I have the HP Latex 115, The color is rarely even similar to what the RIP engine or any other program shows. This usually only exabits with the grayscale, it's usually lighter and sometimes very blue or brown. Which leads to my next question, even directly after one print with all export and RIP setting the same the grayscale color are different shades. For one print the charcoal color is right, then before the printer cools I print the same thing again and it can be much lighter, or a dark blue, or even an earthy brownish-gray.
Based on your explanation, it seems like the issue happens even when printing on the same material. My main recommendation is to do the color calibration and try to generate an ICC profile (using a spectrophotometer), then repeat the color calibration every certain time if you want the color matching. This will compensate for the difference between the printhead status with the passes from the last time you printed in terms of color.
It's important to do this with every single new media loaded and of course, use the proper media preset.
Finally, as a recommendation, you can expect more color consistency if the printer is warm up, so if you are looking for color matching (for example something that was printed 2 days ago), I recommend to print something else before, in order to have the printheads warmed up.
If those tips are not working, the best option is to contact HP support.
The 115 printer is a very basic model of HP Latex series. Your profile selection, as Daniela explained is not going to have all the necessary variables of your environment to produce great colour reproduction.
You have to consider humidity, temperature, air density, saturation levels and how these things affect the media and the ink properties. Colour calibration, with an xrite eye 1 would certainly help you, but understand, throughout the year your environment may change in its conditions, and this will also change your ICC profiles results, you typically will have to revisit your calibrations a couple time a year if not more.
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