MULTI-LAYERED CONFIGURATIONS IN DIFFERENTIALLY ROTATIONAL EQUILIBRIUM

Abstract The balance of inverted pendulum on inclined surfaces is the precursor to their control in unstructured environments. Researchers have devised control algorithms with feedback from contact (encoders - placed at the pendulum joint) and non-contact (gyroscopes, tilt) sensors. We present feedback control of Inverted Pendulum Cart (IPC) on variable inclines using non-contact sensors and a modified error function. The system is in the state of equilibrium when it is not accelerating and not falling over (rotational equilibrium). This is achieved when the pendulum is aligned along the gravity vector. The control feedback is obtained from non-contact sensors comprising of a pair of accelerometers placed on the inverted pendulum and one on the cart. The proposed modified error function is composed of the dynamic (non-gravity) acceleration of the pendulum and the velocity of the cart. We prove that the system is in equilibrium when the modified error is zero. We present algorithm to calculate the dynamic acceleration and angle of the pendulum, and incline angle using accelerometer readings. Here, the cart velocity and acceleration are assumed to be proportional to the motor angular velocity and acceleration. Thereafter, we perform simulation using noisy sensors to illustrate the balance of IPC on surfaces with unknown inclination angles using PID feedback controller with saturated motor torque, including valley profile that resembles a downhill, flat and uphill combination. The successful control of the system using the proposed modified error function and accelerometer feedback argues for future design of controllers for unstructured and unknown environments using all-accelerometer feedback.

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Modulation of Spatial Orientation Processing by Mental Imagery Instructions: A MEG Study of Representational Momentum

Journal of Cognitive Neuroscience ◽

10.1162/089892900562345 ◽

2000 ◽

Vol 12 (4) ◽

pp. 569-582 ◽

Cited By ~ 19

Author(s):

Michel-Ange Amorim ◽

Wilfried Lang ◽

Gerald Lindinger ◽

Dagmar Mayer ◽

Lüder Deecke ◽

...

Keyword(s):

Mental Imagery ◽

Spatial Orientation ◽

Visual Motion ◽

Brain Activity ◽

Representational Momentum ◽

The Body ◽

Body Motion ◽

Body Tilt ◽

Rotational Equilibrium ◽

The Right

Under appropriate conditions, an observer's memory for the final position of an abruptly halted moving object is distorted in the direction of the represented motion. This phenomenon is called “representational momentum” (RM). We examined the effect of mental imagery instructions on the modulation of spatial orientation processing by testing for RM under conditions of picture versus body rotation perception and imagination. Behavioral data were gathered via classical reaction time and error measurements, whereas brain activity was recorded with the help of magnetoence-phalography (MEG). Due to the so-called inverse problem and to signal complexity, results were described at the signal level rather than with the source location modeling. Brain magnetic field strength and spatial distribution, as well as latency of P200m evoked fields were used as neurocognitive markers. A task was devised where a subject examined a rotating sea horizon as seen from a virtual boat in order to extrapolate either the picture motion or the body motion relative to the picture while the latter disappeared temporarily until a test-view was displayed as a final orientation candidate. Results suggest that perceptual interpretation and extrapolation of visual motion in the roll plane capitalize on the fronto-parietal cortical networks involving working memory processes. Extrapolation of the rotational dynamics of sea horizon revealed a RM effect simulating the role of gravity in rotational equilibrium. Modulation of the P200m component reflected spatial orientation processing and a non-voluntary detection of an incongruity between displayed and expected final orientations given the implied motion. Neuromagnetic properties of anticipatory (Contingent Magnetic Variation) and evoked (P200m) brain magnetic fields suggest, respectively, differential allocation of attentional resources by mental imagery instructions (picture vs. body tilt), and a communality of neural structures (in the right centro-parietal region) for the control of both RM and mental rotation processes. Finally, the RM of the body motion is less prone to forward shifts than that of picture motion evidencing an internalization of the implied mass of the virtual body of the observer.

