1. Exercise (Deriving the Transfer function of Nonlinear System) A nonlinear liquid-level system, such as the one shown in the figure 1, has a cross-sectional area of 3.0 m. The valve characteristic is qo(h) = 33h Where q = flow rate, m3/min and h = level above the valve, m. If the average level is 9m, at time zero, the inlet flow is suddenly increased by 2m3/min.the general dynamical differential Equation of the level controlled storage system is as follows: Aan het) = 9:(t) qolt) 44 R 40 Figure 1: A nonlinear liquid-level system (a) (1 point) Find the transfer function H(s)/Qi(s). (b) (0.5 points) Calculate the level h(t = 2) after two minutes of the change? (c) (0.5 points) What is the ultimate final value, new steady-state,h(t = 0), of the level of the liquid in the tank