KDC Assignment 6

What I found most interesting was the number of people reporting almost exactly the same time - 0.28 +/- 0.002 seconds - for their rise time.

For the Kalman filter design, it's a valid strategy to break the encoder reading out into two values. We don't need a one-to-one mapping between instruments and measurements input to the Kalman filter.

1. - Use the position value directly for the position measurement, with a low measurement noise. This indicates that we believe the position measurement to within its resolution.
2. Differentiate the position measurement to provide a synthetic "measurement" of velocity. Use a higher measurement error in the R matrix to indicate that this measurement is less accurate, due to timing and resolution issues.

Some people called the tachometer reading the "actual" velocity. This is a mistake. It's just another measurement instrument with its own error, same as the encoder. It is just as well to filter the position acausally (using e.g. filtfilt) off-line to get an estimate of the "actual" velocity.

Friction and gravity compensation is hard. This page shows a nice video of the gravity and friction compensation in action.