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One could certainly build a circuit that takes the single-sided voltage from the controller and outputs a double-sided voltage for your solenoids. The first thing you need to do is determine how the voltages map from one to the other.
You are going to need two complementary voltage controlled voltage sources, plus the logic to invert the control voltage. Minimally, we are talking about several op amps and two pass transistors of opposite polarity.
That is if the mapping is linear. If it is something more complicated, you might need a microcontroller, or analog circuit (more opamps) to do the mapping.
