PLL closed loop pole/zero and open loop pole/zero

[hearter]

we all know open loop pole zero location, but any one know the relation of closed loop pole zero to the open loop? can we quantify the peaking by closed loop pole/zreo location?

appreciate any insight

thanks
Hearter

 

[saro_k_82]

Ofcourse you can. Rootlocus provides you just that. It is easy to read the damping coefficient from the rootlocus plot which quantifies the peaking.

 

[hearter]

I think we are talking about different things here, can you explain in detail, how to relate root locus plot to the peaking?

appreciate
H

 

[Emanuel_hr]

Well, if you know the open loop poles and zeros(and the gain) then you can write the transfer function. The closed loop transfer function is Hc = Ho/(1+b*Ho), where Ho is the open loop transfer fcn, b is the feedback path transfer fcn.
And yes you can quantify peaking from closed-loop transfer fcn, just calculate ζ and ω(assuming second order response), for higher order is harder to evaluate, a simulation might be required.
Hope this helps.