Dynamics and control of flexible satellite using reaction sphere actuators

Dynamics and Control of Flexible Satellite Using Reaction Sphere Actuators

Recently, the magnetically suspended reaction spherical actuator (RSA) in attitude control of satellite received much attention in the literature. The compact size and low weight of RSA make it suitable for small satellite and space robotics applications. Several studies have suggested the use of control moment gyro (CMG)-based mechanism actuators for attitude control of flexible satellites. However, friction in the CMGs can cause hysteresis and backlash, leading to control errors and reduced accuracy of the attitude control system. Moreover, the vibration of the CMGs can introduce unwanted disturbances into the satellite’s motion, affecting the pointing stability and performance of the attitude control system. In contrast, magnetically suspended reaction sphere actuators are frictionless and have low vibration, making them a promising option for attitude control of flexible satellites. In a research article recently published in Space: Science & Technology, scholars from Nanjing University of Aeronautics and Astronautics and York University propose the attitude stabilization of spacecraft considering the vibration suppression of flexible appendages with magnetically suspended reaction sphere actuators.

First, authors present the satellite attitude dynamics and design the disturbance observer-based linear quadratic Gaussian (DOBLQG) approach for satellite attitude stabilization. The dynamics equations of the flexible satellite (concerning the angular velocity of the spacecraft to the inertial frame, ω_ib^b) are modeled in the body frame, taking the control torque τ and the total disturbance D into consideration. The dynamics equations are linearized via the linearized kinematic equation of the satellite that using Euler angles. To design the DOBLQG approach for satellite attitude stabilization, the linear state-space model of the system is derived, and disturbance and measurement noise are considered. The DOBLQG controller structure combines optimal dynamic regulators with state-space system modeling, a disturbance observer, and a Kalman filter state estimator. The block diagram of the DOBLQG controller is shown in Fig. 2. The state x is also proven bounded via Lyapunov function: V̇ is negative if ||x||₂ > 2(χ₁+χ₂+χ₃)/λ_min(Q); hence, x will converge to the region { x｜||x||₂ ≤ 2(χ₁+χ₂+χ₃)/λ_min(Q)}.

Fig. 2. Block diagram of the DOBLQG strategy.

Then, authors establish the reaction sphere dynamics and design the steering law. The magnetically suspended reaction sphere actuator (RSA) is a type of angular momentum-based actuator. It uses magnetic bearings to suspend a single reaction sphere in a frictionless environment. The rotor is capable of rotating in any direction, providing 3-axis control of a spacecraft’s attitude. The rotor is suspended by a series of permanent and electromagnetic poles that generate a magnetic field to levitate the sphere. The stator can drive and tilt the rotor through various methods such as permanent magnet, electromagnetic induction, and piezo and ultrasonic motors. Two virtual gimbals are considered for dynamic modeling of the RSA. The configuration of 3 orthogonal RSAs is illustrated in Fig. 4. By adjusting the currents or magnetic fields applied to the electromagnets or permanent magnets, the actuator can change the forces and torques acting on the reaction sphere, consequently changing the angles α (the rotation angle about x_r) and β (the rotation angle about y_r). In light of the small angle assumptions, it is possible to disregard the square tilt angles rate and the satellite’s angular acceleration. Consequently, the output torque of each RSA can be determined by taking the time derivative of h_RS. The tilt angles and rotor speed rate can be calculated utilizing a steering law. In the numerical simulation, the control command τ is considered as an input parameter to the steering block. A steering law is designed as λ = WJ^T(JWJ^T+μN)^-1τ. After calculating the tilt angle rates, the torque produced by the orthogonal cluster of reaction sphere actuators can be determined.

Fig. 4. Configuration of 3 orthogonal RS actuators.

Finally, authors carry out the numerical simulation and draw a conclusion. A sample attitude stabilization scenario is considered with DOBLQG in this simulation. In this scenario, the satellite starts an attitude stabilization maneuver from [0.17 0.087 0.087]^T rad to [0 0 0]^T with the proposed strategy. These maneuvers have been performed using the orthogonal cluster of RSAs. The random variables representing the uncertainty associated with the disturbances are added to the nominal values of the disturbance torques to obtain disturbed torque values that include the uncertainty. The simulation results show that the maneuver completes in less than 30 s (see Fig. 5). The tilt angles of RSA are less than 0.1 rad in the stabilization mode and do not reach saturation state. The numerical simulation results demonstrated that the orthogonal reaction sphere actuators provide sufficient torque for agile stabilization and damping disturbances when considering the DOBLQG control strategy.

Fig. 5. Euler angle diagram.