Vibration Of Flexible Appendages Research Articles

Attitude Maneuvering and Vibration Reducing Control of Flexible Spacecraft Subject to Actuator Saturation and Misalignment

A robust adaptive constrained control scheme is proposed for flexible spacecraft attitude maneuver and vibration suppression, in which multiple constraints are simultaneously considered, such as uncertain inertia parameters, external disturbance, unmeasured elastic vibration, actuator saturation, and even actuator misalignment. More specifically, a novel path planning scheme based on quintic polynomial transition is firstly developed to realize smooth acceleration variate and therefore decrease the vibration of flexible appendages. Secondly, an elastic modal estimator is employed to estimate the unmeasured variables, such as the modal position and velocity. Thirdly, an adaptive updating technique is used to spare the extra knowledge of system parameters and the bound of the external disturbance. In addition, an auxiliary design system is constructed to address the actuator saturation problem, and a compensation term is synthesized and integrated into the controller to handle the actuator misalignment. Finally, overall system stabilization is proved within the framework of Lyapunov theory, and numerical simulation results are presented to illustrate the effectiveness of the proposed scheme.

Observer-Based Terminal Sliding Mode Control for Attitude Stabilization of Flexible Spacecraft with Fuel Slosh

In this paper, an observer-based terminal sliding mode control approach is proposed and applied to the attitude control system of the flexible spacecraft with fuel slosh. The disturbances from the vibration of the flexible appendage and fuel slosh are modelled as derivative-bounded disturbances which can be estimated and rejected by the disturbance-observer-based-control (DOBC). Next, by combining the DOBC with terminal sliding mode controller (TSMC), a composite controller is proposed to realize the finite time convergence. Therefore, anti-disturbance and finite time attitude stabilization can be guaranteed by the proposed composite controller. Linear matrix inequality (LMI) -based algorithm is used to compute the observer parameters. Finally, theoretical analysis and simulation results are given to verify the effectiveness of the proposed method.

Attitude control of towed space debris using only tether

Tethered towing for Active Debris Removal (ADR) is promising but vulnerable to entanglement and collision due to the debris rotation. This paper proposes a novel way to control the attitude of debris towed with off-centered capture using only tether. For this purpose, a tethered manipulator (TM) on the bottom of gripper is employed to move the tether attachment point. Since the tether cannot yield a torque along itself and the TM motions are constrained, the underactuated problem subject to input saturation arises as a critical control challenge. This is tackled by using backstepping-based hierarchical sliding mode control (HSMC) with anti-windup technique. And a disturbance observer is developed to render the controller robust to the dynamics uncertainty and flexible appendages vibration. To avoid collision, by designing an impedance controller the tether tension is stabilized with a reel mechanism in platform for changing the tether length. Finally, the proposed method is verified numerically by the first impulsive maneuver of Hohmann transfer.

Sliding mode friction observer based control for flexible spacecraft with reaction wheel

A novel composite anti-disturbance control scheme is proposed for attitude control system (ACS) of flexible spacecraft with the reaction wheel friction. The proposed control scheme can overcome the performance degradation of controller under the condition of reaction wheel friction and flexible appendage vibration. First, the dynamic model of the flexible spacecraft is modelled, including disturbance torque of the reaction wheel. A sliding mode friction observer is designed to estimate the reaction wheel friction torque for feed-forward compensation. Then, a flexible appendage vibration observer is constructed to estimate and compensate for the flexible appendage vibration. Finally, an H ∞ controller is adopted to attenuate the estimation error and other bounded disturbances, such as the environment disturbance. Simulations on the ACS of a flexible spacecraft demonstrate the robustness and effectiveness of the proposed method.

