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To make this clear colin55 is saying take 3 NiCd cells, wire them in parallel, and then connect them in series with the 12 volt battery.The simpest thing to do is get a 12v battery and connect it to the output of the bridge. Now get a 2 or 3 NiCd rechargeable cells and put them in parallel and add them to the 12v battery. You now have a (12.6v plus 1.2v) capacitor at many Farads to act an input for your controller.
This will fix your problem and you don't have to ask any more questions.