  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 becomes the dominate error term of the AO
system. While the AO system measures the wavefront error and subsequently
applies a correction (taking a total of 1 to 2 milli-seconds), the atmospheric
turbulence above the telescope has changed. 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. Our predictive
wavefront control algorithm minimizes the delay in a mean square sense 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 on the basis of both daytime
laboratory tests and on-sky tests. We show a reduction in residual-mean-square
wavefront error for the predictor compare to the leaky integrator implemented
on Keck. Finally, we present contrast improvements for both day time and on-sky
tests. Using the L-band vortex coronagraph for Keck's NIRC2 instrument, we find
a contrast gain of 2.03 at separation of 3~$\lambda/D$ and up to 3 for larger
separations (4-6~$\lambda/D$).
