Correct spelling, explanation: the origin of the word controller can be found in contreroller, which was an Anglo-Norman term used to describe the activity of keeping a copy of a roll of accounts. When controller appeared in English in the times of Middle English, it means a person who kept a double register of accounts. In modern English controller refers to either a person or a device.

Definition of controller:
noun – a device used to operate another device or a person who controls or operates something,
Press the red button on the controller to activate the device.
The controller of our radio approved the new program so it will be on next week.

Collocations with controller:
A few common collocations include: program controller, financial controller, and regional controller.
The new program controller for BBC wants to present his vision at the meeting today.
We all feel stressed because of the financial controller who has been sitting here for over a week.
The regional controller wants to introduce some important changes in our sector.

Incorrect spelling, explanation: an English verb to control is spelled with a single -l letter, and probably because of that a lot of English users spell the noun controller as controler. The version with a single -l letter, however, is wrong and the only correct spelling is controller.