SMARTDAMP Algorithm

Our custom approach to PID tuning

More content soon.  TLDR: if you have the kV and kA feedforward values.  we can use that as a model for our system.  
Then, we solve for the poles of the system.  After some math, we arrive at the following: 
KD=2KaKP−KvK_D=2\sqrt{K_aK_P}-K_vKD​=2Ka​KP​​−Kv​
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This will guarantee a critically damped PID response for a PD controller, given an arbitrary choice of Kp 
It is recommended that the following inequality is true: 
Kp≥Kv24KaK_p \geq \frac{K_v^2}{4K_a}Kp​≥4Ka​Kv2​​
Otherwise, Kd will be negative and you get a scary non-minimum phase system.  
Specifying percent overshoot
A Critically damped system is not necessarily the fastest possible response, sometimes you are okay with a bit of overshoot.  This modified version of the SMARTDAMP algorithm allows you to specify a percent overshoot in addition to your proportional gain to give you your optimal choice for Kd
Kd=2ζKaKp−KvK_d = 2 \zeta \sqrt{K_a K_p} - K_vKd​=2ζKa​Kp​​−Kv​
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where Zeta is our dampening ratio.
We can find zeta using the following equation given PO (Percent overshoot)
ζ=−ln⁡PO100π2+ln⁡2PO100\zeta =\frac{-\ln{\frac{PO}{100}}}{\sqrt{\pi^2 + \ln^2{\frac{PO}{100}}}}ζ=π2+ln2100PO​​−ln100PO​​
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Last modified 2mo ago