Consider the PCM furnace module of Appendix E. Assume that

Chapter 12, Problem 12.17

(choose chapter or problem)

Consider the PCM furnace module of Appendix E. Assume that hydrocarbon temperature \(T_{H C}\) is the \(\mathrm{CV}\), that fuel gas flow rate \(F_{F G}\) is the \(\text { MV }\), and that they are related by the following transfer function model:

\(\frac{T_{H C}}{F_{F G}}=G_{p}=\frac{220 e^{-2 s}}{6.5 s+1}, \quad G_{v}=G_{m}=1\)

(a) Design a PID controller based on the IMC tuning relations and a reasonable choice for \(\tau_{C}\)

(b) Design a PID controller based on the relay auto-tuning feature of the PCM, and the Ziegler-Nichols settings.

(c) Simulate each controller for a sudden change in an unmeasured disturbance, the hydrocarbon flow rate \(F_{H C}\) at \(t = 10\) min, from \(0.035\) to \(0.040\) \(m^3/min\). Which controller is superior? Justify your answer.

(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.