Question #4 (30 marks) The diagram below is from a Department of Energy underground storage tank. Suchs are used throughout the United States for storing gasoline for sale to the public. Recently, engineers believe that a leak has developed and can threatens the environement. Your supervisor has assigned you the task of moedeling the height in the tank as a function of the supply flow Fi(t), the sales flow F2(t) and the unmeasured flow Fs(t). It is assumed that the lead is proportional to the height of the liquid in the tank, simply Fs(t)=h(t) and is a constant. The tank is a cylinder of constant cross-section area A and the gasoline density is 0.78g/cm. a) Determine dynamic model b) Any linearization required? Justify your answer (10 marks) (4 marks) c) Find the transfer function of the storage tank relating the liquid level to the supply flow Fi (s) and the sales flow F2(s); where Fi(s)and F2(s) are Laplace transforms of Fi(t) and F2 (t), respectively. (10 marks) d) Which of the input variables, would you select as a control variable and which ones as disturbance variables. (6 marks) F1 A h 1 1 1 Fa F Note: in Fs(t) is a constant. All variables Fi(t), F2 (t), and Fs(t) are time dependent.