$(20$ pts$)$ PID Controller with an error function: We can use the PD controller for room temperature control. If the error function is

$f(x)=-x^2+6$

$Kp=2,K_D=0\mathrm{.}125$

Questions:

What is the error for the proportional controller at $t=2$

What action a PD controller should take at $t=2($hint: consider both P and D$)$

What if $K_p=2,K_D=0\mathrm{.}25,$ what action a PD controller should take at $t=2$

What if $K_p=2,K_D=0\mathrm{.}5,$ what action a PD controller should take at $t=2$