# How do I select an appropriate controller gain for this roll control autopilot?

I'm trying to select a suitable K value for this roll control autopilot, based on:

Instead of the Gyro, I've also just considered a negative unity proportional gain feedback. How do I select the appropriate controller gain K for the system? (I'm feeding a step impulse into the system). I know that for each aircraft it would be different, for a fighter jet you want quick response times, but maybe not so much on a commercial airliner. What I'm trying to find out/understand is there design criteria/a method to selecting this value?

• Is there a overshoot(%) I should aim for?
• Is there a required damping ratio set?
• Or do I eyeball it, and find a balance between the time to settle and overshoot(%)?

You want fast response, but not any overshoot. The perfect response to a step input in this case would be a critically damped one. Matlab/Simulink are your friends here.

Things to consider in your feedback loop:

• Aircraft dynamics - is the initial inertia response modelled? Meaning, does the aircraft roll spool up to its final roll rate upon aileron deflection?
• Is aerodynamic resistance to roll modelled?
• Is it a digital loop, and if so what integrators are you using? If Euler your loop rates need to be high.

I've seen a similar design for a helicopter with a controller gain of 20 and an additional roll compensator $\frac {s + 1}{s}$ in the forward loop, and a negative unity feedback.

You could eyeball the response, use different settings for the feedback gain, and find the fastest response without overshoot. You'd have to testcase it for several extremes. You do need some form of damping feedback as well, I reckon your first task would be to find a response that is not oscillating.

• <You could eyeball the response, use different settings for the feedback gain, and find the fastest response without overshoot.> There are analytic methods for that. – Federico Aug 18 '17 at 7:13
• What sort of methods are you referring to? Plotting the root locus? – Liam Aug 18 '17 at 8:16
• @Liam for example. then the Bode plot, or Nyquist. The peak of the overshoot is given through some simple formulas: en.wikipedia.org/wiki/Step_response#Control_of_overshoot ecee.colorado.edu/~ecen2270/materials/TransResp2ndOrdSys.pdf [eq. at page 8, unfortunately overlapped with the picture] – Federico Aug 18 '17 at 9:01
• @Federico thanks, that's helped me clear up my understanding of what I'm trying to achieve here. – Liam Aug 18 '17 at 10:53