If your ribs have a thin membrane over the bones on the backside, remove it by carefully sliding a knife under the membrane and peeling it away.
In a small bowl, combine brown sugar, salt, garlic powder, paprika, pepper, mustard powder, and cayenne. Rub mixture all over ribs.
Place trivet in Instant Pot and add water. Place ribs on trivet so that they are standing up.
Secure lid and set to Pressure Cook on High for 20 minutes.
Follow manufacturer’s guide for quick release, making sure to wait until the cycle is complete before unlocking and removing lid.
Using tongs, carefully remove ribs from Instant Pot and lay them flat on a large baking sheet. Brush both sides all over with barbecue sauce before serving.