RPM PI control structure

[MChehadeh]

Hi,
May I know the structure of the PI controller used for control of RPM governor? this would help with tuning. For example, does the error get multiplied by Kp and Ki and then the results get summed-up together to produce the control action? or is it some other arrangement?

Thanks,,,

[Alex Kushleyev]

@MChehadeh

Here is how the RPM controller works (without going into too much detail...). It is a basic PI controller with feed-forward. This should clarify the formula and how the ESC parameters are used in RPM control mode

#RPM controller is running on each ESC at 10Khz update rate

#duty_cycle is between 0 and 999 (999 = 100% duty cycle). This is duty cycle of pwm applied to motor
duty_cycle = ff_term + p_term + i_term  

#explanation of the terms:

#cap the rpm setpoint using actual rpm + max_rpm_delta to prevent very large transitions 
#desired_rpm is rpm sent from flight controller
setpoint_rpm = min(desired_rpm, actual_rpm + params.max_rpm_delta) 

ff_term = compute the feed-forward term based on the setpoint_rpm, ESC calibration params a0, a1, a2 and measured voltage

error_rpm = setpoint_rpm - actual_rpm #note the rpm_error term is capped, since setpoint is capped

p_term = params.kp * error_rpm / 1024      #scale the result to get to units that make sense
i_term += params.ki * error_rpm / 1048576   #scale the result to get to units that make sense. this term persists

bound p_term using params.max_kpe
bound i_term using params.max_kie

Note that there are actually two caps, one that produces setpoint_rpm, but also p and i terms are capped separately. This can help bound different terms.

You can also zero out p or i terms by setting either the gains to zero or the max_kpe / kie to zero.

If you don't want the setpoint to be limited by params.max_rpm_delta, you can set max_rpm_delta to a large value that is greater than your max rpm, but you could have very aggressive response if you command a large rpm transition.

[MChehadeh]

@Alex-Kushleyev Thanks for the response.

What I understood is that there is a constant ratio between p_term and i_term, i.e. 1024/1048576=9.76x10^-4. Is that right?

[Alex Kushleyev]

@MChehadeh yeah it is simply 1/1024. Powers of 2 for faster calculations

Integral is scaled down a lot because it accumulates fast at 10khz update rate