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?