Reaction Wheels Research Articles

The One-Wheel Cubli: A 3D inverted pendulum that can balance with a single reaction wheel

This article presents a novel 3D inverted pendulum that can balance on one of its corners using only a single reaction wheel. This is achieved by a careful design of the mass moment of inertia in such a way that the inertia along the two principal tilt axes is significantly different. The consequence is a time-scale separation of the underlying tilt dynamics, which renders the system controllable. We show that controllability is maximized when the ratio of the two principal inertia values amounts to the square of the silver ratio and discuss a sensor placement that minimizes variance in our tilt estimates. Both of these aspects lead to a principled design of the system. A model is derived from first-principles and used for delay compensation, state estimation, and to design a linear-quadratic regulator that stabilizes the highly underactuated system in its upright equilibrium. Thereby, the modeling and compensation of cantilever deflections, which arise from the lightweight design, is crucial. The article includes experimental results, which underline the efficacy of the system design and highlight an excellent balancing performance of the proposed feedback controller.

Adaptive finite-time fault-tolerant control for nano-satellite attitude tracking under actuator constraints

In this paper, a finite-time fault-tolerant control method is developed for attitude tracking of a nano-satellite with three magnetorquers and one reaction wheel in the presence of actuator faults, inertia uncertainties, external distribution, and actuator constraints. For this purpose, the modified non-singular fast terminal sliding mode control is used due to the ability of robustness against uncertainties and finite-time convergence. In this approach, the modified sliding surface variable is constructed based on angular velocity and attitude error to converge the attitude error to zero in a finite time. In addition, three adaptive parameters are employed to reduce the adverse effect of uncertain expressions and to track the attitude commands with high control accuracy. The adaptive parameters and sliding surface variable are used in the reaching phase of the controller to decrease the chattering phenomenon. The dynamics of adaptive parameters, with regard to the angular velocities of the nano-satellite and reaction wheel and the sliding surface variable, are obtained during the stability proof of the closed-loop system. Also, the finite-time convergence of sliding surface and attitude variables are proved by the extended Lyapunov condition, and the convergence regions of attitude tracking errors are obtained. The simulations are accomplished and compared with an existing adaptive sliding mode control approach to evaluate the performance of the proposed controller. The results verify that the proposed controller performs better than the mentioned controller in terms of finite-time convergence, the accuracy of attitude tracking, and the reduction of the chattering phenomenon.

Rendezvous and Docking of Co-Operative Target with Dual-Axis Gimbaled Electric Thruster

This paper presents a simulation study on the viability of a dual axis gimbaled electric thruster for the relative orbital position control. Relative attitude of the spacecraft is controlled using reaction wheels (RWs). This study considers proportional derivative (PD) algorithm for orbital position control and nonlinear dynamic inversion for relative attitude control. The relative attitude dynamics is derived assuming that the target spacecraft is cooperative and is inactive, therefore, its relative attitude changes only due to its orbital motion around the central body. The dual-gimbal dynamics is approximated for control design due to coupling between gimbal rates. Numerical simulation results are presented to show the efficacy of the control algorithm as well the viability of the dual-axis gimbaled thruster for relative orbital motion control.

A General Method to Obtain the Frequency Response Function from the Disturbance Source to the Sensitive Payload

Microvibrations are one of the main factors contributing to platform jitter and a decline in pointing stability and precision. Among various disturbance sources, reaction wheel assembly (RWA) is one of the most significant ones and has drawn the interest of numerous scholars. How to evaluate the influence of the disturbances of RWA on the pointing accuracy of a spacecraft is an arduous task because it involves multiple disciplines. The acquisition of the frequency response function (FRF) from the disturbance source to the sensitive payload is one of the most crucial stages in integrated modeling. Direct measurement of the FRF in the six directions is challenging because of the restricted room for RWA installation in a spacecraft, particularly in small satellites. In this paper, a general method based on the Hv algorithm to obtain the FRF is presented. This method only needs the RWA, itself, as an excitation source. Then, in order to acquire the FRF, we use an optical remote-sensing satellite as the research object. The peak positions of FRF obtained by different RWAs are basically the same, while the amplitudes are slightly different, indicating that this method is effective. This method takes into consideration the coupling between the RWA and the spacecraft, making it possible to multiply the RWA disturbance measured at a fixed interface with the FRF, to determine the image motion of the sensitive payload.

