U.S. Particle Accelerator School

Control Theory with Application to Accelerators and RF Systems course

Sponsoring University:

Michigan State University


Control Theory with Application to Accelerators and RF Systems


Claudio Rivetta and John D. Fox, SLAC National Accelerator Laboratory

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. Laboratory sessions will introduce students to computer simulations of simple and practical problems and introduce homework problems. Homework problems will be assigned each day as complement of the labs exercises and instructors will be available to help answer questions about the homework during the evening exercise sessions. There will be a final exam on the last day of class or group presentation/project addressing the solution to particular accelerator problems either based on real cases or reported by papers .

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.

Reading Requirements
The material for the course will be provided by the lecturers. Suggested reading (not mandatory) prior to the class: any undergraduate-level book on Control Systems.

“Control Systems Engineering” 4th edition, by Norman Nise, ISBN 0-471-44577-0 (John Wiley & Sons, 2003)

“Feedback Systems: An Introduction for Scientists and Engineers” by Karl J. Astrom and Richard M. Murray, ISBN 0691135762, (Princeton University Press, 2008)

“Feedback Control of Dynamic Systems” 6th edition, by Gene Franklin, J. David Powell, Abbas Emami-Naeini, ISBN 0136019692, (Prentice Hall, 2009.)


Credit Requirements
Students will be evaluated based on performance in the labs (30% of final grade), the homework (40% of final grade) and on the final exam (30% of final grade).

IU/USPAS course: Physics 671