A morphing aircraft with variable sweep wings is studied in this paper. A longitudinal dynamic model is established, and the influence of morphing on aerodynamic parameters is analyzed to reveal its trends and patterns. To address the coordinated control problem between the morphing mechanism and aerodynamic control surfaces, a two-step feedback linearization method is employed to design the baseline control law, resulting in virtual control inputs related to the morphing deflection and control surface deflection. A nonlinear disturbance observer is utilized to estimate unmodeled dynamics. An objective function is designed, incorporating penalty terms for control usage and drag, while hard constraints on direct control inputs and virtual control inputs are transformed into allowable error terms within the objective function. Based on this, the morphing deflection and control surface deflection are obtained by solving a quadratic programming problem with soft constraints, effectively resolving issues such as control input oscillations and infeasible solutions in the quadratic programming solver. By appropriately setting the weight coefficients in the control allocation objective function, the goal of morphing-assisted flight can be achieved. Simulation results demonstrate that morphing, by altering the aerodynamic parameters of the aircraft, can improve tracking accuracy while balancing the requirements of reducing drag and minimizing control surface usage during the morphing process.