A H/sub /spl infin//-weighting scheme for PID-like motion control

For motion control systems PID- or lead-lag-controllers serve well and are industrial standard. But often flexible modes of the mechanism endanger the stability of the control loop and thereby limit the bandwidth of the loop. Tuning and augmenting the controller becomes difficult and expensive at this point. Robust control design methods, first of all the /spl mu/-synthesis, offer a straight design formalism to overcome this problem. Anyhow, the crucial point in H/sub /spl infin// and /spl mu/-synthesis is the proper choice of weighting functions. In most of the known applications of robust control, the weighting functions were shaped ad-hoc. It is often not clear to the engineer how to express the given technical specifications in terms of H/sub /spl infin//-weighting functions. In fact, theory does not give an answer to this question up to now. Therefore, in this paper a H/sub /spl infin//-weighting scheme is presented that leads to closed-loop response similar to the established one obtained by PID-control in the rigid-body range. In this way PID-like high performance motion controllers can systematically be designed in the presence of structural flexibilities. In contrast to other guidelines on weighting functions, the exact shape of the weighting functions is given as well as specific numbers of their parameters.

[1]  S. Skogestad,et al.  Performance weight selection for H-infinity and μ-control methods , 1991 .

[2]  Pieter J.M. Van Groos,et al.  k-SYNTHESIS FOR A COMPACT DISC PLAYER , 1998 .

[3]  S. Font,et al.  H/sub /spl infin// control of a magnetic bearing , 1994, 1994 Proceedings of IEEE International Conference on Control and Applications.

[4]  R.L. Fittro,et al.  Control of a high speed machining spindle via /spl mu/-synthesis , 1997, Proceedings of the 1997 IEEE International Conference on Control Applications.

[5]  M. Dettori,et al.  Performance-robustness trade-off in the control of a CD player using mixed objectives design , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[6]  Decio Crisol Donha,et al.  Automatic weight selection for H ∞ control design , 1997 .

[7]  M Maarten Steinbuch,et al.  μ‐synthesis for a compact disc player , 1998 .

[8]  Sebastian Engell.  Design of Robust Control Systems with Time-domain Specifications , 1993 .

[9]  Jiankun Hu,et al.  Systematic H∞ weighting function selection and its application to the real-time control of a vertical take-off aircraft , 2000 .

[10]  Anna-Karin Christiansson.  A general framework for hybrid H-control , 2000 .

[11]  W. Gawronski,et al.  Frequency weighting for the H-infinity and H2 control design of flexible structures , 1998 .

[12]  W. Gawronski,et al.  On Frequency Weighting for the H and H(sub 2) Control Design of Flexible Structures , 1998 .

[13]  C. C. Lee,et al.  Systematic approach to selecting H/sub /spl infin// weighting functions for DC servos , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[14]  Ian Postlethwaite,et al.  Pole-zero cancellations and closed-loop properties of an H∞ mixed sensitivity design problem , 1992, Autom..

[15]  Maarten Steinbuch,et al.  Advanced Motion Control: An Industrial Perspective , 1998, Eur. J. Control.

[16]  Matthew A. Franchek,et al.  Selecting the Performance Weights for the μ and H∞ Synthesis Methods for SISO Regulating Systems , 1996 .

[17]  Rainer Nordmann,et al.  Implementation results of µ-synthesis control for an energy storage flywheel test rig , 2000 .

[18]  R. Nordmann,et al.  Attitude control of the airborne telescope SOFIA: /spl mu/-synthesis for a large scaled flexible structure , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).