When the string isn't under tension you have a non-linear system (i.e. you're pushing on a rope) which may also make this harder to control. The stiffness of your string is going to limit your bandwidth. (The string acts as a low-pass filter, at least when it's under tension). I've actually worked a little on a similar setup and it was really hard to control.

Since you're sampling the sampling theorem absolutely applies and you must sample at least x2 the highest frequency in your input (either by increasing the sample rate or filtering the input before sampling or both) otherwise you'll get aliasing.

As Kyle points out the other factor is your desired control bandwidth. I concur with the rule of thumb that the loop should run at least ~x10 that frequency.

Both these conditions need to be met.

There's a pretty good discussion of this here:

http://dissertations.ub.rug.nl/FILES/faculties/science/1995/m.d.van.der.laan/c6.pdf

Selection of sampling rates is an important issue. For economical reasons, sampling rates are kept as low as possible: A lower rate means that there is more time available for control algorithm execution, which can thereby be carried out on slower computers. Digitizing well behaved analog control systems can heavily affect system response. If sampling frequencies is too low, the systems may even become unstable. According to the Nyquist criterion, the sampling frequency should at least be twice as high as the bandwidth of the error signal. This bandwidth is bounded by the system bandwidth, hence ws 2wB. However, in order to guarantee satisfactory response, a factor of 10 to 20 may be required

When the string isn't under tension you have a non-linear system (i.e. you're pushing on a rope) which may also make this harder to control. The stiffness of your string is going to limit your bandwidth. (The string acts as a low-pass filter, at least when it's under tension). I've actually worked a little on a similar setup and it was really hard to control.

Since you're sampling the sampling theorem absolutely applies and you must sample at least x2 the highest frequency in your input (either by increasing the sample rate or filtering the input before sampling or both) otherwise you'll get aliasing.

As Kyle points out the other factor is your desired control bandwidth. I concur with the rule of thumb that the loop should run at least ~x10 that frequency.

Both these conditions need to be met.

There's a pretty good discussion of this in Chapter 6: Sampling in closed loop control systems of Marten Derk van der Laan's (1995) dissertation Signal sampling techniques for data acquisition in process control:

Selection of sampling rates is an important issue. For economical reasons, sampling rates are kept as low as possible: A lower rate means that there is more time available for control algorithm execution, which can thereby be carried out on slower computers. Digitizing well behaved analog control systems can heavily affect system response. If sampling frequencies is too low, the systems may even become unstable. According to the Nyquist criterion, the sampling frequency should at least be twice as high as the bandwidth of the error signal. This bandwidth is bounded by the system bandwidth, hence ws 2wB. However, in order to guarantee satisfactory response, a factor of 10 to 20 may be required