Manoeuvring and vibration reduction of a flexible spacecraft integrating optimal sliding mode controller and distributed piezoelectric sensors/actuators

This investigation is to apply optimal sliding mode (OSM) control theory and distributed piezoelectric sensor/actuator technology to vibration control of a flexible spacecraft. An approximate analytical dynamic model of a slewing flexible spacecraft with surface-bonded piezoelectric sensors/actuators is developed using Hamilton's principle with discretization by assumed model method. To satisfy pointing requirements and simultaneously suppress vibration, two separate control loops are adopted. The first uses the piezoceramics as sensors and actuators to actively suppress certain flexible modes by designing a positive position feedback (PPF) compensators that add damping to the flexible structures in certain critical modes in the inner feedback loop; then a second feedback loop is designed using OSM control to slew the spacecraft. The OSM controller minimizes the expected value of a quadratic objective function consisting of only the states with the constraints that the error states always remain on the intersection of sliding surfaces. The advantage in this method is that the vibration reduction and attitude control are achieved separately in the two separate feedback loops, allowing the pointing requirements and simultaneous vibrations suppression to be satisfied independently of one another. An additional attraction of the design method is that the selection of PPF gain is determined by introducing a cost function to be minimized by the feedback gains which are subject to the stability criterion at the same time, such that the feedback gains are selected in a more systematical way to avoid the arbitrary selecting of feedback gains. The proposed control strategy has been implemented on a flexible spacecraft, which is a hub with a cantilever flexible beam appendage and can undergo a single axis rotation. Both analytical and numerical results are presented to show the theoretical and practical merits of this approach.