Consider the furnace shown in the accompanying figure, which is used to heat the supply of air to a catalyst regenerator. Open-loop response data were obtained by making a step change in the output of the controller, from which the following approximate model was determined:

(a) Draw the block diagram of the feedback system, showing the transfer functions in each block, and specifying the units of each signal to or from each block. (b) Determine PI controller settings using: (i) the ITAE tuning relations for set-point response (ii) Direct Synthesis, with c = 25% of the open-loop time constant (iii) the Cohen and Coon relations (iv) Ciancone settings for set-point response (c) By inspection of the controller tuning constants, which approach gives the most conservative settings? Which give the least conservative? (i.e. the most overdamped or underdamped responses) (d) Enter your system into Simulink, and simulate the closed-loop response for a 10 F step change in furnace temperature set-point for each of the controller settings determined above. Do the results confirm your answers in (c)? (e) The process conditions have changed, resulting in an additional effective dead time of 1 min. Modify the process model in Simulink to reflect this change and repeat the simulations in (d), with the same controller settings used before. Which controller settings are the most and least robust (i.e. tolerant to changing process conditions)? Does this correlate with your answer in (c)?

4e~2s T(s) u(s) F % contoller output U 5S + 1 Stack gases Air Air ( TT 23 TC 23 () Fuel 4e~2s T(s) u(s) F % contoller output U 5S + 1 Stack gases Air Air ( TT 23 TC 23 () Fuel