Marco Ruano, Sanzar
Victor Gómez, Sanzar
Marco Ruano, Professor , Sanzar
The growing market for small satellites requires agile, efficient and compact attitude control systems (ACS) to improve mission performance, enable optical satellite communication (quantum) and improve data observation, increasing precision and agility in control.
Reaction wheels are the most widely used active attitude controls; these have the advantages of high angular momentum and reduced space, despite problems such as saturation and maximum torque offered that seriously limit the operability of their satellites with long pointing wait times and recovery of the capacity to generate momentum (de-saturation). CMGs differ from reaction wheels. The latter applies torque simply by changing the rotor spin speed, but the former tilts the rotor’s spin axis without necessarily changing its spin speed. CMGs are also far more power efficient. For a few hundred watts and about 100 kg of mass, large CMGs have produced thousands of Newton meters of torque. A reaction wheel of similar capability would require megawatts of power.[1]
Moment and torque are provided to the satellites through various devices such as reaction wheels, moment control gyros and magnetorques. However, other performances, such as moment-to-weight ratio and moment-to-volume ratio, are required in microsatellites due to space and weight constraints. Satellite operators and manufacturers must choose between performance or space; another problem is the complexity of satellite control devices with problems such as saturation or singularity.
We describe CMG design varieties and CMG cluster configuration (at least three CMG or RW are required for complete control of the satellite, and four consider redundancy and safety issues). Finally, we provide comparison results between diverse CMG configurations and types to show the future capabilities of CMG applications in small satellites to enhance small satellite services and profitability and enable new applications such as quantum and optic communications.
Design varieties of Control Moment Gyroscopes.
Single gimbal
When the gimbal CMG rotates, the change in the rotor’s angular momentum direction represents a torque that reacts onto the body to which the CMG is mounted; single-gimbal CMGs exchange angular momentum in a way that requires very little power, with the result that they can apply very large torques for minimal electrical input.
Dual-gimbal
A Control Moment Gyroscope (CMG) consists of two gimbals per rotor. This design is more versatile than a single-gimbal CMG because it can orient the rotor’s angular momentum vector in any direction. However, the movement of one gimbal often requires the other gimbal to react, which can lead to a higher power requirement for a given torque compared to a single-gimbal CMG. If the objective is to efficiently store angular momentum, as seen in the case of the International Space Station, dual-gimbal CMGs are an excellent choice. On the other hand, if a spacecraft needs to generate significant output torque while minimizing power consumption, single-gimbal CMGs are
Variable-speed
The primary practical benefit of VSCMGs, compared to conventional CMGs, is an additional degree of freedom—afforded by the available rotor torque. This can be harnessed for continuous CMG singularity avoidance and VSCMG cluster reorientation. Research has shown that the rotor torques required for these purposes are very small and within the capability of conventional CMG rotor motors. [2] Thus, the practical benefits of VSCMGs are readily available using conventional CMGs with alterations to CMG cluster steering and control laws for CMG rotor motors, demonstrating the adaptability of existing technology. The VSCMG can also be used as a mechanical battery to store the electric energy of the flywheels as kinetic energy.
Geometrical Configuration.
Pyramidal configuration.
In a pyramidal configuration, the actuator torque T∈R^3 contribution is [3]:
T=(h+ω × h) ̇
The total angular momentum vector h of the CMG cluster equals the summation of individual N CMGs, usually four, angular momentum vectors, hi ∈ R3, i = 1, . . . , N :
The angular momentum of the CMG cluster, with the assumption that each CMG generates a unity magnitude of angular momentum in the case of the CMG pyramid configuration under consideration, may be computed in the spacecraft body frame as a matrix h that depends on re δi, i =, . . . ,N is the gimbal angle, β is the skew angle (inclination of the pyramid faces with the horizonal plane), cβ ≡ cos β, and sβ ≡ sin β. The angular momentum derivative h ̇ of the CMG cluster can then be determined while retaining the skew angle constant as follows:
h ̇=[A] (δ=T-ω× h) ̇
Where [A] is a 4 x 3 matrix which depends on δi, gimbal angle, and β is the skew angle
Linear configuration.
A four CMG linear layout will produce torque to the satellite XYZ axes according to the following equations:
Ï„=[Ï„_X Ï„_Y Ï„_Z ]=Ï„_gimbal+Ï„_cmg+Ï„_pqr Ï„_gimbal
Most of the torque generated by the CMG is by the CMG effect Ï„_cmg. The desired CMG gimbal rates are computed by knowing the satellite attitude, satellite desired attitude, CMG gimbal angles and CMG flywheel spin rates.
