Strange regular spikes in desired acceleration yielding poor performance

I was doing some endurance flight testing on my Pixhawk powered Align M690L hexa, and I noticed regular spikes in the pitch that were causing much higher current draw from the battery than I expected.

Further investigation yielded that the desired acceleration (in my case specifically DAccY) had regular spikes. The discontinuities were also obvious in desired velocity. I am not certain the way guidance works on the ArduCopter and what is computed from what, so it is difficult to get root cause. However, the spikes are very regular, and are clearly a source of the guidance (potentially poor PID settings?).

The spikes were exhibited in front forward auto flight, but not in the RTL back-forward portion of the flight. I am not certain whether this means that this is caused by flying forward, or if the guidance code is subtly different b/w RTL and waypoint flight.

Attaching some pictures of the dacc, dvel, and the pitch.

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Just some additional background. I noticed that during the more "spiky" auto mode the drone was flying slower than we had configured it (11m/s rather than the 15 m/s). This is an indication that the spikes "up" are causing it to slow down and not accelerate as much as it should in ideal circumstances. So it's not that it's going too fast, it's going the right speed but something is causing the drone to constantly want to pitch up.

"something is causing the drone to constantly want to pitch up"
10000 mAh LiPo => your drone is not balanced?

My PIDs (blurred, sorry)

Yeah we have a hefty 10000mAh. Would an unbalanced drone have this behavior? It is somewhat back-heavy, that is true. I'm not an expert in this, but I would expect that a drone that is unbalanced would have trouble keeping a constant pitch, but it's getting commanded to pitch up by the outer loop control loop. Can that be caused by imbalance? 

Sure https://en.wikipedia.org/wiki/Moment_of_inertia ; i guess that when the speed is low is all OK; your angular momentum is not correlated to speed; when you go faster you have a high-momentum in the back  (as it's back-heavy) and a low-momentum in the nose. This doesn't help. 

Try to do exactly the same test, but on the roll axis (not pitch). Everithing should be better. As m690 is symmetrical, the only a-symmetry is the 10k LiPo

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