The continuous$-$time PID controller is given by: y$($t$)=$Kpu$($t$)+$Ki

Z t du$($t$)$

u$($$)$d$+$Kd dt $.$

$1.$ Analyze the causality of this controller. If it is non$-$causal, explain how to make it causal.

$0$

Using the backward difference for differentiation and backward rectangular integration for the integral, derive a discrete$-$time version y$[$kT$]$ of the controller.

Evaluate causality of the discrete$-$time version. Now comment on causality of the new system. If the causality has been changed, comment on what is the reason.