In addition to the default Ubuntu Backups application ... Timeshift is a feature rich system restore utility that can be installed with:
sudo apt install timeshift
It has a simple management GUI that you can launch from applications or from a terminal with:
timeshift-launcher
It also can be extensively managed via command-line ... pleas see man timeshift
That being said, the engine under-the-hood in many backup/restore applications like Timeshift and even CarbonCopy is Rsync ... So you can look at man rsync
and customize the command to do exactly what you want e.g.:
rsync -a -x / /backup/
That simple command will backup(synchronize) your root partition mounted at /
to your destination backup disk partition mounted at /backup/
... That command can be automated e.g. by adding it as a cron-job or you can even use it in a script that detects when you plug-in a certain backup disk and backup/synchronize to that certain disk automatically.