# 1.8: Industrial Process Models

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Industrial processes comprise procedures involving exchange of chemical, electrical or mechanical energy to aid in the manufacturing of industrial products. Industrial process models are mathematical models used to describe those processes.

An industrial process model, in its simplified form, can be represented by a first-order ODE accompanied by a dead-time, i.e., there is a finite time delay between the application of input and the appearance of the process output.

Let \(\tau\) represent the time constant associated with an industrial process, \(\tau _

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We note that the process model involves a transendental function, \(e^{-\tau _

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**Example 1.13:** An industrial process model

The process parameters of a stirred-tank bioreactor are given as: \(\{ K,\; \tau ,\; \tau _

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By using a first-order Pade’ approximation, a rational transfer function model of the industrial process with delay is obtained as: \(G(s)=\frac{20\left(1-0.5s\right)}{\left(0.5s+1\right)^{2} }\).

Further, a model of this kind is called non-minimum phase due to the extra phase added by the right-half-plane zero in the numerator (see Chapter 2 for details).