Virtual passive control of flexible arms with collocated and noncollocatedfeedback

A novel approach to the control of flexible manipulators is proposed. The c ontroller includes both joint-variable and tip-deflection feedback. It is s hown that tip-deflection feedback transforms the original structure into a new system in which the structure parameters are virtually scaled up or dow n. The new system can hence be easily stabilized via a strictly passive fee dback law. A co-hub, lumped-parameter structure with multiple massless link s is first investigated and stability conditions are developed. The results are then applied to a distributed-parameter flexible arm, which is decompo sed into an equivalent lumped-parameter structure via a set of modal functi ons normalized in a particular way. Tip-deflection feedback is shown to be capable of enhancing control performance on a flexible arm, and stability i s ensured as long as the gain associated with the noncollocated feedback sa tisfies a simple inequality. The stability criteria are valid independent o f high-order flexible modes. (C) 2001 John Wiley & Sons, Inc.