Let us consider the problem of controlling the temperature T of a liquid in a tank when the inlet temperature Ti changes. Assume that the inlet and outlet flow rates are equal. Our measurement will be the liquid temperature and the manipulated variable the rate of heat input Q$,$ provided by steam. How does the Q change in order to keep temperature constant? Develop the control law for $($i$)$ proportional control $($ii$)$ integral control and $($iii$)$ proportional$-$integral control.