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I am trying to implement the backstepping techniques for quadrotor described in this article : Backstepping control for a quadrotor helicopter: Madani & Benallegue 2006

Since I am new to the control theory (and I know that my question concerns the most easiest part of this paper), I don't understand how can I generate my desired trajectory from the transfer function they provide at equation (56)

$$ H(s) = \frac{1}{(s+1)^6} $$

Or, generally speaking, how can I link any kind of trajectory to its corresponding transfer function ? Did my question make sense ? Is there a confusion ? I mostly ask to the community some relevant documentations (and not technical answer in this particular case).

I did some "exercises" on controlling cart trajectory for instance but the trajectory equation was always provided: circular, van der pol cycle. There were no transfer functions.

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  • $\begingroup$ Look up the 'internal model principle' in control theory. You can represent classes of signals as transfer-functions; most famously any step can be modelled using 1/s and embedding this model in the control law enables the control law to track any step (given some reasonable assumptions); the same goes for other signal models $\endgroup$
    – Arnfinn
    Nov 30, 2023 at 20:03

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