Consider the PCM furnace module of Appendix E. Assume that hydrocarbon temperature T_HCis the CV, that fuel gas flow rate F_FGis the MV, and that they are related by the following transfer function model:

(a) Design a PID controller based on the IMC tuning relations and a reasonable choice for Ï„_c.

(b) Design a PID controller based on the relay auto-tuning feature of the PCM, and the Z-N settings.
(c) Simulate each controller for a sudden change in an unmeasured disturbance, the hydrocarbon flow rate F_HC, at t = 10 min, from 0.035 to 0.040 m 3 /min. Which controller is superior?
(d) Attempt to obtain improved control system performance by fine tuning your better controller for part (c). For the performance criteria, consider maximum deviation from set point and settling time.

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= 1 220e-25 6.5s +1' G, = Gm THC G,: F FG