Optimal root loci of flexible space structures

It is shown that simple generic properties can be proved for the optimal root loci of flexible space structures (FSS). It is proved that the angles and rates at which closed-loop poles depart from the open-loop poles can be found by inspection for any FSS with sufficiently widely space natural frequencies. Similar results also apply to the angles at which certain loci approach the transmission zeros of any FSS with compatible (physically colocated and coaxial) sensors and actuators, as a consequence of the special properties of the zeros of such systems. Finally, determining the number and orders of the Butterworth configurations of such as FSS is much more straightforward than for a general state-space system: it amounts only to checking whether structural displacements or their rates are the measured outputs. These results depend on the fundamental second-order nature of such systems, and five considerably more insight than is possible a priori for general linear multivariable systems