Example: Water-Tank System
Water-Tank System
This section introduces an example that continues throughout
the remaining sections of this chapter. By following this example,
you will learn the process of linearizing a model using Simulink Control Design functions.
Water enters a tank from the top and leaves through an orifice
in its base. The rate that water enters is proportional to the voltage, V,
applied to the pump. The rate that water leaves is proportional to
the square root of the height of water in the tank.
Schematic Diagram for the Water-Tank System
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Model Equations
A differential equation for the height of water in the tank, H,
is given by
where Vol is the volume of water in the
tank, A is the cross-sectional area of the tank, b is
a constant related to the flow rate into the tank, and a is
a constant related to the flow rate out of the tank. The equation
describes the height of water, H, as a function
of time, due to the difference between flow rates into and out of
the tank.
The equation contains one state, H, one
input, V, and one output, H.
It is nonlinear due to its dependence on the square-root of H.
Linearizing the model simplifies the analysis of this model. For information
on the linearization process, see Exact Linearization Using the GUI.
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