For the spice rub: In a small bowl, combine the brown sugar, smoked paprika, garlic powder, dry mustard, salt, black pepper and cayenne. For the ribs: Remove the membrane from the underside of the ribs. Rub the spice mixture all over. Set aside for 30 minutes, or up to 8 hours (in the refrigerator). Add the Dr Pepper to the Instant Pot and place the trivet (that came with the Instant Pot) over top. Arrange the ribs on the trivet in concentric circles with the meaty side facing out. Cover the Instant Pot and seal to close. Select HIGH PRESSURE and set the timer for 25 minutes. When the timer is up, let the pressure naturally release for 10 minutes, then manually release. Remove the ribs and transfer to a sheet tray, meat-side-up, to let cool slightly. Set the Instant Pot to SAUTE. Cook the liquid to reduce by one-half, about 15 minutes. Add the ketchup, vinegar, brown sugar, soy sauce and black pepper, and whisk well to combine. Cook for 10 to 15 minutes, whisking frequently, until thickened like BBQ sauce. Heat a broiler to high heat. Brush the tops with the BBQ sauce sauce and broil for 4 minutes to slightly caramelize. Brush all over with more sauce and serve immediately.