Adaptive control of nonlinear attitude motions realizing linear closed loop dynamics
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abstract
An adaptive attitude control law is presented to realize linear closed loop dynamics in the attitude error vector. The Modified Rodrigues Parameters (MRPs) are used along with their associated shadow set as the kinematic variables since they form a nonsingular set for all possible rotations. The desired linear closed loop dynamics can be of either PD or PID form. Only a crude estimate of the moment of inertia matrix is assumed to be known. A nonlinear control law is developed which yields linear closed loop dynamics in terms of the MRPs. An adaptive control law is then developed that enforces these desired linear closed loop dynamics in the presence of large inertia and external disturbance model errors. Because the unforced closed loop dynamics are nominally linear, standard linear control methodologies such as pole placement can be employed to satisfy design requirements such as control bandwidth. The adaptive control law is shown to track the desired linear performance asymptotically without requiring apriori knowledge of either the inertia matrix or external disturbance.
