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Process Control: Modeling, Design, and Simulation by B. Wayne Bequette

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2.7. Linear Models and Deviation Variables

Consider the stirred-tank heater model (Example 2.3), when the volume, flow rate, and inlet temperature are constant at their steady-state values (indicated by the subscript s):

Equation 2.70

Deviation Variable Formulation

Control engineers like to think in terms of “deviation variables,” that is, perturbations from a steady-state operating condition. The reader should show that if we define the following deviation variables

Equation 2.71

then Equation (2.70) can be written in the form

Equation 2.72

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