what is it that you ultimately want to do or accomplish? while the beagle bone (black) has IO and capes that will accomplish much of what you list and could likely do everything on the list with appropriate sensors and circuitry interfaced it may or may not be the appropriate platform for your task. The beagle bone has the advantage of having 2 programmable real time units in addition to the arm processor and it runs a full linux operating system thus putting it in the class of a general purpose computer. often tasks such as PID, motor control, and PWM can be simpler to deploy and implement, especially when precise timing is a concern, on a microcontroller platform such as arduino. which you choose, really depends upon what you wish to accomplish.