A Raspberry Pi should be sufficient for the control you intend to do with it.
In designing a controller under a full multitasking operating system, like the Linux operating systems that are available for the Raspberry Pi, you have to be careful about the real-time requirements, and if the time share chunk of processor made available to your software will be enough to keep up with the rt nature of cyber-physical interactions.
In small words: if you don't run much beyond the controller code in the RPi, it should suffice, but if you want to have other pieces of code running, like some higher level supervisory control or even a Java virtual machine for some reason, you will have to assess the response time, and even take the risk of some runaway thread end up blocking your controller for some time.
The solution for that, and if you take it you will most likely have no headaches in the process, is to have non-preemptive multi-tasking OS, or, even better, a Real Time OS running on the Raspberry Pi.
And you can have both (not at the same time, of course!). Raspberry Pi has support for the RISC OS Operating System, which employs cooperative multitasking, where you can give absolute priority for the control loop, and only run other pieces of code once the control loop is done for the cycle.
And, my personal best, you have Xenomai running on it. Xenomai is a hard real-time supervisor that has Linux running under it, so you can have a full deploy of a Linux machine, with all the benefits of having all the pre-packaged software and other amenities, and you also have a Real Time layer where you can run your control loop without any risks of getting interrupted out of time. You can find instructions on how to have Xenomai installed on the RPi here. There used to be a ready SD image of it available, but it seems to have gone offline at this time.
EDIT: A ready to install SD image of Xenomai for the Raspberry Pi can be downloaded from this link.