Single Gimbal Control Moment Gyros Research Articles

Hierarchical attitude stabilization controller design and analysis for underactuated spacecraft on SO(3)

In this paper, the complete attitude stabilization of underactuated spacecraft with two parallel single gimbal control moment gyroscopes (SGCMGs) is explored on 3-dimensional special orthogonal group (SO(3)) and its corresponding Lie algebra (so(3)). Instead of assumption on zero total angular momentum in existing article, a less conservative criterion is adopted to ensure system controllability, which does not simplify system dynamics. On the kinematic level, an ideal controller is proposed to globally stabilize attitude without singular initial condition and stagnation behavior. Besides, the ideal kinematic controller is developed on so(3), which avoids singularity or unwinding phenomenon caused by other attitude parameters. On the dynamic level, a hierarchical controller consisting of two parts is proposed. The high-level sliding mode part enforces finite time stabilization of angular velocity about underactuated axis while the low-level part tracks ideal angular velocity commands about actuated axes. A rigorous proof of the whole dynamic-kinematic system that has not been explored before is given. Analysis of hierarchical control from the perspective of linear algebra provides a novel insight into controller design for underactuated systems. Furthermore, the paradigm of controller design which is applicable to other underactuated systems is derived. Simulation results validate the effectiveness of the proposed control logic.

Deep reinforcement learning-based attitude control for spacecraft using control moment gyros

This paper addresses the development of an attitude control system that steers control moment gyros (CMGs) based on deep reinforcement learning (DRL) for agile spacecraft. The proposed DRL-based attitude control system learns CMG steering strategies to achieve the desired attitude, thus potentially bypassing the singularity issues inherent in the CMG cluster. In particular, it is designed in two-phases to apply the DRL technique efficiently. In the first phase, the attitude control is performed based on DRL up to a certain tolerance, after which it switches to conventional control and steering law for stabilization in the second phase. The rapid pointing capability of the proposed DRL-based attitude control system is demonstrated for an agile spacecraft equipped with pyramid-type single gimbal control moment gyros. Additionally, in realistic scenarios of pointing multiple targets on the ground, the momentum vector recovery that the CMG system needs to consider is also briefly discussed.

Stability Assessment of the High-Speed Flywheel with AMBs on a Rotating Platform

With the continuous improvement of the performance and capabilities of spacecrafts, the application of active magnetic bearings (AMBs) has become a major focus in current research. The AMBs-flywheel system is not only responsible for attitude control but also provides the required energy during shadow periods. In magnetically suspended single gimbal control moment gyroscope (SGCMG), self-excited vibration caused by high-speed rotor rotation significantly affects the stability of the AMB system. The research focus lies in magnetically supporting the flywheel at high speeds with low power consumption to explore gyroscopic mechanics at ultra-high speeds and assess the corresponding stability. This study presents an assessment of the stability performance of a high-speed flywheel equipped on a single gimbal with an angular momentum of 75 Nm. To achieve ultra-high-speed operation under low driving power, a high-precise dynamic balance was performed followed by a novel unbalance control strategy of a radial and axial automatic balancing algorithm to suppress effectively synchronous vibrations due to nutation and precession. Corresponding experiments including static stable suspension experiments as well as low-speed, high-speed, and series-based stability assessments were conducted. Stable suspension at any speed ranging from 0 to 30,000 r/min was successfully implemented. The stability performance of the high-speed flywheel on a rotating platform at different gimbal speeds was verified, with a maximum speed reaching 31,200 r/min. The entire output torque process within the range of 30,000 r/min was revealed.

Adaptive periodic-disturbance observer based composite control for SGCMG gimbal servo system with rotor vibration

This paper presents an adaptive periodic-disturbance observer (APDO)-based composite control scheme to attain accurate velocity-tracking control for the single gimbal control moment gyro (SGCMG). Firstly, a modified periodic-disturbance observer (PDO) is proposed to estimate both the fundamental wave and harmonics of the rotor vibration. Secondly, to ensure the estimation accuracy under variable rotor speed, an APDO is proposed by combining an adaptive frequency estimator with the modified PDO. Integrating with the PI controller, the proposed APDO-based composite control scheme can effectively reduce the influence of rotor vibration, friction, and parameter uncertainties, thereby improving control accuracy. Furthermore, performance and stability analyses show that the observer can achieve accurate estimation under arbitrary initial conditions. Finally, numerical and hardware-in-the-loop simulation results are given to demonstrate the robustness and effectiveness of the proposed scheme.

