incorporating reaction wheels in "Attitude Dynamics" box.

Hi All;

Currently there is a useful, all-in-one box in simulink called "Attitude Dynamics" which is a compact form of simulating the attitude dynamics equations of a satellite. The dynamic equations used in the box is also summarized here. However it does not account for any reaction / momentum wheel dynamics. The wheel torque may be inserted through "Mb" input of the box however in the dynamic equations there should also be a term for "w_b_icrf x wheel_momentum". The question is as follows:

1. Is there a way through the user interface of this box to incorporate wheel momentum and torque?
2. if not is there another attitude dynamics box which takes wheel dynamics as input?
3. if not, can you -in the future releases- include an external wheel momentum / and torque input to this box ?

Thanks

Gökhan

[Brahmadev]

Hi @Gökhan,

Could you please share any references for the equations considering Wheel Dyanmics in the Rotational Dynamics equations?

[Gökhan]

Hi @Brahmadev; Thank you for your response. Just to avoid any misunderstandings, when I say "wheel dynamics" I do not mean a generic or specific model of a reaction wheel.

Following is a more detailed version of the dynamics equation you mention in the help files.

Da stands for time derivative in inertail frame

Ds stands for time derivative in satellite frame

Additional terms are Ds(h_w/s) which is the torque generate by the wheel in satellite frame and ws x h_w/s which is the angular velocity cross wheel assembly angular momentum again in statellite frame. The torque generated by the wheel assembly may be input to the system by using the "external torque" input. However the "ws cross h_w/s" term should be included in the dynamic equations.

So one can not really (as I understand) use momentum wheels in the satellite dynamics model.

Thanks

[Brahmadev]

Hi @Gökhan,

Thank you for sharing more information regarding the equation. Could you also point to any written resources such as papaers or books that mention said equation?

[Gökhan]

Hi @Brahmadev; For example, the book "Spacecraft Dynamics and Control" (https://www.sciencedirect.com/book/9780081007006/spacecraft-dynamics-and-control#book-info) (Canuto, Masotti, Novara, Carlucci, Montenegro) ISBN 978-0-08-100700-6; Section 7.7 (under Chapter 7: Attitude Dynamics: Modeling and control) talks about dynamic equations regarding " Attitude Dynamics with Internal Rotating Masses" in detail.

Thanks

Gökhan

Answer 1

[Brahmadev]

Hi @Gökhan,

Based on the documentation mentioned by you, the "Attitude Dynamics" does not provide a direct method to incorporate wheel momentum into the dynamics equations.

Unfortunately, there are no other blocks which take into consideration the "Wheel dynamics". The "Spacecraft Dynamics" block also uses the same equations for Rotational Dynamics. Refer to the documentation page below:

https://www.mathworks.com/help/aeroblks/getting-started-with-the-spacecraft-dynamics-block.html

Hence, you might need to create a custom subsystem in Simulink that models the dynamics according to your requirement. Alternatively, you can reach out to MathWorks Technical Support and share your use-case. You can create a technical support query at:

https://www.mathworks.com/support/contact_us.html

Hope this helps!