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Chapter 20

Q. 20.10

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

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

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

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

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

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

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

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

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

Process transfer function matrix:

\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}\right]}


Verified Solution

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

c) C_{ O _{2}} Set-point change

The set-point responses in Figs. S20.10a and. S20.10b demonstrate that increasing the elements of the R 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 R matrix are increased to 0.5, the disturbance responses are even more sluggish.