Periodic Signal Suppression in Position Domain Based on Repetitive Control

In this paper, a periodic signal suppression method in position domain based on repetitive control (RC) is proposed to realize high-precision speed control for the gimbal servo system of the single gimbal control moment gyro (SGCMG). To reduce the volume and weight while outputting large torque, the gimbal servo system usually needs to install the harmonic drive. However, the nonlinear transmission characteristics of the harmonic drive are also introduced into the gimbal servo system and make the speed fluctuate. Considering the speed fluctuation signal shown as a fixed frequency in the position domain, a position domain RC method combined with acceleration feedback is designed to realize the speed fluctuation minimization. The position domain RC improves the dynamic characteristics, while the acceleration feedback increases the damping of the system. To analyze the stability, the position domain RC is converted into the time domain through the domain transformation method, and a phase compensator is designed to improve the stability and increase the bandwidth of the position domain RC by compensating for the phase lag of the middle and low frequency, respectively. The feasibility and effectiveness of the proposed method are verified by the simulation and experimental results. These results illustrate that after applying the proposed approach, the output speed fluctuation and harmonic components decrease more than 20% and 24.1%, respectively.

Micro-vibration modeling and analysis of single-gimbal control moment gyros

Micro-vibration modeling and analysis of single-gimbal control moment gyros (SGCMGs) are conducted in this study. Considering the rotation and support effect of the low-speed gimbal, a nonlinear time-varying dynamic model for micro-vibration analysis of an SGCMG is established using the energy theorem. By considering the Hertzian contact, elastohydrodynamic lubrication, and surface waviness, the nonlinear supporting forces and moments of the angular contact ball bearings on the high-speed rotor and low-speed gimbal are derived, and accordingly, an iterative solution method is proposed. Based on a three-axis dynamic force measurement platform, the dynamic characteristics of a real SGCMG are tested to verify the rationality of the proposed micro-vibration model. Subsequently, the effects of unbalance mass, surface waviness amplitude, gimbal lock angle, and rotation angular speed of the gimbal on the three-axis gimbal bearing transmission forces are discussed. The findings of this study provide insights for clarifying the micro-vibration characteristics and provide a theoretical basis for the working state design and structural optimization of SGCMGs.

Backstepping-Based Steering Control for Spacecraft Attitude Control Using Two-Skewed Control Moment Gyroscopes

Numerous control methods that use two reaction wheels have been proposed for the underactuated control problem. However, few studies have applied two single-gimbal control moment gyroscopes (SGCMGs) to the three-axis attitude control problem. In this study, under the assumption that the total initial angular momentum is zero, a steering control law for the three-axis attitude maneuvers of a spacecraft with an array of two-skewed SGCMGs is designed using the backstepping technique without setting a constraint on the range of gimbal angles. The spacecraft attitude is expressed in terms of the parameters, which are suitable for the underactuated attitude control problem. The control gains are appropriately chosen to guarantee controller stability. The proposed steering control law is validated through numerical simulations. The results show that the proposed steering control law can achieve a shorter settling time than that obtained from a control law with a constraint on the range of gimbal angles.

Steering Law for Control Moment Gyroscopes with Online Torque Capacity Maximization

While single-gimbal control moment gyroscopes (CMGs) remain the actuators of choice for agile spacecraft, using over-redundant or overdesigned CMG arrays will cease to be a viable approach as agility requirements increase. The torque envelope of a CMG array under gimbal rate constraints is a zonotope, whose geometrical characteristics can be used to systematically increase the torque capacity around an arbitrarily given axis. For a four-CMG roof array, which consists of two coplanar CMG pairs, the torque capacity is a function of the allocation of angular momentum between the pairs. Based on the latter, a gimbal angle steering law is developed that maximizes the CMG array’s torque capacity around a preferred axis defined by the current slew maneuver. A main feature of the proposed steering law is that this maximization does not require offline computations for any given preferred axis. In addition, an angular-momentum-based attitude tracking control law is formulated. As verified in numerical simulations, the developed steering and attitude control algorithms are able to follow a typical agile reference profile with adequate time domain performance while satisfying actuator constraints.

