Vibration attenuation of spacecraft in the presence of parametric and unmodeled dynamics uncertainties using collocated and noncollocated control: A comparative study

Abstract

µ-control synthesis offers the advantage of maintaining robust performance and stability in the presence of plant uncertainties. Expressions relating the 2-norm of the vector of regulated outputs and closed-loop modal damping to the weights used for µ-control synthesis are derived in this paper. By using these expressions, the amount of damping added to each mode can be controlled individually while maintaining equal importance for each controlled mode. Hence, the selection of weights for synthesizing a suitable µ-controller is greatly simplified. Furthermore, a comparative study of µ-controllers designed by the proposed procedure and positive position feedback (PPF) controllers designed by analytically derived optimal parameters is also presented. The techniques are compared for their vibration attenuation, energy utilization, and stability characteristics, in the presence of parametric and unmodeled dynamics uncertainties. Results for both time domain and frequency domain simulations are presented. As in some cases (sandwich plate structures etc.) the noncollocation of actuator/sensor becomes crucial for achieving good performance, the above-mentioned characteristics are evaluated for both collocated and noncollocated sensor locations.