Many chemical processes can be modeled as first-order systems. The differential equation for a linear first-order process is often written in the following form:

Equation 3.25

This can also be written as

where the parameters (τ_{p} and k_{p}) and variables (y and u) have the following names: τ_{p} is the process time constant (units of time), k_{p} the process gain (units of output/input), y the output variable, and u the input variable. Taking the Laplace transform of each term (notice that we are now using lower-case variables to ...

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