Prepare the ribs by removing the membrane from the back of each rack. This can be done by sliding a knife under the membrane and then pulling it off using a paper towel for grip.
In a small bowl, combine the brown sugar, smoked paprika, garlic powder, onion powder, salt, and black pepper. Mix well to create a dry rub.
Rub the dry rub mixture all over the ribs, making sure to coat them evenly.
Pour the water into the Instant Pot. Place the trivet inside the pot and arrange the ribs vertically, wrapping them around the inside of the pot. If needed, you can cut the racks in half to fit better.
Close the lid of the Instant Pot and set the valve to the sealing position. Cook on high pressure for 25 minutes.
While the ribs are cooking, preheat your grill to medium-high heat.
Once the cooking time is up, perform a quick pressure release by carefully turning the valve to the venting position. Wait for the pressure to fully release before opening the lid.
Carefully remove the ribs from the Instant Pot and transfer them to the preheated grill.
Brush the BBQ sauce generously over both sides of the ribs and grill them for about 5 minutes per side, until the sauce caramelizes and the ribs have a nice char.
Remove the ribs from the grill and let them rest for a few minutes. Slice them into individual ribs or serve them as whole racks.
Serve the Instant Pot BBQ ribs with additional BBQ sauce on the side and your favorite side dishes like coleslaw, cornbread, or roasted vegetables.