TY - GEN
T1 - Boundary stabilization of a reaction-diffusion system weakly coupled at the boundary
AU - Ghattassi, Mohamed
AU - Laleg-Kirati, Taous-Meriem
N1 - KAUST Repository Item: Exported on 2021-09-02
PY - 2020
Y1 - 2020
N2 - This study analyses the boundary stabilization of a system of two parabolic linear PDEs weakly coupled at the boundary. This model is motivated by heat transfer in a membrane distillation based desalination modeled by a two-dimensional advection diffusion equations coupled at the boundary. Based on some physical assumptions, the 2D model can be formulated as a 1D reaction-diffusion system. Two cases were studied: full and under actuated scenarios. In the full actuated case, a backstepping approach is used to map the plant to an exponentially stable target system. The well-posedness of the kernel equations is proved. Moreover, the actuation of only one of the parabolic equations has been considered. The standard backstepping transformations is again used to transform the initial plant to a desired target system where Lyapunov analysis is adequately used. Finally, a numerical example showing the performance of the proposed control design is presented.
AB - This study analyses the boundary stabilization of a system of two parabolic linear PDEs weakly coupled at the boundary. This model is motivated by heat transfer in a membrane distillation based desalination modeled by a two-dimensional advection diffusion equations coupled at the boundary. Based on some physical assumptions, the 2D model can be formulated as a 1D reaction-diffusion system. Two cases were studied: full and under actuated scenarios. In the full actuated case, a backstepping approach is used to map the plant to an exponentially stable target system. The well-posedness of the kernel equations is proved. Moreover, the actuation of only one of the parabolic equations has been considered. The standard backstepping transformations is again used to transform the initial plant to a desired target system where Lyapunov analysis is adequately used. Finally, a numerical example showing the performance of the proposed control design is presented.
UR - http://hdl.handle.net/10754/670897
UR - https://linkinghub.elsevier.com/retrieve/pii/S2405896320310971
U2 - 10.1016/j.ifacol.2020.12.773
DO - 10.1016/j.ifacol.2020.12.773
M3 - Conference contribution
SP - 16537
EP - 16542
BT - IFAC-PapersOnLine
PB - Elsevier BV
ER -