Effects of variations in controller gains on the dynamics of magnetic bearings
Magnetic bearings support turbomachinery by regulating their forces exerted in relation to the displacement of the machine supported. The regulating control system must be tuned for stable and safe operation of the rotor. The ultimate goal of this study is to determine the effects of changing controller gains on the behavior of the rotor during operation in its normal speed range with a known unbalance load. We also endeavor to confirm the model of the rotor supported the magnetic bearings, as an additional goal.
We first investigate the modelling of rotors supported by magnetic bearings, including the model of the control system. We present a finite element model of a magnetic bearing supported rotor, and perform experiments to determine the characteristics of the control system which governs the magnetic forces on the rotor. The experimental control system characteristics confirm the expected characteristics from theory. With this knowledge, we perform simulations and experiments under the same forcing conditions to determine the accuracy of the model in predicting the experimental behavior of an unbalanced rotor. The model exhibits satisfactory ability in predicting the experimental behavior of the rotor under this loading. Our next step is to determine the effects of variation of proportional and integral controller gains on the behavior of the rotor. Both simulations and experiments show that an increase in the proportional controller gain results in an increase in the rotor’s first critical speed. An increase in the integral gain results in a small decrease in the location of the peak response speed in the speed range tested, while leaving the peak amplitude insignificantly changed. Again, simulations and experiments predict this result.
We reach the following three conclusions from this study. First, the finite element model of the rotor/bearing system is a viable model for predicting the behavior of the experimental system. Second, tuning of the proportional gain shows a significant effect on the behavior of the rotor during unbalance loading across its speed range, due to considerable change in bearing stiffness caused by the tuning of this gain. Last, tuning of the integral gain has a small effect on the behavior of the rotor due to the change in bearing damping, too small to be considered significant.