The Simulink® model `watertank` includes the nonlinear Water-Tank System plant and a PI controller in a single-loop feedback system.

The Water-Tank System is shown in the following figure.

Water enters the tank from the top at a rate proportional to the voltage, V, applied to the pump. The water leaves through an opening in the tank base at a rate that is proportional to the square root of the water height, H, in the tank. The presence of the square root in the water flow rate results in a nonlinear plant.

The following table describes the variables, parameters, differential equations, states, inputs, and outputs of the Water-Tank System.

 Variables H is the height of water in the tank.Vol is the volume of water in the tank.V is the voltage applied to the pump. Parameters A is the cross-sectional area of the tank.b is a constant related to the flow rate into the tank.a is a constant related to the flow rate out of the tank. Differential equation `$\frac{d}{dt}Vol=A\frac{dH}{dt}=bV-a\sqrt{H}$` States H Inputs V Outputs H