Digital control of active magnetic bearings

Theoretical relationships are developed to relate the characteristics of a controller transfer function to the stiffness and damping properties of an active magnetic bearing for machine rotors. Both proportional and derivative feedback are shown to be necessary for closed-loop system stability, and, for the ideal case, bearing stiffness and damping properties are shown to be simple linear functions of the proportional and derivative feedback gain constants, respectively. The flexibility of a digitally controlled magnetic bearing is demonstrated by the implementation of algorithms which include second-derivative and integral feedback. Second-derivative feedback is shown to be effective at extending the usable bandwidth of the digital controller, and integral feedback rejects rotor position error in the presence of static loads. The relationship between controller sampling rate and bearing performance is investigated, and it is shown that increased sampling rate and increased amounts of second-derivative feedback have similar effects on the bearing properties     

Fault diagnosis of active magnetic bearings

Active magnetic bearings (AMBs) are intrinsically unstable systems and require feedback control to ensure stable operation. Further, sensors, actuators, and the rotor need to operate under normal conditions, and a fault detection and diagnostics system is necessary to ensure a safe and reliable operation. Accordingly, several studies have developed methods to detect failures associated with the rotor or the electrical system (i.e., AMB). However, prior identification of the dynamic system parameters or the magnetic forces is usually desired, which can be impractical for real machines. To overcome this problem, this study proposes a failure detection method based on a mathematical model and the correlation between the measured states related to the rotor and the control. Artificial neural networks are used to map the states that cannot be measured, and faults are determined by comparing the output correlations of neural networks. Faults in the AMB/rotor system are identified considering various rotor unbalance configurations (mechanical failures) and failures in the position sensor gain and in the magnetic actuator current (electrical failures). Various fault configurations were explored for each case cited. A comparison of the theoretical and experimental results showed good agreement, which demonstrates the adequacy of the method in detecting mechanical and electrical failures in industrial machines.     

Improvements of the integration of active magnetic bearings

Functional and structural integration are tools to improve active magnetic bearing systems. In this paper two aspects of the integration of electromagnetic bearings are presented: (1) The non-linearity of the magnetic force is compensated by software integrated in the digital controller. (2) In self-sensing bearings the rotor position is identified from the electric state variables directly at the power amplifiers.     

Nonlinear system identification

This paper provides an overview of nonlinear system identification methodologies. The theory and application of nonlinear system identification is vast, and this overview is not intended to be comprehensive. Rather, the attempt here is to illustrate some of the salient features and key aspects of nonlinear system identification, especially those most relevant to the practitioner. In particular, this overview focuses on important issues in nonlinear system idenfication that differ from those encountered in linear system identification, including tests for nonlinearity, model selection, and input signal considerations.     

High-efficiency linear power amplifier for active magnetic bearings

A modified class-G linear amplifier has been developed to improve the overall efficiency of a transconductance amplifier loaded with the high inductance and low resistance typical of the magnetic bearing coils. A simple theoretical characterization has been used to provide some diagrams to optimize the power efficiency as a function of a nonconstant load such as that due to a rotor unbalance. Experimental results are reported that show a more than satisfactory agreement with the expected results and the developed theory     

Feedback linearization of active magnetic bearings: current-mode implementation

Feedback linearization is a promising approach to the nonlinear control problem posed by active magnetic bearing systems. In this paper, feedback linearization is employed in combination with robust control techniques for the regulation of a single axis test rig actuated by a multiple pole magnetic bearing. To this end, a nonlinear polynomial model of the magnetic actuator was developed based on its experimental calibration. The effect of the amplifier and measurement system dynamics on the feedback linearization performance, was also examined, and compensation filters were developed. Finally, an uncertainty framework was proposed for the linearized plant, and a robust controller was designed via /spl mu/ synthesis. Experimental results demonstrate that the feedback-linearized active magnetic bearing system can achieve stability and the specified performance over the entire range of bearing clearance. The introduction of compensation filters is shown to be essential to this result.     

