The smart controller enters sleep mode after pushing the power button. The screen then goes dark but after a few minutes the device shuts down but itself
If there is a way to increase that time?
After using the contoller for a while in good weather conditions I was surprise to see that the battery gets low faster than expected

yes there is a way.

1 click on settings

2 scroll down to the (device)  that's highlighted in blue and you will see display.  there you can make the appropriate changes to your liking

If you're going to update the software on the smart controller make sure  you put it on (never sleep) then change it to your liking

thank you Drone Pilot!

Hello there. I am sorry for the trouble this has caused you before and it is great to know that after following the instructions posted by Drone-Pilot on post #2 you were able to set your DJI Smart Controller to your liking. Have a safe and a happy flying always.