Advanced control of non‐isothermal axial dispersion tubular reactors with recycle‐induced state delay

Abstract We develop a delay‐aware estimation and control framework for a non‐isothermal axial dispersion tubular reactor modelled as a coupled parabolic‐hyperbolic PDE system with recycle‐induced state delay. The infinite‐dimensional dynamics are preserved without spatial discretization by representing the delay as a transport PDE and adopting a late‐lumping approach. Closed‐form resolvent operators for the generator and its adjoint are derived, enabling Cayley–Tustin time discretization that maintains key system properties such as stability. The resulting discrete‐time representation is used to design a model predictive controller (MPC) with terminal equality constraints that guarantee closed‐loop stability under input constraints. Concurrently, a moving horizon estimator (MHE) is constructed for output‐based state reconstruction, exploiting inner‐product formulations in the lifted Hilbert space. Estimation and control are integrated via a modular architecture that maintains functional separation while enabling consistent state feedback. Numerical simulations demonstrate that the full‐state MPC successfully stabilizes the unstable reactor under input constraints, while the integrated MHE‐MPC framework enables output‐based feedback control by reconstructing distributed states from noisy measurements, maintaining constraint satisfaction and overall closed‐loop performance.