H∞ Optimal Control for Linear Time Invariant and Parameter Dependent Conditions in Active Magnetic Bearing Systems

Abstract

This thesis mainly focuses on the 𝐻∞ optimal control for the mixed sensitivity problem in rotor/active magnetic bearing (AMB) systems by considering linear time invariant (LTI) and parameter dependent conditions. In order to attenuate vibrations when a rotor runs under contact-free conditions. Riccati based 𝐻∞ optimization is introduced for a rotor/AMB system at particular rotational speeds. A 𝐻∞ controller synthesized by the LMI based gain-scheduling technique was then designed to guarantee stability when the system operates with varying speed. Based on the LMI’s framework, a gain-scheduling controller designed for contact-free recovery, is also presented. The controller’s robust stability and contact-free recovery capability were verified through simulations and experiments.

Finite element modelling (FEM) is introduced into the description of a flexible rotor. The rotor/AMB model, including linearized AMB system actuation under PD control, is then used for robust 𝐻∞ control design as a contact-free plant. In the LTI 𝐻∞ optimization, singular value issues due to discrepancy number of system inputs and outputs is discussed. A solution to that problem is proposed, and examined numerically. In order to extend operating speeds, a switching control system including several LTI 𝐻∞ controllers is introduced and tested in simulation.

Rotor/touchdown bearing contact dynamics are investigated numerically and experimentally. Based on the linearization method for rotor/touchdown bearing contact, a contact-dependent plant including the interaction of the rotor and a movable base was developed for contact-free recovery controller design. It relies on a feedforward contact estimation observer. The LMI based gain-scheduling control action enables the rotor to escape from trapped contact. Additionally, the potential limitation for the contact-recovery controllers is assessed experimentally under significant unbalance. Coast down tests were undertaken to verify contact-free recovery control action when the rotational speed varies in a transient manner.

Date of Award	21 Oct 2016
Original language	English
Awarding Institution	University of Bath
Supervisor	Patrick Keogh (Supervisor), Matthew Cole (Supervisor), Necip Sahinkaya (Supervisor) & Roger Ngwompo (Supervisor)