The first stage of the Saturn V, for example, burned about 26 tons of material in total per second (https://en.wikipedia.org/wiki/Rocketdyne_F-1#Specifications). Therefore the rocket dynamics are changing... very quickly. How does the control/guidance system deal with this? Do they design 100 controllers that they gain-schedule? Thanks for your input!
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According to "Description and Performance of the Saturn Launch Vehicle's Navigation, Guidance, and Control System", the control gain values make scheduled changes twice in each of the first two stages of ascent, and one more during the TLI burn, presumably reducing gain to avoid oversteering the lightened vehicle.
Note that Saturn V first-stage guidance was a pitch-vs-time program, concerned more with staying in a safe aerodynamic regime than with the exact trajectory.
I don't know how this compares with more modern systems; presumably the gain could be made a simple linear or polynomial function of time (since mass versus time should be fairly predictable).
answered Nov 22, 2015 at 16:41
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$\begingroup$ You are describing what is called gain scheduling. It is typical for many aerospace control systems since aerodynamics are so highly non-linear, especially for supersonic aircraft (since they have to fly subsonic, trans-sonic, and supersonic). $\endgroup$ Nov 22, 2015 at 16:48
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$\begingroup$ Thanks! And I will read that whole document, thank you for linking it :) $\endgroup$ Nov 22, 2015 at 17:15
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1$\begingroup$ The document's pretty fascinating. I had no idea they put custom analog filters in the attitude and attitude rate signal paths to keep the control system from overreacting to the structural flexing of the rocket! $\endgroup$ Nov 22, 2015 at 17:31
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$\begingroup$ There are many things to love about space SE, but one I love the most is reading the documents that are proffered up as references. $\endgroup$ Nov 23, 2015 at 1:30