Acceleration profile is a little related to feedback loop. I have worked with 
state feedback control instead of PID for a while and it works great although 
adding integrator have puzzled me a little bit.

Ordinary integrator works between set reference value and measured value and 
this will only work for a dead beat controller. Then gain is lower it will 
integrate not only the current model and measurement errors but also the part 
because real have not yet had enough time to change. Then integrating the model 
error which is the difference between change predicted by model and measured 
value integrator seems to work much better.

In theories for state feedback control they use the zero point and claim it 
could easily be expanded to any point. All articles and books I have read about 
state feedback including linear quadratic control with or without noise (LQR, 
LQG) they use difference between set reference value for position/angle and 
measured position/angle. This must be a little bit wrong and it should be the 
differences for each state because as is now all differences except one is from 
zero. It should be: (angle_ref - angle_mesaured)*gain1 - (velocity_ref - 
velocity_measured)*gain2 - (current_ref - current_measured)*gain3. From the set 
reference value for position the model is used used to calculate set reference 
value for all three values. There may also be an individual integrator for each.


Nicklas Karlsson

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