Question: Consider the PCM furnace module of Appendix E. Assume that hydrocarbon temperature T HC is the output variable and that air flow rate F A

Consider the PCM furnace module of Appendix E. Assume that hydrocarbon temperature T_HCis the output variable and that air flow rate F_Ais the input variable.

(a) Develop an FOPTD model from response data for a step change in F_A at t = 10 min from 17.9 to 20.0 m³/min. Summarize your calculated model parameters in a table and briefly describe the method used to calculate them.

(b) Repeat (a) for an SOPTD model.
(c) Plot the actual T_HC response and the two model responses for the F_A step change of part (a).

(d) Are the two models reasonably accurate? Which model is superior? Justify your answer by considering the least squares index for the prediction errors,

S = E Ly(k) – §(k)I [y(k) – ŷ(k)I² k=1

where N is the number of data points.

S = E Ly(k) (k)I [y(k) (k)I k=1

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