U.S. Particle Accelerator School

Control Theory with Applications to Accelerators and RF Systems

Sponsoring University:

Old Dominion University

Course Name:

Control Theory with Applications to Accelerators and RF Systems


Claudio Rivetta, SLAC

Purpose and Audience
The purpose of this course is to introduce the students to control theory focusing on applications to control beam dynamics, RF accelerating structures and other systems part of accelerators and light sources facilities. This course is suitable for advanced students and entry level graduate students who are considering accelerator physics as a possible career and for engineers and operators who want to learn about feedback systems applied in accelerator/light source complex.

Basic linear algebra, calculus, differential equations, complex analysis (matrix manipulation, Eigenvalue - vectors, Fourier/Laplace transforms, etc.)

Basic knowledge of accelerators/ beam dynamics / RF systems (equiv. first-year graduate level). Problems and Labs will be based on Accelerator system examples.

Must be familiar with Matlab simulation code. (Homeworks and labs are based on Matlab)

It is the responsibility of the student to ensure that he or she meets the course prerequisites or has equivalent experience.

This introductory course will focus on control theory applied to dynamic systems, in particular to systems found in accelerator/light source facilities. Fundamental concepts of control theory and feedback design techniques are explored to then introduce to the student to robust design and optimal design of controllers. On the completion of this course, the students are expected to understand analysis and design of feedback systems applied to linear time invariant systems and be able to understand intrinsic limitations in performance in the feedback system and be prepared to understand and apply in the future modern techniques of controller design.

Instructional Method
The course will be offering a series of lectures during the morning and afternoon followed by laboratory sessions. The first week will cover the control theory material during lectures and the laboratory sessions will introduce students to computer simulations of simple and practical problems. The material introduced in the lectures will be completed by homework problems. Homework problems will be assigned each day as complement to the labs exercises and instructors will be available to help answer questions about the homework during the evening exercise sessions.

During the second week several specific problems in accelerators and RF system will be addressed, covering one different topic each day. A lecture presenting the problem and focusing on the analysis and design of that particular topic will be presented in the morning and during the afternoon it will be dedicated to laboratory work focused in that topic. A report and conclusions on the topic assigned per day should be prepared by the student.   

There will be a partial exam on the last day of the first week. Group presentation/project addressing the solution to particular accelerator problems either based on real cases or reported by papers will be presented the last day of the second week.

Course Content
The course will include lectures on Dynamic Systems and Linear Time Invariant Systems. Basic techniques of closed loop feedback analysis and design will presented to conclude with robust design and fundamental limitations in the feedback design. Introduction to full state feedback, observers and estimation is presented to conclude with general topologies and optimal design criteria of controllers (LQR,LQG, LQGLTR, Hinf). All the examples, laboratory and homework problems are related with systems found in accelerator/light source complex. Specific control problems found in accelerators will be addressed in detail the second week of the course. Topics for the second week of the course include:

Reading Requirements

Credit Requirements
Students will be evaluated based on performance in the labs (30% of final grade), the homework (35% of final grade) and on the final exam (35% of final grade) for the first week. Students will be evaluated based on the Labs reports (65%) and final presentation (35%) for the second week.

Old Dominion University course number:
Phys 852, "Control Theory with Applications to Accelerators and RF Systems"
Indiana University course number: Physics 571, "Special Topics in Physics of Beams"
Michigan State University course number: PHY 963, "U.S. Particle Accelerator School"
MIT course number: 8.790, "Accelerator Physics"