Gyroscopic Devices Research Articles

Utilisation of the Controllable Inertial Morphing for Providing Spacecraft with Acrobatic Attitude Capabilities.

The paper is exploring a new method of controlling of the attitude dynamics of the spacecraft with non-zero angular momentum, using deliberately applied changes to the spacecraft inertial properties, called inertial morphing (IM). This method does not employ classical gyroscopic devices, nevertheless it enables the spacecraft to perform various acrobatics manoeuvres, allowing interchanges between stable and unstable states. In one case scenario, it enables transformation of the stable spin into unstable flipping motion and establishment of the desired periods of the flips at various stages of the procedure. Special consideration is given to the selection of the controllable morphed parameters to impose the desired periods and patterns of the acrobatics. This paper exploits use of the unstable flipping motions of the systems and due to established mini-max relationships for the flipping periods, enables selection of the system parameters, maximizing or minimizing the values of the periods for faster (more agile) maneuvers. In the other scenario, IM is used to transfer the regular spin about one body axis into the regular spin about another nominated body axis. Numerous illustration cases are presented and application of the new enhanced capabilities are discussed in detail. For example, paper presents a scenario of the reconfiguration of the articulated spacecraft with its segments being inverted during the acrobatic procedure in the desired way, which may open new possibilities during the spacecraft operation, including re-boost and landing.

Physics of Gyroscope’s “Antigravity Effect”

The physics of gyroscopic effects are more complex than presented in existing mathematical models. The effects presented by these models do not match the real forces acting on gyroscopic devices. New research in this area has demonstrated that a system of inertial torques, which are generated by the rotating mass of spinning objects, acts upon a gyroscope. The actions of the system of inertial forces are validated by practical tests of the motions of a gyroscope with one side support. The action of external load torque on a gyroscope with one side support demonstrates that the gyroscope’s upward motion is wrongly called an “antigravity” effect. The upward motion of a gyroscope is the result of precession torque around its horizontal axis. The novelty of the present work is related to the mathematical models for the upward and downward motions of gyroscopes influenced by external torque around the vertical axis. This analytical research describes the physics of gyroscopes’ upward motion and validates that gyroscopes do not possess an antigravity property.

Physics of gyroscope nutation

The known publications of the gyroscope property of maintaining its axis are represented by simplified mathematical models formulated on the law of kinetic energy conservation and the action of an inertial torque expressed by the change in the angular momentum. This is the reason that practice does not validate the correctness of such publications and gyroscopic effects remained for a long time as unsolved problems. The new study demonstrates that the origin of gyroscopic effects is more complex and is manifested by the simultaneous and interdependent action of the several inertial resistance and precession torques produced by the rotating mass of a spinning object. These inertial torques are represented by the action of centrifugal, Coriolis, the common inertial forces and the change in the angular momentum of the rotating mass of a gyroscope. In case of the complex gyroscope motion, the inertial torques can deactivate that represent the new property of the matter. The principles of energy conservation, the action of the system of internal and external torques on gyroscopic devices and their new mathematical models enable for the describing all gyroscopic effects. The main contribution and novelty of this paper is the mathematical modeling and describing the physics of the gyroscope nutation called galloping, which was a mostly unsolved problem in engineering.

Fractional-calculus-based control scheme for dynamical systems with input uncertainty

Since the existence of unwanted oscillations should be avoided in practical systems, this article investigates active vibration and oscillation suppression of two-degree-of-freedom dynamical systems using a novel variable structure control methodology. Owing to high stability and generality of the fractional-calculus-based differential equations, a non-integer-order sliding surface is proposed. Afterward, the occurrence of the sliding motion is ensured using a switching control rule. The effects of the input nonlinearities, which are usually existed in mechanical actuators, are fully dealt with using the introduced fractional sliding modes. In addition, unknown lumped uncertainties are considered to disturb the system dynamics. As a result, the proposed controller is robust against system and control fluctuations and can handle bounded external perturbations. Moreover, careful stability synthesis is developed to theoretically confirm the control designs. Finally, two numerical case studies, which include oscillation control of a magnetic bearing system and a gyroscope device, are provided to demonstrate the superior performance of the suggested control technology.

