Optimal control of axial dispersion tubular reactors with recycle: Addressing state‐delay through transport <scp>PDEs</scp>

Abstract The optimal control of an axial tubular reactor with a recycle stream is addressed as a key type of setting for distributed parameter systems in chemical engineering. The intrinsic time delay from the recycle process, thus far overlooked in relevant literature, is modelled as a transport partial differential equation (PDE), resulting in a system of coupled parabolic and hyperbolic PDEs. Utilizing Danckwerts boundary conditions, the reactor is boundary‐controlled with the control input at the inlet. A continuous‐time optimal linear quadratic regulator is developed to stabilize the infinite‐dimensional system, employing a late lumping approach in order to preserve the properties of the original infinite dimensional system in controller design. The full‐state feedback regulator is designed by solving the Operator Riccati Equation (ORE), leveraging the system's Riesz‐spectral properties. To address practical limitations of full‐state feedback, a Luenberger observer is also proposed, enabling state reconstruction from boundary measurements. Numerical simulations are conducted to evaluate the proposed control strategies. The results demonstrate that the full‐state feedback regulator effectively stabilizes the system. A comparison is made between two configurations where different numbers of eigenmodes were selected to design the controller. The observer‐based regulator also stabilizes the system successfully using merely output measurements, effectively overcoming the challenge of limited state access.