How about building an automatic battery charger for lead acid batteries.
First look here:
Read the sections on battery charging, (page 12)
Look at the problems of overcharging, also how to recover a "Deeply Discharged" battery.
Now, design a charger which will:
Detect the state of charge of the battery and charge it at a suitable rate, and stop charging when fully charged.
The state of charge detect must include deeply discharged, and act accordingly.
Does that help?
JimB