Analyze the degrees of freedom.

Perform the following analysis for the stirred-tank heat exchanger under IMC feedback control. To simplify the analysis, assume a perfect model when determining the analytical solution and that Gj(s) = Gp(s). (a) Analyze the degrees of freedom. (b) Derive the linearized model for the process and controller. (c) Determine the analytical solution for the controlled variable for a step set point change. Assume that τf = τ. (d) Determine the analytical solution for the manipulated variable for a step set point change. Assume that τf = τ. (e) Recalculate the results in (c) and id) for Xf = £t, with ft = 0.5 and 0.1. Sketch the shape of the dynamic responses of the controlled and manipulated variables for these three values of tf. (f) Select the best value of Xf for the heat exchanger, not necessarily one of the values considered in previous parts of this question.


 

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