Correct spelling, explanation: controller is an English word that appeared for the first time in Middle English. Back then it referred to a person who kept a duplicate register of accounts. Controller entered English from the Anglo-Norman form contreroller, which used to mean to keep a copy of a roll of accounts. Today, controller functions only as a noun.

Definition of controller:
1. noun – a device which is used to control or operate a machine or some other equipment
To play this game you need to operate a controller, which is equipped with four buttons.
2. noun – a person who is in control of something
The job of an air-traffic controller is highly responsible and if you can’t work under pressure, it’s not for you.

Expressions with controller:
Some common expressions with controller include: air traffic controller, quality controller, food controller;
After a thorough investigation, the air controller was to blame for the accident.
Our quality controllers make sure that we launch products of the highest quality only.
After the inspection of a food controller the restaurant was closed.

Incorrect spelling, explanation: controller is a word with quite a simple spelling, but still many English users make a mistake and spell it with a single -l letter, which gives an incorrect form controler. The mistake is probably the consequence of the fact the verb to control is spelled with a single -l letter. When it comes to the noun, however, the only correct spelling is controller.