  In the framework of the "LHC Injectors Upgrade" (LIU) project, the CERN
Proton Synchrotron (PS) is being prepared as a pre-injector for the Large
Hadron Collider at high luminosity (HL-LHC). RF systems at 20 MHz, 40 MHz and
80 MHz are required for longitudinal beam manipulations to provide 25 ns bunch
spacing and short bunches at transfer to the Super Proton Synchrotron (SPS).
Beam induced voltage in these cavities causes transient beam-loading and
uncontrolled longitudinal emittance blow-up. To reduce the impedance beyond the
reach of the wide-band feedback around the power amplifier, a new
multi-harmonic feedback has been developed and commissioned. Based on
narrow-band filters treating each revolution frequency harmonic separately, the
feedback phase at these harmonics can be dynamically adapted during
acceleration, taking into account the phase of the cavity transfer function.
The beneficial effect on longitudinal beam quality of LHC-type beams is shown.
