Nutation Damper Research Articles

A New Method of Satellite Attitude Control using a Bias-Momentum

In this paper a new method of satellite attitüde control using a bias-momentum called the digital logic coordination control method is described. The key point of method is that the roll-yaw motion state is represented by 8 characteristic codes. codes being processed, the control commands for roll-yaw loop can be generated. The control commands perform the coordination control between precession control and nutation damping. In nutation damping, the absolute value of the attitude error will not increase, but in precession control, the nutation is damped gradually.The controller consists of a number of triggers and gates, so it is simple and reliable.A digital simulation for the attitude control system of a sunpointing satellite has been performed. The result of simulation demonstrates the performance of the new control method.

Damper saturation effects on nutation

Saturation of a nutation damper carried by one of an ensemble of bodies (stack) in a relative angular motion around a common symmetry axis is investigated analytically. Formulae for the nutation angle rate are found for weak and strong saturation, applicable both to “axial” and “tangential” dampers. One of the results is that, under certain conditions, a saturated—i.e. a shorter and thus lighter—damper is more effective than an unsaturated damper.

Satellite attitude acquisition by momentum transfer-the controlled wheel speed method

An implementation of the momentum transfer method for spacecraft attitude acquisition of momentum wheel stabilized geostationary satellites is presented, in which the wheel speed is varied in a predeterminable manner to reduce the nutation usually associated with the method. The implementation is found to be capable of achieving the transfer to the desired zero nutation end point with 5° to 20° of residual nutation in practical situations without additional nutation damping. The transfer time is typically 10–30 min. The implementation is described in terms of the momentum sphere and energy ellipsoid. The detailed functional dynamics and parametric relationships are given in terms of phase planes and elliptic integral solutions. Feasibility of the implementation is shown to be dependent on the moment of inertia configuration and the degree to which tolerances on moments of inertia, satellite spin rate, and wheel speed are predeterminable.

Passive Nutation Damping Using Large Appendages with Application to Galileo

The use of large appendages for passive nutation damping is analyzed, and an analytical expression is developed to predict the nutation damping time constants for a large class of spacecraft including Galileo. It is shown that the use of large appendages for nutation damping can significantly degrade spacecraft stability margins and that the final design of the nutation damper must represent a tradeoff between the damping performance and the stability margin for sufficiently large appendages. The time constant derivation is outlined and the Galileo design is presented, including tradeoffs.

Suppression of wind-induced instabilities using nutation dampers

This paper presents the results of experiments conducted to assess the effectiveness of circular ring-type nutation dampers partially filled with liquid. In the beginning, important system parameters are defined and their effect on the damping coefficient established using a simple static stand facility. This is followed by tests on two- and three-dimensional models, in smooth flow and boundary layer tunnels, with the models undergoing vortex-induced resonance and galloping conditions. Results suggest that nutation dampers can effectively suppress both forms of instabilities over a wide range of wind velocity.

Active damping of nutation of conducting gyroscope rotor

Active damping of nutation of conducting gyroscope rotor

Theory, Simulation, and Practical Tests of a Counterspun Nutation Damper for Prolate Spinners

A nutation damper described in some previous papers is considered. It consists of a flywheel attached by a dissipative tilting mounting on the axle of a motor parallel to the spacecraft spin axis, but spinning in the opposite direction to the spacecraft. It is treated first by theory using differential equations applied to a quasisteady-state showing that it stabilizes oblate and prolate spinners and that it fits into a comparatively unexplored corner of the field that is generally understood. As a result of the theory, some optimization is done and design goals suggested. The equations are simulated on an analog computer and some examination made of performance on spacecraft that are inertially more difficult to treat by theoretical means. Stabilization is demonstrated on triaxial prolate spacecraft and spherical spacecraft are made to spin about a preferred axis. A little success has been achieved with spacecraft spinning about an intermediate inertia axis. A rudimentary damper has been made and fitted to a prolate body with an inertia ratio of 0.6, mounted on a spherical air bearing. Stabilization is demonstrated and it is shown how the results relate to theory. There is some discussion of the shortcomings of the damper tested and probable methods of engineering for space.

