Q1 Consider a liquid level system consisting of two interacting cylindrical tanks of areas of cross-section A1 and A2 respectively shown Figure Q1. The input flow rate to the system is qin(t), the flow rate from tank 1 to tank 2 is qi(t), and the output flow rate from the system is qout(t). The flow rates are given by the following equations: ain(t) hRef (t) R 91(t) h₁(t) R gout (t) h₂(t) = R R is the valve restriction coefficient and it is same for all valves used in the system. Area of cross-section of tank 1, A₁ is such that time constant RA₁ is 2 sec. Area of cross-section of tank 2 is such that time constant RA2 is 4 sec. hRef(t) is the desired height of liquid and it is 1 m for t≥0. (a) Write down the governing differential equation for each tank. (b) Determine the overall transfer function (s) of the system. (2 marks) (10 marks) HRef(s) (c) What is the order of the system? If it is second order, prove that the system is over- damped. (3 marks) R water hi(t) Area, A Tank 1 R 91 Area, 4; water h2(f) Yout Tank 2 Figure Q1