Controller parameterization and bias current reduction of active magnetic bearings for a flexible and gyroscopic spindle

Abstract

A magnetically levitated spindle was designed for fatigue testing of cylinders made of fiber reinforced plastic. In these fatigue tests, the speed of the cylinders is varied cyclically between 15,000 and 30,000 rpm until their mechanical failure occurs. Several eigenfrequencies have to be passed to reach the operational speed range. During long-term operation, the rotor of the spindle is prone to overheating due to various losses. One way of reducing the rotor temperature is to decrease the bias current of the radial active magnetic bearings. Since the bias current influences the dynamic behavior of the system, the control of the bearings has to be adapted as well. This article describes a controller design for the system with different bias currents to determine the smallest usable bias current. A detailed model of the plant is developed, which is then used to optimize the parameters of the utilized controller with a predefined structure using the weighted  ∞ norm as the objective function. Since the rotor is highly gyroscopic, its eigenfrequencies change with the rotational speed. To ensure that the system meets certain robustness criteria at all rotational speeds, the parameters of the controller are simultaneously optimized for the plant model at different speeds. This approach leads to a controller which can be used in the entire speed range without the need for gain scheduling. The functionality of the controller and the influence of the bias current on the rotor temperature are investigated through measurements.

Adapting the control of the magnetic bearings of a highly flexible and gyroscopic rotor to the excitations by the motor

“…This speed-dependent behavior of the rotor as well as sensor noise and the limitations of the system have to be considered while designing the controller for the radial AMB. For the test rig, the parameters of a predefined controller structure were tuned using an optimization process, which is described in detail in [9]. The control of the axial AMB, which is decoupled from the radial direction, is less challenging and was tuned manually.…”

“…The controller parametrization process is described in Section 3.2. The model and the parametrization process are described in more detail in [9]. The adaption of this process to the previously described vibrations is shown in Section 3.3.…”

“…4. Structure of the plant model [9] without noise, the controller output u is calculated by u(s) = −C(s) y(s) (1) and u is equal to U set . However, noise and disturbances should be considered in the controller parametrization process.…”

“…Furthermore, to incorporate frequency-dependent design goals and the limitations of the system in the parametrization process, stable weighting functions W are introduced for the disturbance inputs F un , U d and n as well as the evaluation outputs ∆q, I c and u (e.g., [18,21,22,31]). The weighting functions are chosen in such a way that the maximum amplitudes of the inputs are one and the outputs have to be smaller or equal to one (see [9]). Finally, the disturbance inputs are combined in the vector w and the weighted evaluation outputs in the vector z.…”

“…A more detailed description of this approach will be shown in Section 3.2. It was developed and successfully applied to the system to reduce rotor heating [9]. However, during operation, rotor vibrations occurred which limited the performance of the system.…”