1) A liquid-level control system has a process model that is given by: 30 dh (t ) dt = q; (t)- q(t) where h(t) is actual liquid level [in], qi(t) is actual inlet flow rate [gpm], and q(t) is actual outlet flow rate. Additional information: Sensor-transmitter: fast acting with gain 0.5 [V/in] Controller: proportional, with Kc = 10 [V/V] setpoint Valve: fast acting with gain 2.5 [gpm/V] qi(t) Transducer: none, controller output units and valve input units are the same. LT LC a) Derive equation H(s) = f(Qi(s), Q(s)) V b) Draw a block diagram of the control system. h(t) c) Determine H(t) for a unit step change in setpoint. Is this result expected? Why or why not? XD q(t) d) Repeat parts b and c for the case where Kc = -10 [V/V]. Discuss result. L(s) 3