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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Experimental Safe Extremum Seeking for Accelerators

Here, we demonstrate the recent designs of safe extremum seeking (Safe ES) on the 1-km-long charged particle accelerator at the Los Alamos Neutron Science Center (LANSCE). Safe ES is a modification of extremum seeking (ES) which, in addition to minimizing an analytically unknown cost, also employs a safety filter based on an analytically unknown control barrier function (CBF) safety metric. Tuning is necessitated by accelerators being large complex systems, with many drifting parameters due to thermal effects and degradation. At the same time, safe operation (the maintenance of state constraints) is crucial, as damage brings astronomical costs, both financially and in operation downtime. Our measured (but analytically unknown) safety metric is the beam current. We perform multivariable Safe ES on three accelerator applications, in which we adapt 4, 6, and 3 magnet strength parameters, respectively. Two of the three applications are for validated simulation models of beamlines at LANSCE: the first for the proton radiography (pRad) beamline of 800-MeV protons for spot size tuning; the second on a high-performance code, HPSim, for tuning the low-energy beam transport (LEBT) region that contains a beam of 750-keV protons. The third is an experimental tuning of the steering magnets in the LEBT at LANSCE.

43 PARTICLE ACCELERATORS↗
DOE OSTI2025

Local practically safe extremum seeking with assignable rate of attractivity to the safe set

We present Assignably Safe Extremum Seeking (ASfES), an algorithm designed to minimize a measured, static objective function while maintaining a measured, static metric of safety (a control barrier function or CBF) to be positive in a practical sense. We ensure that for trajectories with safe initial conditions, the violation of safety can be made arbitrarily small through appropriately chosen design constants. We also guarantee an assignable “attractivity” rate: from unsafe initial conditions, the trajectories approach the safe set, in the sense of the measured CBF, at a rate no slower than a user-assigned rate. Similarly, from safe initial conditions, the trajectories approach the unsafe set, in the sense of the CBF, no faster than the assigned attractivity rate. The feature of assignable attractivity is not present in the semiglobal version of safe extremum seeking, where the semiglobality of convergence is achieved by slowing the adaptation. We also demonstrate local convergence of the parameter to a neighborhood of the minimum of a quadratic objective function constrained to the safe set with a linear CBF. The ASfES algorithm and analysis are multivariable, but we also extend the algorithm to a Newton-Based ASfES scheme which we show is only useful in the scalar case. The proven properties of the designs are illustrated through simulation examples.

42 ENGINEERING↗
DOE OSTI2024

Semiglobal Safety-Filtered Extremum Seeking With Unknown CBFs

We introduce a safe extremum-seeking (Safe ES) algorithm which achieves the minimization of an unknown objective function while ensuring that an unknown, yet measured, control barrier function (CBF) remains above an arbitrarily small negative value for all time. In other words, “practical safety” is maintained during the entire period of convergence to the constrained extremum. Our design is based on quadratic program (QP) CBF style filters for safety, which is applied in an average and estimated sense. Using nonsmooth analysis tools, we guarantee semiglobal practical asymptotic (SPA) stability of the global constrained optimum, practical convergence to the safe set if starting in a condition violating the CBF, and practical safety for all time—semiglobally—if starting in safe set. The safety result of the paper is analogous with modern notions of SPA stability, guaranteeing that, for any small violation of safety, there exist design coefficients which guarantee that such a small violation is not exceeded. The paper outlines a set of sufficient conditions on the barrier and objective functions, and by way of a Lyapunov argument, we demonstrate that nonconvex constrained optimization problems can be solved. We present these results in the setting of a static map and a dynamical system. A simulation example illustrates the results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Model-free stabilization via Extremum Seeking using a cost neural estimator

In this paper, a fully model-free architecture for vertical stabilization of thermonuclear plasmas in tokamak experimental reactors is presented. For the first time, an Extremum Seeking control algorithm is combined with neural networks to estimate the Lyapunov function to be minimized, resulting in a fully data-driven control architecture. The performance of different neural networks are compared. Specifically, Multilayer Perceptrons and Extreme Learning Machines are considered. The proposed architecture is tested in simulation to show that it can counteract relevant plasma disturbances, resulting in a significant improvement in terms of the achievable operative space compared to the Extremum Seeking algorithm, which still relies on model-based cost estimator.

42 ENGINEERING↗
DOE OSTI2021

Field Demonstration of Inverter-based Voltage Management using Extremum Seeking Control

The influx of Distributed Energy Resources (DER) throughout the distribution system presents a challenge and an opportunity for maintaining power quality standards throughout the system. As such, DER Management systems have become a burgeoning field in both industry and academia. This work presents results from a field test of a model-free, distributed control approach, Extremum Seeking, applied to voltage management on a live feeder in Riverside, CA. The paper presents selected results to highlight the successes and challenges the control approach faced. The work shows that despite slow inverter response, extremum seeking control is able to drive voltage toward a target without knowledge of the system it is operating on.

