A Model-based Optimal Control Approach for CERNs AWAKE Electron Line Trajectory Correction Problem
Author
Michalik, David
Term
4. term
Education
Publication year
2021
Submitted on
2021-08-31
Pages
81
Abstract
This thesis explores whether a model-based optimal control method can correct the path of the electron beam in CERN’s AWAKE beam line. In this setting, using a Linear Quadratic Regulator (LQR) in this way had not previously been attempted. After a short introduction to CERN’s accelerators and to the AWAKE experiment, the work focuses on the electron beam line and on how to keep the beam close to a desired trajectory. A physics-based model is built by describing how charged particles move under magnetic fields and simplifying the result to linear equations of motion. A review of current control practices at CERN helps formulate the requirements and control objective. To test feasibility for extremely fast beams (near the speed of light), the system is modeled in a simple form, written in state space and discretized. This leads to a bilinear mathematical model that is controlled with an LQR, a standard optimal control algorithm that balances tracking accuracy against control effort through feedback. Simulations are run in a reinforcement-learning simulation environment that is adapted to include the beam-line elements’ physical properties for the LQR study. The results show that the LQR feedback controller can steer the beam toward its reference path in simulation. However, because there was no access to the physical hardware, the real-world performance could not be assessed.
Dette speciale undersøger, om en modelbaseret optimal styringsmetode kan korrigere banen for elektronstrålen i AWAKE-strålelinjen på CERN. I denne sammenhæng var det ikke tidligere forsøgt at anvende en lineær kvadratisk regulator (LQR) på denne måde. Efter en kort introduktion til CERNs acceleratorer og AWAKE-eksperimentet fokuserer arbejdet på elektronstrålelinjen og på at holde strålen tæt på en ønsket referencebane. Der opstilles en fysikbaseret model ved at beskrive, hvordan ladede partikler bevæger sig i magnetfelter, og ved at forenkle dette til lineære bevægelsesligninger. En gennemgang af de kontrolmetoder, der aktuelt anvendes på CERN, bruges til at formulere krav og styremål. For at teste gennemførlighed for ekstremt hurtige stråler (næsten lyshastighed) modelleres systemet i en enkel form, skrives i tilstandsrum og diskretiseres. Dette giver et bilineært matematisk system, som styres med en LQR, en standard optimal kontrolmetode, der afvejer sporingsnøjagtighed mod styreindsats via feedback. Simulationer gennemføres i et forstærkningslæringsbaseret simulationsmiljø (Reinforcement Learning), som tilpasses til at indkode de fysiske egenskaber af strålelinjens elementer til LQR-studiet. Resultaterne viser, at LQR-feedbackregulatoren kan styre strålen mod referencebanen i simulation. Uden adgang til fysisk hardware er det dog ikke muligt at vurdere ydeevnen i praksis.
[This apstract has been rewritten with the help of AI based on the project's original abstract]