Boundary model predictive control of thin film thickness modelled by the Kuramoto–Sivashinsky equation with input and state constraints

Abstract

In this work, a model modal predictive control (MMPC) strategy is proposed to stabilize the falling liquid film thickness in the vertical tubes modelled by the Kuramoto–Sivashinsky (K–S) equation in the presence of naturally present state and input constraints. The novel features of proposed synthesis is the development of an infinite dimensional PDE state representation which incorporates the exact transformation of boundary into the distributed control setting and benefits arising from the property of decoupled boundary applied input actuation and K–S PDE modal states. Furthermore, the dissipative structure of the K–S spectral operator provides the foundation for the model modal based predictive controller (MMPC) synthesis which utilizes the finite dimensional state representation to formulate the quadratic objective function while the infinite dimensional K–S PDE state constraints are appropriately defined and cast in the form of a constrained quadratic programme. Finally, we demonstrate that if feasible, the MMPC achieves stabilization of the thin film thickness and satisfies naturally present state and input constraints. Numerical simulation of the boundary applied actuation evaluates the proposed method's performance.