Dilyana Domont-Yankulova

Technical communique: A fast nonlinear control method for linear systems with input saturation

We present a novel, fast saturating nonlinear feedback law for single input systems with linear dynamics and input saturation. It is fast in the sense that it yields a better performance than a saturating linear control law. The control law is based on implicit soft variable-structure control. A convex optimization procedure for the controller synthesis based on linear matrix inequalities (LMIs) is derived at the price of some conservatism. As an example, we consider the control of a submarine.

Vereinfachte schnelle Regelung von linearen Systemen mit Stellgrößenbeschränkungen

Zusammenfassung Sättigende, weiche strukturvariable Regelungen mittels impliziter Lyapunov-Funktionen eignen sich zur schnellen Regelung von linearen Systemen mit Stellgrößenbeschränkungen. Der vorliegende Beitrag stellt eine Vereinfachung dieses Regelungstyps bei gleichzeitiger Verbesserung des Regelverhaltens vor. Die Vereinfachung führt auf weniger restriktive Stabilitätsbedingungen. Hierdurch vergrößert sich die Menge regelbarer Strecken, und die Anwendung dieses Regelungstyps auf bestimmte instabile Strecken ist erstmals möglich. Des Weiteren wird ein LMI-basiertes Verfahren zur effizienten Bestimmung von Reglerparametern vorgestellt. Damit werden Entwürfe von schnellen Regelungen für zwei Benchmarkstrecken vorgenommen. Eine Nachoptimierung der Reglerparameter mittels Suchverfahren führt zu fast zeitoptimalem Verhalten. Abstract Saturating, soft variable-structure controls using implicit Lyapunov functions are suited for fast control of linear systems subject to input constraints. We present a simplified version of this type of control. It shows an improved performance mainly due to less restrictive stability constraints. The set of controlable plants is enlarged so this type of control can be applied to certain unstable systems for the first time. A design procedure using LMIs is presented to calculate the parameters of the controller. This procedure is used to design fast controls for two benchmark problems. Further optimisation using local noncovex optimisation leads to nearly time-optimal results.

Cavity Impedance Reduction Strategies During Multi Cavity Operation in the SIS100 High Intensity Hadron Synchrotron

The planned SIS100 heavy ion synchrotron at the GSI Helmholtzzentrum für Schwerionenforschung will possess twenty ferrite accelerating cavities in its final stage of extension. As at injection and at flat top during slow extraction of the planned acceleration cycles the RF voltage will be relatively low, not all cavities will be active in this part of operation. It is important to analyse the impact of the inactive cavities on the overall RF voltage and subsequently their implication on the longitudinal particle dynamics. Classical approaches for reducing the beam impedance consist of active detuning of the cavities to pre-described parking frequencies. The fact that two out of ten buckets have to stay empty in all SIS100 scenarios is of particular interest as additional frequency components appear in the excitatory beam current, which have to be considered when the cavity is detuned. Therefore multi-cavity particle tracking simulations, consisting of twenty cavities and their attached LLRF control systems, are carried out in order to analyse different possibilities to minimize the impact on the beam dynamics and emittance growth.

Tuning of 3-Tap Bandpass Filter during Acceleration for Longitudinal Beam-Stabilization at FAIR

During acceleration in the heavy-ion synchrotrons SIS18/SIS100 at GSI/FAIR longitudinal beam oscillations are expected to occur. To reduce longitudinal emittance blow-up, dedicated LLRF beam feedback systems are planned. To date, damping of longitudinal beam oscillations has been demonstrated in SIS18 machine experiments with a 3-tap filter controller (e.g. [1]), which is robust in regard to control parameters and also to noise. On acceleration ramps the control parameters have to be adjusted to the varying synchrotron frequency. Previous results from beam experiments at GSI indicate that a proportional tuning rule for one parameter and an inversely proportional tuning rule for a second parameter is feasible, but the obtained damping rate may not be optimal for all synchrotron frequencies during the ramp. In this work, macro-particle simulations are performed to evaluate, whether it is sufficient to adjust the control parameters proportionally (inversely proportionally) to the change in the linear synchrotron frequency, or if it is necessary to take more parameters, such as bunch-length and synchronous phase, into account to achieve stability and a considerable high damping rate for excited longitudinal dipole beam oscillations. This is done for singleand dual-harmonic acceleration ramps.

