Wobbling Issue only when battery is in Low Voltage

We are facing wobbling and slightly diagonal oscillation, when we are giving YAW input in LOW battery. Same thing is repeating every time at around 12.6V (Li-ion 4S, 16.8V, 16800mah). We tried to improve PID tunes, later we tried to improve YAW tune.
Yaw_P = 0.45
Yaw_I = 0.045

Yaw_P = 0.9
Yaw_I = 0.09

Yaw_P = 0.35
Yaw_I = 0.035

Yaw_P = 0.2
Yaw_I = 0.02

when we did last set up (P=0.2 & I=0.02) wobbling decreased, but are not sure- is it a proper solution? <log>

Is that a problem, how to solve - please guide anyone.

Have you configured the voltage monitoring and failsafes properly?
And update to ArduCopter 4.4.1. Why are you using 4.0?

Yaa we updated voltage monitoring properly…
It’s Already 4.4.1 sir, that showing in mission planner log viewer^

Perhaps that battery cannot supply the current demand. The outputs are maxing out which triggered a Thrust Loss error. Stabilization will be compromised.

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At 3.15 V/cell a Li-Ion battery is fully discharged, isn’t it?

we are using li-ion, As our Battery Manufacturer certified we can drain till 2.7/cell but not 2.5

What percentage of charge do you think you have left at 12.6V?
Who is the manufacturer and what is the discharge current rating for the battery?

10C
Manufacturer: MPower (India)

How many mAh have you drawn from the battery from full charge down to 12.6V?

Without enough voltage there will be not enough RPM. It is that simple. You will need to redimension your Powertrain to be able to cope with such low voltages. It is not a software isssue, it is an hardware issue.

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Yaaa, I accept that, but same motor (TMotor MN3510 700kv) worked properly till 12V with another ESC AIR 40 but not the same with current ESC F35A…

for that confusion happened… its all about optimisation, as much I can.