the 13.5 volt source with the 70 milliohm resistor in series is the (lead acid) battery with its ESR
1.1 volt across a 2.2 ohm current sense resistor with my selected max charge current (0.5 A) flowing.
26.3 ohm resistor is the load being powered
Potentiometer sets current amount
Red LED lights when battery voltage is =< 11 volts, regardless of which power source is currently in use.
Yes, the voltage drops a bit when the main input is lost. Devices requiring a more stable voltage will need an additional regulator on the output. Because the battery is always connected (while being charged) no switchover is necessary as with a standby power supply.
No safety devices are shown. A real system should have fail safes for battery overheat, output overcurrent, input overvoltage, and so on.
