Robust Tracking for the diffusion equation using sliding-mode boundary control

Diego Gutierrez-Oribio (1, 2) , Yury Orlov (3) , Ioannis Stefanou (1, 2) , Franck Plestan (4, 2)

1 GeM - Institut de Recherche en Génie Civil et Mécanique
2 Nantes Univ - ECN - NANTES UNIVERSITÉ - École Centrale de Nantes
3 CICESE - Centro de Investigacion Cientifica y de Education Superior de Ensenada [Mexico]
4 LS2N - Laboratoire des Sciences du Numérique de Nantes

Robust output tracking is addressed in this paper for a diffusion equation with Neumann boundary conditions and anti-collocated boundary input and output. The desired reference tracking is solved using the well-known flatness and Lyapunov approaches. The reference profile is obtained by solving the motion planning problem for the nominal plant. To robustify the closed-loop system in the presence of the disturbances and uncertainties, it is then augmented with PI feedback plus a discontinuous component responsible for rejecting matched disturbances with a priori known magnitude bounds. Such control law only requires the information of the system at the same boundary as the control input is located. The resulting dynamic controller globally exponentially stabilizes the error dynamics while also attenuating the influence of Lipschitz-intime external disturbances and parameter uncertainties. The proposed controller relies on a discontinuous term that however passes through an integrator, thereby minimizing the chattering effect in the plant dynamics. The performance of the closedloop system, thus designed, is illustrated in simulations under different kinds of reference trajectories in the presence of external disturbances and parameter uncertainties.

Domaines: Optimisation et contrôle [math.OC]

Diego Gutierrez-Oribio, Yury Orlov, Ioannis Stefanou, Franck Plestan. Robust Tracking for the diffusion equation using sliding-mode boundary control. 61st IEEE Conference on Decision and Control, Dec 2022, Cancum, Mexico. ⟨hal-03774397⟩