System identification and mechanical resonance frequency suppression for servo control used in single gimbal control moment gyroscope.

Effective identification of the control model is one of the key aspects in improving the performance of the single gimbal control moment gyroscope (SGCMG) servo system. The accuracy and stability of the servo system can be improved by studying system identification and mechanical resonance frequency. In this study, firstly, the SGCMG gimbal servo system was simplified to a two-mass block model. The theoretical mathematical model of the system's transfer function and mechanical resonance frequency was derived. Secondly, this paper studied the effective suppression method for mechanical resonance. Thirdly, the mathematical model of the orthogonal correlation analysis method was deduced for system identification. Then, an experimental platform was investigated to obtain the frequency characteristic curve and the transfer function. Finally, the frequency characteristic curve obtained using the transfer function model was plotted and compared with the frequency characteristic curve obtained experimentally. Our results indicate that the orthogonal correlation analysis has a high identification accuracy.

Agile rest-to-rest attitude maneuvering of spacecraft using pyramid-type SGCMG based on iteratively recalculated optimal trajectory

This paper is concerned with the agile rest-to-rest attitude maneuvering of spacecraft using pyramid-type single-gimbal control moment gyroscopes (SGCMGs). In this method, the gimbal rate command to the SGCMGs is determined by calculating the pair of optimal trajectories of the attitude and the gimbal angles without any “steering law”. Thus, the proposed method does not suffer from the singularity problem causing the increase in control error and settling time. Before maneuvering, the pair of the initial optimal trajectories of the attitude and the gimbal angles is calculated by the minimum-time problem. Then, to compensate for errors in maneuvering caused by disturbances and/or modeling errors, the trajectories of the attitude and the gimbal angles are recalculated and updated frequently during the control. In this paper, optimization problems for generating and updating the trajectories are formulated, and specific control algorithms are provided. Finally, numerical simulations and ground experiments with an air floating table are performed to verify the feasibility and effectiveness of the proposed control method. For the rest-to-rest attitude maneuver, the proposed method can be adapted not only to the presence of modeling error in the inertia tensor, but also to the failure of one or two CMGs in the SGCMG system, without changing the control algorithm. These demonstrate the high robustness and practicality of the proposed method.

High-Precision Speed Control for Low-Speed Gimbal Systems Using Discrete Sliding Mode Observer and Controller

The high-precision control of angular speed in low-speed gimbal servo systems is an essential topic in the operation of the single gimbal control moment gyro (SGCMG). This article proposes a discrete control algorithm to suppress the influence of various disturbances on the low-speed gimbal servo system and the constraint between controller parameters and sampling time is established to ensure the stability of the system. To begin with, the disturbance analysis of the low-speed gimbal servo system is presented, including the torque ripple in the permanent magnet synchronous motor (PMSM), nonlinear friction, coupling torque caused by the spacecraft motion, and the parameter uncertainties. Then, a composite control method combining the sliding mode controller (SMC) with sliding mode observer (SMO) is applied to the speed loop and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> -axis current loop. The interferences are estimated by two SMOs, while SMCs are designed to eliminate the influence brought by the residual disturbances. The stability of the overall system is proven based on the Lyapunov criterion. Finally, simulation and experimental results verify the effectiveness of the proposed composite control method.

A Steering Method With Multiobjective Optimizing for Nonredundant Single-Gimbal Control Moment Gyro Systems

The steering problems are investigated for nonredundant three single-gimbal control moment gyros (SGCMGs), in which no null-motion can be utilized to avoid the singular gimbal configurations. A gimbal configuration far away from the singularity is selected as a candidate nominal configuration, and a comprehensive multiobjective optimal cost function is constructed with respect to the actual gimbal angular vector error, the gimbal command variation, and the torque output error. By minimizing the cost function, an optimal gimbal angle command formula is derived consequently, and a corresponding equivalent gimbal angular rate command formula is also presented. Moreover, according to the pattern of the rest-to-rest attitude maneuver, dynamically weight-adjusting strategies for the cost function are designed, and a complete steering scheme for the nonredundant SGCMG system is built up based on the derived algorithms of the gimbal command. The proposed steering method can guarantee successful singularity-avoiding during the attitude maneuver and gimbal-returning back to the vicinity of the nominal angles at the end of the maneuver, and its effectiveness is verified by both numerical simulations and experimental tests.