ОСОБЛИВОСТІ ВИЗНАЧЕННЯ ТОЧНОСТІ ВИМІРЮВАНЬ ІНЕРЦІАЛЬНИХ ПРИЛАДІВ ВИЗНАЧЕННЯ КООРДИНАТ

В статті показано, що в основу функціонування існуючих приладів інерціальних навігаційних систем літальних апаратів покладено властивість швидкообертових гіроскопів зберігати незмінним напрямок осі обертання в просторі (гіроскопічний ефект). При цьому у загальному випадку похибки гіроскопічних пристроїв (приладів) залежать як від їх конструкції, так і від умов їх роботи. Обґрунтовано актуальну наукову задачу – проведення аналізу особливостей визначення точності вимірювань інерціальних навігаційних систем при розрахунку координат літального апарату. Наведено, що відомий метод часткової компенсації похибок вимірювань аналітичним шляхом на основі обчислення їхніх значень, є недосконалим. Пропонується для обчислення й подальшої компенсації похибок навігаційних вимірювань розробити математичну модель похибок інерціальних навігаційних систем. Така модель аналітично описує зв'язок між вхідними похибками інерціальних навігаційних систем, обумовленими недоліками гіроскопів й акселерометрів, та її вихідними похибками у визначенні координат літального апарату. Запропоновані три складові математичної моделі – блоки розрахунку координат літального апарату. Обґрунтовано, що діапазон вихідних похибок інерціальних навігаційних систем є невеликим, що дозволяє застосувати для дослідження динаміки похибок відомі методи лінеаризації функцій. Розглянуто динаміку утворення похибок у блоку обчислення кутових швидкостей і моментів. Ефективність компенсації зростаючих з часом функціонування похибок інерціальних навігаційних систем залежить від того, наскільки точно апріорно відомі чисельні значення дрейфів гіроскопів і похибок акселерометрів. Подальші дослідження пропонується направити для перевірки адекватності запропонованої математичної моделі похибок інерціальних навігаційних систем реальним процесам за допомогою результатів імітаційного моделювання з використанням нелінійної моделі формування похибок.

A Mathematical Model for Top Nutation Based on Inertial Forces of Distributed Masses

The main property of gyroscopic devices is maintaining the axis of a spinning rotor, a mathematical model formulated on the principle of the change in the angular momentum. This principle is used for mathematical modeling of the motions of a top at known publications. Nevertheless, practical tests of gyroscopic devices do not correspond to this analytical approach. Recent investigations have demonstrated that the origin of gyroscope properties is more complex than that represented in known publications. The applied torque on a gyroscope produces internal torques of the spinning rotor based on the action of the several inertial forces. These forces are the centrifugal, Coriolis, and common inertial forces as well as the change in the angular momentum generated by the mass elements and center-mass of the spinning rotor. The action of these torques manifests itself in the resistance and precession torques of the gyroscopic devices. These inertial torques act simultaneously and interdependently around two axes and represent the fundamental principles of the gyroscope theory. The new inertial torques enable deriving mathematical models for the motions of well-known top that is the simplest form of gyroscopic devices. The novelty of the work is mathematical models for the motions of the top based on action of eight inertial forces acting around its two axes. The obtained mathematical models for the top nutation and self-stabilization are represented in terms of machine dynamics and vibration analysis. The new analytical approach for motions of the well-balanced top and top with eccentricity of the center-mass definitely responds to the practical results.

Inertial forces acting on a gyroscope

Gyroscopic devices for navigation and control systems are widely applied in various industries, such as shipping and aerospace. A remarkable property of gyroscopes is that their axes can be maintained within a particular space. This interesting property of a spinning disc mounted on an axle is represented by a mathematical model formulated based on L. Euler’s principle of change in angular momentum. Nevertheless, numerous publications and analytical approaches in known gyroscope theories do not correspond to practical tests on gyroscopes. A simple rotating disc creates problems that do not have long-term solutions. Recent investigations in this area have demonstrated that the origin of gyroscope properties is more sophisticated than that described in known hypotheses. Researchers have not considered the action of inertial forces produced by the mass elements and center mass of the spinning rotor that create internal resistance and precession torques. Resistance torque is established through the actions of centrifugal and Coriolis forces. Precession torque is established through the actions of common inertial forces and a change in angular momentum. These internal torques act simultaneously and interdependently on two axes and represent the fundamental principles of gyroscope theory. Equations for internal inertial torques of a spinning disc have been formulated through mathematical analysis and differential and integral equations. These calculus methods provide a basis for understanding the rates of change in inertial forces acting on a gyroscope and include the use of functions, their derivatives, and integrals in modeling the physical processes in gyroscopes. This paper presents mathematical models for several internal inertial torques generated by the load torque acting on a spinning rotor. These models can describe all gyroscope properties and represent their novelty for machine dynamics and engineering.

