  Recently, the Hamiltonian Control Theory was used in [Boreux et al.] to
increase the dynamic aperture of a ring particle accelerator having a localized
thin sextupole magnet. In this letter, these results are extended by proving
that a simplified version of the obtained general control term leads to
significant improvements of the dynamic aperture of the uncontrolled model. In
addition, the dynamics of flat beams based on the same accelerator model can be
significantly improved by a reduced controlled term applied in only 1 degree of
freedom.
