Adaptive fault estimation and accommodation for distributed parameter systems with coupled parabolic partial differential equations

This paper presents a novel model-based approach for fault detection, estimation and accommodation in linear distributed parameter systems (DPS) governed by parabolic partial differential equations (PDEs), prone to sensor and actuator faults. Unlike traditional methods, our approach utilises a filter-based observer directly employing the PDE representation and relies solely on boundary measurements, eliminating the need for extensive sensor arrays. By generating fault detection residuals from a comparison of measured and observer outputs, our method offers efficient fault detection. Innovative parameter update laws facilitate accurate estimation of fault parameters, enabling precise adjustment of the nominal controller to mitigate fault effects. Rigorous Lyapunov analysis ensures the robustness of our approach. Additionally, we derive a formula for estimating time-to-accommodation (TTA), providing valuable insights into fault resolution timelines. Simulations on a linearised diffusion process validate the effectiveness of our scheme, highlighting its superiority over existing approaches.