Energy-Sink Analysis of Systems Containing Driven Rotors

Introduction T simulation of attitude motions of highly deformable, dissipative spacecraft is so difficult that one is highly motivated to resort to heuristic methods of analysis, particularly when the deformability and/or dissipation characteristics of the spacecraft are not well defined, as during preliminary design. One such method is the so-called energy-sink approach, which has been used extensively' to obtain qualitative and quantitative information regarding attitude motions of relatively simple spacecraft. However, the use of this technique is frequently accompanied by rather strong disclaimers,'''' which suggests that the designer is well-advised to view it with suspicion. More particularly, when the spacecraft under consideration contains driven rotors, as when momentum wheels or control moment gyros are employed for attitude control, one must entertain doubts regarding the validity of energy-sink arguments, for such components of a spacecraft can play the roles of energy sources, a fact first pointed out by Landon and Stewart. Nevertheless, the method has been employed even under these circumstances; and, although some published work contains material showing that incorrect conclusions can be reached in this way, failure of the energy-sink approach has not been the central issue in anything that has appeared in print to date, with the result that the dangers inherent in the use of the method remain obscure. The present paper is intended to remedy this situation. This paper begins with the development of a formula that enables one to find the angle (nutation angle) between the central angular momentum vector and the symmetry axis of a torque-free, axisymmetric gyrostat as a function of the system's kinetic energy of rotation. A suitable kinetic energy time-history reflecting energy dissipation is then postulated, and the formula is used to construct a plot of the nutation angle as a function of time. To compare this energy-sink prediction with the actual motion of a deformable spacecraft, a gyrostat carrying a nutation damper is. considered next. This system has deformability and energy dissipation capabilities of the kind one must deal with when analyzing large, flexible spacecraft, but it is sufficiently simple to permit the formulation of exact differential equations of motion.

Nutation Dampers vs Precession Dampers for Asymmetric Spacecraft

The energy dissipation efficiencies of ball-in-tube dampers oriented with their sensitive axes orthogonal to (nutation) and parallel to (precession) the nominal spin axis of an asymmetric spacecraft are studied using the energy-sink method and numerical integration. Energy-sink equations for each of the two types of dampers are obtained in the forms of damped, periodically forced Hill-type equations. The stability of solutions to Mathieu equation approximations to these equations is considered. An approximate analytical expression for the ratio of the average energy dissipation rates of the two types of dampers is obtained. Results for ideally tuned, identical (except for their spring constants and orientations) dampers are presented and compared with those of a previous study. For a particular spacecraft configuration, analytical results for the energy dissipation ratio are compared with numerical results, and excellent agreement is achieved.

Dual-Spin Spacecraft Nutation Control Using Articulated Payloads

A technique is presented for achieving active control of nutation on a dual-spin spacecraft with an articulated payload through use of the payload's control system. Using the Orbiting Solar Observatory (OSO)-8 as an illustration, the closed-form solution to the nutation/control system dynamic interaction is presented. Control system design criteria are developed which establish the basic stability of the interaction. Design procedures are described to achieve the most effective nutation damping. Limitations on the amount of damping which can be achieved are characterized as functions of spacecraft and payload mass properties and servodesign parameters. The design techniques presented are verified through a series of on-orbit tests recently conducted on the OSO-8 spacecraft.

Galileo Dual-Spin Attitude and Articulation Control System

Galileo, the first outer planet explorer to be configured as a dual spinner, will conduct intensive investigation of Jupiter's atmosphere, satellites, and magnetosphere. The exacting mission, coupled with the inherently complex spin and flexible body dynamics of the vehicle, demands careful design of the Galileo Attitude and Articulation Control System (AACS). A brief overview of the Galileo mission and spacecraft is presented, followed by a detailed discussion on the mechanization of the AACS and the many factors that influence its design. Included are discussions on attitude determination and control, high-gain antenna pointing, science scan platform pointing, nutation damping, wobble compensation, spin and despin control, and propellant migration and boom flexibility effects.

Apple Magnetic Attitude Control (AMAC) - A New Attitude Control Concept

A novel closed loop magnetic attitude control scheme for momentum biased, near equatorial orbit satellites is described. Unlike the other schemes proposed so far, the controller presented here performs both the attitude correction and nutation damping, thus obviating the need for a seperate nutation damping mechanism.The magnetic torquer is placed along the roll axis of the spacecraft. The roll error, ϕ, obtained from earth sensor, is filtered out into two components viz., one varying at orbital frequency, ϕo, and the other varying at nutational frequency ϕn. The control dipole moment, Mc, of the magnetotorquer is governed by the control law, Mc=K2′ϕn−K1′ϕo where K1′K2′ are constants.Analytical expressions for time response of the system and conditions for stability are derived, using linearised equations of motion. The roll/yaw dynamics of the satellite was simulated on an analog computer and the simulation and analytical results matched well. Also, the simulation results indicate that enough damping is provided in the yaw channel; design aspects such as choice of feedback gains and saturation characteristics of the magneto-torquer are discussed.

Magnetic Attitude Control of a Momentum-Biased Satellite in Near-Equatorial Orbit

A novel closed-loop magnetic attitude control scheme is described for momentum-biased, near-equatorial orbit satellites. Unlike the other schemes proposed so far, the controller presented here performs both the attitude correction and nutation damping, thus obviating the need for a separate nutation damping mechanism. The magnetic torquer is placed along the roll axis of the spacecraft. The roll error , obtained from the Earth sensor, is filtered out into two components; one varying at orbital frequency 0 , and the other varying at nutational frequency „. The control dipole moment .Mc of the magneto-torquer is governed by the control law, Mc = K2 n -K'l^0, where K'j and K'2 are constants. Analytical expressions for time response of the system and conditions for stability are derived, using linearized equations of motion. The roll/yaw dynamics of the satellite were simulated on an analog computer, and the simulation and analytical results matched well. Also, the simulation results indicate that enough damping is provided in the yaw channel. Design aspects such as choice of feedback gains and saturation characteristics of the magneto-torquer are discussed.