A Nonlinear Sampled-Data Observer of Vehicle Lateral Velocity

Modeling and control of ground vehicles have become a major research field in the last few years, due to the increasing diffusion of driver assistance technologies and the persistent need for guaranteeing safety and comfort of driver and passengers. Although vehicle control systems require a large set of measurements to perform accurate computations, due to the possible unavailability and the non-negligible cost of sensors, it is not always possible to assume the direct knowledge of some important dynamic quantities involved, among which a major role is taken by its lateral velocity. In this letter, we address the design and implementation of an asymptotic sampled-data state observer for the vehicle single-track model. The observer only exploits the knowledge of sparse yaw-rate samples, which are obtained by relatively cheap digital gyroscopic devices, to reconstruct the continuous behavior of lateral velocity and yaw rate. However, due to the inherent properties of the vehicle single-track model, the observer is theoretically guaranteed to work only in the presence of sufficiently bounded driver maneuvers. Consequently and in view of a practical exploitation in a realistic setting, we preliminarily validate the approach by means of simulations of the observer applied to a more general vehicle model, including parameter variations, unmodeled dynamics, and quantization. The results seem to confirm the potential of the approach.

Математична модель багаторежимної системи визначення повної просторової орієнтації рухомого об’єкта

Мета: У статті представлено математичний опис системи визначення просторової орієнтації рухомого об’єкта, яка може бути використана у високоточних системах стратегічного призначення. Методи дослідження: Для розв’язання даної проблеми було використано класичну теорію механіки, теорію гіроскопів та теорію інерціальної навігації. Результати: Отримано повну математичну модель платформної системи визначення просторової орієнтації, включаючи опис різних режимів функціонування. Представлено результати моделювання. Висновки: Представлені результати підтверджують ефективність запропонованих моделей. Розроблені математичні моделі можуть бути корисними для навігаційних систем рухомих об’єктів широкого класу.

Prospects for the use of ion-plasma and beam technologies when creating precision assemblies of gyroscopic devices

Prospects for the use of ion-plasma and beam technologies when creating precision assemblies of gyroscopic devices

Синтез цифровых регуляторов гироскопических командных приборов

Синтез цифровых регуляторов гироскопических командных приборов

Analytical approximations to the dynamics of an array of coupled DC SQUIDs

Coupled dynamical systems that operate near the onset of a bifurcation can lead, under certain conditions, to strong signal amplification effects. Over the past years we have studied this generic feature on a wide range of systems, including: magnetic and electric fields sensors, gyroscopic devices, and arrays of loops of superconducting quantum interference devices, also known as SQUIDs. In this work, we consider an array of SQUID loops connected in series as a case study to derive asymptotic analytical approximations to the exact solutions through perturbation analysis. Two approaches are considered. First, a straightforward expansion in which the non-linear parameter related to the inductance of the DC SQUID is treated as the small perturbation parameter. Second, a more accurate procedure that considers the SQUID phase dynamics as non-uniform motion on a circle. This second procedure is readily extended to the series array and it could serve as a mathematical framework to find approximate solutions to related complex systems with high-dimensionality. To the best of our knowledge, an approximate analytical solutions to an array of SQUIDs has not been reported yet in the literature.

Design, fabrication and characterization of a low-noise Z-axis micromachined gyroscope

This paper presents the design, fabrication and characterization of a low-noise Z-axis micromachined gyroscope. A triple-mass scheme is adopted to obtain a decoupled mode and matched vibration structure. The gyroscope was fabricated based on a 30-μm silicon on insulator wafer. A DRIE, lag-effect-based, dicing-free process was used to easily and rapidly create the gyroscope devices without requiring normal dicing. The fabricated gyroscopes were vacuum packaged (pressure of approximately 2,000 Pa) and tested. The measured power spectral density of the noises is as low as 17.5 μV/?Hz, and the resolution of the fabricated gyroscope is 7.1 × 10---4°/s/?Hz (2.52°/h/?Hz).

Bias Contributions in a MEMS Tuning Fork Gyroscope

This paper analyzes the bias sources of mechanical and electrostatic origin in a tuning fork microelectromechanical systems (MEMS) gyroscope. In a gyroscope which is symmetrical and has no defect, there would be no bias; technological defects should be investigated in order to identify and quantify bias sources, which arise from quadrature and in-phase errors. Technological dispersions within the etching step of the mechanical structure are a major source of errors. Dispersions at the scale of a single MEMS particularly matter by impacting springs and electrodes. Design rules are defined for a z-axis gyroscope in order to curb these errors: In particular, specific drive springs, which are very stiff in the sense direction, and a mechanical decoupling between drive and sense are indicated to decrease errors. Local dispersion of the width of beams has been assessed with a network of electrical test structures and leads to a local standard deviation of 3-6 nm at the scale of a MEMS gyroscope device. The optimized design enables to obtain a total error of less than 300°/s on very compact z-axis gyroscopes with an area of mechanical part of 0.5 mm2.

