  This letter investigates the design of a class of infinite-dimensional
observers for one dimensional (1D) boundary controlled port-Hamiltonian systems
(BC-PHS) defined by differential operators of order $N \geq 1$. The convergence
of the proposed observer depends on the number and location of available
boundary measurements. \textcolor{hector}{Asymptotic convergence is assured for
$N\geq 1$, and provided that enough boundary measurements are available,
exponential convergence can be assured for the cases $N=1$ and $N=2$.}
Furthermore, in the case of partitioned BC-PHS with $N=2$, such as the
Euler-Bernoulli beam, \textcolor{hector}{it is shown} that exponential
convergence can be assured considering less available measurements. The
Euler-Bernoulli beam model is used to illustrate the design of the proposed
observers and to perform numerical simulations.
