Unbalance Compensation of AMB Systems with Input Delay: A Truncated Predictor Feedback Based Output Regulation Approach

Active magnetic bearings (AMBs) adopt electromagnetic forces to support the rotating shaft and do not have physical contact with the rotary structure. Compared to conventional mechanical bearings, AMBs do not require lubrication; the non-contact working environment improves the efficiency and reduces maintenance cost caused by mechanical wear; the dynamic forces also help the machinery to achieve higher rotational speeds. These appealing features of AMBs have gradually expanded their application in different industries, especially those involving high speed rotating machineries, such as compressors, where efficiency and reliability are highly desired.

Emerging applications in offshore drilling for oil and gas production require compressors to operate in a remote and harsh environment for long periods of time. By adopting AMB technologies, these remotely operated applications have become technically and economically more feasible. Motivated by the challenges in those applications, this dissertation first addresses controlling high speed compressors supported by AMBs in offshore oil and gas development, where the control and sensor measurement signals are transmitted through long cables between the control unit on the shore and the compressor on the seabed. These cables, which may extend for several kilometers, introduce significant time delays to the system and the delays can degrade the system performance and even cause instability. Therefore, control methods that effectively contain the delay effect become indispensable. In this dissertation, the truncated predictor feedback (TPF) control law is applied to handle the time delay. The TPF control method utilizes the prediction of future states in the control signal calculation to eliminate the delay effect. The controller corresponding to the maximized input delay that the closed-loop system can tolerate is obtained iteratively from the solution of a linear matrix inequality (LMI) problem. It is demonstrated in the dissertation that the TPF controller can tolerate a significant amount of input delay for AMB system levitation and outperforms a properly designed µ-synthesis robust controller.

The second topic of this dissertation is unbalance compensation of AMB systems at both constant and time-varying rotational speeds. Any rotating machines are subject to disturbance forces caused by residual unbalance and the disturbance force is synchronous to the rotational speed. Therefore, unbalance compensation is crucial for reducing rotor vibration and preserving the system stability in high speed rotating machines. A properly controlled compressor supported by AMBs needs to confine the vibration to a small level to satisfy industrial standards. To mitigate the adverse effects of unbalance forces, this dissertation proposes a novel unbalance compensation technique based on the output regulation mechanism. The problem of output regulation is to design a controller for disturbance rejection and/or reference tracking, while the disturbance or reference signal is generated by a known dynamic system called exosystem. For a time-invariant exosystem, the regulation error can be fully eliminated while for a time-varying exosystem, it is observed that a small residual error exists in the regulated output for a non-minimum phase system, such as an AMB system. A unified gradient method is adopted to ensure that the error is small. To apply the output regulation mechanism, the unbalance forces are modeled as the output of the exosystem and the compensator gains are obtained based on the solution of static regulator equations for the constant speed case and differential regulator equations for the time-varying speed case.

Eventually, the TPF control law and the output regulation based unbalance compensation method are combined to achieve the control requirements of a remotely located compressor supported by AMBs at different rotational speeds. To demonstrate the effectiveness and applicability of the proposed methods, extensive simulations and experiments have been performed using precise AMB system models and AMB test rigs.