Reactor_abg.tex

MTT command:

mtt Reactor abg tex

Figure 1.1: System Reactor: acausal bond graph

Figure 1.2: System Reactor, Schematic

Figure 1.2 (on page ) is the schematic diagram od a chemical reactor. The acausal bond graph of system Reactor is displayed in Figure 1.1 (on page ) and its label file is listed in Section 1.1.1 (on page ). The subsystems are listed in Section 1.1.2 (on page ).

This example of a (nonlinear) chemical reactor is due to Trickett and Bogle^1.1 is used in this section. The reactor has two reaction mechanisms: A$\rightarrow$   B$\rightarrow$   C and 2A$\rightarrow$   D. The reactor mass inflow and outflow $f_r$ are identical. $q$ represents the heat inflow to the reactor.

This is a two input, two-output unstable nonlinear system with unstable zero dynamics. The following figures illustrate the properties of the linearised system.

Figure 1.3: System Reactor: poles 1 and 2 v. steady-state flow $f_s$

Figure 1.4: System Reactor: pole 3 v. steady-state flow $f_s$

Figure 1.5: System Reactor: zero of system with $t$ and $c_a$ as output v. steady-state flow $f_s$

Figure 1.6: System Reactor: pole 3 v. steady-state flow $f_s$

• Figures 1.3 (on page ) and 1.4 (on page ) show the three poles of the linearised system as the steady-state flow varies.
• Figure 1.5 (on page ) shows the system zero (when $t$ and $c_a$ are the two system outputs) as the linearised system as the steady-state flow varies.
• Figure 1.6 (on page ) shows the system zero (when $t$ and $c_b$ are the two system outputs) as the linearised system as the steady-state flow varies.