Robustness Analysis of a Self-Sensing AMB by Means of µ-Analysis

The stabilitymargin of a two degree-of-freedomself-sensing AMB is estimated bymeans of µ-analysis. The specific self-sensing algorithm implemented in this study is the direct current measurement (DCM) method. 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 LTI 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 resultant µ-analyses show that self-sensing AMBs are rather sensitive for variations in the controller and the self-sensing module.