As fast as your processor can handle?

If you use discrete time design, as  long as you have the precise model, sample rate can be just twice the reciprocal of the time constant.  If you use a continuous time design and then discretise the controller, then the sample rate should be around 20 times the reciprocal of the time constant.  

A given control-loop should be faster than the corresponding open-loop system, otherwise no point having that controller. You can use direct synthesis approach to design a controller (could be PID) where the closed-loop time constant can be specified a faction of the open-loop one. For more recent approach, try using the multi-scale control scheme, which allows one to adjust desired closed-loop speed relative to the open-loop one.

You should specify control quality requirements firstly. If you want to estimate the order of sampling time only, and if you apply a discrete time controller you should set the sample rate at least 20..100  times lower the time constant. So, in your application this will give quite nice value around several tenths of microseconds. You must also be aware if your actuating system has appropriate bandwidth.

Zigang Pan Prof. Pan, I have a question almost idential to the OP's. I have a discrete control system with known dead time and negligible process time constant. In order to obtain a stable control, how should I determine my sampling interval? I came across the websites and saw numbers like 10, 20, or even 100 times smaller than the dead time. Is there a theory giving these results? Thanks a lot.

Mr Dai, if you have a discrete-time control system, then there is no need to choose sampling interval. Just get the model of the control system and design a discrete time controller for the system.

ZP

Zigang Pan Prof. Pan, there is a limit for the sampling rate in my controller, so I need to know if the sampling rate is enough for the stability of the control system.