Vibration suppression of a large flexible spacecraft for on-orbit operation

Flexible appendages, such as solar panels, communication antennas and other large structures, are mounted on the base of a space robot and target satellite. The vibration of the flexible structure is excited by operations of a space manipulator. It is very challenging to control the vibration of large flexible appendages for on-orbit operation and, especially when the manipulator operates a non-cooperative target with unknown structural parameters and vibration information. In this study, a hybrid control method is proposed based on wave-based control and PD control methods to control the motion of a manipulator while suppressing the vibration of appendages. First, the rigid-flexible coupled dynamic model of a compounded system is established. This is followed by designing a hybrid control strategy combining wave-based control and PD control for rest-to-rest maneuvers based on the characteristics of the compounded system. Finally, the simulation of a 3D compounded system is provided to verify the effectiveness of the presented approach. The simulation results indicate that the space robot can successfully berth the target while suppressing the vibrations of the structure.

Space robots with flexible appendages: Dynamic modeling, coupling measurement, and vibration suppression

For a space robot with flexible appendages, vibrations of flexible structure can be easily excited during both orbit and/or attitude maneuvers of the base and the operation of the manipulators. Hence, the pose (position and attitude) of the manipulator's end-effector will greatly deviate from the desired values, and furthermore, the motion of the manipulator will trigger and exacerbate vibrations of flexible appendages. Given lack of the atmospheric damping in orbit, the vibrations will last for quite a while and cause the on-orbital tasks to fail. We derived the rigid-flexible coupling dynamics of a space robot system with flexible appendages and established a coupling model between the flexible base and the space manipulator. A specific index was defined to measure the coupling degree between the flexible motion of the appendages and the rigid motion of the end-effector. Then, we analyzed the dynamic coupling for different conditions, such as modal displacements, joint angles (manipulator configuration), and mass properties. Moreover, the coupling map was adopted and drawn to represent the coupling motion. Based on this map, a trajectory planning method was addressed to suppress structure vibration. Finally, simulation studies of typical cases were performed, which verified the proposed models and method. This work provides a theoretic basis for the system design, performance evaluation, trajectory planning, and control of such space robots.

Attitude stabilization of flexible spacecrafts via extended disturbance observer based controller

To achieve the high-precision attitude stabilization for the flexible spacecraft in the presence of space environmental disturbances, unmodeled dynamics, and the disturbances caused by the elastic vibration of flexible appendages, an extended disturbance observer (EDO) based controller is proposed. The proposed controller is formulated by combining EDO and a backstepping feedback controller. EDO is used to estimate the disturbance, which is modeled as an unknown high-order differentiable equation and the rth-order derivative of the disturbance is assumed to be bounded. Compared to the conventional first-order disturbance observer, the higher order EDO offers improvement in estimate accuracy, if the absolute values of poles for EDO transfer function are chosen larger than the frequency content of the disturbance. Then, the output of EDO plus the backstepping feedback controller are applied to stabilize the attitude with high precision by rejecting disturbances for the flexible spacecraft. Finally, numerical simulations have been conducted to verify the effectiveness of the proposed controller.

Nonlinear model and attitude dynamics of flexible spacecraft with large amplitude slosh

This paper is focused on the nonlinearly modelling and attitude dynamics of spacecraft coupled with large amplitude liquid sloshing dynamics and flexible appendage vibration. The large amplitude fuel slosh dynamics is included by using an improved moving pulsating ball model. The moving pulsating ball model is an equivalent mechanical model that is capable of imitating the whole liquid reorientation process. A modification is introduced in the capillary force computation in order to more precisely estimate the settling location of liquid in microgravity or zero-g environment. The flexible appendage is modelled as a three dimensional Bernoulli-Euler beam and the assumed modal method is employed to derive the nonlinear mechanical model for the overall coupled system of liquid filled spacecraft with appendage. The attitude maneuver is implemented by the momentum transfer technique, and a feedback controller is designed. The simulation results show that the liquid sloshing can always result in nutation behavior, but the effect of flexible deformation of appendage depends on the amplitude and direction of attitude maneuver performed by spacecraft. Moreover, it is found that the liquid sloshing and the vibration of flexible appendage are coupled with each other, and the coupling becomes more significant with more rapid motion of spacecraft. This study reveals that the appendage's flexibility has influence on the liquid's location and settling time in microgravity. The presented nonlinear system model can provide an important reference for the overall design of the modern spacecraft composed of rigid platform, liquid filled tank and flexible appendage.

