Convergence analysis of filtered-X LMS algorithm with secondary path modeling error

A more relaxed sufficient condition for the convergence of filtered-X LMS (FXLMS) algorithm is presented. It is pointed out that if some positive real condition for secondary path transfer function and its estimates is satisfied within all the frequency bands, FXLMS algorithm converges whatever the reference signal is like. But if the above positive real condition is satisfied only within some frequency bands, the convergence of FXLMS algorithm is dependent on the distribution of power spectral density of the reference signal, and the convergence step size is determined by the distribution of some specific correlation matrix eigenvalues.Applying the conclusion above to the Delayed LMS (DLMS) algorithm, it is shown that DLMS algorithm with some error of time delay estimation converges in certain discrete frequency bands, and the width of which are determined only by the 'time-delay estimation error frequency' which is equal to one fourth of the inverse of estimated error of the time delay.

Performance analysis of FXLMS algorithm with secondary path modeling error

Performance analysis of filtered-X LMS (FXLMS) algorithm with secondary path modeling error is carried out in both time and frequency domain. It is shown firstly that the effects of secondary path modeling error on the performance of FXLMS algorithm are determined by the distribution of the relative error of secondary path model along with frequency. In case of that the distribution of relative error is uniform the modeling error of secondary path will have no effects on the performance of the algorithm. In addition, a limitation property of FXLMS algorithm is proved, which implies that the negative effects of secondary path modeling error can be compensated by increasing the adaptive filter length. At last, some insights into the 'spillover' phenomenon of FXLMS algorithm are given.

PRINCIPLES AND PARAMETER DESIGN FOR AC-DC THREE-DEGREE FREEDOM HYBRID MAGNETIC BEARINGS

To simplify the mechanical structure, decrease the overall system size of the 3-degree freedom axial-radial magnetic bearings and reduce the manufacturing costs as well as operating costs, an innovated AC-DC 3-degree freedom hybrid magnetic bearing is proposed, which is driven by a DC amplifier in axial direction and a 3-phase power converter in radial directions respectively, and the axial and radial bias magnetic fluxes are provided with a common radial polarized permanent magnet ring. The principle producing magnetic suspension forces is introduced. By using equivalent magnetic circuit method, the calculation formulas of magnetic suspension forces and the mathematics models of the system are deduced. Nonlinearities of suspension forces and cross coupling between different degree freedoms are studied further by calculating the suspension forces at different displacements and control currents to validate the feasibility of the mathematics model. Then based on the mathematics models of the bearing, a control method of this novel bearing is designed. Lastly, the methods on parameter design and calculations of the bearing are presented, and an applicable prototype is simulated to analyze the magnetic path by using finite element analysis. The theory analysis and simulation results have shown that this magnetic bearing incorporates the merits of 3-phase AC drive, permanent magnet flux biased and axial-radial combined control, and reduces overall system size and has higher efficiency and lower cost, This innovated magnetic bearing has a wide application in super-speed and super-precision numerical control machine tools, bearingless motors, high-speed flywheels, satellites, etc.