What does "Controlling Object" mean in FAA documentation?
'Controlling object' is, as far as I can tell, the old term for 'controlling obstacle'.

From the TERPS manual (Appendix B):


  Controlling Obstacle. The obstacle on which the design of a procedure or establishment of a minimum altitude or angle is based on. See also Order 8260.19, Flight Procedures and Airspace.


Controlling object is mentioned as a field in the Public Use Airport Runways database:

Attribute_Label: BE_CTL_OBJ
Attribute_Definition:
Description of the controlling object at the base end of the runway
(e.g., trees, bldg, fence, none).
Attribute_Definition_Source: FAA
Attribute_Domain_Values:


And as you can see, it can be trees, a building, and so on.