INFLUENCE OF UNCERTAINTIES ONPD TUNING

The aim of this work is to present a method for tuning theparameters of PD controller under the influences of the uncertainties, inorder to stabilize the position of a rotor supported by active magneticbearings (AMBs). The uncertainties are relative to mass, transverse andpolar moment of inertia of the rotor. The introduction of the uncertainties isdue to an incomplete modeled dynamic of the system or in the case thesystem being subjected to a parametric variation. The presence of theuncertainties produces a set of differences among the values of the output.Poles displacement method is used to reach the asymptotically stabilitycondition characterized by a periodic oscillation during the transientresponse as a consequence of the impulse input. In this way we carried outsome particular condition under graphical representation which helpsmaking a prevision when the phenomena of instability occurs. In the presentapproach the poles displacement is obtained by imposing respectively thecondition on the real part, which must be negative, and in the discriminantof a second degree equation, which must be less than zero, both depend onthe uncertainties and the angular speed of the rotor. All calculations areperformed through a 4-axis AMB rigid rotor to validate the PD controllermethod rule introduced in this work.