Cavity Field Control for Linear Particle Accelerators

High-energy linear particle accelerators enable exploration of the microscopic structure of pharmaceuticals, solar cells, fuel cells, high-temperature superconductors, and the universe itself. These accelerators accelerate charged particles using oscillating magnetic fields that are confined in metal cavities. The amplitudes and phases of the electromagnetic fields need to be accurately controlled by fast feedback loops for proper accelerator operation.This thesis is based on the author's work on performance analysis and control design for the field control loops of the linear accelerator at the European Spallation Source (ESS), a neutron microscope that is under construction in Lund, Sweden. The main contribution of the thesis is a comprehensive treatment of the field control problem during flat-top, which gives more insight into the control aspects than previous work. The thesis demonstrates that a key to understand the dynamics of the field control loop is to represent it as a single-input single-output system with complex coefficients. This representation is not new itself but has seen limited use for field control analysis.The thesis starts by developing practical and theoretical tools for analysis and control design for complex-coefficients systems. This is followed by two main parts on cavity field control. The first part introduces parametrizations that enable a better understanding of the cavity dynamics and discusses the most essential aspects of cavity field control. The second part builds on the first one and treats a selection of more advanced topics that all benefit from the complex-coefficient representation: analysis of a polar controller structure, field control design in the presence of parasitic cavity resonances, digital downconversion for low-latency feedback, energy-optimal excitation of accelerating cavities, and an intuitive design method for narrowband disturbance rejection. The results of the investigations in this thesis provide a better understanding of the field control problem and have influenced the design of the field controllers at ESS

Five-Full-Block Structured Singular Values of Real Matrices Equal Their Upper Bounds

We show that the structured singular value of a real matrix with respect to five full complex uncertainty blocks equals its convex upper bound. This is done by formulating the equality conditions as a feasibility SDP and invoking a result on the existence of a low-rank solution. A counterexample is given for the case of six uncertainty blocks. Known results are also revisited using the proposed approach

Complex-coefficient systems in control

Complex-valued dynamics can be used for modeling rotationally invariant two-input two-output systems and bandpass systems when they are considered in the baseband. In a few instances, control design has been done in the complex domain, which facilitated analysis and synthesis. While previous work has been application specific, we will discuss more generally how complex valued dynamics arise, basic properties of these systems, revisit some classic control theoretic results in the complex setting, and discuss two novel examples of control design in the complex domain - accelerator cavity field control and feedback linearization of RF amplifiers

Control Problems at the European Spallation Source

A background on the Europan Spallation Source is given, and our work on three control problems important for the design of its linear accelerator are presented

Trade-offs in Control of Switched Reluctance Motors (Avvägningar vid reglering av switchade reluktansmotorer)

Soaring prices for rare earth metals have led to significantly increased production costs for permanent magnet motors. This has motivated research into alternative motor types, one of them, the switched reluctance motor (SRM), will be discussed in this thesis. The SRM has several positive and negative characteristics as well as highly nonlinear dynamics. It is not clear how trade-offs between these characteristics should be made in an optimal fashion when designing the motor hardware and control algorithm. An optimal control problem is formulated and the possibilities of using control to make trade-offs between torque ripple and efficiency is investigated. Based on the optimization results some possible improvements in SRM control are highlighted

Cavity Field Control for High-Intensity Linear Proton Accelerators

The European Spallation Source will, once fully operational in 2025, be the world's brightest neutron source. The neutrons will be generated by bombarding a tungsten target with protons accelerated to 96\% the speed of light by electromagnetic fields confined in 155 radio-frequency cavities along the world's most powerful linear accelerator.This thesis has been motivated by the strict control specifications on the amplitudes and phases of the accelerating electromagnetic fields. By considering the field control problem from an automatic control perspective, the thesis aims at improving the understanding of the problem and to explain important aspects of the control design.Throughout the thesis it has been helpful to model the cavity and RF system by complex-coefficient single-input single-output systems. The complex-coefficient representation was particularly useful for discussing: (1) the control design for cavities with parasitic resonance modes; (2) the effect of loop phase variations on feedback stability; (3) the directionality of the disturbances and the objective function.The thesis presents a non-standard parametrization and derivation of the cavity field dynamics that make it easier to relate the physical cavity process to the model, and simplifies the understanding of how the cavity parameters affect the achievable control performance.The control performance of simple PI(D)-controllers and general linear time-invariant controller was compared using the Youla parametrization and convex optimization; it was found that PI(D)-controllers in many cases achieved performance similar to the more general linear time-invariant controller; this indicates that simple PI(D)-controllers in many cases are an excellent choice for cavity field control.Lastly, the energy-optimal strategy to build up the electromagnetic cavity fields is derived, allowing the sustainability of the European Spallation Source to be further improved

An Intuitive Design Method for Disturbance-Rejecting Peak Filters

We present a method for augmenting a nominal controller with a peak filter to achieve improved rejection of narrowband disturbances. The method is based on consideration of the open-loop Nyquist curve, which arguably makes it more intuitive and flexible than previous approaches. We also comment on some implementation aspects, and give an application example based on a control problem at a particle accelerator

Transient beam loading based calibration for cavity phase and amplitude setting

Traditional phase scan method for cavity phase and amplitude setting is offline and hard to track the variations of environment and operation points. An alternative beam loading based calibration method is investigated in this paper, which might become useful online/real time calibration method