So, just a quick update. The derivative control is programmed and ready to go. It's very simple. The proportional part of the term moves the canards to 7.5° if there is 7.5° of tilt. The canards stay at 7.5° max for tilts above 7.5°, and 7.5° of tilt corresponds to the saturation value of 250 us to the servos. The derivative term just opposes the change in the tilt. We think a gain of 50°/s would result in critical damping. So, as an example, if the tilt was 3 degrees and the rocket was moving at 20°/s towards 0° of tilt, the proportional correction would be 3 / 7.5 x 250 = 100 us in the direction of zero tilt. The derivative term would be 20 / 50 x 250 = 100 us in the direction away from zero tilt. So, for this example, the canards would be at 3° without the derivative term and 0° with that term. We will likely start with a lower derivative gain and work up.
Also, I was looking at more of the data from the flight. I previously posted tilt data from the EasyMega. However, the corresponding data from the UDB5 (which is actually doing the controlling) is slightly different. The data for the EasyMega and the UDB5 are posted below. What is interesting in the UDB5 data is that the rocket oscillates
before it reaches 10° of tilt. At that point, the canards should still have been trying to get the rocket to the 10° set point. So, why did the rocket turn away from the 10° set point? I have concluded that what is happening is that the rocket flexes when requested to make a sharp turn to 10°. At 7.5°, the canards start to back off, and the rocket un-flexes, which shows up on the tilt graph as an oscillation that isn't real. This isn't the sort of response that is suitable for derivative control.
The "Test Rocket" was originally designed as a two-stage platform just to test the concept of controlling to vertical from below the sustainer. It was an inexpensive rocket, relatively speaking, made from thin-wall Wildman fiberglass tubing. It was supposed to fly a few times in preparation for Balls flights, and that was it. As it turns out, it has flow many more times than I ever expected under increasingly stressful conditions, and I added a spin can to the sustainer. So, for this on-going testing, I need to strengthen the upper air frame a little to elimimate this flexing. In keeping with the blue collar character of this rocket, I'm going to experiment with a Soller carbon sleeve with heat shrink tubing. I've never tried that, and never expected to try it, but it seems like the perfect application under the circumstances. I'll report back....
Jim