In §6.3, the standard tri-spin solar sail configuration on a CubeSat sized satellite was implemented. As mentioned in §3.2.1.4 and §5.3.3.4, an advanced actuator can be created by placing the two rotating structures on 2-axis gimbals. The performance of such a system was investigated within a simulation.
6.5.1 Simulation Parameters
The simulation for a CMG controlled tri-spin solar sail was based on the same parameters defined in §6.3. The reaction wheel model within the simulation environment was replaced with a DGCMG model. The CMG controlled tri-spin satellite was implemented as a 3U CubeSat technology demonstrator. The satellite started in its deployed state and with all control angles (andλ) at zero. A number of attitude manoeuvres relative to the orbit-frame were implemented. The same attitude manoeuvres were executed with the satellite mentioned in §6.3 and a version of the CMG solar sail satellite containing control inaccuracies. In the application with inaccuracies, the angular momentum of the sail and the MCS were assumed not to cancel precisely (Hs 6= Hc), a gimbal control error was induced (s 6= c) and the satellite was to start
with a non-zero gimbal angle (0 6= 0◦). The CMG controller was assumed to have knowledge of the initial
conditions of the gimbal angles, but was not aware of the angular momentum or control angle errors. The CMG controller had a control period of1 s.
6.5.2 Simulation Results
The simulation results are shown in Figures 6.26 and 6.27. The Euler angle step responses for the three control cases are shown in Figure 6.26. Figure 6.26a shows the step response when applying the required torque with conventional reaction wheels and the MCS, as was done in §6.3. All the references were reached with a critically damped quaternion feedback controller. The same responses as for the CMG control case are shown in Figure 6.26b. Almost no discrepancy can be seen in the step responses when compared to the reaction wheel control case. The inaccuracies applied to the CMG control did affect the output (see Figure 6.26c). The transients between the steps were larger, but the satellite still reached the references. It is also visible (especially after the last step) that the satellite was struggling to maintain the required attitude reference.
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(c) Euler angles of CMG control inaccuracies
The control inputs for the step responses of the different scenarios are shown in Figure 6.27. The required torque, in the case of the standard reaction wheels, is shown in Figure 6.27a, which shows the torque pulses during each step. The CMG control signals are shown in Figures 6.27b and 6.27c. It is clear that the inaccuracies in the CMG control increased the control signals required, as evident in the step response. The attitude references are relative to the orbit frame. The angular momentum of the rotating sail and MCS was not equal (Hs6= Hc) and the satellite had an angular momentum bias. This angular momentum needed to be continually precessed to maintain the required attitude relative to the orbit frame. Such precession induces a gyroscopic disturbance torque, which has to be absorbed by the actuator.
For the simulation case with control inaccuracies, the CMG gimbal angles did not return to zero. These gimbal angles should be managed and actively controlled back to zero after a manoeuvre had completed (similar to momentum management case in §6.3.5.6). The CMG control could generate the required torques with small changes in gimbal control angles.
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wz(a) Reaction wheel control torque
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c(c) Angular momentum during CMG control
Figure 6.27 – Control inputs for reaction wheel and CMG control
The full-state EKF requires the current known angular momentum of the satellite to propagate the model successfully. The error in the angular momentum becomes large when an unknown angle error exist
within the CMG. The effect of this error can be reduced by making use of estimation methods that do not require the angular momentum. The gyro-based EKF and the TRIAD algorithm are able to still estimate the attitude accurately in the presence of an unknown angular momentum bias.
6.6
Conclusion
This chapter has presented the attitude simulation of a solar sail satellite. Dynamic equations and control methods that were derived and designed in earlier chapters were used to produce a simulation environment in which the feasibility of the ADCS of different spinning solar sail configurations could be assessed. The simulation program was developed in Matlab Simulink and different components of the simulation program were discussed.
The attitude simulation for a tri-spin satellite was completed. The simulation was able to illustrate the performance of all the ADCS control modes required for a tri-spin satellite to detumble after release, deploy its sail and MCS and generate solar thrust to either increase or decrease its orbit energy. The simulation introduced estimators that are viable for such a technology demonstrator mission. The results of the simulation reveal that the system can be improved by using rate sensors during deployment. The addition of angular rate sensors would provide accurate information during deployment and will increase the performance of the rate controller. Combinations of solar tracking controllers to increase and reduce the orbit energy were presented to generate the correct thrust to change the orbit altitude. A gravity gradient disturbance torque was present due to the large moment of inertia of the sail. Methods to manage the angular momentum build-up due to this effect would be a necessity for solar sails orbiting around earth.
