Spike at the start of discrete integration.

I have an angular displacement in Yaw at a 100Hz sampling rate. When I try to differentiate it, I get a spIke at the first sample point of velocity and 2 spikes in the first 2 samples of acceleration. I plan on passing this into a low pass filter so I can't ignore these samples either unfortunately. What am I doing wrong that causes the spikes at the start of my differentiated channel?

The Blue line is Velocity and yellow is Acceleration in the attached scope image.

[Paul]

Probably relate to the Initial Condition parameter of the Discrete Derivative block(s).

Can you upload Yaw_Data in a .mat file (use the paper clip icon on the Insert menu) or show the three signals on three separate scopes?

[Andrew Gilliam]

This is my yaw data displacement to acceleration left to right.

[Paul]

Zoom in on each scope for the first 0.040 seconds like in the attached JPEG so we can see what's going on with each signal in the time of interest.

[Andrew Gilliam]

Here's the first few samples. The only thing to note is the offset from zero on the displacement data but the dispalcement value doesn't change in this zoom window.

Answer 1

[Paul]

In the first Discrete Derivative block that computes the rate, try setting the parameter "Initial condition for previous weighted input K*u/Ts — Initial condition" to Yaw_Data(1)/Ts, where Ts is 0.01 (or whatever is the Sample Time of the signal driving that block). That should smoot things out for the first couple of sample when Yaw_Data is constant. There will still be a transient when the Yaw_Data changes. Hopefully it doesn't change too much from sample to sample. Estimating acceleration from position can be difficult. Instead of a pure differentiator, maybe a high pass filter would be better.

Also, perhaps combining the differentation and the low pass filter into a single filter would be beneficial, unless you need the rate and acceleration signals explicitly for some other reason.

[Andrew Gilliam]

Thank you so much for this!!