Magnetic Bearing Test Rig Research Articles

Robust Design of a Fractional-Delay Repetitive Controller for Uncertain Feedback Control Systems and Its Validation on a Magnetic Bearing Test Rig

This article presents a robust design of a fractional-delay repetitive controller in the frequency domain. The control goal is to accurately suppress the control error caused by a disturbance whose period may be a non-integer multiple of the sampling period. Coefficients of the repetitive controller finite impulse response (FIR) filters are calculated by solving a convex optimization problem that includes constraints limiting both the sensitivity function and the control sensitivity function. The proposed new design algorithm is verified by experiments on a test rig to efficiently damp shaft vibrations of an active magnetic bearing (AMB).

Adaptive odd repetitive control for magnetically suspended rotor harmonic currents suppression

Magnetic levitation rotating machinery has been widely used in industrial applications. Odd harmonic currents in the active magnetic bearing coils, which are caused by rotor mass unbalance and sensor runout, increase the power consumption and the base vibration. Repetitive control has recently been used to suppress harmonic currents in magnetic bearing systems. However, repetitive control needs the rotor rotational speed information and has some limitations without a speed sensor. In this paper, an adaptive odd repetitive control which does not need the speed sensors is proposed to suppress the active magnetic bearing odd harmonic currents. Compared to the conventional repetitive control, the second-order generalized integral frequency-locked loop is applied in adaptive odd repetitive control to estimate the rotor speed in real time without additional speed sensors. The magnetically suspended rotor with harmonic disturbances is modeled. The work principle, structure, and design of the adaptive odd repetitive control are addressed. The simulation and experiments are carried out on a rotor active magnetic bearing test rig to validate the effectiveness of the proposed adaptive odd repetitive control, and the results show that the active magnetic bearing odd harmonic currents are well suppressed.

Measurement and simulation of the dynamic characteristics of plain and profiled annular seals

The performance and reliability of turbomachinery is often limited by shaft vibrations induced by fluid forces of (i) plain or profiled annular seals, (ii) pistons and (iii) journal bearings. The rotordynamic coefficients namely, stiffness, damping and inertia of plain annular seals are in general calculated using the bulk-flow approach developed by Childs. However, when applying the calculation method to profiled gaps, especially those with non-symmetrical profiles, large differences between simulation and experimental data are reported. Furthermore, reliable experimental data as well as large databases including experimental and simulation results from a single author are limited. To overcome this, the paper introduces a unique active magnetic bearing test rig, built and operated at the Technische Universität Darmstadt as well as the corresponding simulation method to determine the rotordynamic influence of annular seals. An extensive experimental study is carried out investigating plain, symmetrically profiled and non-symmetrically profiled annular seals within the relevant parameter range for turbulent flow in pumps. The results are compared to the simulation results showing a significant influence of profiled gaps on the dynamic characteristics in comparison to plain annular seals. Furthermore, it is shown that symmetric and non-symmetric profiles have a different influence on the dynamic quantities inertia, damping and stiffness.

Instability Study of Magnetic Journal Bearing under S-CO2 Condition

A supercritical CO2 (S-CO2)-cooled Brayton cycle is under development for distributed power applications for remote regions. In order to successfully develop it, issues of controlling shaft levitation with bearings have to be solved. From several studies, magnetic bearings have been suggested for reliable levitation performance with reduced cost and complexity. However, several studies on magnetic bearing show that instability issues under high-pressure fluid and high-speed operating conditions may exist. The purpose of this research is to provide background for understanding the instability of magnetic bearings under S-CO2 conditions and propose functional requirements of the magnetic bearing. Thus, the rotating shaft with magnetic bearings operating under high pressure fluid was first analyzed. To test the theory, a magnetic bearing test rig was constructed. By comparing experimental data to the analysis results, the analysis results were verified. Therefore, the analysis results can be used for predicting instability in the future and can contribute to the development of better magnetic bearing controllers.

Radial self-stabilizing reluctance magnetic bearing

A novel design for a minimum loss reluctance magnetic bearing, with only one active control loop, will be presented in this paper. On the basis of extensive numerical simulations, the suitability of the bearing concept for machine tools and other possible applications are discussed. The results of the mostly finite element method simulations are being validated and verified by means of tests on a magnetic bearing test rig. At the end of the paper an outlook on possible improvements and further developments will be given.

Robust control of active magnetic bearing systems with an add-on controller to cancel gyroscopic effects: Is it worth it?

