In this paper, we present a high bandwidth frequency lock of a rigid tunable Fabry Perot cavity based on a set of lead zirconate titanate (PZT) actuators. The cavity spacer was specifically designed such that the frequency of the first resonance of the whole assembly under PZT excitation is above 35 kHz, thus allowing a servo-loop bandwidth of 13 kHz. It is demonstrated that no significant noise is added by the cavity to the output beam with respect to the input beam over the servo-loop bandwidth. This cavity can be used as a pre-mode cleaner in interferometric gravitational wave detectors such as the Laser Interferometer Gravitational-Wave Observatory (LIGO) and Virgo.