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I'm trying to implement two PIDs for stabilizing quadrotor for position tracking. The inputs are $x_{d}(t), y_{d}(t), z_{d}(t)$ and $\psi_{d}(t)$. For position tracking, usually the small angle assumption is assumed. This assumption allows for acquiring $\theta_{d}$ and $\phi_{d}$. These are the results

enter image description here

The x-axis position is driving me crazy. After alot of attempts for tuning the PIDs, I felt something wrong is going on. Is this a normal behavior for PID controller? Also, what I've noticed is that once $\psi$ reaches to zero, the platform starts oscillating (after 1.5 second in the figure).

For solving ODEs and computing the derivatives for the velocities, I use Euler methods.

It is simulation in Matlab.

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  • $\begingroup$ Explain in more detail how you tuned your PID controller. $\endgroup$
    – Paul
    Apr 17, 2015 at 15:33
  • $\begingroup$ @Paul, do you want to know the actual values of the gains? $\endgroup$
    – CroCo
    Apr 17, 2015 at 20:20
  • $\begingroup$ Not the values, just the steps you took to arrive at those values. $\endgroup$
    – Paul
    Apr 17, 2015 at 21:30
  • $\begingroup$ @Paul, after a deep thinking, I believe these results are good (not perfect). I've double checked the trajectory, it seems from 0 sec to 1.5 sec, the trajectory is fixed. After 1.5 sec, the trajectory starts varying. I've implemented backstepping controller and the results are perfect. Thank you. $\endgroup$
    – CroCo
    Apr 18, 2015 at 18:42

2 Answers 2

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is it real or simulation application?

If simulation there is good examples in matlab codes/models you can look deeper

If real:

1- filter the sensor data

2- use tan2 function for angular error calculations

3- begin PID calculations with all P, I and D constants. if you use just one of them stabilization is not possible. PI or PD control is possible. Be carefefull first constants P>I>D than you can use :

http://sts.bwk.tue.nl/7y500/readers/.%5CInstellingenRegelaars_ExtraStof.pdf

or

http://www.expertune.com/tutor.aspx

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  • $\begingroup$ simulation in matlab. yes there are a lot of matlab codes, but the majority of them use simulink. I'm using script. $\endgroup$
    – CroCo
    Apr 17, 2015 at 20:24
  • $\begingroup$ This is a good thesis I did simulink model from this and works fine. Also be carefull about using tan2 in angular calculations. also If you can send or share the code may be(if familiar language) I can help/fix your code $\endgroup$
    – acs
    Apr 17, 2015 at 23:16
  • $\begingroup$ @cagdasecking, after a deep thinking, I believe these results are good (not perfect). I've double checked the trajectory, it seems from 0 sec to 1.5 sec, the trajectory is fixed. After 1.5 sec, the trajectory starts varying. I've implemented backstepping controller and the results are perfect. Thank you. $\endgroup$
    – CroCo
    Apr 18, 2015 at 18:42
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The controller has a definite performance problem after t=1.5sec. [This can be due to the system model or some other coding error.]

The system (model + controller) behaves smooth until t=1.5sec. It is best to magnify and debug the code at that region. The controller behaves as expected until then. Only the X has no error from T0, which makes assessing the X-axis controller impossible.

Another point also worth noting is that, the Y and Z errors should have caused some error in X, but we don't see this. So the simulation model could be simplified (like decoupled in X direction from others maybe?)

Euler angles sometimes cause computational errors in attitudes (for exact zero, or pi or pi/2's). That might be the reason.

For an understanding of the maths behind euler representation singularities, and their solutions, please refer to textbooks or articles, one example is: http://lairs.eng.buffalo.edu/pdffiles/pconf/C10.pdf

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  • $\begingroup$ The problem was with the trajectory. From 0-1.5 sec, the trajectory is fixed. This explains why the error decays, after 1.5 sec, the trajectory started varying and hence the error doesn't decay, therefore I just hoped to reduce the error which I've done. I've implemented backstepping controller and the results are much better than PID but still PID is a valid choice. $\endgroup$
    – CroCo
    Apr 23, 2015 at 22:28

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