Robust frequency control - Application to magnetic bearings

H _∞ synthesis is becoming increasingly important among corrector calculation methods. Its main feature is that it can be used to model different transfers of a servo system, while guaranteeing closed-loop stability. It also allows certain robustness objectives to be taken into account, such as guaranteeing stability margins or robustness to poorly known or unmodeled high-frequency dynamics.

We have implemented this approach with the aim of developing a methodology for synthesizing controllers for magnetic bearings. This is a problem with many very precise specifications. In many cases, it can be solved by conventional methods, but not in a systematic way, resulting in longer design times. It is also difficult to carry out test campaigns to optimize a particular aspect of the specifications.

To design the control system, we used a flexible rotor model in modal form, with six bending modes in addition to inertia. Synthesis is first performed continuously. A discrete synthesis is then performed, using the w-transform.

In paragraph 1 , we explain the principles of the H _∞ synthesis. Paragraph 2 presents the physical system and its model, as well as the specifications addressed. The H _∞ synthesis is described in paragraph 3 , indicating how the specifications (bandwidth, disturbance...