Finite-time composite control for gimbal system in SGCMG under high-frequency disturbance

This paper investigates the velocity-tracking problem of the gimbal system in a single gimbal control moment gyro (SGCMG) suffering from high-frequency disturbance. In order to accurately and quickly reject the high-frequency disturbance resulted from nonuniform mass distribution and manufacturing imperfection, a finite-time harmonic disturbance observer (FTHDO) is constructed according to the available information about the high-frequency disturbance. Then, a composite controller is developed to achieve simultaneous disturbance rejection and attenuation. The nominal control performance can be recovered under the high-frequency disturbance. It has been demonstrated that the velocity-tracking error can be stabilized by the proposed composite controller within finite time. Finally, numerical simulation results are presented to verify the superiority of the proposed method.

Neural network-based fault diagnosis for spacecraft with single-gimbal control moment gyros

This paper proposes a neural network-based fault diagnosis scheme to address the problem of fault isolation and estimation for the Single-Gimbal Control Moment Gyroscopes (SGCMGs) of spacecraft in a periodic orbit. To this end, a disturbance observer based on neural network is developed for active anti-disturbance, so as to improve the accuracy of fault diagnosis. The periodic disturbance on orbit can be decoupled with fault by resorting to the fitting and memory ability of neural network. Subsequently, the fault diagnosis scheme is established based on the idea of information fusion. The data of spacecraft attitude and gimbals position are combined to implement fault isolation and estimation based on adaptive estimator and neural network. Then, an adaptive sliding mode controller incorporating the disturbance and fault estimation results is designed to achieve active fault-tolerant control. In addition, the paper gives the proof of the stability of the proposed schemes, and the simulation results show that the proposed scheme achieves better diagnosis and control results than compared algorithm.

Robust gimbal reorientation singularity-avoidance steering strategy for regular pentagonal pyramid configuration with two control moment gyroscopes failed

The failure configuration which consists of four single-gimbal control moment gyroscopes (SGCMGs) of the widely-used regular pentagonal pyramid SGCMG system, i.e. failure 4-SGCMG configuration, is investigated in this paper. On account of the symmetry of regular pentagonal pyramid configuration, a conversion method which could transform any failure 4-SGCMG configuration to the chosen failure system is introduced. Then, the zero-momentum gimbal angle of the chosen failure system is derived and its distribution in gimbal angle space is analyzed. In order to avoid internal singularity, preferred initial gimbal angles are calculated basing on derivation of zero-momentum gimbal angles and the corresponding terminal singular surfaces are obtained through numerical simulations. Furthermore, a constraint about maneuver direction is introduced and a robust gimbal reorientation steering strategy is proposed. Finally, simulations on a non-chosen failure configuration with inertia matrix uncertainty demonstrate the effectiveness of the conversion method and robustness of the proposed steering law.

Singularity-robust control moment gyro allocation strategy for spacecraft attitude control in the presence of disturbances

In this paper, a disturbance and singularity robust steering law for a set of single gimbal control moment gyros (SGCMGs) is addressed to improve the agile rotational maneuverability of spacecraft. A roof array is selected and investigated in this work because of the simplicity of the singularity envelope. Also, a feasible angular momentum chart, which provides a singularity-free bound for the roof array, is utilized. It is very important to recover the momentum vector to the initial gimbal direction to overcome the singularity problem. Thus, an optimization technique is described to restore the gimbal vectors back to their original angular position after the rest-to-rest attitude reorientation. Another issue to be examined is that external disturbances interrupt the gimbal vector going back to the initial position. Therefore, a robust allocation logic based on the optimization technique is exploited to handle the effect of external disturbances adequately by using a magnetic torquer. Finally, several numerical simulations are performed to highlight that the allocation logics proposed can overcome the singularity problem and be operated reliably for the spacecraft installed with a roof array of CMGs generating the control torque required for all time exactly.

