a truss dob like a plettstone on its own uses no power at all. do you have some sort of servocat system on yours ? how many amps does it draw under typical usage?
I've been using a 12V 20AH panasonic burglar alarm/motorcycle sized AGM (absorbed glass mat, often misnamed SLA for sealed lead acid) to power various things with quite good results, I charge it with a car battery charger on a 2 amp setting.
if you don't know how much power your system actually draws, hook it all up, and put a digital multi-meter in 10 amp mode in series with the battery... like, battery + lead to DMM - lead, DMM + lead to your device(s) + side, then the device(s) - side to the battery ground. 10 amp mode on most meters requires moving the + lead to a special socket just for AMPS mode. now, with it hooked up this way, power your load, run through all the various things you do with it, and note the amps on the meter. fudge a working average amps based on the peaks and dips of the readings, and figure hours * amps == amp-hours (AH), also figure that a 20AH battery really shouldn't have more than 15 AH actually used if you want the battery to last many charge-discharge cycles. also, derate the battery by as much as 50% in cold weather, like near freezing.
when you're done with the amp readings, be sure to put the meter back in a normal volts scale, and put the + lead back in the normal + hole. you never EVER want to put an 'amp' meter across a voltage, its always used in series with a load.
p.s. those Li-Phosphate batteries are a poor choice for this application, they are optimized as engine starting batteries, to deliver a high current for a few seconds, rather than sustained discharge cycles. they are NOT 7-9 AH, thats a bogus 'lead battery equivalent' number. Li*** batteries are very expensive, their main advantage in a motorcycle application is they are very light, this counts for dirt bikes and race bikes.