# Impulse and step response related to the angular position of a spacecraft

#### Imagin_e

Hi!

I don't know if I'm in the right forum of this site but I'm trying anyway. I was just wondering if someone could explain how the step- and impulse response is related to an angular position (of e.g. a spacecraft)? Just a little about the theory since I am trying to actually understand how/why my matlab plots and the results are related to this subject.

Thanks!

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#### FactChecker

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2018 Award
It is important when trying to control something like the angular position (i.e. orientation). Its response to an impulse or step input shows how it will respond to any disturbance or frequency input. Obviously, when you try to correct an error, you do not want to push it in the wrong direction. That would just cause it to go off exponentially. Just as important is that you don't want to be too slow and then overdo it. That would cause it to oscillate back and forth. To analyse which frequencies of oscillation will die out and which will grow (diverge), it is necessary to know how the system responds to every frequency. Any divergent frequency is bad unless it is so slow that it is easy to control in other ways.

#### Imagin_e

It is important when trying to control something like the angular position (i.e. orientation). Its response to an impulse or step input shows how it will respond to any disturbance or frequency input. Obviously, when you try to correct an error, you do not want to push it in the wrong direction. That would just cause it to go off exponentially. Just as important is that you don't want to be too slow and then overdo it. That would cause it to oscillate back and forth. To analyse which frequencies of oscillation will die out and which will grow (diverge), it is necessary to know how the system responds to every frequency. Any divergent frequency is bad unless it is so slow that it is easy to control in other ways.
Thanks buddy!

#### JBA

For a spacecraft orientation change or rotation, as opposed to a change in velocity or direction of travel, any impulse force-time sum in one direction must be countered with an equal impulse force-time sum in the opposite direction in order to arrest the imposed rotation of the craft.

#### FactChecker

Gold Member
2018 Award
For a spacecraft orientation change or rotation, as opposed to a change in velocity or direction of travel, any impulse force-time sum in one direction must be countered with an equal impulse force-time sum in the opposite direction in order to arrest the imposed rotation of the craft.
Good point. I guess that stopping the rotation would boil down to just canceling the disturbance impulse because there is no aerodynamics to mess it up. Unless you want to get it back to some particular orientation, the problem would be solved. Getting it back to a desired orientation would reintroduce the threat of oscillatory control behavior.

#### Baluncore

The orientation of a satellite is usually adjusted so it points it's antennas towards the Earth while pointing it's solar panels towards the Sun. Under normal conditions the satellite rotates about it's centre of mass at a fixed rate that maintains those orientation directions. As an axis orientation or rotation rate error begins to accumulate, and so becomes apparent, a short correction impulse is applied to correct the drift of rotation. Over time that impulse will accumulate to bring the satellite back towards the required orientation.

Satellites move in elliptical orbits. To change position from an old orbit to a new orbit, two impulses are usually required. An intermediate elliptical orbit is used that intersects both the old and then the new orbit. The first impulse transfers it from the old orbit to the intermediate orbit, the second impulse, applied at the appropriate time, takes it onto the final required new orbit.

#### Imagin_e

Thank you for explaining, now I understand. Cheers!!

"Impulse and step response related to the angular position of a spacecraft"

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