For the CSTR case study, we consider the well studied nonlinear benchmark problem
of the Van der Vusse scheme [Chen et al.(1995)Chen, Kremling, and Allgöwer,Engell and Klatt(1993)]. This model represents a
first-order reaction for
with two competing reactions
and
.
All reaction models use temperature
dependent Arrhenius reaction rates. The model has four states: concentration
of A, concentration of B, reactor temperature, and cooling jacket temperature.
With this process, it is desirable to maximize the concentration of product
B. This system exhibits many highly nonlinear characteristics which include:
input multiplicity, gain sign change, asymmetric response, and transformation
from minimum to nonminimum phase behavior. These nonlinear characteristics
are most prevalent at the optimal operating point. See Figure 4
for a comparison of dynamic response to a step change in the feed flow rate.
From this figure, one can see that inverse response is observed for changing
to a low flow rate and not observed at higher flow rates. As seen from the
process values at steady-state, the process gain changes from positive to negative,
causing input multiplicity. The optimal operating point is at the convergence
of changing steady-state gains and inverse to non-inverse dynamic response.
The process model equations, parameters, and operating conditions may be found in Appendix A. All simulation results were performed using MATLAB 5.3.
