Ramírez, Hector Miguel

The observer design for 1D boundary controlled infinite-dimensional systems is addressed using the port-Hamiltonian approach. The observer is defined by the same partial differential equations as the original system and the boundary conditions depend on the available information from sensors and actuators. The convergence of the observers is proved to be asymptotically or exponentially under some conditions. The vibrating string and the Timoshenko beam are used to illustrate the observer convergence in different scenarios.

This paper investigates the observer design for the 1D boundary controlled port-Hamiltonian systems (BC-PHS) using the late lumping approach. Different observers are proposed for BC-PHS with different measured boundary variables. Based on the passivity propriety of the BC-PHS, sufficient conditions of the observer error convergence are provided for the different proposed observers. The wave equation is used to illustrate the effectiveness of the proposed observers with different boundary sensing.