Virtual passive control of flexible arms with collocated and noncollocated feedback

A novel approach to the control of flexible manipulators is proposed. The controller includes both joint‐variable and tip‐deflection feedback. It is shown that tip‐deflection feedback transforms the original structure into new system in which the structure parameters are virtually scaled up or down. The new system can hence be easily stabilized via a strictly passive feedback law. A co‐hub, lumped‐parameter structure with multiple massless links is first investigated and stability conditions are developed. The results are then applied to a distributed‐parameter flexible arm, which is decomposed into an equivalent lumped‐parameter structure via a set of modal functions normalized in a particular way. Tip‐deflection feedback is shown to be capable of enhancing control performance on a flexible arm, and stability is ensured as long as the gain associated with the noncollocated feedback satisfies a simple inequality. The stability criteria re valid independent of high‐order flexible modes.