On Transfer Functions and Control of a Flexible Slewing Link

An unconstrained mode expansion (UMM) for the solution to the linear equations of motion of a flexible slewing link is used to obtain single-input/single-output transfer functions for tip-position control purposes. Attention is given to the zero locations of the tip-position to hub-torque transfer function in terms of the flexible-to-rigid inertia ratio. We define a local tip-position to hub-torque transfer function and find that it is minimum-phase and not passive. A sequential root locus design approach is then used to determine suitable stabilizing hub angle, hub rate and local tip position feedback gains. Simulations indicate that for certain gain values, a constrained-mode expansion (CMM) leads to erroneous conclusions regarding system performance and even stability. Based on these results, it is suggested that the UMM be used for all future controller designs.