14 SOLAR ENERGY↗
DOE OSTI2026

Adaptive Model-Free Vehicle Path-Tracking via Fast-Converging Prescribed-Time Newton-Based Extremum-Seeking Control

Model-free control (MFC) offers a simple and effective approach to automated vehicle path-tracking without requiring an explicit plant model for control law design. However, gain tuning in MFC is typically carried out through trial-and-error, which can be time-consuming and may lead to suboptimal performance. To address this limitation, extremum-seeking-based adaptive MFC has shown promise by enabling real-time adaptation of control gains, without relying on a predefined vehicle model. Nonetheless, existing ESC approaches often suffer from slow convergence. This paper integrates MFC, employing longitudinal and lateral ultra-local models of a rear-wheel-drive vehicle, with a novel prescribed-time (PT) Newton-based extremum-seeking control (ESC) strategy that ensures rapid convergence of control gains within the prescribed time. Unlike conventional gradient-based ESC methods, the PT Newton-based ESC leverages artificial delays and time-periodic gains, not only to guarantee convergence within the specified time, but also to compensate for feedback delays. Simulation results demonstrate that the proposed approach significantly improves gain adaptation speed and tracking accuracy. This work advances adaptive model-free vehicle control by offering a high-performance, delay-resilient alternative to existing ESCMFC frameworks.

Waleed khan, Muhammad [The University of Texas at ↗
DOE OSTI2022

Extremum-Seeking-Based Ultra-local Model Predictive Control and Its Application to Electric Motor Speed Regulation

Electric vehicle (EV) market is rapidly expanding. As a critical component of EV, an electric motor needs to accurately follow a reference speed signal while respecting the electrical current constraint for safety. Those requirements are usually formulated as a model predictive control (MPC) problem. However, the performance of traditional model-based MPC depends on the accuracy of the system model, which may not always be guaranteed in reality. Therefore, we utilize a data-driven, model-free predictive control strategy, called ultra-local MPC (ULMPC), to control the speed of an electric motor. To further enhance the control performance of ULMPC, we employ the extremum-seeking control (ESC) to tune the control gain of the ULMPC online. Simulation and hardware experiments demonstrate the enhancement of the extremum-seeking-based ULMPC over a constant-gain ULMPC.

Zhou, Yujing↗
DOE OSTI2024

A New Simple-to-Configure Self-Perturbing Multivariable Extremum-Seeking Controller

This paper presents a new stochastic relay-based extremum-seeking controller (ESC) for multi-input-single-output (MISO) systems. The algorithm was developed with the goal of simplifying configuration to enable easier deployment to real-world problems. A solution is developed first for a static map and then adapted for a general class of dynamic systems. The number of configurable parameters is one per input channel for the static case and only one additional parameter is needed for the dynamic version. The problem of gradient identifiability is solved via the use of stochastic relay gains and a simple stability proof for the static case is presented. Simulation tests demonstrate the performance of the strategy for optimizing both static and dynamic systems.

Salsbury, Timothy [BATTELLE (PACIFIC NW LAB)]↗
DOE OSTI2021

Adaptive Extremum Seeking Control Based LCL Filter Resonant Frequency Online Estimation

The LCL filter has been widely used in the grid-tied inverter systems. However, the resonance of the LCL filter can reduce the system stability margin and the control performance. Moreover, the grid impedance variations can lead to the drift of the resonant frequency, which can further worsen the system robustness. Thus, it is important to know the actual resonant frequency of the LCL filter. In this letter, an adaptive extremum seeking control (AESC) based estimation scheme is proposed to estimate the resonant frequency of the LCL filter online. Further by injecting a high-frequency (HF) signal into the inverter output voltage, the AESC scheme can identify the extremum of the LCL filter amplitude response, i.e., resonant peak. The amplitude of injection signal is adaptive based on the inverter HF response, which can address the tradeoff between the dynamic response and inverter output current quality. Most importantly, compare to other method, the proposed scheme has very low computational complexity, which minimizes the burden to the normal inverter controller operation. Stability analysis is given in this letter, and experimental studies are conducted to validate the effectiveness of the proposed scheme.

