Question $1$:

$13$

$1\mathrm{.}1.$ List the different combinations of continuous controllers and explain why is there a need for this.

$1\mathrm{.}2$ A Pl controller is used to control the temperature in a continuous stirred tank heater $($CSTH$).$ The temperature in CSTH varies $20-220C.$ The control valve on the steam inlet goes from a fully open to a fully closed state whelithis signal varies from $100$KPa te $20.$ KPaA temperature variation of $+1-10C$ around the set point of $120C$ changes the pressure signal of the valve by $80$KPa. Upon error change by $+5C,$ the control valve got fully closed after $1$min. Calculate the reset rate and the proportional band. Assume that the valve was $50\%$ open, and the temperature was at the set point at the begining.