One of the performance-limiting factors in the design of robust controllers for active magnetic bearing systems is the fact that the controller needs to be robust to the gyroscopic effects, that is rotational speed-dependent dynamics of the system. Studies in the literature show that better performance and stability can be achieved when gyroscopic effects are explicitly handled by a cross-feedback control for rigid rotor-active magnetic bearing systems. For flexible rotor-active magnetic bearing systems, gyroscopic effects are mainly dealt by defining the rotational speed as an uncertain parameter of the model or with linear parameter-varying controllers. This study explores the novel idea of compensating gyroscopic effects of a flexible rotor-active magnetic bearing system with an add-on controller and investigates its effects on the achieved performance of μ-controllers. The study is carried out on an experimental active magnetic bearing test rig with relatively high gyroscopic effects. An add-on controller is designed to compensate the gyroscopic effects of the first and second flexible modes of the rotor. Two μ-controllers are designed for the system: (1) benchmark controller that is designed using a standard control approach for active magnetic bearing systems and (2) controller designed with a modified model of the system in which the gyroscopic effects for the first and second flexible modes are reduced because of the presence of the add-on controller. Both controllers are implemented, and their performances are compared for initial levitation, run-up test from 0 to 10,000 r/min, orbit sizes at various speeds, and the computational cost of implementing each controller. The results suggest that better performance is potentially possible at the cost of significant increase in the computational complexity of the controller.

Flux density measurement of radial magnetic bearing with a rotating rotor based on fiber Bragg grating-giant magnetostrictive material sensors.

The rotational magnetic field of radial magnetic bearings characterizes remarkable time and spatial nonlinearity due to the eddy current and induced electromagnetic field. It is significant to experimentally obtain the features of the rotational magnetic field of the radial magnetic bearings to validate the theoretical analysis and reveal the discipline of a rotational magnetic field. This paper developed thin-slice fiber Bragg grating-giant magnetostrictive material (FBG-GMM) magnetic sensors to measure air-gap flux density of a radial magnetic bearing with a rotating rotor; a radial magnetic bearing test rig was constructed and the rotational magnetic field with different rotation speed was measured. Moreover, the finite element method (FEM) was used to simulate the rotational magnetic field; the measurement results and FEM results were investigated, and it was concluded that the FBG-GMM sensors were capable of measuring the radial magnetic bearing's air gap flux density with a rotating rotor, and the measurement results showed a certain degree of accuracy.

Harmonic disturbance attenuation in a three-pole active magnetic bearing test rig using a modified notch filter

This study is concerned with the problem of harmonic disturbance rejection in active magnetic bearing systems. A modified notch filter is presented to identify both constant and harmonic disturbances caused by sensor runout and mass unbalance. The proposed method can attenuate harmonic displacement and currents at the synchronous frequency and its integer multiples. The reduction of stability is a common problem in adaptive techniques because they alter the original closed-loop system. The main advantage of the proposed method is that it is possible to determine the stability margins of the system by few parameters. The negative phase shift of the modified notch filter can be tuned to achieve a desired phase margin, while the gain margin can also be adjusted separately. It is shown that the modified notch filter can be designed to suppress multiple harmonics at the same time. It is implemented on a three-pole magnetic bearing test rig to evaluate its performance. Simulation and experimental results indicate that the presented method can be successfully applied to compensate the periodic disturbances such as sensor runout and mass unbalance in active magnetic bearing systems.

Control of a flexible rotor active magnetic bearing test rig: a characteristic model based all-coefficient adaptive control approach

Active magnetic bearings (AMBs) have found a wide range of applications in high-speed rotating machinery industry. The instability and nonlinearity of AMBs make controller designs difficult, and when AMBs are coupled with a flexible rotor, the resulting complex dynamics make the problems of stabilization and disturbance rejection, which are critical for a stable and smooth operation of the rotor AMB system, even more difficult. Proportional-integral-derivative (PID) control dominates the current AMB applications in the field. Even though PID controllers are easy to implement, there are critical performance limitations associated with them that prevent the more advanced applications of AMBs, which usually require stronger robustness and performance offered by modern control methods such as H-infinity control and µ-synthesis. However, these advanced control designs rely heavily on the relatively accurate plant models and uncertainty characterizations, which are sometimes difficult to obtain. In this paper, we explore and report on the use of the characteristic model based all-coefficient adaptive control method to stabilize a flexible rotor AMB test rig. In spite of the simple structure of such a characteristic model based all-coefficient adaptive controller, both simulation and experimental results show its strong performance.

