Numerically Integrating a Damped-Oscillating Mass System

[Wolff]

Hi all. My first time posting. Hopefully it will go well. :)

For my ME Lab 1 class I need to numerically differentiate LVDT data to find acceleration of an damped-oscillating mass system and I need to numerically integrate accelerometer data to find displacement of the same damped-oscillating mass system. This data is supposed to be compared.

I did not have any problem numerically differentiating the data. It came out perfect.

Now when I go to numerically integrate the accelerometer data, the displacement data seems to drift off into space. The drift is slightly apparent in the velocity data but the displacement data doesn't even come close to resembling the LVDT displacement.

I have been told that this is integration drift. I have no clue how to remove this and was hoping someone here could guide me in the right way.

Thanks for all your help in advance!

 

[lewando]

I have been told that this is integration drift. I have no clue how to remove this and was hoping someone here could guide me in the right way.

Short answer: You can't. Tiny errors in acceleration measurement become (relatively) big errors in displacement.

 

[viscousflow]

I have been told that this is integration drift. I have no clue how to remove this and was hoping someone here could guide me in the right way.

Thanks for all your help in advance!

All small accelerometers drift rapidly over small periods of time (on the order of 20ft/s/s). As lewando said, this cannot be stopped. This assignment should show you why dead reckoning is an abandoned tool.

 

[Wolff]

Thanks for your help!

 

[lewando]

Slightly longer answer: You can reduce your drift somewhat by doing a couple of things:

1) Make sure your accelerometer is well-calibrated. Gain error and offset error should be minimized. For a single z-axis (+z=up, -z=down) accelerometer, resting on a perfectly flat, non-vibrating surface, you should be gettting as close to 1 g as you can. Any deviation from this, either generated by the accelerometer or by your measuring device, will result in drift.

2) Accelerometers respond to acceleration dynamically over a (somewhat large) range of frequencies. This allows a window of opportunity for unwanted noise sources to creep into your measurements. Depending on your application's operating frequency range, you can use an appropriate band-limiting filter to filter out unwanted noise sources.

3) Do not tilt the accelerometer. Keep it perfectly level or else the tilt will look like an acceleration when there is none.

 

[viscousflow]

3) Do not tilt the accelerometer. Keep it perfectly level or else the tilt will look like an acceleration when there is none.

Just wanted to add to that. Tilt looks like an insanely major acceleration. I was doing some readings on a control system where I estimated angles from the accelerations (inaccurate obviously) but when I tilted it at around 30 degrees for a short period of time, one of my motors used for roll instantly saturated at full throttle. Good thing I had the saturation in place, because the readings became unbounded (on the order of 3million ft/s/s).