42 ENGINEERING↗
DOE OSTI2020

Batch Measurement Extremum Seeking Control of Distributed Energy Resources to Account for Communication Delays and Information Loss

Distributed Energy Resources (DER) have great potential to enhance the operation of electric power distribution systems. Previously, we explored the use of 2 Dimensional Extremum Seeking (2D-ES) control algorithms to enable model-free optimal control of DER to provide grid services to both the distribution and transmissions systems. Motivated by preliminary deployments of DER managed by 2D-ES algorithms in hardware-in-the-loop tests and in operational distribution grids, in this work, we extend the control scheme to accommodate communication delays and information loss. We propose a modification to the 2D-ES scheme to allow for the processing of batches of possibly noncontiguous objective function measurements at unknown and possibly uneven intervals. We provide a proof of the convergence of the batch 2D-ES (2D-BES) scheme when optimizing a generic convex objective function, as well as simulation results that demonstrate the suitability of the approach for substation active and reactive power target tracking.

Sankur, Michael↗
DOE OSTI2024

Extremum seeking control of distributed energy resources with decaying dither and equilibrium-based switching

Embodiments relate to an operating system coupled to and controlling at least one Distributed Energy Resource (DER) in a smart grid and includes an electricity distribution network and a 2-dimensional Extremum Seeking (2D-ES) controller coupled to network. The electricity distribution network has first and second inputs and one output and maps all active power and reactive power inputs to the smart grid providing measurements of an objective function. The 2D-ES controller controls the DER and includes an active power loop and a reactive power loop. The active power loop is in communication with the first input and the output, governs active power contribution, and receives measurements of the objective function which contain static and oscillatory components. The reactive power loop is in communication with the second input and the output, governs reactive power contribution, and receives measurements of the objective function which contain static and oscillatory components.

Arnold, Daniel↗
DOE OSTI2022

Black-box optimization of a closed-circuit reverse osmosis system for desalination through extremum seeking control

We study the minimization of the cost function of a closed-circuit desalination reverse osmosis (CCRO) system, which is used for producing drinking water. The cost function is a trade-off between the specific energy consumption and the specific brine management cost. The extremum-seeking controller (ESC) manipulates the critical electric conductivity of the brine to minimize the cost function. Experiments were designed in which the composition of the feed salinity is increased to test the controller’s ability to converge to a new optimum. The ESC was able to shift the critical conductivity to a new optimum, which resulted in a 9% improvement in the cost function.

Chowdhury, Dhruba↗
DOE OSTI2020

Extremum seeking for optimal control problems with unknown time-varying systems and unknown objective functions

We consider the problem of optimal feedback control of an unknown, noisy, time-varying, dynamic system that is initialized repeatedly. Examples include a robotic manipulator which must perform the same motion, such as assisting a human, repeatedly and accelerating cavities in particle accelerators which are turned on for a fraction of a second with given initial conditions and vary slowly due to temperature fluctuations. In this paper, we present an approach that applies to systems of practical interest. The method presented here is model independent; does not require knowledge of the objective function; is robust to measurement noise; is applicable for any set of initial conditions; is applicable to simultaneously controlling an arbitrary number of parameters; and may be implemented with a broad range of continuous or discontinuous functions such as sine or square waves. For systems with convex cost functions we prove that our algorithm will produce controllers that approach the minimal cost. For linear systems we reproduce the cost minimizing linear quadratic regulator optimal controller that could have been designed analytically had the system and cost function been known. We demonstrate the effectiveness of the algorithm with simulation studies of noisy and time-varying systems.

42 ENGINEERING↗
DOE OSTI2021

Extremum Seeking-Based Control System for Particle Accelerator Beam Loss Minimization

Particle accelerators throughout the world vary widely in terms of age and availability of advanced noninvasive diagnostics that provide varying levels of detail about the accelerated beams. Additionally, beam loss measurements and current monitors are ubiquitous in the accelerator community, they are noninvasive, and they are some of the most important metrics in terms of preventing damage or irradiation of beam pipes and equipment for high-energy machines. However, beam loss and current measurements are difficult to use for feedback tuning because of a lack of a known analytic relationship between scalar loss measurements throughout an accelerator and the hundreds of thousands of parameters that influence the beam and time variation of the beam source itself. In this work, we present a model-independent extremum seeking (ES) controller, which has been implemented for automated tuning and optimization of the Los Alamos Neutron Science Center (LANSCE) linear ion accelerator based only on scalar quantities, such as beam loss or flux measurements. We demonstrate the approach on various accelerator subsystems, including groups of radio frequency (RF) accelerating cavities, quadrupole magnets, bending magnets, and steering magnets. This tool is now available as a use graphical user interface (GUI) in the LANSCE control room, allowing beam physicists to choose arbitrary groups of parameters and beam loss or current monitors for adaptive tuning.

43 PARTICLE ACCELERATORS↗