Wholly satin sheets are pretty useless, slip and slide all over the place.
Partially satin, or similar, with all outside edges made of a grip like material like towelling are better.
www.easymovesheets.com and the secure sit & slide fitted sheet is really good.
No doubt the link in this post may be deleted so just Google, 'easy move sheets' with no spaces, and then dot com.and there are 3 types to choose from with the one I mentioned having proved the best.... not the easy slide,(all satin), not the easy turn, (mostly satin except for the bottom part), but the secure sit & slide, (satin on the central part where your body is but with a grip material on all sides and the bottom)
I do wonder why PUK have not found this supplier and still advise satin sheets.You can order online, but as we have an electric adjustable bed with a deep mattress, I phoned them and they were most helpful in advising which size, depth wise, was the best.
Hope this helps.