PCB-integrated embedded planar magnetorquers for small satellites intelligent detumbling

The challenge of damping high tumbling rates after deployment of spacecraft from a rocket using PCB-integrated (printed circuit board) embedded planar coils that acts as pseudo- 2D magnetorquers is explored for higher form factor small satellites (2 U and 4 U). The magnetorquers cannot generate the torque if their axes are lined up with the local geomagnetic field and generally the reaction wheels are actuated to generate this torque component. CubeSats are small satellites that have cube units of 10 cm along each axis and they are usually detumbled using magnetorquer rods bringing norm to the point where reaction wheels take over to reduce the body rates to zero. In this paper, the task of removing the initial angular velocities is undertaken by using the embedded planar coils without relying on the secondary actuators using an intelligent projection based form of the B-Dot control. The proposed reconfigurable planar coils can effectively detumble the higher form factor small satellites using application-specific optimal coil configuration. The performance parameters for various possible combinations of the coils are thermally evaluated to sustain a stable thermal profile as the planar coils are embedded inside the multilayered PCB in the form of copper traces. Lastly, the proposed coils are compared with the performance parameters of the commercial actuators in the formal studies. It is found that the suggested embedded planar magnetorquers outperforms the competition.

Dynamic Vibration Absorbing Performance of 5-DoF Magnetically Suspended Momentum Wheel Based on Damping Regulation

The vibration performance is critical to the suspension control and the torque precision of the magnetically suspended momentum flywheel (MSMW). The translational and torsional vibration of the MSMW are investigated in this article, and the damping regulation method is proposed to improve the anti-vibration performance of the MSMW. Firstly, the modellings of the MSMW, including the dynamic models and the displacement coordinate, are developed, and the comprehensive damping characteristics of the MSMW are investigated. Moreover, the transfer functions of the translational and the torsional vibrations are established using the dimensionless model, and the relationship between the dynamic response and the stiffness/damping coefficient is studied. Furthermore, the numerical simulations of the dynamic response of the translational and torsional vibration are conducted. Finally, the experiments are designed to verify the vibration characteristics of the MSMW, and the dynamic displacements are measured to analyze the anti-vibration performance of the proposed damping regulation method. The results indicate that the displacement deflection of the translational vibration is reduced by 68.8%, and the angle deflection of the torsional vibration is mitigated by 71.2% by regulating the damping coefficient.

Time-Domain Electromagnetic Characterization of Reaction Wheel for Space Applications

The electromagnetic characterization of reaction wheels is crucial to comply with the demanding ac magnetic field cleanliness requirements of space science missions, thus, preventing interference on sensitive onboard instrumentation. Therefore, a complete assessment, including the measurement of the magnetic flux vector at different operational modes and under dynamic conditions, is proposed as a contribution beyond conventional testing methodologies. This article investigates the worst-case magnetic field emissions experimentally, using a test setup based on a multichannel acquisition and multidomain postprocessing system. The focus of the measurement campaign was on the low-frequency range (10 Hz–2 kHz). Moreover, capturing the B-field in the time-domain enabled further analysis, that is, complementary outputs for understanding the electromagnetic performance of the reaction wheel. As a result, we can relate the wheel rotation with the current and the magnetic fields, compute the field orientation, and evaluate in-band interference for the magnetic field.

Applied nonlinear control of spacecraft simulator with constraints on torque and momentum of reaction wheels

In this paper, the attitude of a spacecraft simulator is controlled in the presence of nonlinearities, uncertainties and constraints of the system. An optimization-based controller is developed in the closed form based on predicting the nonlinear responses of spacecraft system. For practical requirements of the spacecraft actuated by the reaction wheels (RWs), the control method considers the actuator limitation in the torques applied to RWs and the restriction in the angular momentum of the wheels due to the limited rotational speed of motors. In this way, the momentum constraint is equated with the torque constraint by a prediction-based transformation. Then, the constrained optimal control law is calculated by solving an equivalent optimization formulation. The constrained stability is analyzed by the Lyapunov second method and the bound of system response is obtained in terms of the prediction time. In the results, at first, the performance of the unconstrained version of the proposed controller, which leads to the feedback linearization like controller, is evaluated in the presence of uncertainties through computer simulations. Finally, the constrained version is simulated and experimentally implemented as hardware in the loop on the spacecraft simulator. The obtained comparative results indicate a good performance for the constrained controller in realistic conditions.

