Understanding a PLL: Determine H(s) from Transfer Functions

[anon6912]

I'm trying to implement a basic PLL. The diagram is given as follows:

Where the transfer functions are given as follows:

To implement the PLL I need it to be as follows:

How do I determine H(s) from the transfer functions that are given?

Thank you for your help

 

[Baarken]

Based on your 3rd picture, the block diagram reminds me of the so-called synchronous frame-PLL shown below (see attached pdf for more details). Here the loop filter is basically a PI regulator.

Se also "Operation of a phase locked loop system under distorted utility conditions" by V. Kaura and V. Blasko if you are interested in PLL under distorted inputs.