Robustness estimation of self-sensing active magnetic bearings via system identification
Van Vuuren, Pieter Andries
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Due to their frictionless operation active magnetic bearings (AMBs) are essential components in high-speed rotating machinery. Active magnetic control of a high speed rotating rotor requires precise knowledge of its position. Self-sensing endeavours to eliminate the required position sensors by deducing the rotor’s position from the voltages and currents with which it is levitated. For self-sensing AMBs to be of practical worth, they have to be robust. Robustness analysis aims to quantify a control system’s tolerance for uncertainty. In this study the stability margin of a two degree-of-freedom self-sensing AMB is estimated by means of μ-analysis. Detailed black-box models are developed for the main subsystems in the AMB by means of discrete-time system identification. Suitable excitation signals are generated for system identification in cognisance of frequency induced nonlinear behaviour of the AMB. Novel graphs that characterize an AMB’s behaviour for input signals of different amplitudes and frequency content are quite useful in this regard. In order to obtain models for dynamic uncertainty in the various subsystems (namely the power amplifier, self-sensing module and AMB plant), the identified models are combined to form a closed-loop model for the self-sensing AMB. The response of this closed-loop model is compared to the original AMB’s response and models for the dynamic uncertainty are empirically deduced. Finally, the system’s stability margin for the modelled uncertainty is estimated by means of μ-analysis. The potentially destabilizing effects of parametric uncertainty in the controller coefficients as well as dynamic uncertainty in the AMB plant and self-sensing module are examined. The resultant μ-analyses show that self sensing AMBs are much less robust for parametric uncertainty in the controller than AMBs equipped with sensors. The μ-analyses for dynamic uncertainty confirm that self-sensing AMBs are rather sensitive for variations in the plant or the self-sensing algorithm. Validation of the stability margins estimated by μ-analysis reveal that μ-analysis is overoptimistic for parametric uncertainty on the controller and conservative for dynamic uncertainty. (Validation is performed by means of Monte Carlo simulations.) The accuracy of μ-analysis is critically dependent on the accuracy of the uncertainty model and the degree to which the system is linear or not. If either of these conditions are violated, μ-analysis is essentially worthless.
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