On imperfection of elasticity in the Earth's interior

Attempts are made to estimate the distribution of damping with depth, based on the observed damping of P waves, of free vibrations, and of surface waves and partly on a discussion by D. L. Anderson and R. S. Hart. Results are consistent in order of magnitude, but could easily be wrong by a factor of 2. Comments are added on the need for further work. Stress is laid on the damping of the free nutation, which indicates that α in the modified Lomnitz law is about 0.2 on an average.

An overview of the ‘Aryabhata’ project

Aryabhata, India’s first satellite, was successfully launched into a nearearth orbit on 19 April 1975, from a USSR Cosmodrome. The primary objective ofAryabhata was to establish the indigenous capability in satellite technology.Aryabhata, weighing 358 kg, was quasispherical in shape, and had body-mounted solar cells and Ni-Cd chemical batteries as primary power sources. Other features of the spacecraft include power control systems, passive thermal control system, PCM/FM/PM telemetry system transmitting data at 256 bits/s in real time and 2560 bits/s in the stored mode, PDM/AM/AM telecommand system, cold gas spin stabilisation system with nutation damper and a number of sensors. The satellite also included three scientific experiments—one on x-ray astronomy, the second for observing solar neutrons and gamma rays and the third on aeronomy. The present paper gives an overview of the basic features of the satellite, associated ground stations and a brief account of the fabrication, testing and (in-orbit) performance of the satellite. Results of some of the technological experiments carried out inAryabhata are also briefly described.

COMSTAR Spacecraft Product-of-Inertia Coupled Electronic Nutation Damper

The design and flight performance of an innovative scheme for active nutation control flown on the COMSTAR spacecraft is described. This spacecraft is a dual-spin configuration stabilized in a maximum energy state spinning about an axis of minimum inertia. The damping mechanization implemented employs a rotor-mounted accelerometer for sensing and the despin motor as actuator, applying transverse axis damping torques through the despun product of inertia. Significant advantages of the scheme are that a broadly tuned damper, insensitive to parameter uncertainties, is provided with very low hardware weight, complexity and cost.

Passive magnetic momentum wheel unloading

Rotational kinetic energy may be extracted from the momentum wheels of a spacecraft by converting the rotational energy to electrical energy with a dynamo effect using the Earth's magnetic field, and dissipating the resultant kinetic energy as heat. This is an extension of the magnetic spin and nutation damping schemes used with spinning spacecraft. A three-axis momentum wheel assembly can be constructed with the desired inertial and autounloading characteristics that will operate in low Earth orbit. For synchronous altitudes, such a system is also possible, but the wheel design is affected greatly. The passive system is essentially failure-proof and results in a simplification of onboard systems and ground operations.

対称スピン衛星のウォブル

In recent years accuracy requirement for satellite attitude control system is getting increasingly stringent and wobble of a spinning satellite has received attention.In this paper attitude dynamics of an axisymmetric spinning satellite is analyzed and the beat of nutation and wobble is found to exist.A wobble reducer composed of two movable masses is proposed. Canadian communication satellites adopted a wobble reducer composed of three masses. The reduction of mass number from three to two contributes to the reduction of weight and the simplification of mass control logic. The possibility of wobble elimination using this wobble reducer is shown theoretically.Computer simulation is conducted and the transient attitude stability is confirmed when the wobble reducer together with a dash-pot-type nutation damper is used even if the mass of the nutation damper moves in a way unfavourable to dynamic balance.An experiment using a spherical-air-bearingsupported satellite model and mini-computer was carried out. The result of the experiment confirmed the attitude dynamics analysis including wobble and nutation. The performance of the wobble reducer was also confirmed through the experiment.

Simulation of attitude motions of torque-free, deformable spacecraft

Equations of motion are derived for torque-free, elastic, dissipative systems possessing a finite number of degrees of freedom. The equations are linearized about a particular solution in the variables describing the “internal” configuration of the system, and then SAM, a computer program based on these equations, is described. The program permits the user to obtain information about motions of a given system without writing any computer code. The paper concludes with an illustrative example involving a comparison of results obtained, on the one hand, by solving the exact equations of motion and, on the other hand, by using SAM to explore the behavior of a satellite containing a passive nutation damper. The example shows rather vividly both that relatively small deformational motions can give rise to large attitude motions and that SAM can describe these motions satisfactorily.

The damping of P waves

The results found for the damping of P between about 10° and 90° by Berzon, Passechnik & Polikarpov are analysed for the parameters in the modified Lomnitz law. They are decisive against elasticoviscosity (α= 1), but do not decide between the possible values 0 and 0.2 for a in that law. Comparison with the damping of the 14-monthly free nutation suggests about 0.13.