The following open-loop continuous-time transfer function represents a second-order system that is to be controlled using a digital computer with \(\mathrm{ZOH}\) :

\[G(s)=\frac{1}{(s+1)(s+10)}\]

Choose a suitable sampling interval \(T\) and design a digital PID controller that ensures that the settling time \(t_{s} \leq 1\) sec, damping ratio \(\xi \geq 0.5\) and there is zero steady-state error to a step input.