# Why do autopilot controllers use $\theta$ as the input signal rather than $\gamma$?

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.

• 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... Mar 7 at 4:42
• @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. Mar 7 at 8:29
• @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) Mar 7 at 16:16
• @MichaelHall I proposed the edit to the community Mar 8 at 11:14
• Just fixed. Thanks! Mar 9 at 14:59

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

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.

• 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. Mar 7 at 9:13
• It includes a nice picture. Mar 8 at 18:07
• @MichaelHall then keep your pictures Mar 10 at 9:58
• @Federico, chill out dude… competing answers is how this site works. You ought to know that, aren’t you a moderator? Mar 10 at 15:13