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Study of solvent effects in association and rotational equilibrium in haloacetamides

Spectrochimica Acta Part A Molecular Spectroscopy ◽

10.1016/0584-8539(94)80113-4 ◽

1994 ◽

Vol 50 (1) ◽

pp. 41-48 ◽

Cited By ~ 5

Author(s):

E.Sánchez de la Blanca ◽

M.V. García ◽

D. Troitiño

Keyword(s):

Solvent Effects ◽

Rotational Equilibrium

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The influence of azimuthal motion on ion resonance instability for a non-neutral plasma column

Journal of Plasma Physics ◽

10.1017/s0022377800018432 ◽

1995 ◽

Vol 54 (2) ◽

pp. 173-183 ◽

Cited By ~ 3

Author(s):

H. C. Chen

Keyword(s):

Plasma Column ◽

Cyclotron Frequency ◽

Plasma Frequency ◽

Maxwell Model ◽

Threshold Value ◽

General Treatment ◽

Plasma Rotation ◽

Rotational Equilibrium ◽

Neutral Plasma ◽

Fast Ion

A general treatment of ion resonance instability for a non-neutral plasma column is performed using a macroscopic cold-fluid-Maxwell model. The azimuthal motion of the plasma components has an important influence on the behaviour of the instability. When the electrons are in slow rotational equilibrium, the instability occurs in both slow and fast ion rotational equilibrium. However, there is stability when the electrons are in fast rotational equilibrium except that the l = 1 mode becomes unstable and independent of plasma rotation. The kink (l = 1) mode only occurs when the plasma column boundary exceeds a certain threshold value that depends on the ratio of the plasma frequency to the cyclotron frequency.

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SYNOPTIC: Breakdown of Translational and Rotational Equilibrium in Gaseous Expansions

AIAA Journal ◽

10.2514/3.49883 ◽

1970 ◽

Vol 8 (11) ◽

pp. 1997-1997 ◽

Cited By ~ 12

Author(s):

G. A. Bird

Keyword(s):

Rotational Equilibrium

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On rotational equilibrium in infrared laser cavities

Journal of Applied Physics ◽

10.1063/1.326682 ◽

1979 ◽

Vol 50 (9) ◽

pp. 5994-5995

Author(s):

B. Steverding

Keyword(s):

Infrared Laser ◽

Rotational Equilibrium

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Breakdown of translational and rotational equilibrium in gaseous expansions

AIAA Journal ◽

10.2514/3.6037 ◽

1970 ◽

Vol 8 (11) ◽

pp. 1998-2003 ◽

Cited By ~ 114

Author(s):

G. A. BIRD

Keyword(s):

Rotational Equilibrium

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Gaia-DR2 extended kinematical maps

Astronomy and Astrophysics ◽

10.1051/0004-6361/201833849 ◽

2019 ◽

Vol 621 ◽

pp. A48 ◽

Cited By ~ 18

Author(s):

M. López-Corredoira ◽

F. Sylos Labini

Keyword(s):

Azimuthal Velocity ◽

Fredholm Integral Equations ◽

Inversion Method ◽

Velocity Measurements ◽

Dynamical Models ◽

Velocity Gradients ◽

Stationary Configuration ◽

Rotational Equilibrium ◽

The Mean ◽

Gaia Dr2

Context. The Gaia Collaboration has used Gaia-DR2 sources with six-dimensional (6D) phase space information to derive kinematical maps within 5 kpc of the Sun, which is a reachable range for stars with relative error in distance lower than 20%. Aims. Here we aim to extend the range of distances by a factor of two to three, thus adding the range of Galactocentric distances between 13 kpc and 20 kpc to the previous maps, with their corresponding error and root mean square values. Methods. We make use of the whole sample of stars of Gaia-DR2 including radial velocity measurements, which consists in more than seven million sources, and we apply a statistical deconvolution of the parallax errors based on the Lucy’s inversion method of the Fredholm integral equations of the first kind, without assuming any prior. Results. The new extended maps provide lots of new and corroborated information about the disk kinematics: significant departures of circularity in the mean orbits with radial Galactocentric velocities between −20 and +20 km s−1 and vertical velocities between −10 and +10 km s−1; variations of the azimuthal velocity with position; asymmetries between the northern and the southern Galactic hemispheres, especially towards the anticenter that includes a larger azimuthal velocity in the south; and others. Conclusions. These extended kinematical maps can be used to investigate the different dynamical models of our Galaxy, and we will present our own analyses in the forthcoming second part of this paper. At present, it is evident that the Milky Way is far from a simple stationary configuration in rotational equilibrium, but is characterized by streaming motions in all velocity components with conspicuous velocity gradients.

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