  We show that the technique known as concatenated continuous dynamical
decoupling (CCD) can be applied to a trapped-ion setup for a robust
implementation of the quantum Rabi model in a variety of parameter regimes.
These include the case where the Dirac equation emerges, and the limit in which
a quantum phase transition takes place. We discuss the applicability of the CCD
scheme in terms of the fidelity between different initial states evolving under
an ideal quantum Rabi model and their corresponding trapped-ion realization,
and demonstrate the effectiveness of noise suppression of our method.