A composite anti-disturbance control scheme for attitude stabilization and vibration suppression of flexible spacecrafts

: There exist multiple disturbances resulting from the structural vibrations of flexible appendages, unknown external and internal disturbances, and parameter uncertainties, which affect the attitude control performance seriously. To enhance the disturbance attenuation performance and vibration suppression ability, a composite anti-disturbance control scheme (CADCS) based on disturbance observer is proposed for attitude stabilization and vibration reduction of flexible spacecraft. The CADCS combines a composite disturbance observer (CDO) and a PD controller with feedforward. The multiple disturbances are equivalent to slowly varying disturbance and harmonic disturbance. The CDO can estimate two types of disturbance and compensate for them through feedforward. The PD controller realizes the asymptotic convergence by compensating the disturbance from CDO. The CADCS based on CDO and PD controller is not only simple and easy to realize, but also yields better vibration suppression and anti-disturbance performance. Simulation results of a certain spacecraft demonstrate the effectiveness of the proposed CADCS.

Dynamics, analytical solutions and choice of parameters for towed space debris with flexible appendages

Active debris removal is one of the promising techniques that will decrease the population of large, non-functional spacecraft (space debris) on orbit. Properties of space debris should be taken into account during planning an active debris removal mission. In this paper the thrusting phase of tethered deorbit of large space debris with flexible appendages is considered. The goal of the work is to investigate the mutual influence of the tether vibrations and the vibrations of flexible appendages during thrusting phase. A mathematical model of the space tug and the towed space debris with flexible appendages is developed. Parameters of the system are determined with assumptions that the system is moving in straight line, avoiding high amplitude vibrations of flexible appendages. The expression of the discriminant indicates that the vibrations of the tether and flexible appendages influence each other. A critical tether stiffness exists for the given space tug mass that should be avoided.

Nonsmooth attitude stabilization of a flexible spacecraft

A flexible spacecraft is a kind of complex systems consisting of rigid bodies and flexible appendages. The attitude maneuvering or external disturbances will unavoidably lead to a continuous vibration of flexible appendages. It is known that the finite-time control technique offers better convergence and disturbance rejection properties. To achieve the high-accuracy attitude stabilization, a nonsmooth attitude-stabilizing control strategy based on the finite-time control technique is investigated for flexible spacecrafts in this paper. The rigorous mathematical stability analysis of the overall closed-loop system is made by means of cascaded systems theory. The novelty of the paper is that the relation between the convergence region of states and the control parameters can be obtained, which indicates that the steady-state error can be preestimated when the control parameters are determined. Simulation results show that not only can the attitude be stabilized precisely, but the elastic vibration of flexible appendages can be suppressed effectively as well.

Sinusoidal Path Planning for Attitude Maneuver of Flexible Spacecraft

Considering the complex of space environment, the influence of flexible attachments, the restraint of measurement and control precision, it makes difficult to control the attitude precisely. In order to improve the attitude maneuver's rapidity and its stability, this paper studied the attitude maneuver's path programming method of satellite with the flexible attachments. Through the establishment of the dynamic model of flexible satellites, and using multi-objective optimization algorithm to select the optimal parameter, an asymmetric sinusoidal maneuver path was planned. Simulation results show that the planned path could suppress flexible appendages vibration which brought by attitude changes, then the effectiveness of the planning algorithm is demonstrated.

High Accuracy Attitude Control System Design for Satellite with Flexible Appendages

In order to realize the high accuracy attitude control of satellite with flexible appendages, attitude control system consisting of the controller and structural filter was designed. When the low order vibration frequency of flexible appendages is approximating the bandwidth of attitude control system, the vibration signal will enter the control system through measurement device to bring impact on the accuracy or even the stability. In order to reduce the impact of vibration of appendages on the attitude control system, the structural filter is designed in terms of rejecting the vibration of flexible appendages. Considering the potential problem of in-orbit frequency variation of the flexible appendages, the design method for the adaptive notch filter is proposed based on the in-orbit identification technology. Finally, the simulation results are given to demonstrate the feasibility and effectiveness of the proposed design techniques.

