Efficient reduced order controller design for dissipative PDE systems with strong convective phenomena

The control of dissipative distributed parameter systems with strong convective phenomena is considered, employing model order reduction. The accuracy of the derived reduced order model (ROM) and the associated observer may decrease as the system behavior switches from diffusion-dominant to convection-dominant. To mitigate the issue, we propose to use adaptive proper orthogonal decomposition (APOD) to capture the changing behavior of the system. A Lyapunov controller is designed based on the ROM to control the system in the presence of disturbance and strong convective phenomena. Galerkin method is used to construct the ROM. The basis functions needed in Galerkin method are updated using APOD. A case study of regulating a tubular reactor at an open-loop unstable steady state is presented, where the performance of the ROM-based observer is evaluated. It's also demonstrated that APOD can improve the accuracy of the observer when an unexpected disturbance occurs.