Using LMIs to optimize robustness of observer‐based state‐feedback for a synchrotron

SUMMARY In this article, a synthesis method for linear systems subject to uncertain time-varying parameters is proposed. Starting with the given values for the nominal parameters, the first objective is to find a constant state feedback such that the controlled system is stabilized and given dynamic specifications, such as a minimal decay rate, are met. In a second step, the constant feedback is then locally optimized such that the uncertain system parameters are allowed to vary around their nominal point as much as possible, whereas stabilization and dynamic specifications still hold. In addition, the procedure is extended toward observer-based state feedback. Finally, this approach is applied to a synchrotron example, where the particle beam in longitudinal direction is to be stabilized and the coherent synchrotron frequency as well as the damping rate are uncertain. Copyright © 2013 John Wiley & Sons, Ltd.

[1]  P. Gahinet,et al.  H∞ design with pole placement constraints: an LMI approach , 1996, IEEE Trans. Autom. Control..

[2]  Hendrik Lens.  Fast robust stabilization by saturating output feedback of uncertain linear systems with input constraints , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[3]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[4]  H. Klingbeil,et al.  A Digital Beam-Phase Control System for Heavy-Ion Synchrotrons , 2007, IEEE Transactions on Nuclear Science.

[5]  J. Adamy,et al.  A METHOD TO OBTAIN THE FREQUENCY OF THE LONGITUDINAL DIPOLE OSCILLATION FOR MODELING AND CONTROL IN SYNCHROTRONS WITH SINGLE OR DOUBLE HARMONIC RF SYSTEMS , 2012 .

[6]  Frank James Sacherer,et al.  RMS Envelope Equations with Space Charge , 1971 .

[7]  E. Ostertag,et al.  An Improved Path-Following Method for Mixed ${H} _{2} /{H}_{\infty}$ Controller Design , 2008, IEEE Transactions on Automatic Control.

[8]  Ulrich Laier,et al.  DUAL HARMONIC OPERATION AT SIS18 , 2010 .

[9]  F. Sacherer,et al.  Theory and Performance of the Longitudinal Active Damping System for the CERN PS Booster , 1977, IEEE Transactions on Nuclear Science.

[10]  Analysis of acceleration control loops of a synchrotron , 1992 .

[11]  H. Horisberger,et al.  Regulators for linear, time invariant plants with uncertain parameters , 1976 .

[12]  J. Ackermann,et al.  A common controller for a family of plant models , 1982, 1982 21st IEEE Conference on Decision and Control.

[13]  A. Levant.  Robust exact differentiation via sliding mode technique , 1998 .

[14]  Pedro L. D. Peres,et al.  An LMI approach to compute robust stability domains for uncertain linear systems , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[15]  Jürgen Adamy,et al.  Observer Based Controller Design for Linear Systems with Input Constraints , 2008 .

[16]  S. Y. Lee,et al.  Accelerator Physics , 2019 .

[17]  Stephen P. Boyd,et al.  A path-following method for solving BMI problems in control , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[18]  Frank James Sacherer,et al.  A Longitudinal Stability Criterion for Bunched Beams , 1973 .

[19]  C. Scherer,et al.  Multiobjective output-feedback control via LMI optimization , 1997, IEEE Trans. Autom. Control..

[20]  Pierre Apkarian,et al.  Robust pole placement in LMI regions , 1999, IEEE Trans. Autom. Control..