I'm an electronics newbie.
The part I'm talking about is this:
DC 10-50v 12V 24V 48V 3000W 60A amps DC Motor Speed Control PWM HHO Controller
My question is, can this type of part be used to control brushless DC motors?
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Practically all brushless motors require 3 independent power connections, each one at the appropriate frequency and 3 different phases. Those 3 power cables are typically connected to a brushless ESC.
Practically all DC motor speed controllers (including DC electronic speed controllers for brushed DC motors), including the one you link to, only have 2 output power connections.
The 2 outputs of a DC motor speed controller are not enough to drive the 3 inputs of a brushless motor
(photo from "RC Hobby Mysteries: What is Brushless Motor?")
(diagram from "Esky Helicopters FAQ: Brushed vs Brushless Motors")
DC motor speed controllers -- with 2 output power connections -- work with brushed DC motors that have 2 power connections.
Brushless ESCs -- with 3 output power connections -- work with brushless motors that have 3 power connections.
As far as I can tell, any other connection between any two of a DC motor speed controller, a brushless ESC, a brushed DC motor, and a brushless motor, won't do anything useful.