Distribution Voltage Regulation using Extremum Seeking Control with Power Hardware-in-the-Loop.
Abstract not provided.
Johnson, Jay Tillay↗
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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↗
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↗
Bounded extremum seeking with discontinuous dithers
The analysis of discontinuous extremum seeking (ES) controllers, e.g. those applicable to digital systems, has historically been more complicated than that of continuous controllers. We establish a simple and general extension of a recently developed bounded form of ES to a general class of oscillatory functions, including functions discontinuous with respect to time, such as triangle or square waves with dead time. We establish our main results by combining a novel idea for oscillatory control with an extension of functional analytic techniques originally utilized by Kurzweil, Jarnik, Sussmann, and Liu in the late 80s and early 90s and recently studied by Durr et al. Lastly, we demonstrate the value of the result with an application to inverter switching control.
97 MATHEMATICS AND COMPUTING↗
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↗
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↗
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↗
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 ↗
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↗
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)]↗
Bounded extremum seeking for angular velocity actuated control of nonholonomic unicycle
Here, we study control of the angular-velocity actuated nonholonomic unicycle, via a simple, bounded extremum seeking controller which is robust to external disturbances and measurement noise. The vehicle performs source seeking despite not having any position information about itself or the source, able only to sense a noise corrupted scalar value whose extremum coincides with the unknown source location. In order to control the angular velocity, rather than the angular heading directly, a controller is developed such that the closed loop system exhibits multiple time scales and requires an analysis approach expanding the previous work of Kurzweil, Jarnik, Sussmann, and Liu, utilizing weak limits. We provide analytic proof of stability and demonstrate how this simple scheme can be extended to include position-independent source seeking, tracking, and collision avoidance of groups on autonomous vehicles in GPS-denied environments, based only on a measure of distance to an obstacle, which is an especially important feature for an autonomous agent.
33 ADVANCED PROPULSION SYSTEMS↗
Application of extremum seeking for time-varying systems to resonance control of RF cavities
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. Lastly, 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.
47 OTHER INSTRUMENTATION↗
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↗
Extremum Seeking Library (ESL) v1.0
The software developed is a library for the Modelica language. The library includes different extremum seeking control algorithms and examples of possible usecases. It is also intended to export the models as so called Functional Mock-up Units, which are models supported by any kind of software which supports the Functional Mock-up Interface standard.
Mueller, Joscha↗
Hierarchical Management of Distributed Energy Resources Using Chance-Constrained OPF and Extremum Seeking Control: Preprint
Distributed energy resources (DERs) are becoming an important part of distribution systems because of their economic and environmental benefits. Although their inherent intermittency and volatility introduce uncertainties into the system, they have potential to provide controllability to the system under proper coordination. In this paper, we propose a hierarchical control algorithm for distribution systems with DERs so that they have controllability similar to that of a generator bus. The upper level scheduler solves a chance-constrained optimal power flow (OPF) problem to plan the operation of the DERs based on forecasts, and the lower level distributed DER controllers leverage the extremum seeking approach to deliver the planned power at the feeder head. The proposed algorithm is tested on a modified IEEE 13-node feeder, demonstrating its effectiveness.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Hierarchical Management of Distributed Energy Resources Using Chance-Constrained OPF and Extremum Seeking Control
Distributed energy resources (DERs) are becoming an important part of distribution systems, because of their economic and environmental benefits. Although their inherent intermittency and volatility introduce uncertainties into the electric power system, they have the potential to provide controllability to the system under proper coordination. In this paper, we propose a hierarchical control algorithm for distribution systems with DERs so that they have controllability similar to a generator bus. The upper level scheduler solves a chance-constrained optimal power flow (OPF) problem to plan the operation of the DERs based on forecasts, and the lower level distributed DER controllers leverage the extremum seeking approach to deliver the planned power at the feeder head. The proposed algorithm is tested on a modified IEEE 13-node feeder, demonstrating its effectiveness.
24 POWER TRANSMISSION AND DISTRIBUTION↗