Estimation for AMB-Supported Rotor Systems: A Feasibility Study for Going Beyond the Kalman Filter

Abstract

As a key enabler for rotating machinery operating at very high speeds with higher efficiency, active magnetic bearings (AMBs) bring many advantages, including lubricant-, and friction-free operation. As AMBs are open-loop unstable, they require feedback control, and good results for multiple-input multiple-output AMB-rotor-systems are typically achieved with state-space methods, requiring state estimators. Further, AMBs’ performance in rotor systems is impacted by effects such as unbalances and changing loading, which can be interpreted as unknown parameters that one may want to estimate. Today, in rotor-AMB systems, commonly, variants of the Kalman filter are employed. By design, they approximate the system dynamics, e.g., in the form of linearization, and are often tuned for a specific operation speed. Parameter estimation introduces further nonlinearities in the problem, and parameters are rarely subject to purely aleatoric uncertainty or following a Gaussian distribution. Often, bounds for physical parameters are known from engineering insight, but cannot be directly used in variants of the Kalman filter. In contrast, moving horizon estimation (MHE), an estimation method formulating and solving online the underlying estimation problem as a nonlinear optimization problem over a moving window of past measurements, can overcome these deficiencies. It can naturally deal with nonlinear dynamics and with bounded parameters to estimate, where the latter is useful also for diagnostic purposes. Due to its numerical and theoretical complexity, it is presently not as popular as Kalman filtering in engineering applications. This contribution investigates whether MHE can realize foundational theoretical advantages in a prototypical test scenario for AMB-rotor systems. The estimation results practically confirm the theoretical differences between the Kalman filter and the moving-horizon estimator. However, subsequent work will try to improve MHE’s estimates by using more of its capabilities.