Integral action for setpoint regulation control of a reaction–diffusion equation in the presence of a state delay. (December 2021)

• Record Type: Journal Article
• Authors: Lhachemi, Hugo; Malik, Ammar; Shorten, Robert
• Is Part Of: Automatica. Volume 134(2021)
• Publication Date: 2021-12
• Subjects: PI regulation -- Reaction–diffusion equation -- State-delay -- Partial differential equation -- Input-to-state stability; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2021.109935
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: This paper is concerned with the regulation control of a one-dimensional reaction–diffusion equation in the presence of a state-delay in the reaction term. The objective is to achieve the PI regulation of the right Dirichlet trace with a command selected as the left Dirichlet trace. The control design strategy consists of the design of a PI controller on a finite dimensional truncated model obtained by spectral reduction. By an adequate selection of the number of modes of the original infinite-dimensional system, we show that the proposed control design procedure achieves both the exponential stabilization of the original infinite-dimensional system as well as the setpoint regulation of the right Dirichlet trace.