Develop first-order-plus-time-delay (FOPTD) transfer function models from simulated distillation column response data obtained from the PCM Distillation Column Module Tutorial.
Do the following:

1. Prepare labeled plots of the simulated data for the overhead composition for step changes in reflux ratio and vapor flow rate (boilup). Use three values of the magnitude of the step change for each input (change only one input at a time). For vapor rate, use +5%, +10%, +15%. For reflux ratios, use +10%, +20%, +30%.
2. Develop FOPTD models that relate bottom composition, y, to the input variable, u. Use one of the methods described in Chapter 7. Determine an individual transfer function model for each of the three step changes.
3. Summarize the calculated model parameters in a table. Also, briefly describe the method that you used to calculate the model parameters.
4. Plot the responses for composition y, and the transfer function model response, ymod, for the step changes used in the Tutorial

After analyzing the modeling results, answer the following questions and justify your answers:

1. Does the column behavior appear to be approximately linear or nonlinear over the simulated range of conditions? (Hint: compare the transfer function models obtained for the three step changes).
2. Are the response times for the two inputs approximately the same?