Integral action for setpoint regulation control of a reaction–diffusion equation in the presence of a state delay

Hugo Lhachemi (1, 2) , Ammar Malik (3) , Robert Shorten (4)

1 L2S - Laboratoire des signaux et systèmes
2 CentraleSupélec
3 UCD - University College Dublin [Dublin]
4 Imperial College London

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.

Mots clés: PI regulation; Reaction–diffusion equation; State-delay; Partial differential equation; Input-to-state stability

Domaines: Optimisation et contrôle [math.OC]; Automatique / Robotique

Hugo Lhachemi, Ammar Malik, Robert Shorten. Integral action for setpoint regulation control of a reaction–diffusion equation in the presence of a state delay. Automatica, 2021, 134, pp.109935. ⟨10.1016/j.automatica.2021.109935⟩. ⟨hal-03377110⟩