Parameter‐dependent observer‐based feedback compensator design of a space‐time‐varying PDE with application to a class of steelmaking processes

Abstract

AbstractThis article deals with the problem of observer‐based feedback compensator design for a linear reaction–advection–diffusion equation subject to a time‐varying diffusion coefficient, a time‐varying advection coefficient, and a space‐time‐varying reaction coefficient. To solve such a problem, these coefficients are written in parametric forms under their boundedness assumptions. By considering these parametric forms of the coefficients and the distribution functions for control actuation and non‐collocated measurement, a parameter‐dependent observer‐based feedback compensator is constructed such that the resulting closed‐loop coupled equation exponentially converges to a bounded set of the equilibrium profile in the spatial norm. With the aid of the Lyapunov technique and variants of Poincaré–Wirtinger's inequality, a sufficient condition for the existence of such feedback compensator is presented in the form of convex constraints. Finally, extensive simulation results for a numerical example and a class of steelmaking processes are presented to support the proposed design method. For the collocated measurement case, both theoretical and simulation results show that the proposed observer‐based feedback compensator can provide a better control performance than the static feedback compensator in the presence of measurement disturbances.