Control

"I have full control" is correct.

'Controls' in the plural of the noun form of 'control'. 'Controls' are objects that allow you to control something.

When you say you have control, you have control OF something... Even if the 'of' is not said, it is implied. While it is also the noun form of control, it is an entirely separate meaning as it is used to describe your relation to something, rather than the thing itself.

I really wish I knew the terms in English grammar as well as I do Spanish Grammar. Le sigh.

'a' is redundant.

'Controls' can be used as a verb depending on the pronoun, eg:
"She controls the situation well." or "They control the situation well."

'Control' can also be used as a noun, singularly or plurally, eg:
"He is manning the controls." or "We have taken control."

I apologize for the English language, but there isn't a great deal of difference between the following phrases:

I am in control of the ship.
I am in full control of the ship.
I have the ship under control.
I have control of the ship.
I have the controls.

The last phrase is the only one with a significantly different meaning. "I have the controls" means "I am the person operating the control mechanisms," but doesn't necessarily imply that that person is in control of anything else that's going on. You can have the controls and still be no more than a pair of hands executing someone else's verbal orders.

When saying "I have a..." you are referring to something you are in posession of, whether tangible (I have a shirt) or intangible (I have an idea) that can exist in singular or plural form (shirts, ideas). Then the "a" refers to "one".

In this context, the word control is a concept (i.e.: the ability to control) rather than the noun "control" (e.g.: the mechanical device that controls). As such, you simply say "I have full control".