Advanced manufacturing concept of a bio-inspired reaction wheel rotor for small- and medium-sized constellation satellites

The increasing number of constellation satellites requires re-thinking of the design and manufacturing process for reaction wheel rotors. Mass optimisation of reaction wheel rotors leads to cost reduction and performance increase. Those optimisations can be realised by taking ideas from nature. Therefore, design principles of diatoms were screened, abstracted and implemented in an algorithm-based design process. In this way, a bio-inspired rotor was created, which considers launch and in-operation loads, is capable of up to 7500 RPM and shows a compact design with a diameter of 282,text {mm}. Regarding mechanical performance, an energy density of 4661,text {J kg}^{-1} and a mass moment of inertia ratio of 0.7584, which considers the component and an idealized design, could be achieved. Compared to a commercial rotor, this is equivalent to a similar inertia ratio and +85 % energy density, but +44 % mass due to manufacturing restrictions. Based on different boundary conditions, different first natural frequency for launch and operation conditions were obtained (658,text {Hz} and 210,text {Hz}). The new design was cast from nano-reinforced aluminium alloy (AlSi10Mg + Al2O3) in 3D-printed sand moulds that were produced via binder-jetting process. Thus, a hybrid manufacturing process was used, by combining additive manufacturing and casting. Post-processing of the cast part via turning and milling was performed to compensate distortion and achieve the required surface quality. Preliminary vibration measurements were performed, showing a large need for balancing to achieve low vibration emissions.

Robust stabilization control of live working robot under wind load based on angular momentum conservation principle

In respond to the problem that the live working robot is easy to be affected by wind load in the process of field high altitude operation, which result in robot body rolling with poor stability and low operation efficiency, a robot momentum wheel balance control method under wind load action based on the principle of angular momentum conservation has been proposed in this paper. The moment generated by the rotation of the momentum wheel is used to offset the wind load moment so as to realize the robot online balance control. Through the analysis of the influence mechanism for the live working robot on the wind load, the coupling relationship model of three kinds typical parameters namely, wind force, robot rolling angle, and momentum wheel drive moment have been established. Based on the virtual prototype size of the live working robot, the physical model of the momentum wheel device is established and the dynamic model of robot balance system under the wind load is established by Lagrange method. Finally, the disturbance environment of the robot under the wind load action in ADAMS and MATLAB-SIMULINK software, a fuzzy PID controller has been adopt to control the robot online in real time wind load. Compared with computational torque control and gravity compensation control, the simulation result show that the momentum wheel balance can reduce the rolling angle under the wind load and keep the robot in a balance posture with strong robustness. The research of this paper has important theoretical significance and practical application value for promoting the practical application of robot in actual wind load operation environment.

Active Damping, Vibration Isolation, and Shape Control of Space Structures: A Tutorial

This tutorial reviews the author’s contributions to the active control of precision space structures over the past 35 years. It is based on the Santini lecture presented at the IAC-2022 Astronautical Congress in Paris in September 2022. The first part is devoted to the active damping of space trusses with an emphasis on robustness. Guaranteed stability is achieved by using decentralized collocated actuator–sensor pairs. The so-called integral force feedback (IFF) is simple, robust, and effective, and the performances can be predicted easily with simple formulae based on modal analyses. These predictions have been confirmed by numerous experiments. The damping strategy for trusses has been extended to cable structures, and also confirmed experimentally. The second part addresses the problem of vibration isolation: isolating a sensitive payload from the vibration induced by the spacecraft (i.e., the unbalanced mass of attitude control reaction wheels and gyros). A six-axis isolator based on a Gough–Stewart platform is discussed; once again, the approach emphasizes robustness. Two different solutions are presented: The first one (active isolation) uses a decentralized controller with collocated pairs of the actuator and force sensor, with IFF control. It is demonstrated that this special implementation of the skyhook, unlike the classical one, has guaranteed stability, even if the two substructures it connects are flexible (typical of large space structures). A second approach (passive) discusses an electromagnetic implementation of the relaxation isolator where the classical dash-pot of the linear damper is substituted by a Maxwell unit, leading to an asymptotic decay rate of −40 dB/decade, similar to the skyhook (although much simpler in terms of electronics). The third part of the lecture summarizes more recent work done on the control of flexible mirrors: (i) flat mirrors for adaptive optics (AO) controlled by an array of piezoelectric ceramic (PZT) actuators and (ii) spherical thin shell polymer reflectors controlled by an array of piezoelectric polymer actuators (PVDF-TrFE) aimed at being deployed in space.

