Bounded extremum seeking with discontinuous dithers

Summary
Recently, a form of extremum seeking for control (ESC) was developed for the stabilization of uncertain nonlinear systems. In ESC, the extremum seeker itself directly controls the systems through feedback rather than fine tuning a controller. The ESC results, and other related results, apply only to systems affine in control. However, in most physical systems, the control effort enters the system's dynamics through a nonlinear function, such as an input with deadzone and saturation. In this work, we use our previous results on ESC to develop constrained extremum seeking stabilizing controllers for systems of practical interest that are nonaffine in control. Considering that any odd function can be approximated arbitrarily well by an odd polynomial, we present analytic results for designing controllers for systems in which control enters the system dynamics through an odd polynomial. Furthermore, we study the robustness of the scheme to uncertainty in the odd polynomial degree as well as robustness to even-powered perturbations.

Constrained extremum seeking stabilization of systems not affine in control

Beam-driven plasma wakefield acceleration (PWFA) achieves the same energy gain in a single meter, for which conventional accelerators require several kilometers, however much work is still required to match the beam quality of conventional accelerators. The PWFA processes to be studied at the FACET-II facility will utilize extremely short (down to a few fs) high energy (10 GeV), high charge (few nC) electron and eventually positron bunches. The PWFA process is extremely sensitive to the detailed longitudinal current profiles of these bunches and it would be of great benefit to have precise measurement and control of these profiles. We present an adaptive model tuning technique for FACET-II to adaptively tune online models based on real time accelerator and beam data to continuously provide a non-invasive diagnostic which predicts the longitudinal phase space (LPS) of extremely short and highly compressed electron beams, which otherwise require destructive X-band transverse deflecting cavity (XTCAV)-based measurements. Based on simulation studies, our method has the potential for: (1). The development of a non-invasive longitudinal phase space diagnostic by adaptively tuning models based on non-invasive measurements such as energy spread spectra which could be recorded at all of the bunch compressors in the facility. (2). Utilize these diagnostic to perform model-independent feedback-based to achieve desired longitudinal phase space distributions. (3). Utilize the model-independent feedback approach to maximize energy gain while minimizing emittance growth and energy gain variance of the PWFA process by tuning accelerator parameters, while monitoring what longitudinal phase space the algorithm has found, information that will be useful for further analytical and simulation studies.

Adaptive model tuning studies for non-invasive diagnostics and feedback control of plasma wakefield acceleration at FACET-II

A recently developed form of extremum seeking for time-varying systems is implemented in hardware for the resonance control of radio-frequency cavities without phase measurements. Normal conducting RF cavity resonance control is performed via a slug tuner, while superconducting TESLA-type cavity resonance control is performed via piezo actuators. The controller maintains resonance by minimizing reflected power by utilizing model-independent adaptive feedback. Unlike standard phase-measurement-based resonance control, the presented approach is not sensitive to arbitrary phase shifts of the RF signals due to temperature-dependent cable length or phasemeasurement hardware changes. The phase independence of this method removes common slowly varying drifts and required periodic recalibration of phase-based methods. A general overview of the adaptive controller is presented along with the proof of principle experimental results at room temperature. This method allows us to both maintain a cavity at a desired resonance frequency and also to dynamically modify its resonance frequency to track the unknown time-varying frequency of an RF source, thereby maintaining maximal cavity field strength, based only on power-level measurements.

Application of Extremum Seeking for Time-Varying Systems to Resonance Control of RF Cavities

The radiation generated by a seeded free-electron laser (FEL) is characterized by a high temporal coherence, which is close to the Fourier limit in the ideal case. The setup and optimization of a FEL is a non-trivial and challenging operation. This is due to the plethora of highly sensitive machine parameters and to the complex correlations between them. The fine tuning of the FEL process is normally supervised by physicists and is carried out by scanning various parameters with the aim of optimizing the spectrum of the emitted pulses in terms of intensity and line-width. In this article we introduce a novel quantitative method for the evaluation of the FEL spectrum via a quality index. Moreover, we investigate the possibility of optimization of the FEL parameters using this index as the objective function of an automatic procedure. We also present the results of the preliminary tests performed in the FERMI FEL focused on the effectiveness and ability of the automatic procedure to assist in the task of machine tuning and optimization.

Free-electron laser spectrum evaluation and automatic optimization

In this work, an implementation of a recently developed model-independent adaptive control scheme, for tuning uncertain and time varying systems, is demonstrated on the Los Alamos linear particle accelerator. The main benefits of the algorithm are its simplicity, ability to handle an arbitrary number of components without increased complexity, and the approach is extremely robust to measurement noise, a property which is both analytically proven and demonstrated in the experiments performed. We report on the application of this algorithm for simultaneous tuning of two buncher radio frequency (RF) cavities, in order to maximize beam acceptance into the accelerating electromagnetic field cavities of the machine, with the tuning based only on a noisy measurement of the surviving beam current downstream from the two bunching cavities. The algorithm automatically responds to arbitrary phase shift of the cavity phases, automatically re-tuning the cavity settings and maximizing beam acceptance. Because it is model independent it can be utilized for continuous adaptation to time-variation of a large system, such as due to thermal drift, or damage to components, in which the remaining, functional components would be automatically re-tuned to compensate for the failing ones. We start by discussing the general model-independent adaptive scheme and how it may be digitally applied to a large class of multi-parameter uncertain systems, and then present our experimental results.

In-hardware demonstration of model-independent adaptive tuning of noisy systems with arbitrary phase drift

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In-hardware demonstration of model-independent adaptive tuning of noisy systems with arbitrary phase drift