A Gimballed Control Moment Gyroscope Cluster Design for Spacecraft Attitude Control

This paper addresses the problem of singularity avoidance in a cluster of four Single-Gimbal Control Moment Gyroscopes (SGCMGs) in a pyramid configuration when used for the attitude control of a satellite by introducing a new gimballed control moment gyroscope (GCMG) cluster scheme. Four SGCMGs were used in a pyramid configuration, along with an additional small and simple stepper motor that was used to gimbal the full cluster around its vertical (z) axis. Contrary to the use of four variable-speed control moment gyroscopes (VSCMGs), where eight degrees of freedom are available for singularity avoidance, the proposed GCMG design uses only five degrees of freedom (DoFs), and a modified steering law was designed for the new setup. The proposed design offers the advantages of SGCMGs, such as a low weight, size, and reduced complexity, with the additional benefit of overcoming the internal elliptic singularities, which create a minor attitude error. A comparison with the four-VSCMG cluster was conducted through numerical simulations, and the results indicated that the GCMG design was considerably more efficient in terms of power while achieving a better gimbal configuration at the end of the simulation, which is essential when it is desired for different manoeuvres to be consecutively executed. Additionally, for a nano-satellite of a few kilograms, the results prove that it is feasible to manufacture the GCMG concept by using affordable and lightweight commercial off-the-shelf (COTS) stepper motors.

An active force controlled of small CMG-based satellite

Purpose This paper aims to investigate the attitude control pointing improvement for a small satellite with control moment gyroscopes (CMGs) using the active force control (AFC) method. Design/methodology/approach The AFC method is developed with its governing equations and integrated into the conventional proportional-derivative (PD) controller of a closed-loop satellite attitude control system. Two numerical simulations of an identical attitude control mission namely the PD controller and the PD+AFC controller were carried out using the MATLAB®-SimulinkTM software and their attitude control performances were demonstrated accordingly. Findings Having the PD+AFC controller, the attitude maneuver can be completed within the desired slew rate, which is about 2.14 degree/s and the attitude pointing accuracies for the roll, pitch and yaw angles have improved significantly by more than 85% in comparison with the PD controller alone. Moreover, the implementation of the AFC into the conventional PD controller does not cause significant difference on the physical structure of the four single gimbal CMGs (4-SGCMGs). Practical implications To achieve a precise attitude pointing mission, the AFC method can be applied directly to the existing conventional PD attitude control system of a CMG-based satellite. In this case, the AFC is indeed the backbone for the satellite attitude performance improvement. Originality/value The present study demonstrates that the attitude pointing of a small satellite with CMGs is improved through the implementation of the AFC scheme into the PD controller.

Feedback attitude control of spacecraft using two single gimbal control moment gyros

In this paper, feedback attitude control of an underactuated spacecraft with two single gimbal control moment gyros (SGCMGs) is considered. For a two-SGCMG system in an arbitrary configuration, a feedback control method based on a real-time optimization approach is proposed. Here, the gimbal angle trajectories as the solution to the minimum-time control are parameterized by the time polynomials, and their coefficients are modified at each sampling period. Numerical simulations are performed to demonstrate the validity of the proposed method as well as a certain robustness against unmodeled dynamics. Furthermore, the experimental verification is also conducted to demonstrate the actual effectiveness.

Design of Sliding Mode Techniques for a CMG-based Testbed Attitude Control System

Abstract Precise pointing accuracy and rapid maneuvering are two key features for attitude control missions of small spacecraft. Control moment gyroscopes (CMGs) are applied as ideal actuator for large torque output capability but are usually limited due to the problem of inherent mechanical singularity. This paper proposes a robust attitude control methodology, based on Sliding Mode Control (SMC) techniques, in presence of CMG practical restrictions and disturbances. Two second-order SMC techniques are designed, to guarantee accuracy and limited convergence time. Moreover, attitude control torques are generated by means of four single gimbal CMGs in pyramidal configuration, considering the design of an experimental testbed. The effectiveness of the proposed methodologies are shown in simulations, for different mission scenarios, including singularity points.