What model of the system do people usually use? (input is Torque? if yes do they model the motor?

[pierfabre]

• This paper uses the torque as the control input of the system. They then uses an inner loop on their DC motor to control the torque using a PI : "an analog servo drive AZBDC12A8 from Advanced Motion Controls that includes an inner current-loop driven by a PI controller. This allows assuming that the current flowing through the DC motor terminals reaches the current imposed by the control signal and, in consequence, torque can be used as the control signal."
• The other way of doing it is neglecting the inductive effect in the motor and use the voltage as control input just like in this example
  
  This second method allows us to by-pass the need for a feedback on the current sensor. We will test the viability of the hypothesis made during the system identification work
• Alternatively to the inner curretn loop, we could also take the motor dynamic into account directly in the NMPC
• Another alternative would be to have the torque in input of our NMPC and then we calculate the state of the system at the next iteration if we apply this torque thanks to the model of the NMPC. From this state we take the motor position and speed and we control our motor over this target! In mathematical terms
  
  
  This solution might be easier and doesn't rely on an additional sensor

[pierfabre]

See the current output if we feed this voltage input

[pierfabre]

Inner current loop

Only feedforward

Only Ki (no feedforward, no Kp)

Ki + feedforward

Ki + Kp + feedforward

[pierfabre]

Control position and speed of the motor

with loaded pendulum

TODO : add video

Kp = 5.0
Kd = 0.02

Use scipy.lfilter

More efficient than np.convolve!
now we have 3430Hz frequency!

Kp = 2.0
Kd = 0.01

order = 2.0
fs = 3400.0
cutoff = 50.0