Hacking a LED fluorescent tube
Even though you saw 18 volts across the LEDs with your multi-meter, this does not necessarily mean that you can just put 18 volts across the LEDs and get the same result. LEDs are diodes (the D in LED) and so act a lot like a short when lit. Very small changes in voltage can result in very large changes in current, so it is not practical to drive LEDs with a constand voltage source. You can read more about it here...

https://www.sparkfun.com/tutorials/219

For a single LED, you can usually get away with just putting a resistor in series with the LED and then driving with a constant voltage source. This works because the voltage drop across the resistor will increase as the current though it (and the LED) increases. 

You could potentially power your string from a fixed DC voltage by putting a resistor in series with it. You'd need to make sure that the resistor could handle the maximum power it might need to dissipate. 

But to do it right, you will want probably want to use a constant current LED driver. The one you currently have converts a 220VAC input into a constant current output where the amount of current is configured to match the LED string. You can google "buck converter schematic" and "constant current LED driver" to get an idea of how that board works, but looking at the photo, it probably has these sections...


A rectifier that turns the incoming AC into DC.
A chopper that turns the rectified DC in high frequency pulses.
A transformer that turns the high voltage pulses into low voltage pulses.
A filtering cap that smooths the output pulses.
A a current sense resistor that is in series with the output current that converts the output current level into a voltage that is then used to adjust the width of the high voltage pulses to keep the output current at the desired level.


(Your board could be different in several ways - for example the sensing could happen on the high voltage side, or instead of a full rectifier you could only have a single diode to half rectify the incoming AC. you'll need to look at the board carefully and figure out what is happening). 

I have had some luck with tricking boards like this to do my bidding with very little additional components. The jist is that you mess with the voltage that the pulse generator sees to trick it into decreasing the input duty cycle, which lowers the output current and dims or turns off the LEDs. 

It is possible to use an arduino to control all this, but again it is dependent on the specific board you have. 

Alternately, you can just buy an AC/DC dimmable constant current power supply pretty cheaply and use that.