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

Abstract

SUMMARYIn 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.

Offset-free output feedback predictive control for longitudinal beam dynamics in heavy ion synchrotrons

“…The QP (15) is solved via a Matlab implementation of the FGM with 17 iterations. 4 For the sake of realistic simulation results we add uncorrelated white noise to the measurements (13). The noise level is chosen consistent with available measurement data from the SIS18 synchrotron.…”

“…Very few papers exist that focus on the feedback design. In [4], a synchrotron beam serves as an example for a robust observer based state feedback controller, but no implementation issues are discussed. In this paper, we consider the specific setup of the synchrotron SIS18 at GSI Helmholtz Center for Heavy Ion Research [5] and consider open problems that are essential for a successful implementation of Model Predictive Control (MPC) scheme.…”

Predictive control for longitudinal beam dynamics in heavy ion synchrotrons

“…The aim of this paper is to show that MPC is feasible in principle for SIS18, although the sample rate is about 375 kHz. In [5], the SIS18 synchrotron serves as an example for a robust observer based state feedback controller, but no implementation and timing issues are discussed. In this work, we aim to make a considerable step towards the implementation of MPC on digital hardware for heavy-ion synchrotrons.…”

Entwurf robuster modellbasierter Fehlerisolationsfilter

“…Weitere LMIs zur Beschreibung von D-Regionen finden sich zum Beispiel in [83] [98,145,186,187,190,191,196,207,211,212,264]. Da in der historischen Entwicklung der Begrifflichkeiten nicht immer konsistente Bezeichnungen verwendet wurden, dient der Abschnitt auch dazu, die im Rahmen dieser Arbeit verwendeten Begriffe zu definieren.…”