagnosis and the rehabilitation of vestibular disorder with “VERTIGO STATIC PLATFORM”

minimal acceleration [1]. In normal circumstances, this allows for the minimisation of the head acceleration with the consequent reduction of inertial loads and stabilisation of the optic flow. In patients with muscular myopathies causing impairments at trunk level, the ability to control upper body accelerations and ensure head stability is expected to be reduced. Aim of this study is to test the above hypothesis, as a paradigmic example, in subjects with facioscapulohumeral dystrophy. Methods: Twenty control healthy subjects (CS, 25 ± 6 years, 1.6 ± 0.1 m, 58 ± 8 kg) and 12 subjects with facioscapulohumeral dystrophy (DS, 38 ± 10 years, 1.8 ± 0.1 m, 85 ± 23 kg) participated in this study. They were asked to walk at their self-selected speed, and a 9-camera VICON MX was used to reconstruct the trajectories of 10 markers (anterior and posterior superior iliac spines, jugular notch, C7 spine process, front and back of the head, and heels). Head (H), upper trunk (T), and pelvis (P) movements were described using the trajectories of the midpoints between the head markers, between C7 and jugular notch, and the centroid of the iliac spines, respectively. The root mean square of the accelerations (aRMS) of H, T, and P were computed along the antero-posterior (AP), medio-lateral (ML) and vertical (V) directions. To investigate the differences between the two groups in the ability to attenuate the accelerations from pelvis to head level, the following coefficients were computed: cPT =( aRMSP − aRMST)/aRMSP, and cPH =( aRMSP − aRMSH)/aRMSP. The t-test was used for statistical analysis. Results: For the CS, at all levels, the aRMS was not correlated with the speed of progression. For the DS, a moderate, but not significant, inverse correlation between speed and head acceleration was found in the ML and AP directions. Both groups (figure) showed no significant aRMS attenuations along the V direction. In the CS, along the AP direction, pelvis acceleration was significantly higher (p < 0.01) than that at trunk and head levels. The DS, on the contrary, were less able to reduce the amplitude of the acceleration from pelvis to trunk and head levels, as shown by the lower (p < 0.01) attenuation coefficients. In the ML direction, finally, the head acceleration was attenuated with respect to the pelvis in the CS (p = 0.03), whereas it was higher (p < 0.01) than the pelvis acceleration in the DS, as shown by the negative cPT and cPH. Discussion: The ability to control head stability during walking is a characteristic of healthy adults, which is preserved in aging [2], but it was significantly compromised in the subjects with a myopathy. Along mediolateral direction, the head acceleration was even higher than that of the pelvis. A possible explanation for this result could be the adoption of a strategy to compensate for hip abductor weakness, but further studies are needed to validate this hypothesis.

Tropical Cyclone Energy Dispersion in a Three-Dimensional Primitive Equation Model: Upper-Tropospheric Influence*

Abstract The three-dimensional (3D) Rossby wave energy dispersion of a tropical cyclone (TC) is studied using a baroclinic primitive equation model. The model is initialized with a symmetric vortex on a beta plane in an environment at rest. The vortex intensifies while becoming asymmetric and moving northwestward because of the beta effect. A synoptic-scale wave train forms in its wake a few days later. The energy-dispersion-induced Rossby wave train has a noticeable baroclinic structure with alternating cyclonic–anticyclonic–cyclonic (anticyclonic–cyclonic–anticyclonic) circulations in the lower (upper) troposphere. A key feature associated with the 3D wave train development is a downward propagation of the relative vorticity and kinetic energy. Because of the vertical differential inertial stability, the upper-level wave train develops faster than the lower-level counterpart. The upper anticyclonic circulation rapidly induces an intense asymmetric outflow jet in the southeast quadrant, and then further influences the lower-level Rossby wave train. On one hand, the outflow jet exerts an indirect effect on the lower-level wave train strength through changing TC intensity and structure. On the other hand, it triggers downward energy propagation that further enhances the lower-level Rossby wave train. A sudden removal of the diabatic heating may initially accelerate the energy dispersion through the increase of the radius of maximum wind and the reduction of the lower-level inflow. The latter may modulate the group velocity of the Rossby wave train through the Doppler shift effect. The 3D numerical results illustrate more complicated Rossby wave energy dispersion characteristics than 2D barotropic dynamics.

