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. © 2001 John Wiley & Sons, Inc.

[1]  H. Harry Asada,et al.  Integrated structure/control design of mechatronic systems using a recursive experimental optimization method , 1996 .

[2]  Kamal Youcef-Toumi,et al.  Modeling, design, and control integration: a necessary step in mechatronics , 1996 .

[3]  Christopher J. Damaren,et al.  Passivity and Noncollocation in the Control of Flexible Multibody Systems , 2000 .

[4]  Kirsten Morris,et al.  Dissipative controller designs for second-order dynamic systems , 1994, IEEE Trans. Autom. Control..

[5]  Wayne J. Book,et al.  Performance limitations of joint variable-feedback controllers due to manipulator structural flexibility , 1990, IEEE Trans. Robotics Autom..

[6]  Bruce H. Wilson,et al.  Optimal Design of a Vibration Isolation Mount Using Physical Programming , 1999 .

[7]  Bruce A. Francis,et al.  Feedback Control Theory , 1992 .

[8]  Toshiyuki Ohtsuka,et al.  Mission function control for a slew maneuver experiment , 1991 .

[9]  M. Balas,et al.  Feedback control of flexible systems , 1978 .

[10]  Shuzhi Sam Ge,et al.  Improving regulation of a single-link flexible manipulator with strain feedback , 1998, IEEE Trans. Robotics Autom..

[11]  Shang-Teh Wu.  Time-optimal control and high-gain linear state feedback , 1999 .

[12]  Carlos Cerrada,et al.  Load adaptive control of single-link flexible arms based on a new modeling technique , 1999, IEEE Trans. Robotics Autom..

[13]  Wayne J. Book,et al.  Controlled Motion in an Elastic World , 1993 .

[14]  Robert H. Cannon,et al.  Design and Experimental Demonstration of Rapid, Precise End-Point Control of a Wrist Carried by a Very Flexible Manipulator , 1991, Int. J. Robotics Res..

[15]  William J. O'Connor,et al.  Position control of flexible robot arms using mechanical waves , 1998 .

[16]  F. Matsuno,et al.  On robustness of passivity of manipulators , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).