Flatness-based boundary control of a nonlinear parabolic equation modelling a tubular reactor

A nonlinear parabolic equation modelling an isothermal tubular reactor in one space dimension is considered. The control acts at the boundary of the inflow. It is shown that the system is "flat" with the outflow concentration playing the role of a flat output. Hence, the concentration field throughout the reactor and the control can be parametrized using an infinite series expansion depending on the flat output and its derivatives. This series is shown to have a non-zero radius of convergence provided the flat output trajectory is chosen as a Gevrey-function of class two. A simulation result illustrates the usefulness of the approach in achieving finite-time transitions between stationary concentration profiles.