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In particular, referencing how the Matlab/Simulink controller here uses $\theta$ (absolute pitch angle), rather than $\gamma$ (flight path angle). (Autopilot controller starts at 59:26)

It seems if you wanted to control flight path angle, your input signal should be $\gamma$. I'm sure I am missing something here.

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    $\begingroup$ If you are talking about angle of climb/descent, then according to Principles of Flight by Oxford (this page), it is appropriate to use both $θ$ and $γ$ to denote that... $\endgroup$ Commented Mar 7, 2023 at 4:42
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    $\begingroup$ @Aditya Sharma The symbols of the pitch angle $\theta$ and the flight path angle $\gamma$ are defined and accepted throughout the community. For example the DIN9300 (unfortunately this norm is not open source) or in pretty much every book, e.g. Flight Dznamics principles by Michael Cook. $\endgroup$
    – U_flow
    Commented Mar 7, 2023 at 8:29
  • $\begingroup$ @MichaelHall, I agree. I would propose a corresponding edit of the question, but I only seem to be able to directly edit it (without approval) $\endgroup$
    – U_flow
    Commented Mar 7, 2023 at 16:16
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    $\begingroup$ @MichaelHall I proposed the edit to the community $\endgroup$
    – Quentin H
    Commented Mar 8, 2023 at 11:14
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    $\begingroup$ Just fixed. Thanks! $\endgroup$
    – Nate Poon
    Commented Mar 9, 2023 at 14:59

1 Answer 1

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You are right, your input should be $\gamma$. However the control of $\theta$ is important. To combine both variables, typically a nested control structure is adopted.

For this, two control loops, an outer loop and and inner loop is connected in series. I have drawn a short sketch

Overview of a nested control structure. Picture drawn by the author.

Here you can see that the climb angle error $\Delta \gamma = \gamma_{cmd} - \gamma$ (the difference between the measured and commanded climb angle) is fed to the outer loop, which calculates a pitch command. The pitch error is then calculated by $\Delta \theta = \theta_{cmd} - \theta$. This pitch command is then fed to the inner loop controller which finally computes an elevator deflection for the aircraft.

In most applications the outer and inner loops are simple PID controllers, which are gain-scheduled over the flight envelope. Additionally it should be noted that the inner loops itself is often divided into a rate controller (controlling the rotational rate $q$ for the pitch axis) and and attitude controller controlling $\theta$.

However, this should serve as a general overview how controlling pitch and the flight path angle at the same time can be achieved.

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  • $\begingroup$ how does this differ at all from my answer? you're simply limiting the choice of external control loop to a $\gamma$ one, where that limitation is not needed at all. $\endgroup$
    – Federico
    Commented Mar 7, 2023 at 9:13
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    $\begingroup$ It includes a nice picture. $\endgroup$ Commented Mar 8, 2023 at 18:07
  • $\begingroup$ @MichaelHall then keep your pictures $\endgroup$
    – Federico
    Commented Mar 10, 2023 at 9:58
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    $\begingroup$ @Federico, chill out dude… competing answers is how this site works. You ought to know that, aren’t you a moderator? $\endgroup$ Commented Mar 10, 2023 at 15:13

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