There are several types of controllers, but they fall into basically four categories. 1) time based (usually cheaper type controllers) 2) Inertia (Prodigy being the most popular) - - works as you described 3) Surge - uses a sensor in the hitch (usually) to determine how hard the trailer is pushing forward on the hitch because the truck is trying to stop and applies trailer brakes accordingly - only operates when the brake lights are on 4) tow vehicle brake operation - two of the more popular being Jordan Ultima using a wire attached to the brake arm and Brakesmart which uses a tee in the brake fluid system.
Jordan and Brakesmart will apply trailer brakes most smoothly in direct proportion to the amount of braking of the tow vehicle.
2003 Dodge HO 6 speed Laramie Dually, Jordan controller, RDS fuel tank, Air Ride 25K hitch
Carriage 36' fiver, Onan 6500, Prosine 2K inverter, 3 slides, MORyde IS and Kingpin