Dynamic response of a multilayer prismatic structure to impulsive loads incident from water

The dynamic crush response of a low relative density, multilayered corrugated core is investigated by combining insights from experiments and 3D finite element simulations. The test structures have been fabricated from 304 stainless steel corrugations with 0°/90° lay-up orientation and bonded by means of a transient liquid phase method. Characterization of the dynamic crushing of these structures has revealed that at low rates, interlayer interactions induce a buckling-dominated soft response. This softness is diminished at high rates by inertial stabilization and the response of the structure transitions to yield-dominated behavior. Unidirectional dynamic crushing experiments conducted using a dynamic test facility reveal a soft response, consistent with lower rate crushing mechanisms. The 3D simulation predictions of crushing strain, pulse amplitude/duration and impulse delivery rate correspond closely with the measurements. The application of core homogenization schemes has revealed that by calibrating with a multilayer unit cell, high fidelity continuum level predictions are possible. Moreover, even simplified hardening curves based on equivalent energy absorption provide remarkably accurate predictions of the crush strains and the impulse transmitted through the core. The multilayered structures investigated here significantly reduced the transmitted pressures of an impulsive load.

Dynamics of kink band formation in columnar thermal barrier oxides

The dynamics of kink band formation in columnar yttria-stabilized zirconia (YSZ) have been investigated via dynamic finite element modeling. A microstructure-based constitutive law models each column as a low-porosity solid and the intercolumnar zones as a high-porosity elastic–plastic foam. In the simulations, a rigid particle impacts a YSZ coating at fixed velocity. At the lowest velocities, kink bands develop having the characteristic location, orientation, and width established in previous quasi-static assessments. However, with increasing impact velocity and/or decreasing YSZ yield strength, kink bands are observed to form at increasingly shallower declinations. Thus a yield-strength-dependent velocity threshold exists, above which kink bands become non-penetrating. Kink band suppression is attributed to inertial stabilization of the columns against buckling. Further interrogation reveals that, for a given particle and YSZ yield strength, there exists a critical coating thickness above which kink-band-induced spallation cannot occur, regardless of impact velocity.

Some dynamical aspects of tropical cyclone concentric eyewalls

AbstractThe intensification of tropical cyclones is often interrupted by an eyewall replacement cycle, a process in which an outer eyewall forms, contracts, and replaces an inner eyewall. The radial distributions of inertial stability and diabatic heating change during such events, impacting the transverse circulation. To examine the effects of such changes, an analytical solution of the transverse circulation equation associated with a balanced vortex model is derived using a parameterization that distinguishes five radial regions subdividing the domain by each region's values of inertial stability and diabatic heating. These regions define the eye, inner eyewall, moat, outer eyewall, and far‐field. In mature concentric eyewall situations, the solutions do not support the hypothesis that the inner eyewall collapses as a direct result of subsidence from the outer eyewall. However, the results suggest subsidence and warming temperatures in the moat are governed by enhanced inertial stability associated with a strengthening outer eyewall. The model solutions also illustrate how the diabatic heating in the inner eyewall, imbedded in a region of high inertial stability, induces larger temperature tendencies than the diabatic heating in the outer eyewall, which borders the far‐field region of low inertial stability. Thus, as the inner eyewall dies, the storm temporarily loses its ability to produce an intense, localized warm region. This ability is restored during the contraction and intensification of the outer eyewall. These results provide a partial dynamical explanation of how an eyewall replacement cycle can act as a temporary brake on tropical cyclone intensification. Copyright © 2008 Royal Meteorological Society

Climate variation and prediction of rapid intensification in tropical cyclones in the western North Pacific

One of the greatest challenges in tropical weather forecasting is the rapid intensification (RI) of the tropical cyclone (TC), during which its one-minute maximum sustained wind speed increases at least 30 knots per 24 hours. Here we identify and elucidate the climatic conditions that are critical to the frequency and location of the RI on annual, intraseasonal, and interannual time scales. Whereas RI and formation share common environmental preferences, we found that the percentage of TCs with RI varies annually and from year to year. In August, only 30% of TC actually experiences RI, in contrast to the annual maximum of 47% in November. The proportion of RI in July–September is higher during El Nino years (53%) than the corresponding one in the La Nina years (37%). Three climate factors may contribute to the increase in the proportion of RI: the southward shift in the monthly or seasonal mean location of the TC formation, the increase in the low-level westerly meridional shear vorticity, and the decrease in northerly vertical shear. When the mean latitude of TC formation increases, the mixed-layer heat content decreases while TC’s inertial stability increases; both are more detrimental to the RI than to TC formation because the RI requires large amount of latent heat energy being extracted efficiently from the ocean mixed layer and requires accelerated low-level radial inflow that carries latent heat reaching the inner core region.

Biomimetic control for adaptive camera stabilization in driver-assistance systems

Throughout the last decade, a large number of electronic driver-assistance systems have been developed in order to improve vehicles’ comfort and safety. Up to now, they more or less all rely on odometric data. However in the future, a new form of information is likely to be used: visual sensors, e.g. cameras, can provide additional knowledge on traffic and the vicinity. This paper presents an inertially stabilized camera platform for high precision tracking of points of interest, that has been developed within the project FORBIAS (Research cooperation for biomimetic assistance systems). The inertial stabilization is based on a specially designed sensor system that uses MEMS components in connection with a biologically inspired control algorithm for adaptive enhancement and online calibration of the gaze stabilization system.