Robustness of Velocity Feedback Controllers for Flexible Spacecraft

Abstract

The robustness properties of collocated velocity feedback controllers used for damping enhancement in large, flexible space structures are investigated. It is proved that the closed-loop system using such controllers is asymptotically stable in the large when: 1) unmodeled linear time-invariant dynamics (such as sensors/ actuators) are present, provided that the phase angle of such dynamics is between -90°and 900, 2) time-varying or invariant nonlinearities lying in the first and the third quadrant (i.e., belonging to the (0, m) sector) are present, or 3) sector-type nonlinearities following first-order stable dynamics are present in the feedback loop.

An exploration of active hard mount vibration isolation for precision equipment

“…DVF control is considered first, which is known to possess excellent stability robustness properties in case the velocity sensor and the force actuator are collocated [Balas (1979);Joshi (1985)]. In that case, the sensor and actuator form a dual pair, meaning that the inner product of the sensor and actuator signals represents the total power supplied to the system by the actuator T u is a quadratic matrix product and is therefore at least positive semi-definite.…”

“…It does not depend on the system's mass and stiffness parameters. Moreover, robust stability is maintained when small collocation errors occur and in the presence of certain sensor dynamics and/or non-linearities [Joshi (1985)]. Clearly, the DVF approach can be easily used in MIMO systems, provided that the feedback gain matrix G is chosen as a positive definite matrix.…”