Coupled position and attitude control of a servicer spacecraft in rendezvous with an orbiting target

Rendezvous is one of the fundamental phases of on-orbit servicing (OOS) missions. Since it requires high accuracy and safety, modeling is an indispensable part. Therefore, this article puts forward an approach for boosting the exactitude of the final proximity phase of a servicer spacecraft using precise modeling. Unlike other similar works that solely use linear models to design controllers, this paper employs a fully nonlinear model and considers most possible uncertainties and disturbances. In this regard, first a complete nonlinear relative pose (i.e., concurrent position attitude) motion dynamic is developed, which includes (1) the role of the reaction wheels and (2) the major environmental force and torque model. Second, taking the thruster's adverse torque into account, two sliding mode-based control techniques with different nonlinear sliding surfaces are designed. Moreover, the Lyapunov stability criterion is used to handle high nonlinearity effects, control input saturation, actuator misalignment, external disturbance torque/force, measurement error, uncertainties of both inertia parameters, and control inputs. Even the PWPF modulator of the thrusters has been considered to make the outcomes more realistic. Finally, three different scenarios are comprehensively simulated to illustrate the feasibility and efficiency of the designed scheme. The results prove that the proposed closed-form controller is more executable to implement than other existing approaches.

Fault Diagnosis for Momentum Wheels of Communication Satellite Based on Artificial Neural Network

With the advent of several fault detection techniques in modern control systems design, this paper adopted the Artificial Neural Network (ANN) Fault Detection scheme for the Fault Detection of the Attitude Control System for a Communication Satellite. In satellite applications, telemetry data can be very large, and ANN is best suited for network modeling involving large sets of data. The availability of real satellite data from Nigcomsat-1R communication satellite provided a practical platform to assess the fault detection algorithm. Results obtained showed a good correlation between raw satellite telemetry data and Neural Network model-generated results for subsequent fault detection. The fault detection models were able to detect faults, log them and provide a notification to enhance subsequent isolation and rectification. Momentum Wheel Speed and Torque were used to investigate the performance of the wheels while the Momentum Wheel Voltage and Current helped to monitor the wheel’s health state. A fault is detected if the absolute difference between original output (MW Torque) and the NN Torque output is greater than 0.012. With this, an accuracy of 100% and mean squared error of 9.8489e-6 were achieved.

Fixed-Time Constrained Model Predictive Sliding Mode Control of Spacecraft Simulator

In this article, two dual-loop control methods are proposed for attitude control and reaction wheels momentum management of the spacecraft simulator by assimilating the advantages of sliding mode and model predictive control (MPC). In the first method, by utilizing the high accuracy and constrained features of the MPC, an optimal controller is designed in the inner loop. MPC drives the angular velocity to the desired value while keeping the reaction wheel velocity to a small region near the origin, considering the constraints of the actuators. Furthermore, based on the fixed-time terminal sliding mode (TSM) the proper angular velocity is produced in the outer layer of this composite controller for the MPC part. In the second method, contrary to the first one, in the exterior loop MPC and in the interior loop finite-time TSM have been designed. The incorporated twofold nonlinear controllers’ policy insures a good dynamic and robustness against external disturbances. The high yielding of the control algorithms has been analyzed by simulation and experimental validation utilizing MATLAB software with real-time connection based on LabVIEW.

Ground test results of the microvibration interference for the x-ray microcalorimeter onboard x-ray imaging and spectroscopy mission

Resolve is a payload hosting an X-ray microcalorimeter detector operated at 50 mK in the X-Ray Imaging and Spectroscopy Mission (XRISM). It is currently under development as part of an international collaboration and is planned to be launched in 2023. A primary technical concern is the micro-vibration interference in the sensitive microcalorimeter detector caused by the spacecraft bus components. We conducted a series of verification tests in 2021-2022 on the ground, the results of which are reported here. We defined the micro-vibration interface between the spacecraft and the Resolve instrument. In the instrument-level test, the flight-model hardware was tested against the interface level by injecting it with micro-vibrations and evaluating the instrument response using the 50 mK stage temperature stability, ADR magnet current consumption rate, and detector noise spectra. We found strong responses when injecting micro-vibration at about 200, 380, and 610 Hz. In the former two cases, the beat between the injected frequency and cryocooler frequency harmonics were observed in the detector noise spectra. In the spacecraft-level test, the acceleration and instrument responses were measured with and without suspension of the entire spacecraft. The reaction wheels (RWs) and inertial reference units (IRUs), two major sources of micro-vibration among the bus components, were operated. In conclusion, the observed responses of Resolve are within the acceptable levels in the nominal operational range of the RWs and IRUs. There is no evidence that the resultant energy resolution degradation is beyond the current allocation of noise budget.

