ReactorTF_abg.tex

MTT command:

mtt ReactorTF abg tex

Figure 2.1: System ReactorTF: acausal bond graph

Figure 2.2: System ReactorTF, Schematic

Figure 2.2 (on page ) is the schematic diagram of a chemical reactor.

The acausal bond graph of system ReactorTF is displayed in Figure 2.1 (on page ) and its label file is listed in Section 2.1.1 (on page ). The subsystems are listed in Section 2.1.2 (on page ).

This example of a (nonlinear) chemical reactor is due to Trickett and Bogle^2.1 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.

The control loop $t$/ has been inverted. The resulting SISO system has two interpretations:

1. the dynamics of the $c_b$/$q$ loop when the $t$/ loop is under perfect control and
2. the inverse dynamics of the $t$/ loop.

Figure 2.3: SystemReactorTF: zero 1 v flow

Figure 2.4: SystemReactorTF: zero 2 v flow

Figures 2.3 (on page ) and 2.4 (on page ) shows the poles of the linearised system as the steady-state flow varies: these are the zeros of the $t$/ control-loop when the $c_b$/$q$ loop is open.