I have a set of shafts that need to be rotated at a high frequency (~1000 RPM) but not at a constant speed. That is to say, the angular velocity of the shaft needs to be a periodic function of the shaft's angular position.
This bizarre predicament has arisen in the context of operating an unsteady, transonic wind tunnel. We have a set of vanes whose angular positions determine the Mach number of the flow through the tunnel's test section. For the research we hope to conduct, the test section Mach number will have to oscillate in a specific pattern as a function of time. Technically, there are several ways we could modify the tunnel's design to accomplish this. We are looking into all of them, but in theory, having a motor whose angular velocity is precisely controlled as a function of its angular position would be the most ideal solution to our problem.
I'm no expert in electrical engineering. I understand that some motors, like servomotors, are made to rotate at any desired speed within their operating range, and that their speed can be precisely controlled by a closed-loop feedback system. Does this mean that I might be able to program a servomotor to rotate in such a way that its angular velocity is constantly changing as it rotates, even at average rotation speeds of up to 1000 RPM?
If so, what type of equipment might I need to do this? Is this what a Variable-Frequency Drive (VDF) is for?
If a servomotor is not appropriate for this task, what type of motor might I need?