Attitude control with cold gas thrusters

Question

Consider the cold gas thrusters on a Falcon 9.

There are two thruster pods on stage 1 and two on stage 2.

Each pod has four orifices to fire along the x, y, and z axes of the scacecraft. By varying the orifices you fire, you can control for roll, pitch, and yaw.

Would the thrusters ever fire to control more than one axis at a time? Or would they fire to correct the error measured on one axis before moving on to another axis?

If the thrusters fire to control more than one axis at a time, is there a reduction in the thrust produced per axis? (If the thrusters are powered by a single gas tank at some pressure P, then it seems you would have to split the flow rate given by P between the multiple orifices on a pod?)

No worries if you don't know about Falcon 9 specifically. I'm using it only as an example. I'm just trying to get a better sense of how cold gas thrusters might fire so that I can more properly simulate them. My only goal is to get a bit closer to "reasonable."

Answer 1

Yes, most GNC systems will correct multiple axes at once.

GNC systems can get quite complex. Typically, each letter is its own piece of software.

The Guidance determines where the spacecraft should be pointing at a given time or mission phase: it outputs a desired attitude (MRP, quaternion, etc). Navigation will determine where the spacecraft is currently pointing at using a set of sensors and thereby determine the difference between the desired attitude and the current attitude. Finally, Control will determine which attitude trajectory the spacecraft should follow based on a steering law (e.g. Lyapunov controllers, cf. 8.3.2 of Schaub & Junkins) and which thrusters to fire to minimize the difference between the desired attitude and the current attitude.