Consider the PCM furnace module of Appendix E with the following variables (HC denotes hydrocarbon): CVs: HC exit temperature THC and oxygen exit concentration cO2 MVs: fuel gas flow rate FFG and air flow rate FA DV: HC flow rate FHC Do the following, using the transfer function models given below:

Question

Consider the PCM furnace module of Appendix [latex]E[/latex] with the following variables ( [latex]H C[/latex] denotes hydrocarbon):

CVs: HC exit temperature [latex]T_{H C}[/latex] and oxygen exit concentration [latex]c_{ O _{2}}[/latex]

MVs: fuel gas flow rate [latex]F_{F G}[/latex] and air flow rate [latex]F_{A}[/latex] DV: HC flow rate [latex]F_{H C}[/latex]

Do the following, using the transfer function models given below:

(a) Design an MPC system using the following design parameters: [latex]\Delta t=1 \min , Q =[/latex] diagonal [latex][0.1,1], R =[/latex] diagonal [latex][0.1,0.1][/latex], [latex]P=20[/latex], and [latex]M =1[/latex].

(b) Repeat part (a) for the same design parameters, but where [latex]R =[/latex] diagonal [latex][0.5,0.5][/latex].

(c) Simulate the two MPC controllers for a step change in the [latex]c_{ O _{2}}[/latex] set point to [latex]1.0143 mol / m ^{3}[/latex] at [latex]t=10 min[/latex].

(d) Repeat part (c) for a step change in [latex]F_{H C}[/latex] at [latex]t=10 min[/latex] to [latex]0.035 m ^{3} / min[/latex].

(e) Based on your results for parts (c) and (d), which MPC controller is superior? Justify your answer.

Process transfer function matrix:

[latex]\begin{matrix} T_{HC} \ C_{O_{2}}\end{matrix}\overset{\begin{matrix} F_{FG} & F_{A}\end{matrix} }{\left[\begin{array}{cc}\frac{220 e^{-2 s}}{6.5 s+1} & \frac{-13 e^{-2 s}}{6.2 s+1} \\frac{-2.0 e^{-4 s}}{3.8 s+1} & \frac{0.14 e^{-4 s}}{4.2 s+1}\end{array} ight]}[/latex]

Accepted Answer

Note: These results were generated using the PCM Furnace Module, MPC option

c) [latex]C_{ O _{2}}[/latex] Set-point change

The set-point responses in Figs. S20.10a and. S20.10b demonstrate that increasing the elements of the [latex]R[/latex] matrix makes the controller more conservative and results in more sluggish responses.

d) Step disturbance in hydrocarbon flow rate

The disturbance responses in Fig. S20.10b are sluggish after an initial oscillatory period, and the two MVs change very slowly. When the diagonal elements of the [latex]R[/latex] matrix are increased to [latex]0.5[/latex], the disturbance responses are even more sluggish.

Question 20.10: Consider the PCM furnace module of Appendix E with the follo...

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