This Library is licensed under the MIT License
For an ultra-detailed explanation of why the code is the way it is, please visit: http://brettbeauregard.com/blog/2011/04/improving-the-beginners-pid-introduction/
For function documentation see: http://playground.arduino.cc/Code/PIDLibrary (Click "Libraries" on the left panel. The link to the documentation is listed as "PIDLibrary - Provides basic feedback control".)