A standard spinning solar sail and the CMG controlled tri-spin solar sail configuration were also simulated. The standard spinning satellite was able to maintain a controlled spin while slowly precessing towards the sun. The control torques to achieve this result can be generated by magnetorquers or other actuators like thrusters and solar torques methods described in §2.4. The standard spinning solar sail cannot complete the tracking manoeuvres quickly enough to able to generate the solar thrust required to change the orbit energy within a LEO. Standard spinning solar sails are perfectly suited for maintaining a required angle relative to the sun in a sun-centred orbit.
The CMG controlled tri-spin satellite was able to produce similar torque to a satellite containing reaction wheels. Comparable step responses could be achieved with small changes in gimbal angles. The simulation also highlighted the effect of gyroscopic disturbance torques in the presence of angular momentum bias that may exist. It would be important for the angular momentum of a tri-spin satellite system to be tightly controlled to prevent significant control errors.
Chapter 7
Conclusion
This thesis has introduced a spinning solar sail satellite configuration that is able to rapidly change the solar thrust vector direction during orbit manoeuvres, for example to increase and decrease the orbit altitude in a low earth orbit. The new spinning solar sail design presented in the thesis succeeded in combining the advantages of a spinning sail with the manoeuvrability of a zero-biased 3-axis stabilised satellite. A 3-axis stabilised satellites can make use of conventional actuators to perform agile attitude manoeuvres and in the case of solar sailing to obtain the required solar thrust vector direction. The main advantages of a spinning sail are:
• It is more resistant to disturbance torques from misalignment of CoM and CoP, than non-rotating sails, and
• It produces a constant centrifugal force, which reduces sail billowing and makes it possible to use wire booms that are simple to deploy as supporting structures.
With the new tri-spin solar sail satellite, the satellite body is despun from the rotating sail. This results in a stabilised platform where conventional actuators can be used. The spinning sail becomes effectively a large momentum wheel. The system has a large angular momentum bias and large control torques are required to change the attitude. An additional rotating mechanism is therefore proposed to zero the angular momentum bias, resulting in a more manoeuvrable solar sailing satellite.
The novel contributions in this study are:
• Conceptualisation of a tri-spin and CMG controlled tri-spin satellite
• Application of the tri-spin and CMG controlled tri-spin satellite concepts to solar sailing satellites • The derivation of simplified dynamic equations for investigating the angular accelerations of the
offset angles of rotating wire booms
• The use of the moment of inertia and its time derivative as a coupling term between the non-rigid and rigid satellite elements influencing the attitude dynamics
• The design and development of a deployment controller for a friction or passive deployment mechanism to deploy wire booms
• The development of model estimation methods to determine the current wire boom lengths of the sail during deployment
• Developing attitude and rate estimators and controllers for a tri-spin satellite • Deriving the steering laws for the CMG controlled tri-spin satellite
• Implementing and simulation testing of the attitude estimators and controllers on a tri-spin and CMG controlled tri-spin solar sail satellite to generate a solar thrust to change its orbit altitude
7.1
Satellite Model Evaluation
The tri-spin satellite contains overall dynamics similar to that of conventional spinning satellites. The standard Newton-Euler equations were rewritten to include, not only the three rotating parts of the satellite, but also the change in inertia that will occur when deploying and rotating the non-rigid elements. The moment of inertia of the sail and the MCS were used as cross-coupling elements to couple the normal rigid dynamics with the non-rigid dynamics of the wire booms. These dynamic equations were reduced to also describe the dynamics of other spinning solar sail configurations.
The effect of attitude changes on rotating wire booms was analysed by making use of Lagrangian mechanics. A dynamic model that was developed described the accelerations of the wire boom offset angles when performing attitude manoeuvres. Analysis of the resultant wire boom dynamics revealed that the angular rate of the wire booms is the dominant parameter. Choosing the nominal angular rate correctly will decrease the influence that the oscillations of the wire booms will have on the rest of the satellite system.
The thrust generated from a solar sail has a significant effect on a satellite’s orbit when in earth-centred or sun-centred orbit. Two manoeuvre-sets were identified that will produce altitude changes for a satellite orbiting around the earth. A simulation was used to compare the performance of these sets, and the influence of each set on the satellite’s orbital parameters.