Optimal Configuration of Four Reaction Wheels in Momentum Management Performance and Reliability Point of View

Optimal Configuration of Four Reaction Wheels in Momentum Management Performance and Reliability Point of View

Small-Satellite Attitude Control Using Continuous Sinusoids With Strict Amplitude Constraints

This article considers attitude control of a rigid body (e.g., small satellite) with internal rotating-mass actuators that, unlike reaction wheels, cannot perform unrestricted rotations. Instead, the rotational stroke of each actuator is limited to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$[-\alpha,\alpha]$ </tex-math></inline-formula> rad, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha &gt; 0$ </tex-math></inline-formula> . We present two attitude-feedback control methods. The first method addresses setpoint tracking of constant attitude commands, whereas the second approach addresses command following of time-varying attitude commands. Both methods use control signals that are continuous and piecewise sinusoidal but whose derivatives can contain discontinuities. The main analytic results show that these attitude-feedback controls achieve asymptotic setpoint tracking for a constant attitude command and approximate command following for a time-varying attitude command. The results also show that the controls satisfy the strict actuator amplitude constraint. Each control method is demonstrated in numerical simulations of a small satellite in deep space. Finally, we present single-axis closed-loop attitude control experiments for a small-satellite system on an air bearing.

Fault tolerant attitude control of under-actuated spacecraft: Theory and experiment

This paper investigates fault tolerant attitude control theory and experiment for under-actuated spacecraft with one reaction wheel completely broken and two others suffering actuator faults of partial loss of effectiveness or bias. A non-smooth robust adaptive fault tolerant control law is proposed under the zero-momentum and input saturation conditions. It shows that the available reaction wheels need to produce sufficient control torque for the fault tolerance. Such a new control method is implemented in a semi-physical simulation system of an air-bearing platform. Experimental results show the effectiveness of the proposed method in spacecraft practical engineering.

One-Winged Momentum-Biased Solar Sail: A New Methodology for Propellantless Attitude Control

This paper proposes a new methodology for solar-sail attitude control that uses only momentum wheels. Different from conventional solar sails packaged in a central hub, the sailcraft is deployed in the direction of one side of the storage. In this single-wing configuration, the offset between the center of mass (c.m.) and center of pressure (c.p.) is large and lies in the sail plane. When specular reflection is dominant, solar-radiation-pressure (SRP) force vector points in the out-of-plane direction, thus causing an in-plane SRP torque orthogonal to the c.m./c.p. offset vector. Therefore, by placing a bias momentum in the c.m./c.p. direction, the sailcraft keeps rotating in the same plane while maintaining its orientation relative to the sun. Analysis reveals that the attitude motion of the one-winged momentum-biased solar sail is basically unstable, but the system can be stabilized in a neutral manner through minor control of the bias momentum. Furthermore, adding another control moment in the out-of-plane direction enables asymptotic stability. Control in the remaining in-plane direction makes it possible to avoid wheel saturation. Numerical simulations demonstrate that both attitude maintenance and maneuver can be performed and that the controller is robust to parameter errors.

Identification and Removal of Reaction Wheel Interference From In‐Situ Magnetic Field Data Using Multichannel Singular Spectrum Analysis

AbstractIn situ magnetic field measurements are critical to our understanding of a variety of space physics phenomena including field‐aligned currents and plasma waves. Unfortunately, high‐fidelity magnetometer measurements are often degraded by stray magnetic fields from the host spacecraft, its subsystems, and other instruments. One dominant source of magnetic interference on many missions are reaction wheels—spinning platters of varying rates used to control spacecraft attitude. This manuscript presents a novel approach to the mitigation of reaction wheel interference on magnetometer measurements aboard spacecraft where multiple magnetometer sensors are deployed. Specifically, multichannel singular spectrum analysis is employed to decompose multiple time series simultaneously. A technique for automatic component selection is proposed that classifies the decomposed signals into common geophysical signals and disparate locally generated signals enabling the robust estimation and removal of the local interference without requiring any assumptions about its characteristics or source. The utility of this proposed method is demonstrated empirically using in situ data from the CASSIOPE/Swarm‐Echo mission, and a data interval with near‐constant background field was shown to have its local reaction wheel interference reduced from 1.90 nT RMS, for the uncorrected outboard sensor, to 0.21 nT RMS (an 89.0% reduction). This technique can be generalized to arrays of more than two sensors, and should apply to additional types of magnetic interference.