Saturation and Singularity.
The Reaction wheels have a saturation issue: no more torque can be delivered to a specific direction if the flywheel reaches its maximum speed. Thus, the system stops the wheel and restarts its acceleration, with the associated loss of time and the need for heavier motors.
The Pyramidal Control Moment Gyroscope (CMG) and linear solutions have a singularity issue at specific gimbal angles that limit the torque delivery in particular directions.
The pyramidal layout uses 2.14 times the volume of the proposed linear layout. The performance of a pyramidal CMG layout is shown below in the simulation results. The Root-mean-square error (RMSE) is just over a tenth of the CMG linear layouts.
The CMG pyramidal layout increases the volume of the linear layout by more than 100%. Additionally, using variable speed control (VSCMG), the linear layout offers an 18% torque increment in the earth’s direction.
VSCMGs use double modes of control: a) CMG mode and b) RW mode, taking advantage of both according to mission requirements.
On a linear VSCMG, the total generated torque is:
Ï„=Ï„_gimbal+Ï„_cmg+Ï„_pqr+Ï„_rw
The desired VSCMG flywheel spin acceleration can be calculated using the VSCMG flywheel acceleration controller. This controller gathers the unitary torque control force value computed for each satellite XYZ body by the attitude controller according to the satellite’s actual and desired attitude.
CMGs generate a much higher torque than RWs because CMG torques rely by the interaction of CMG flywheel angular momentum and gimbal rate. For this reason, CMGs flywheel and gimbal motors do not need to be too large because they only generate enough torque to overcome the flywheel and gimbal assembly inertia moments, respectively. Moreover, RWs peak torque is directly limited by the RW flywheel motor peak torque.
For this reason, a VSCMG can generate much more torque by controlling its gimbal rate rather than controlling its flywheel acceleration. However, by using larger flywheel motors, higher accelerations can be achieved. Moreover, the ACS desired torques can be directed in such a way that the gimbal executes the higher torque demands travels and lower torque demands are executed by accelerating the flywheels.
Simulation results
A series of ACS performance simulations are showing considering the same conditions of J_sat,[ϕ ̂,θ ̂,ψ ̂ ],ω_init,ω_max,〖 J〗_cmg,J_gimbal, 〖T_wheel〗_max, θ ̇_max,λ
ACS type Performance parameter Rise time [s] Overshoot [%] Root-mean-square error [deg]
Linear CMG 12,77 (0,00001) 0,00780 (0,00550) 0,00330 (0,00280)
Linear VSCMG 11,81 (0,00004) 0,00071 (0,00022) 0,00021 (0,00004)
Pyramidal CMG 10,72 (0,00001) 0,00083 (0,00018) 0,00018 (0,00003)
Table 1: ACS control on Roll axis simulation results with standard deviation in parenthesis
ACS type Performance parameter Rise time [s] Overshoot [%] Root-mean-square error [deg]
Linear CMG 12,90 (0.00001) 0,05530 (0,03120) 0,00880 (0,00580)
Linear VSCMG 11,21 (0,00001) 0,00053 (0,00014) 0,00008 (0,00001)
Pyramidal CMG 10,78 (0.00001) 0,00110 (0,00032) 0,00016 (0,00003)
Table 2: ACS control on Pitch axis simulation results with standard deviation in parenthesis
ACS type Performance parameter Root-mean-square error [deg]
Linear CMG 0,00610 (0,00570)
Linear VSCMG 0,00011 (0,00002)
Pyramidal CMG 0,00017 (0,00005)
Table 3: ACS control on Yaw axis simulation results with standard deviation in parenthesis
[1] “R Votel, D Sinclair. “Comparison of control moment gyros and reaction wheels for small Earth-observing satellites.” 26th Annual AIAA/USU Conference on Small Satellites”. [2] Schaub, Hanspeter; Junkins, John L. (January 2000). “Singularity Avoidance Using Null Motion and Variable-Speed Control Moment Gyros”. Journal of Guidance, Control, and Dynamics. 23 (1): 11–16. Bibcode:2000JGCD…23…11S. doi:10.2514/2.4514. [3] Wie B 2008 Space vehicle dynamics and control (American Institute of Aeronautics and Astronautics)