fast rotations

[Roby]

Hi Bill,

First let me thank you for the amazing research you have done for fast gyro rotations,

and thanks for sharing the community. 

On the other hand, can you please explain how you obtained equation 5 in the document Fastrotations.pdf .

Best Regards,

Roby

[william premerlani]

Hi Roby,

Thank you for your very kind words. I had a lot of fun with this, and I am grateful that there is still some interest in this topic.

There are a couple of ways you can derive equation 5. One way is to go back to equation 1 and include the two terms for the integral feedback and then make some approximations based insights from equation 2. You would add  IY to the first line of equation 1 and subtract IX from the second line.

The easier way is to recognize that the integrators will change slowly, so that they can be treated as slowly changing tilt offsets. All we need to do is figure out what their inputs would be in the case of a slowly changing tilt error. In other words, you go to equation 4 and add the terms introduced by the equivalent tilt of the integrator. The dynamics of the integrators is then found by integrating their inputs, which is found by the cross-coupling structure of equation 1.

Best regards,

Bill

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