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 |