GAIN SCHEDULING CONTROLLER FOR AIRCRAFT WITH MASS AND INERTIA VARIATION
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Robustness is one of the main control design requirements for aircraft control. Robustness is sought in the stability and performance of closed loop system against various factors such as disturbance, measurement error, modeling error or un-modeled dynamics. In aircraft control design, it is common to assume that the mass and inertia properties of aircraft are constant. Further, aircraft is assumed to have symmetry in its mass distribution relative to its mid-vertical plane. There are, however, cases where the aircraft mass changes rapidly, most notably in aerial refueling operation. The mass change also results in changes in the inertia matrix. An aircraft may also lose its mass symmetry in the case of, for example, asymmetric fuel loading or internal fuel transfer between fuel tanks. If a control design is carried out based on a speci c mass and inertia con guration, the stability and performance of the closed loop system may degrade when the aircraft ies with a di erent con guration. This research e ort focuses on addressing this issue in aerial refueling and formation ight by employing gain scheduling based on the aircraft mass and inertia con guration. The fuel mass in each fuel tank is considered as gain scheduling variables in addition to the ones associated with aircraft dynamics such as airspeed and turn rate. The rst step of this research is to determine the number of nominal ight conditions to be included in the gain scheduling control design. Eigenvalue and Bode plot analyses are carried out based on the linearized equations of motion for various ight conditions, and symmetric and asymmetric fuel mass con gurations. To reduce the number of cases included in the gain scheduling, "similar" cases are combined. An LQR-based MIMO (Multi Input Multi Output) integral control is designed for each nominal ight and mass con guration. An interpolation scheme based on the "mass distance" is developed to combine this linear controllers into the gain scheduling controller. The "mass distance" is de ned as the norm of the di erences between the current fuel tank amounts and those of each nominal mass con guration. This gain scheduling controller is implemented in aerial refueling simulation for a tailless delta wing aircraft with thrust vectoring capability. The simulation environment includes the 6-DOF models of both tanker and receiver, mass and inertial variation of the receiver aircraft in terms of the fuel mass in each fuel tank, aerodynamic coupling due to the tanker wake induced nonuniform wind. The controller of the tanker aircraft is to y the aircraft at commanded altitude, speed, and turn rate. The gain scheduling controller of the receiver aircraft is to track the commanded position relative to the body frame of the tanker aircraft. The receiver controller was tuned in three control allocation cases: (1) no thrust vectoring; only aerodynamic control e ects in use, (2) both aerodynamic e ectors and thrust vectoring in use, and (3) no elevator or rudder used; only thrust vectoring and aileron in use. The performance of the gain scheduling controller is evaluated through the aerial refueling maneuver when the receiver moves between the observation position, point on the side and behind the tanker, and the refueling position, a point right behind and slightly below the tanker. The simulation results rst of all demonstrates that a linear controller designed based on a nominal ight condition and mass con guration cannot safely complete the refueling maneuver when the aircraft has a di erent mass con guration. The simulation results further shows that the gain scheduling controller employing mass con guration as additional scheduling variables can successfully carry out the refueling maneuver with various symmetric and asymmetric fuel tank con guration.