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C2000WARE-DIGITALPOWER-SDK: Different values used for software PLL coefficient calculations in design guides. Cannot say which one is correct

Part Number: C2000WARE-DIGITALPOWER-SDK
Other Parts Discussed in Thread: SFRA

Hi all

I am studying the software PLL codes provided by TI.  
There are two documents for the explanation of that implementation. One is SPRABT3A  and other one is in the digital power sdk library reference guide. 
For kp and ki calculation, both guides used same exact parameters but somehow ended up with different answers. Please provide explanation for this. 

Following two lines from sdk design guide and the SPRABT3A  document. 


"Now using settling time to be 30ms and the error band to be 5% and damping ratio to be 0.7 we can obtain the natural frequency to be 119.014 and then back substituting we get  kp=166.6 and ki=27755.55. "

"Using settling time as 30 ms, and the error band as 5% and damping ratio to be 0.7, the natural frequency is obtained to be 158.6859. Back substituting Kp =222.1603 and Ki = 25181.22"

Also what is the meaning of Ti in following equation. 

 


Cannot find how ki value was calculated. 

Also, here are some strange relationships i encountered in above values.  

1st statement-  ki is eqal to square of kp. 166.6^2=27755.56

2nd statement- ki is equal to square of wn.  158.6859^2 =25181.2148 



Regards
Damith