Single-input/single-output transfer functions for a flexible slewing link

Truncated linear models based on constrained and unconstrained mode expansions for a flexible link with torque actuation at its hub led us to examine the behavior of the open-loop-zeros of five commonly used SISO transfer functions. We arrive at new conclusions with regard to minimum- and non-minimum-phase zeros, and passivity of the transfer functions. The flexible-to-rigid inertia (FRI) ratio plays an important role in the determination of these characteristics. This paper illustrates how the zero locations of some of the transfer functions are dramatically affected by the FRI ratio. We also investigate the performance of a hub angle, hub rate, and relative tip position static feedback controller based on a reduced-order constrained mode model when applied to both unconstrained and constrained mode models of the same dimension. Simulations indicate that the constrained model can be stable while the unconstrained model is not for high FRI ratios. Our findings can provide useful information to designers in cases where the controller is sensitive to the 1ocation of the plant's zeros.