Optimal Design of Structure Predefined Discrete Control for Rotors in Magnetic Bearings

Many layout techniques of time-discrete control algorithms for magnetic bearings are based on quasi-continuous approximations of traditional time-continuous controllers, although this approach does not provide the full dynamic range and may even lead to instability. State-feedback methods require an observer since the number of measured signals is usually less than the number of states in the mathematical rotor model. In case of flexible rotor structures this observer approach leads to a high-order fully coupled controller and often shows untolerable parameter sensitivity. The goal of this paper is to present a layout method for optimal discrete dynamic compensators with structural constraints typical in magnetic bearing applications, i.e. a predefined controller order or a decentralized feedback structure, in order to fill the gap between well known PD-algorithms and state-LQ-schemes. Similar to the latter method the optimal feedback coefficients are obtained by minimization of a quadratic perfom1ance index. Both the perfom1ance index and the corresponding vector gradient can be computed easily for every set of feedback parameters. Quick convergence can be achieved by a powerfull numerical optimization routine. Results of a SPOC-D (Structure-Predefined Optimal Control for Discrete systems) layed out simple magnetic bearing system are presented and compared with the system properties obtained by standard controller design methods.