Spectrum Analysis in Postural Strategy on Static Tests in a Healthy Population

Introduction and objectivesThe power spectral density can be used to find a hidden behaviour in a physical system. We studied postural behaviour in a healthy population, by means of power spectral density, and compared it with a situation of complete immobility. MethodsA group of healthy volunteers carried out the modified Clinical Test for Sensory Interaction in Balance. A fibre optic gyroscope device was used to record the data. We compared the power spectral density in these tests and with another recording where the device was motionless. We looked for significant differences using the ANOVA test. ResultsA power peak appeared at 8.4Hz in all static tests. The static group showed significant differences with all the other tests. We found no statistically significant differences when visual input discriminated between 2 tests. There were statistically significant differences for the proprioceptive input. ConclusionsBrief movements are needed to maintain the quiet stance. The distinctive feature of these movements is a fundamental frequency at 1.4Hz and a harmonic frequency at 8.4Hz. Proprioceptive input is essential for balance.

Estudio espectral de la estrategia postural de una población sana en pruebas estáticas

Introduction and objectivesThe power spectral density can be used to find a hidden behaviour in a physical system. We studied postural behaviour in a healthy population, by means of power spectral density, and compared it with a situation of complete immobility. MethodsA group of healthy volunteers carried out the modified Clinical Test for Sensory Interaction in Balance. A fibre optic gyroscope device was used to record the data. We compared the power spectral density in these tests and with another recording where the device was motionless. We looked for significant differences using the ANOVA test. ResultsA power peak appeared at 8.4Hz in all static tests. The static group showed significant differences with all the other tests. We found no statistically significant differences when visual input discriminated between 2 tests. There were statistically significant differences for the proprioceptive input. ConclusionsBrief movements are needed to maintain the quiet stance. The distinctive feature of these movements is a fundamental frequency at 1.4Hz and a harmonic frequency at 8.4Hz. Proprioceptive input is essential for balance.

Magnetoelectric drive with transformer current leads for float gyroscopic devices

Magnetoelectric drive with transformer current leads for float gyroscopic devices

Nonlinear Control Analysis of a Double-Gimbal Variable-Speed Control Moment Gyroscope

A single double-gimbal variable-speed controlmoment gyroscope is considered as amethod for three-dimensional spacecraft attitude control. First, the system’s equations of motion are developed, where gimbal and wheel accelerations are prescribed as control inputs. The resulting necessary motor torques as well as system energy rates are computed for verification. Next, a novel control algorithm is developed from the stability constraint for reference trajectory tracking. In contrast with the control development for single-gimbal variable-speed gyros, a Newton–Raphson scheme is required to solve for the desired double-gimbal variable-speed control moment gyroscope control variables because they appear in cross product and quadratic form, preventing analytical solutions. Analysis of the control theory suggests that the same torque amplification effects exist as in a single-gimbal control moment gyro, but control by a single double-gimbal variable-speed control moment gyroscope device is not robust due to potential configurations that result in control singularities. When these singularities are avoided, a simulation with successful reference trajectory tracking is achieved. Allowing double-gimbal gyros to have variable wheel speeds provides additional torquing capabilities, which is significant if failure modes are considered. As will be shown, a single double-gimbal variable-speed control moment gyroscope device can provide limited threedimensional attitude control.

Evolution of the gyrotrons

Based on a retrospective analysis of the domestic and foreign works dealing with a variety of gyrotron applications and performed in the past decades, we show the main trends in the development of gyrotrons of different frequency ranges and different levels of output power. The main areas of application of modern gyrotrons and the specific requirements of each field are described. An overview of recent achievements, as well as major problems that hinder the further progess in gyroscopic devices toward higher frequencies and capacities is given. The methods of solution of these problems by the world’s leading research organizations and manufacturing companies are considered.

Low vibration rectification in a closed-loop, in-plane MEMS device

A method for a geometry of a lateral comb drive for an in-plane, electrostatic force feedback, closed-loop, micromachined accelerometer or closed-loop Coriolis rate gyroscope device, or closed-loop capacitive pressure or force measuring device. When vibration is applied to the device, the error in the time-average output, which is vibration rectification error, due to this input vibration is minimized or eliminated. The geometry resulting from practice of the present invention is space-efficient because drive force is maximized while vibration rectification is minimized or eliminated.