Example 1 – Transfer Function of a liquid-level system

We take into account the liquid-level system of Figure 3-23.

In accordance with the definitions of the previous article (Dinámica de un sistema de nivel de líquidos), we focus on the capacitances C1 and C2, as well as on the resistors R1 and R2. Thus, the dynamics of this system is determined by the following equations:

From here we can obtain the transfer function depending on what variables we define as input and output. For example, suppose the input to the system is q and the output variable is q2, so to find the transfer function of the system we execute the following operations:

So:

That is to say:

In the other hand:

That is:

Also: 

Applying Laplace to equations a, b and c, we obtain:

Clearing H1(s) of e and substituting this value in d we obtain:

An due to f  the latter is:

The transfer function of the system is:

 

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