I have 12v power source [Mean well PSC-60A](https://www.mouser.com/ds/2/260/PSC-60-SPEC-806374.pdf) with UPS function and acid buttery. 
In datasheet says, that output can be regulated from 12-15V - but it's not true, because tested results for output was:

* from 11v(when not connected to 220v and buttery discharged)
* to 13.8v(when connected to 220v and battery charged)
* impossible to regulate output to 12v on charging(min about 13v)
* regulating output voltage affects to battery charging voltage (

How to get a output with voltage of not more than <=12 volts (+/- 0.5V) with max 2A load on peak (avg load 500-800mA) from this 11-13.8v source ?

Output should be less or equal to 12v.

Which option is better, how right:

* use DC-DC buck converter, like [D-SUN MP1584](https://www.google.ro/search?q=d-sun%20MP1584&tbm=isch&tbo=u&source=univ&sa=X&ved=0ahUKEwi59KvRkN_ZAhUIthQKHRf1BasQsAQIKQ&biw=1920&bih=974) ?
* or simple shunt regulator with zener like [1SMB5927BT3G](https://www.onsemi.com/pub/Collateral/1SMB5913BT3-D.PDF) ?

Help me please with this.
[![enter image description here](https://i.stack.imgur.com/Gelx9.png)](https://i.stack.imgur.com/Gelx9.png)

Part of used scheme 
[![enter image description here](https://i.stack.imgur.com/ZpmUW.png)](https://i.stack.imgur.com/ZpmUW.png)