Aerial manipulation has been widely studied to be employed in various tasks such as exploration and transportation. To incorporate aerial manipulation into more sophisticated tasks like pulling or pushing a heavy cargo, an active interaction with surrounding structures should be considered. Unlike physical contact with a static structure which was mainly studied in previous papers, interaction with a movable structure requires a consideration of dynamics of the structure which makes the scenario more complex. In this paper, an aerial manipulator opening a hinged door is presented. Coupled dynamics between an aerial manipulator and a hinged door is derived, and a model predictive control (MPC) algorithm using iterative Linear Quadratic Regulator (iLQR) method for the derived dynamic equation is proposed. Through our proposed control strategy, sub-optimal state and input trajectories robust to model uncertainties while satisfying input constraints are generated. Our dynamic model and control algorithm are validated through simulations.