The invention provides a clearance control system which includes one or more clearance control devices that include features for controlling the clearances between rotating and stationary components of an engine. In one exemplary aspect, a clearance control device utilizes a fluid to pressurize an actuation chamber defined by a compliant member of the clearance control device. The pressurization of the actuation chamber causes the actuation chamber to expand in a direction that changes the clearance between the stationary and rotating components of the engine.