Approximate analytical solutions of an axially moving spacecraft appendage subjected to tip mass

Approximate solutions for vibrations of flexible beam-type appendages subjected to tip mass are studied while uniform and exponential profiles for arm deployment are simulated. Applying an equivalent dynamical system and following Lagrangian approach, the equations of motion of the system are derived as nonlinear ordinary differential equations (ODEs) (with time-varying coefficients), in which the effect of the tip mass can be considered as some nonlinearity added to the ‘no tip mass’ case dynamics. The approximate closed-form solutions are obtained through a novel methodology using a computer algorithm, in which the solutions of the ‘no tip mass’ case are expanded by imposing quadratic perturbations on the independent variable. The mean square of errors (MSEs) for the obtained approximate analytical solution is computed. Using this method, the amplitude and frequency of the arm response are presented by the algebraic equations, which help the parametric design of such systems. In addition, effects of tip mass as an indicator of nonlinearities added to the system dynamics, on the amplitude and frequency of the beam response, are investigated during arm deployment.

Robust Attitude Control of Large Flexible Spacecraft (Application of Input Constrained Model Predictive Control)

This paper presents an application of the model predictive control to flexible spacecraft attitude maneuver. The objective of the study is to demonstrate an experimental feasibility of optimal attitude controllers suppressing the flexible appendage vibration under the actuator saturation. For the purpose, we study two approaches in the model predictive control framework. One is to use the frequency-shaped linear quadratic cost with finite horizon, and the other is to apply the robust control theory. Through ground experiments using a single axis air bearing table, as well as numerical studies for ETS-VIII spacecraft, their abilities are shown and compared.

Study on the Chaotic Dynamics in Attitude Maneuver of Liquid-Filled Flexible Spacecraft

In this paper, the chaotic dynamics in an attitude transitionmaneuver of a coupled slosh–spacecraft with a flexible appendage in going fromminor axis tomajor axis spin under the influence of dissipative effects due to fuel slosh and a small flexible appendage constrained to undergo only torsional vibration is investigated. The coupled slosh– spacecraftwith aflexible appendage in attitudemaneuver carrying a sloshing liquid is considered amultibody system with the sloshing motion modeled as a spherical pendulum. The focus in this paper is on the way in which the dynamics of the liquid and the flexible appendage vibration are coupled. The equations of motion are derived and then transformed into a form suitable for the application of the Melnikov method. The Melnikov integral is used to predict the transversal intersections of the stable and unstable manifolds for the perturbed system. An analytical criterion for chaotic motion is derived in terms of the system parameters. This criterion is evaluated for its significance to the design of spacecraft. The dependence of the onset of chaos on quantities such as body shape and magnitude of damping values, fuel fraction, and torsional vibration frequency of the flexible appendage are investigated. In addition, extensive numerical simulations are carried out to check the range of validity of the Melnikov result.

Heteroclinic bifurcations in attitude maneuver of coupled slosh-spacecraft with flexible appendage

In this paper, the chaotic dynamics in an attitude transition maneuver of a slosh-spacecraft coupled with flexible appendage in going from minor axis to major axis spin under the influence of dissipative effects due to fuel slosh and a small flexible appendage constrained to only torsional vibration is investigated. The slosh-spacecraft coupled with flexible appendage in attitude maneuver carrying a sloshing liquid is considered as multi-body system with the sloshing motion modeled as a spherical pendulum. The focus in this paper is that the dynamics of the liquid and flexible appendage vibration are coupled. The equations of motion are derived and transformed into a form suitable for the application of Melnikov’s method. Melnikov’s integral is used to predict the transversal intersections of the stable and unstable manifolds for the perturbed system. An analytical criterion for chaotic motion is derived in terms of system parameters. This criterion is evaluated for its significance to the design of spacecraft. The dependence of the onset of chaos on quantities such as body shape and magnitude of damping values, fuel fraction and torsional vibration frequency of flexible appendage are investigated. In addition, we show that a spacecraft carrying a sloshing liquid, after passive reorientation maneuver, will end up with periodic limit motion other than a final major axis spin because of the intrinsic non-linearity of fuel slosh. Furthermore, an extensive numerical simulation is carried out to validate the Melnikov’s analytical result.

