Problems with PIDs copter 4.0.4 . 130 cm & 14 KG

Hello everyone, I have a 130cm quadcopter, 4x Hobbywing x8 motor and ESC with 3090 propeller. I have fitted a Pixhawk 4 Holybro controller with 2x Holybro GPS and HereLink.
I have meticulously followed all Tuning instructions and all advice on this forum. It also has the parameter indicated by making the estimated minimum and maximum weight operation.
The drone flies from the beginning correctly, rises, moves roll pitch yaw from the beginning without apparent problem.
It does not fly perfect of course, so I dedicate myself to Autotuning, the drone behaves well, it does not do very strange things, it only loses some height in Althold mode although it recovers later.
After Autotining the Loiter was tested and already in a more serious flight doing movements etc, from time to time it made gas blows and at one point it entered oscillations from which it seemed that it was not going to recover, it changed to Althold mode and landed .
After this and several more attempts to make PIDs with Autotune, we performed Autotune again in a closed room to avoid any disturbance, tested only in Althold, it flies correctly, but makes a strange movement in “Althold”, if it moves forward or forward. back (Pitch), when releasing the stick the drone makes a braking movement as if it were releasing sticks in Loiter, let’s say braking the drone, stabilize for a second, and perform another smaller “braking” movement and return to stabilize.

I share two LOGS, # 47 of the day that I loop and almost crashed, and the second # 60 of the last day of flight with the strange result after Autotuning.

https://drive.google.com/drive/folders/1vLlLfhgPUAOlaM0bp4QsKvRCwSA3YOwT?usp=sharing

I dare not touch anything without someone with experience doing the great favor of reviewing the LOGs and commenting if you see an obvious problem, and if so, indicate the starting point to find a solution.

Thank you very much, greetings to all.

It is not braking, it is oscillating, and over compensating.
Try to do autotune with a less aggressivity (0.05 for start). 0.1 is usually too tight for large, overpowered copters. Also decrease filter settings from 10 to 8 (as recommended in the tuning guide for 30’’ props)

Also use gps blend instead of use_best, your FC constantly switching GPS. It can cause small twitches in loiter/poshold mode.
Your compass is too close to the battery or to the motor wires, it is heavily impacted by motor thrust, auto and loiter modes will not work correctly until you fix it. Disable compasses in the flight controller, and use only the one in the GPS (but move it away from interference sources)
Do you have any payload which could move in flight, the ROLL and PITCH P values are differ significantly, but if it is a symmetrical frame and balanced well, then they should be close (if not identical)

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Hello, thanks for your quick response, I will do everything as you are telling me, the frame is symmetrical although the legs-load areas are not, the controller is in front of the chassis not up in the center but its position is indicated. I am going to make the settings you indicate right now and try PIDs again, I will tell you the result, thank you very much.