Robust Control of Rotordynamic Instability in Rotating Machinery Supported by Active Magnetic Bearings

This dissertation addresses the control challenges for a practical mechatronic system subject to self-excited instability modeled as a parametric uncertainty. Achieving a balance between the conflicting requirements of performance and robustness in the face of system uncertainty is the primary objective of feedback control. Practical issues such as unstable open-loop plant dynamics, finite actuator capacity, the presence structural flexibility and suboptimal sensor/actuator placement limit the achievable performance through the use of feedback.

The ROMAC Magnetic Bearing Test Rig for Rotordynamic Instability (MBTRI) is a state-of-the-art experiment designed to investigate algorithms that may affect the region of stability of a rotor-bearing system with respect to rotordynamic instability as a result of aerodynamic cross-coupled stiffness. The onset of rotordynamic instability is a significant challenge to successful design and operation of high speed rotating machinery particularly gas compressors. The unique design of the test rig includes several features of an industrial centrifugal gas compressor with a flexible rotor designed to operate above its first bending critical speed. The impellers and gas seals within compressors are the primary source of load-dependent aerodynamic cross-coupled stiffness forces which can lead to self-excited instability and serious machine damage in the absence of sufficient support damping. During the design phase of rotating machines the accurate prediction of the onset of instability is made difficult by reliance on semi-empirical dynamic models with significant uncertainty. Literature on the rotordynamic instability mechanism reveals that in the presence of optimum support damping, a maximum achievable stability threshold can be derived as a function of physical parameters of the rotor-bearing system. This presents an ideal opportunity for the exploration of optimal robust active vibration control algorithms using active magnetic bearings (AMBs). A notable advantage of AMBs is their ability to generate optimal support stiffness and damping characteristics. Unlike passive mechanical bearings, the support characteristics of AMBs may be modified over the operating life of the system without any major hardware changes.

A general framework is presented whereby properties of the rotor-AMB system that impose fundamental limitations on achievable performance of the closed-loop system are evaluated as a nominal model of the MBTRI plant dynamic is constructed. This model was validated using system identification techniques, and augmented with uncertainty models representing the effects of variation in parameters such operating speed and the magnitude of the destabilizing stiffness. Using \mu -synthesis several robust controllers were designed and implemented on the MBTRI hardware to investigate their effect on the stability threshold. The best controller established a thirty-six percent increase in the stability threshold over an existing benchmark controller. This represented an increase from fifty-six percent of the maximum achievable stability threshold to seventy-six percent. Robust stability and performance analysis was performed to discern the extent that either the engineering specifications for the desired control performance or uncertainty model or a combination of the two may be altered to more closely approach the maximum stability threshold.