Defesa de Tese de Doutorado – André Francisco Caldeira – 10/03/2017
10/03/2017 16:37
| Defesa de Tese de Doutorado | |
| Aluno | André Francisco Caldeira |
| Orientador
Orientador Coorientador |
Prof. Daniel Ferreira Coutinho, Dr. – DAS/UFSC
Prof. Christophe Prieur, Dr – GIPSA/Grenoble Prof. Valter Juinor da Souza Leite, Dr. – CEFET/MG |
| Data
Local |
10/03/2017 09h30 (sexta-feira)
Sala PPGEAS I (piso superior) |
| Prof. Daniel Ferreira Coutinho, Dr. – DAS/UFSC (orientador)
Prof. Leonardo Antônio Borges Torres, Dr. – UFMG Profa. Sophie Tarbouriech, Dra. – LAAS/França Prof. Eugênio de Bona Castelan Neto, Dr. – DAS/UFSC Prof. Edson Roberto De Pieri, Dr. – DAS/UFSC Prof. Ubirajara Franco Moreno, Dr. – DAS/UFSC Prof. Hector Bessa Silveira, Dr. – DAS/UFSC (suplente) |
|
| Título
|
Static and Dynamic Boundary Control of Coupled PDE-ODE Systems |
| Abstract: This work studies boundary control strategies for stability analysis and stabilization of first-order hyperbolic system coupled with nonlinear dynamic boundary conditions. The modeling of a flow inside a pipe (fluid transport phenomenon) with boundary control strategy applied in a physical experimental setup is considered as a case study to evaluate the proposed strategies. Firstly, in the context of finite dimension systems, classical control tools are applied to deal with first-order hyperbolic systems having boundary conditions given by the coupling of a heating column dynamical model and a ventilator static model. The tracking problem of this complex dynamics is addressed in a simple manner considering linear approximations, finite difference schemes and an integral action leading to an augmented discrete-time linear system with dimension depending on the step size of discretization in space. Hence, for the infinite dimensional counterpart, two strategies are proposed to address the boundary control problem of first-order hyperbolic systems coupled with nonlinear dynamic boundary conditions. The first one approximates the first-order hyperbolic system dynamics by a pure delay. Then, convex stability and stabilization conditions of uncertain input delayed nonlinear quadratic systems are proposed based on the Lyapunov–Krasovskii (L-K) stability theory which are formulated in terms of Linear Matrix Inequality (LMI) constraints with additional slack variables (introduced by the Finsler’s lemma). Thus, strictly Lyapunov functions are used to derive an LMI based approach for the robust regional boundary stability and stabilization of first-order hyperbolic systems with a boundary condition defined by means of a nonlinear quadratic dynamic system. The proposed stability and stabilization LMI conditions are evaluated considering several academic examples and also the flow inside a pipe case study. | |