Design, Construction, and Modeling of a Flexible Rotor Active Magnetic Bearing Test Rig

A successful industrial application of flexible rotors supported on active magnetic bearings (AMBs) requires careful attention not only to rotordynamic design aspects but also to electromagnetic and feedback control design aspects. Model-based control design provides the framework to ensure efficient, reliable, and safe operation of turbomachinery on AMBs. This paper describes in detail the design, construction, and modeling process for a high performance AMB test rig which typifies a small industrial super-critical centrifugal compressor. A unique aspect of the design are the two additional radial AMBs to allow the application of simulated destabilizing fluid or electromagnetic forces to the rotor. These forces are difficult to predict and can lead to rotordynamic instability of industrial machinery if not properly accounted for. This test rig provides a realistic platform to evaluate stabilizing control algorithms for high performance turbomachinery. A complete model of rotor, AMB actuators and accompanying electronics, is constructed from individually verified component models. Model validation is confirmed through the successful design and implementation of a μ-synthesis controller.

Self-Sensing of Non-Laminated Axial Magnetic Bearings: Modelling and Validation

The present paper proposes a refined nonlinear axial bearing model not too complex for real–time applications, which may potentially improve the estimator quality of modulation–based self–sensing. Measurements show that the AC component (ripple) of the bearing current is an underlinear function of the AC excitation voltage, which causes the bearing admittance amplitude |Y (jω, iac)| to considerably increase at low amplitudes of iac. The non– consideration of this effect might explain the poor dynamic performance observed in former implementations of modulation–based self–sensing. The model proposed in this paper includes a dynamic (rate dependent) hysteresis model of the Bertotti type, where the magnetic H field is a nonlinear function of the time derivative of flux density dB/dt. Eddy currents are modelled by a linear lumped RL ladder network (Cauer type). The proposed model gives encouraging results and is able to reproduce some of the observed phenomena. INTRODUCTION Self–sensing permits active magnetic bearings to dispense with dedicated position sensors and, instead, reconstruct rotor position information from the voltage and current signals of the actuator coils. Thus, the hardware amount in the machine environment and the amount of cabling can be reduced, which potentially increases hardware reliability. Although self–sensing technology has progressed in terms of theoretical understanding [1, 2] and by the launching of commercial applications, some unsolved technical challenges impede the application of self–sensing to a broader range of applications. One of these technical challenges concerns self–sensing for non–laminated axial bearings. Non–laminated thrust bearings are a difficult candidate for self– sensing because of both the presence of strong eddy current effects and magnetic material nonlinearity. FIGURE 1: Magnetic Bearing Test Rig from MECOS. FIGURE 2: Flux density obtained by linear FEM simulation (COMSOL) @20 Hz, with μr = 5′000 and σ = 2 · 10 S/m.

Estimating Model Uncertainty using Confidence Interval Networks: Applications to Robust Control

Robust control techniques require a dynamic model of the plant and bounds on model uncertainty to formulate control laws with guaranteed stability. Although techniques for modeling dynamic systems and estimating model parameters are well established, very few procedures exist for estimating uncertainty bounds. In the case of H∞ control synthesis, a conservative weighting function for model uncertainty is usually chosen to ensure closed-loop stability over the entire operating space. The primary drawback of this conservative, “hard computing” approach is reduced performance. This paper demonstrates a novel “soft computing” approach to estimate bounds of model uncertainty resulting from parameter variations, unmodeled dynamics, and nondeterministic processes in dynamic plants. This approach uses confidence interval networks (CINs), radial basis function networks trained using asymmetric bilinear error cost functions, to estimate confidence intervals associated with nominal models for robust control synthesis. This research couples the “hard computing” features of H∞ control with the “soft computing” characteristics of intelligent system identification, and realizes the combined advantages of both. Simulations and experimental demonstrations conducted on an active magnetic bearing test rig confirm these capabilities.

Feedback linearization of an active magnetic bearing with voltage control

A feedback linearization controller is presented for a single-degree-of-freedom (DOF) magnetic bearing test rig. The feedback linearization controller is derived from a detailed nonlinear electromagnet model using both analytic relationships and experimental calibration data. The controller is implemented on the test rig in voltage mode, and measured open-loop transfer functions are used to demonstrate the effectiveness of the feedback linearization controller in transforming the nonlinear system to a linear plant. Next, a high-performance controller for the feedback linearized plant is designed with /spl mu/-synthesis to guarantee a beam compliance performance specification. A common problem associated with voltage control in magnetic suspensions and coil resistance variation, is successfully handled by augmenting the feedback linearized plant with a structured uncertainty. Experimental results demonstrate that the /spl mu/ controller with feedback linearization achieves the performance specified during design for the nonlinear plant independent of the disturbance force level or displacement incurred.