First I want to say good luck on the actual construction. I hope you're not going to try to make it small.
I think that a wired hydraulic would be your best bet. In that case you could make a simple E-gate to do the job for you, then have the inputs go to a wired keypad.
You would need to find out the length on the hydrolic at 0 then it's lengths at 30 and -30.
The E-gate might look something like this, assume that I measured the hydraulic and it is 16.4 units long at 0deg, 31.4 at 30deg, and 2.1 at -30deg. I am assuming that your tierods will be behind the wheel's axis.
Inputs: NumpadLeft NumpadRight
Outputs: Length
Length = 16.4
NumpadLeft == 1 -> Length = 31.4;
NumpadRight == 1 -> Length = 2.1;
NumpadLeft == 1 & NumpadRight == 1 -> Length = 16.4;
(this would be the perfect application for a wired stepping motor, but I'll keep dreaming about that one)


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