Development of an ERL RF Control System

The Mainz Energy-recovering Superconducting Accelerator (MESA), currently under construction at Johannes Gutenberg-Universität Mainz, requires a newly designed digital low-level radio frequency (LLRF) system. Challenging requirements have to be fulfilled to ensure high beam quality and beam parameter stability. First, the layout with two recirculations and the requirements will be shown from an LLRF point of view. Afterwards, different options for the control system are presented. This includes the generator-driven system, the self-excited loop and classical PID controller as well as more sophisticated solutions. OVERVIEW AND REQUIREMENTS OF MESA At Johannes Gutenberg-Universität Mainz a new accelerator will be built: The Mainz Energy-recovering Superconducting Accelerator (MESA). This accelerator will not only feature high current beams, feasible by means of energy recovery, but will also be operated as conventional multi-turn linac with a polarized electron beam. A part of the building is yet to be constructed and civil works will begin in 2018. The accelerator itself is scheduled to be constructed in 2020, but some parts can already be tested in existing halls [1]. Figure 1 shows a (preliminary) lattice [2]. The source Figure 1: MESA lattice as of 2016. called STEAM [1] (“Small Thermalized Electron-source At Mainz”) will deliver a beam of polarized electrons which are pre-accelerated up to 5 MeV in the injector MAMBO (“Milli Ampere Booster”) before they enter the main linac. MESA uses a double-sided layout with two cryomodules, providing an energy gain of up to 25 MeV each. After passing the cryomodules the beam is guided through the arcs for multi-turn operation. Separator magnets split the beams of different energies and recombine them before entering the cryomodules again or before experimental use. ∗ Work supported by DFG: GRK 2128 “AccelencE” † orth@temf.tu-darmstadt.de Two experimental sides are foreseen: If MESA works as a 3-turn linac without energy recovery, the beam will be used in the so-called “external target P2” for high precision measurements of the Electro-Weak mixing angle [1]. In this mode, a 0.15 mA polarized electron beam will be accelerated to 155 MeV. Since there will be no energy recovery after P2 the beam will be dumped at high energy. This makes heavier shielding for radiation protection necessary. The other operation mode will be the energy-recovery mode. In this mode, the beam will interact with the pseudo internal target called MAGIX which is a windowless gas target [1]. There will only be two passes, since this experiment only needs lower energies—but ideally, the available energies range from quite as low as 25 MeV up to a maximum of 105 MeV. The use of energy recovery makes higher currents feasible. In the first stage, a current of 1 mA is planned which shall be upgraded to 10 mA in the second stage. Currently, discussions are ongoing whether this mode will also make use of polarized electrons [1]. There are many possible experiments in MAGIX’ portfolio, from nuclear physics to the search for dark matter [1]. All the experiments will require high accuracy and stability of the accelerating RF field while a wide variety of parameters (e. g. beam current and energy) has to be dealt with. The RF control system will have to handle this on demand. Multi-Turn ERL Layout In this paper, the focus is set to the energy-recovery mode. The path a beam takes is sketched in Fig. 2, starting from the injector through the main linac to the internal experiment and back on the decelerating phase ending in the beam dump. The beam re-enters the cavities 180° out of phase Figure 2: Sketch of the way a beam travels through MESA in the energy-recovery mode. Red: accelerating phase. Blue: decelerating phase. Note that the spatial separation is meant to clarify the different ways—in reality, the bunches are interleaved and those with the same energy share also the same beampipes in the arcs. 59th ICFA Advanced Beam Dynamics Workshop on Energy Recovery Linacs ERL2017, Geneva, Switzerland JACoW Publishing ISBN: 978-3-95450-190-8 doi:10.18429/JACoW-ERL2017-THIBCC005 THIBCC005 70 Co nt en tf ro m th is w or k m ay be us ed un de rt he te rm so ft he CC BY 3. 0 lic en ce (© 20 18 ). A ny di str ib ut io n of th is w or k m us tm ai nt ai n at tri bu tio n to th e au th or (s ), tit le of th e w or k, pu bl ish er ,a nd D O I. WG4: Superconducting RF with respect to the accelerating field. This is achieved by path-length variation in the last arc with the internal target. As can be seen in Fig. 2, there will be four different beams in each cryomodule. MESA will be operated in continuouswave (CW) mode and in the upgraded stage 2 this would result in a DC current of 40 mA in each cryomodule and thereby a very high beam loading. But since two of the four beams are on the decelerating phase their energy is given to the accelerating beams so that for perfect energy recovery the “RF currents” cancel each other. This results in a significantly reduced RF power demand, as can be seen from Eq. (1) and Eq. (2), which describe the required RF power in terms of the amplitude of the accelerating voltage Vacc , the (resulting) beam current Ibeam, the beam phase relative to the crest φbeam, the cavity’s R Q , the loaded quality factor QL , the coupling factor βc , the detuning δω and the 3 dB bandwidth ∆ωBW [3]. PRF = V acc 4 R Q QL 1 + βc βc [