# Analog to digital controller- What sampling rate?

I'm studying about the design of controller in digital control systems. Right now I see the method in which I design my controller in the s domain and then convert it to the z domain.

However, in order to achieve specifications I must choose a suitable sampling period. Otherwise the transfer function in the z domain might have (for example) different poles from those I was going for.

What I do I know is that the bigger the sampling period T the greater the problem. Seeing some examples they choose a T which is 0.1-0.5 times the smallest time constant of the transfer function. In other examples of second order systems T is chosen so $$T<2π/(40ω_d)$$ where ω_d is the natural frequency.

So how should I choose my sampling period?

• Have you gone through the Bilinear Transformation?. – A_A Sep 21 '17 at 8:58
• I'm familiar with it but I'm only interested in the choice of the proper sampling rate here without using the bilinear transform. – John Katsantas Sep 21 '17 at 9:32
• How about using a $T$ that transforms $s$ to $z$ coefficients with a adequately small error between the produced impulse responses from the two models(?) – A_A Sep 21 '17 at 10:10
• This will do I suppose. The thing is I'm having an exam tomorrow without computers so I can't draw the impulse responses. I have to use a certain rule to get the T and I've come across these two ways in textbooks plus one that says that the sampling rate should be 10 times the bandwidth.It's just that every textbook uses a different way to choose a T and this doesn't happen often. I guess they are all correct but I got confused seeing different stuff. – John Katsantas Sep 21 '17 at 10:21