Study on the global chaotic dynamics and control of liquid-filled spacecraft with flexible appendage

This paper investigates the global chaotic attitude dynamics and control of completely viscous liquid-filled spacecraft with flexible appendage. The focus in this paper is on the way in which the dynamics of the liquid and flexible appendage vibration are coupled. The equations of motion are derived and then transformed into a form suitable for the application of Melnikov’s method. Melnikov’s integral is used to predict the transversal intersections of the stable and unstable manifolds for the perturbed system. An analytical criterion for chaotic motion is derived in terms of the system parameters. This criterion is evaluated for its significance to the design of spacecraft. In addition, the Melnikov criterion is compared with numerical simulations of the system. Numerical solutions to these equations show that the attitude dynamics of liquid-filled flexible spacecraft possesses characteristics common to random, non-periodic solutions and chaos. This paper demonstrated that the desired final polarity control is guaranteed by using a pair of thruster impulses. The control strategy for a reorientation maneuver is designed and the numerical simulation results are presented for both the uncontrolled and controlled spin transition.

MIMO Active Vibration Control of Magnetically Suspended Flywheels for Satellite IPAC Service

Theory and simulation results have demonstrated that four, variable speed flywheels could potentially provide the energy storage and attitude control functions of existing batteries and control moment gyros on a satellite. Past modeling and control algorithms were based on the assumption of rigidity in the flywheel’s bearings and the satellite structure. This paper provides simulation results and theory, which eliminates this assumption utilizing control algorithms for active vibration control (AVC), flywheel shaft levitation, and integrated power transfer and attitude control (IPAC), that are effective even with low stiffness active magnetic bearings (AMBs) and flexible satellite appendages. The flywheel AVC and levitation tasks are provided by a multiple input–multiple output control law that enhances stability by reducing the dependence of the forward and backward gyroscopic poles with changes in flywheel speed. The control law is shown to be effective even for (1) large polar to transverse inertia ratios, which increases the stored energy density while causing the poles to become more speed dependent, and for (2) low bandwidth controllers shaped to suppress high frequency noise. Passive vibration dampers are designed to reduce the vibrations of flexible appendages of the satellite. Notch, low-pass, and bandpass filters are implemented in the AMB system to reduce and cancel high frequency, dynamic bearing forces and motor torques due to flywheel mass imbalance. Successful IPAC simulation results are presented with a 12% initial attitude error, large polar to transverse inertia ratio (IP∕IT), structural flexibility, and unbalance mass disturbance.

Attitude manoeuvre and vibration control of flexible spacecraft using computed feed-forward input commands and proportional-derivative feedback

The current paper presents an investigation into development of feed-forward and feedback control strategies for active vibration and attitude control of a flexible spacecraft. In this approach, the feed-forward loop consists of a computed-torque scheme and a command shaping technique based on component synthesis vibration suppression (CSVS) method for shaping the input signal. For relaxing the requirement of dynamic linearity in traditional CSVS, a new approach is developed for designing the input component command by utilizing a structure, in which the modal forces of flexible modes vibration are shaped according to a predefined trajectory, to achieve the vibration suppression for the non-linear attitude dynamics. In addition, to follow the predefined trajectory identically or at least as closely as possible, a model-independent feedback control loop is employed, which can accomplish further reduction of the residual vibration of flexible appendages. This proposed control strategy is practical as it does not require direct measurement of mode vibration, and also has a simple structure with low online computational load. Numerical simulations demonstrate the effectiveness of the control strategy.