Standardized measurements of interaction forces in autostable superconducting magnetic bearings

Passive magnetic bearings involving superconductors combined with permanent magnets have great potential for future utilization in systems that are exceptionally critical concerning friction and wear. In the field of power systems, possible applications of these superconducting magnetic bearings include flywheels and cold machines such as generators, motors and cold compressors. Present bearing designs are based on the high-temperature superconductor YBa₂Cu₃O₇. In order to investigate the capabilities of these materials and to establish an optimized bearing design, we have built a system that allows precise and reproducible measurements of interaction forces between permanent magnets and superconductors. Different sizes and geometries and various configurations can be accommodated. Our intention is to contribute to a standardization of the experimental technique.     

Improved blind channel identification using a parametric approach

In wireless communications, the channel has a known manifold structure due to the sensor array response, pulse-shaping function, and sampling phase. By exploiting this information, the method presented in this article achieves improved performance over unstructured blind channel estimation schemes. The approach is subspace-based, and can take advantage of multiple channel estimates if available, e.g., from different time slots in TDMA systems. Its performance is numerically simulated and compared against the original unstructured channel subspace method     

A parametric blind subspace identification: robustness issue

Subspace techniques became in recent years a popular tool for blind identification of single-input multiple output finite-impulse response (SIMO-FIR) systems. However, a serious drawback of these methods is high sensitivity to the order modeling errors. In this contribution, we show that a parametric approach of subspace methods, i.e., exploiting the specular structure of the propagation channel, is intrinsically robust to channel order overestimation     

Nonlinear self-consistent theory of superheterodyne and parametric free electron lasers

A new approach to a nonlinear self-consistent theory of superheterodyne and parametrical FEL has been formulated. The method of averaged kinetic equation was taken as a principle. Efficiency and capacity for work of the developed approach were illustrated by series of concrete examples.     

Blind identification of multipath channels: a parametric subspaceapproach

In this paper, blind identification of single-input multiple-output (SIMO) systems using second-order statistics (SOS) only is considered. Using the assumption of a specular multipath channel, we investigate a parametric variant of the so-called subspace method. Nonparametric subspace-based methods require precise estimation of the model order; overestimation of the model order leads to inconsistent channel estimates. We show that the parametric subspace method gives consistent channel estimates when only an upper bound of the channel order is known. A new algorithm, which exploits parametric information on the channel structure, is presented. A statistical performance analysis of the proposed parametric subspace criterion is presented; limited Monte Carlo experiments show that the proposed algorithm is second-order optimal for a large class of channels     

A new method for improving the dynamics of superconducting magnetic bearings

This paper describes a new method for improving the dynamics of passive type superconducting magnetic bearings (SMBs). The SMBs are composed of two kinds of superconductors and a permanent magnet. The superconductors of the SMBs were field-cooled in the experiments. After the field-cooling, impulse responses were performed for various horizontal displacements. Then, changes in stiffness and damping coefficient of the SMBs were investigated. From the experimental results, it is found that the stiffness and the damping coefficient are affected by the maximum displacements and by use of sintered superconductors, respectively. The stiffness and the damping coefficient are also evaluated by using frequency responses. Then, the results by frequency responses are compared with those by impulse responses. As a result, it is found that we can control bearing stiffness by changing horizontal displacements and damping coefficient by using sintered superconductors.     

Spectral decomposition in multichannel recordings based onmultivariate parametric identification

A method of spectral decomposition in multichannel recordings is proposed, which represents the results of multivariate (MV) parametric identification in terms of classification and quantification of different oscillating mechanisms. For this purpose, a class of MV dynamic adjustment (MDA) models in which a MV autoregressive (MAR) network of causal interactions is fed by uncorrelated autoregressive (AR) processes is defined. Poles relevant to the MAR network closed-loop interactions (cl-poles) and poles relevant to each AR input are disentangled and accordingly classified. The autospectrum of each channel can be divided into partial spectra each relevant to an input. Each partial spectrum is affected by the cl-poles and by the poles of the corresponding input; consequently, it is decomposed into the relevant components by means of the residual method. Therefore, different oscillating mechanisms, even at similar frequencies, are classified by different poles and quantified by the corresponding components. The structure of MDA models is quite flexible and can be adapted to various sets of available signals and a priori hypotheses about the existing interactions; a graphical layout is proposed that emphasizes the oscillation sources and the corresponding closed-loop interactions. Application examples relevant to cardiovascular variability are briefly illustrated     

