Consider the two-tank liquid-level system shown below with cross-sectional areas, A₁ and A2, respectively. The liquidenters tank 1 through a pipe with a volumetric flow rate of q. The liquid can flow between the two tanks through a valve oflinear resistance R₁. The liquid discharges to atmospheric pressure from tank 2 through a valve of resistance R₂. Assumeboth tanks are exposed to atmospheric pressure and the density p of the liquid is constant.Your tasks:9100A₁/hiR₁A2TheR₂C-A. Derive a differential equation model for the system behavior in terms of the liquid heights h₁ and h2.B. Determine the transfer function G(s) = H₂(s)/Q₁(s) for the system in terms of flow resistances R₁ and R₂, hydrauliccapacitance values C₁ and C2, and gravity, g. (1

To Find:A. The differential equation model for the system behavior in terms of the liquid heights and B. The second-order matrix form of the differential equation.Calculation:Mass balance for Tank 1:The rate of change of liquid in Tank 1 is given by the difference between the flow in and the flow out.The flow in is due to the pump, and the flow out is due to the valve connecting tank 1 to tank 2.Mass balance for Tank 2:The rate of change of liquid in tank 2 is given by the difference between the flow in from tank 1 and the flow out through the valve connected to tank 2Combine the equations to obtain the differential equation model for the system.Calculation:The system of differential equations can be expressed in matrix form: Here,X is the state vector.u is the input vector.A is the state matrix.B is the input matrix.Let be the state vector and be the input vector.The state matrix A and input matrix B can be extracted from the differential equations.Therefore, The second-order matrix is,This matrix form allows for a systematic analysis and control design for the liquid-level system.A. The differential equation model for the system behavior in terms of the liquid heights h1 and h2:B. The second-order matrix form of the differential equation: