Spatio‐Temporal Residual Extended State Observer‐Based Control for Complex Distributed Parameter Systems

ABSTRACT It is difficult to control the complex distributed parameter system (DPS) for uniform spatial performance. In this paper, a spatio‐temporal residual extended state observer‐based control method is proposed for the DPS with both nonlinearities and unknown exogenous disturbances to achieve uniform performance throughout the entire workspace. The proposed control method encompasses four crucial components: An auxiliary DPS, a spatial mapping filter (SMF), a spatio‐temporal residual extended state observer (S‐T‐R‐ESO), and a disturbance feedback controller. Based on the auxiliary DPS and the SMF, feedback information is supplied to the S‐T‐R‐ESO. Subsequently, the observer is capable of estimating the distributed “overall disturbance” (the undesired dynamics), which includes both nonlinearities and exogenous disturbances. Thereafter, based on the estimation of the “overall disturbance”, a feedback controller is implemented to suppress disturbances, enabling the state variables of the controlled plant to achieve spatially uniform stability. It is worth noting that both the proposed observer and the observer‐based controller are proven to converge based on the input‐state stability analysis method. The feasibility and effectiveness of the proposed control method are validated through the temperature control of a catalytic rod, which serves as a benchmark in chemical reactors.