Minimum Time/Minimum Fuel Control of an Axisymmetric Rigid Body

Abstract

Many times it is necessary to reorient an aerial vehicle during flight in a minimum time or minimum fuel fashion. This thesis will present a minimum time/fuel control solution to reorienting an axisymmetric rigid body using eigenaxis maneuvers. Any fixed desired attitude can be achieved by rotating the rigid body about its eigenaxis. While an eigenaxis is not a time-optimal maneuver, it will produce the shortest angular trajectory between the rigid bodys current attitude and the desired attitude. Using the eigenaxis, a reference frame will be defined with the third unit vector direction parallel to the eigenaxis. In this reference frame, the controls and the equations of motion will be developed. A control weight will dictate whether the controller will drive the vehicle to the desired orientation in minimum time, minimum fuel, or a hybrid between minimum time and fuel. The controls can then be translated to the body frame through an attitude matrix that relates the body frame to the eigenaxis frame. After a minimum time/fuel controller has been developed, a minimum time/energy controller will then be designed. This minimum time/energy controller will then be compared against the minimum time/fuel controller by examining two fuel performance indices. Comparing these two controllers results in the most efficient controller being dependent on the cost function that describes the actuator type. Therefore, it is not feasible to select one controller over another independent of the fuel cost function. A minimum time/fuel controller has been designed using an eigenaxis maneuver in order to reorient itself. A comparison between the minimum time/fuel and minimum time/energy controller has been investigated using the two cost functions resulting in neither controller being the most efficient independent of the fuel cost function.