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,

where N is the number of data points.

Transcribed Image Text:

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