Department of Chemical Engineering

University of California, Santa Barbara

 

 

 

Ch.E 152A                                                                                      Due:  October 29, 2008

 

 

Home Problem 4:

 Empirical Models of the Purdue Furnace

(60 points)

 

 

Note: In order to receive credit for this home problem, each of your MATLAB plots must include your name in the title and your MATLAB code for Question 2 must be included.

 

1.      (20 points) Develop first-order-plus-time-delay (FOPTD) transfer function models from your simulated furnace response data that you obtained from the PCM Furnace Module Tutorial. 

Do the following:

a.       Include labeled plots of the simulated data for the three process variables of interest: air flow rate, qA; hydrocarbon exit temperature, T; and the O2 exit concentration, cO2. 

b.      Develop FOPTD models that relate output variable, T, to the input variable, qA. Use one of the methods described in Chapter 7 of the SEM textbook. Determine an individual transfer function model for each of the three qA step changes.

c.       Summarize your calculated model parameters in a table. Also, briefly describe the method that you used to calculate the model parameters.

d.      Plot the responses for furnace temperature, T, and the transfer function model response, Tmod, for the qA step changes used in  the Tutorial.

 

2.      (20 points) Develop a second-order discrete-time model of the form, 

from your simulated furnace response data that you obtained from the PCM Furnace Module Tutorial. Use MATLAB and a least squares approach.


Do the following:

a.       Convert your simulated T and qA data to deviation form by using the initial values as the nominal values.  Then form the X matrix and Y vector, as per Section 7.5 of the textbook (pages 176-177). 

b.      Calculate the least squares estimate of parameter vector, b,. Using the MATLAB command,

B =REGRESS (Y,X) 

c.       Calculate the 95% confidence intervals for the parameter estimates using the MATLAB command,

[B,BINT] = REGRESS(Y,X)

d.      Graphically compare the actual temperature response, T, and the discrete-time model response, Tdm, for the qA input data from the Tutorial.

e.       In your memo (Question 3), report your parameter estimates and their confidence intervals. Include your MATLAB code in an appendix. (Your name should appear as a comment in the first line of the code.)

 

1.      (20 points) Prepare a memo summarizing and analyzing your modeling results. In particular, answer the following questions and justify your answers:

a.       Does the furnace behavior appear to be approximately linear or nonlinear over the simulated range of conditions? (Hint: compare the transfer function models obtained for the three qA step changes.)

b.      Are the response times for T and cO2 approximately the same?

c.       Are the model parameters of the discrete-time model reasonably accurate?

d.      Which type of dynamic model is more accurate, the transfer function models or the discrete-time model?