PID band for power savings

I'm running  a modified version of the some labview single input PID control to control the position of a linear actuator.  My processing variable is a voltage reading from an LVDT, which has a small ripple voltage associated with it.  My output variable is a voltage, which controls the length of the linear actuator.  The PID control works fine, and I can track signals.  BUT, when I try to hold the actuator at a single position, I want the input voltage to turn off.  That is, once the set point and actual position come close enough, I want the controller to reduce it's output voltage to approaching zero.  I tried changing the relay amplitude and noise level, but neither worked.  Right now, once the actual position reaches the set point, the output voltage osciallates between the max and min.
Thanks for any suggestions!

We need more information.  What are all of the hardware components involved?  What PID code are you using?  Is the actuator horizontal or vertical?

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