ATTITUDE REGULATING CONTROL OF A RIGID SPACECRAFT MODEL IN ACTUATING FAILURE MODE

Fazal-ur-Rehman and L. Khan

Keywords

Stabilizing feedback control, nonholonomic systems, Lie bracket extension, controllability Lie algebra, logarithmic coordinates

Abstract

This paper presents two different kinds of attitude regulating control strategies for a rigid spacecraft model in actuator failure mode, which is an example of drift less non-holonomic control systems. The first strategy presents piece-wise constant, states dependent feedback control laws. The method is based on the construction of a cost function V (not a Lyapunov function), which is sum of two semi-positive definite functions V1 and V2 . The semi-positive definite function V1 is dependent on first m state variables which can be steered along the given vector fields and V2 is dependent on the remaining n − m state variables which can be steered along the missing Lie brackets. The values of the functions V1 and V2 allow in determining a desired direction of system motion and permit to construct a sequence of controls such that the sum of these functions decreases in an average sense. The second strategy presents a time-varying feedback law based on the model reference approach, where the trajectory of the extended system is chosen as the model reference trajectory. The controllers are designed in such a way that after each time period T , the trajectory of the rigid body model intersects the trajectory of the model reference, which can be made asymptotically stable. The proposed feedback law is as a composition of a standard stabilizing feedback control for a Lie bracket extension of the original system and a periodic continuation of a specific solution to an open loop control problem stated for an abstract equation on a Lie group. m z= ˙ i=1 gi (z) ui , z ∈ n (1)

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