In SX Microcontrollers, SX/B Compiler and SX-Key Tool, JonnyMac wrote:

You may have to experiment with the PWM frequency to the solenoid; it the frequency is too fast a lower levels you may not be able to overcome the spring/magnetics, etc.  I wish I could tell you more, but it's a bit of a mystery to me, too.  I've attached a quick demo that does PWM in an interrupt.  The original code is by Guenther Daubach with a couple small mods by me (there was not trouble with G's code, I just wanted slightly different behavior).

I've also attached a schematic for you to consider; this circuit is similar to something I used in a high-voltage DC project.

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