Nonlinear system identification using Gaussian inputs

The paper is concerned with the identification of nonlinear systems represented by Volterra expansions and driven by stationary, zero mean Gaussian inputs, with arbitrary spectra that are not necessarily white. Procedures for the computation of the Volterra kernels both in the time as well as in the frequency domain are developed based on cross-cumulant information. The derived kernels are optimal in the mean squared error sense for noncausal systems. Order recursive procedures based on minimum mean squared error reduction are derived. More general input output representations that result when the Volterra kernels are expanded in a given orthogonal base are also considered     

Optimal control of the magnetic bearings for a flywheel energy storage system

With the advances of high strength/light weight composite material, high performance magnetic bearings, and power electronics technology, flywheel energy storage systems (FESS) with magnetically assisted bearings are becoming an exciting alternative to traditional battery systems. One of the challenging problems for such systems is to stabilize the sensitive rotor due to disturbances and plant uncertainties. In this paper, an optimal control system is proposed by incorporating cross-coupling technology into the control architecture, so that the synchronization performance of the rotor in the radial direction can be improved. The control scheme is based on minimization of a new quadratic performance index in which the synchronization errors in the radial direction are embedded. Stability of the control scheme is investigated through Linear Quadratic Gaussian (LQG) optimal control technique. It has been shown that with adequate control parameters the closed-loop stability can be guaranteed theoretically, and the resulting control system can provide satisfactory synchronization performance. Simulations on a compact and efficient FESS with integrated magnetic bearings demonstrate that the proposed approach is very effective to suppress the gyroscopic effort caused by the outside disturbances and model uncertainties.     

A parametric method of identification of single-trial event-relatedpotentials in the brain

A parametric method of identification of event-related (or evoked) potentials on a single-trial basis through an ARX (autoregressive with exogenous input) algorithm is discussed. The basic estimation of the information contained in the single trial is taken from an average carried out on a sufficient number of trials, while the noise sources, EEG and EOG, are characterized as exogenous inputs in the model. The simulations as well as the experimental results confirm the capability of the model of drastically improving the S/N (signal-to-noise) ratio in each single trial and satisfactorily identifying the contributions of signal and noise to the overall recording. A particularly efficient reduction of ocular artifacts is also achieved     

Nonlinear system identification and prediction using orthogonalfunctions

We describe a systematic scheme for the nonlinear adaptive filtering of signals that are generated by nonlinear dynamical systems. The complete filter consists of three sections: a signal-independent standard orthonormal expansion, a scaling derived from an estimate of the vector probability density function (PDF), and an adaptive linear combiner. The orthonormal property of the expansions has two significant implications for adaptive filtering: first, model order reduction is trivial since the contribution of each term to the mean squared error is directly related to the coefficient in the final linear combiner; and second, consistent and rapid convergence of stochastic gradient algorithms is assured. A technique based on the inverse Fourier transform for obtaining a PDF estimate from the characteristic function is also presented. The prediction and identification performance of this nonlinear structure is examined for a number of signals, and it is contrasted with common radial basis function and linear networks     

Generation in crossed fields under parametric variation in the magnetic field

Signal generation in systems with crossed electric and magnetic fields is demonstrated. The generation effect is obtained in an ac magnetic field.     

Application of autoregressive moving average parametric modeling in magnetic resonance image reconstruction

The modeling of data is an alternative to conventional use of the fast Fourier transform (FFT) algorithm in the reconstruction of magnetic resonance (MR) images. The application of the FFT leads to artifacts and resolution loss in the image associated with the effective window on the experimentally-truncated phase encoded MR data. The transient error modeling method treats the MR data as a subset of the transient response of an infinite impulse filter (H(z) = B(z)IA(z)). Thus, the data are approximated by a deterministic autoregressive moving average (ARMA) model. The algorithm for calculating the filter coefficients is described. It is demonstrated that using the filter coefficients to reconstruct the image removes the truncation artifacts and improves the resolution. However, determining the autoregressive (AR) portion of the ARMA filter by algorithms that minimize the forward and backward prediction errors (e.g., Burg) leads to significant image degradation. The moving average (MA) portion is determined by a computationally efficient method of solving a finite difference equation with initial values. Special features of the MR data are incorporated into the transient error model. The sensitivity to noise and the choice of the best model order are discussed. MR images formed using versions of the transient error reconstruction (TERE) method and the conventional FFT algorithm are compared using data from a phantom and a human subject. Finally, the computational requirements of the algorithm are addressed.