I've seen with drones that the norm of programming them is to create three loops, for each axis, but I'm not quite sure what a control loop is when the code must run in a sequential manner.
Programmatically, what IS a control loop?
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A control loop is:
This process continuously repeats.
Generally, if you have multiple control loops on one controller, you perform each step in turn for each control loop - get all references, get all feedbacks, run the actual control algorithm to generate the control signal, then write the control signal as appropriate.
I think Chuck's answer is quite accurate. Just to add, there are two types of control loops. What Chuck has described is a closed control loop, and hence has a feedback loop to make sure the output is same as reference input or the set point.
Open loop, on the other hand, doesn't need a feedback loop as the control action is independent of the process output.