On Tuesday, the City Council gave the green light for the Santa Barbara Museum of Natural History’s renovation plan, rejecting an appeal by neighbors Mark and Lauren Carey of Las Encinas Lane, who wanted more controls on outdoor speakers, construction timing, and the placement of trash cans. Dozens of public speakers packed the chambers to support the museum; no one spoke against it other than the Careys. The council’s blessing of the plan — which will not expand the museum’s footprint or attendance — allows the remodel to begin.