This research addresses the regulator problem in a boundary control system that is generated by Sturm-Liouville dynamics. The primary purpose is to ensure the tracking of a desired reference trajectory while compensating for disturbances originating from a distributed parameter exosystem. At the start, a stabilizing state feedback regulator is constructed by employing a series representation based on the eigenvectors of the Sturm-Liouville generator, guiding the system output to align with the reference trajectory. Following this, a dynamic error-feedback regulator is formulated, utilizing the tracking error as the control input. In addition, the closed-loop system achieves exponential stability, with the tracking error converging to zero over time.

This work focuses on the design of a boundary output feedback regulator for a catalytic cracking reactor model which can be represented by a set of partial differential equations (PDEs). Based on the linear abstract state-space infinite-dimensional version of the PDEs model and the fact that the system generator is a Riesz spectral operator, a stabilizing compensator is developed by using the spectral properties of the system. Simulations are conducted to test the achievement of the developed algorithm.