  The behavior of an adaptive optics (AO) system for ground-based high contrast
imaging (HCI) dictates the achievable contrast of the instrument. In conditions
where the coherence time of the atmosphere is short compared to the speed of
the AO system, the servo-lag error can become the dominant error term of the AO
system. While the AO system measures the wavefront error and subsequently
applies a correction (typically taking a total of one or a few milliseconds),
the atmospheric turbulence above the telescope has changed resulting in the
servo-lag error. In addition to reducing the Strehl ratio, the servo-lag error
causes a build-up of speckles along the direction of the dominant wind vector
in the coronagraphic image, severely limiting the contrast at small angular
separations. One strategy to mitigate this problem is to predict the evolution
of the turbulence over the delay time. Our predictive wavefront control
algorithm minimizes, in a mean square sense, the wavefront error over the delay
and has been implemented on the Keck II AO bench. In this paper, we report on
the latest results of our algorithm and discuss updates to the algorithm
itself. We explore how to tune various filter parameters based on both daytime
laboratory tests and on-sky tests. We show a reduction in the
residual-mean-square wavefront error for the predictor compared to the leaky
integrator (the standard controller for Keck) implemented on Keck for three
separate nights. Finally, we present contrast improvements for daytime and
on-sky tests for the first time. Using the L-band vortex coronagraph for Keck's
NIRC2 instrument, we find a contrast gain of up to 2 at a separation of 3
lambda/D and up to 3 for larger separations (3-7 lambda/D).
