Proportional Control

Proportional controllers are the easiest to understand so it makes sense to start discussing them.

Assume that the quadrotor has a sensor that can perfectly measure its altitude, perhaps using a barometer, GPS, or ultrasonic transducer. Initially the quadrotor is powered on but sitting at rest on the launchpad. Once activated, the pre-programmed flight path has the quadrotor ascend maximally to 10 meters, hover in place for 5 seconds, and then proceed in a northeasterly direction while maintaining a constant altitude.

In the first instant that the quadrotor begins executing the flight plan, the error in altitude is,

The controller senses the large error and commands the motors to produce a vertical thrust that is proportional to the error, i.e.,

Can you see why it's called proportional control?

As the quadrotor approaches the desired altitude, the error decreases and thus the controller input also decreases.

Notice how the proportional gain amplifies the “present” (current time-step) error, with no consideration of past or future errors.