Adaptive Compensation of Sensor Runout for Magnetic Bearings With Uncertain Parameters: Theory and Experiments

1999 ◽  
Vol 123 (2) ◽  
pp. 211-218 ◽  
Author(s):  
Joga D. Setiawan ◽  
Ranjan Mukherjee ◽  
Eric H. Maslen
Keyword(s):  
Magnetic Bearing ◽  
Magnetic Bearings ◽  
Parameter Uncertainties ◽  
Persistent Excitation ◽  
Electrical And Magnetic Properties ◽  
Periodic Disturbances ◽  
Mass Unbalance ◽  
On Line ◽  
The Stability ◽  
Rotor Balancing

The problem of sensor runout in magnetic bearing systems has been largely overlooked due to similarities with mass unbalance in creating periodic disturbances. While the effect of mass unbalance can be significantly reduced, if not eliminated, through rotor balancing, sensor runout disturbance is unavoidable since it originates from physical nonconcentricity between rotor and stator. Sensor runout is also caused by nonuniform electrical and magnetic properties around the sensing surface. To improve performance of magnetic bearings, we present an adaptive algorithm for sensor runout compensation. It guarantees asymptotic stability of the rotor geometric center and on-line feedforward cancellation of runout disturbances using persistent excitation. Some of the advantages of our algorithm include simplicity of design and implementation, stability, and robustness to plant parameter uncertainties. The stability and robustness properties are derived from passivity of the closed-loop system. Numerical simulations are presented to demonstrate efficacy of the algorithm and experimental results confirm stability and robustness for large variation in plant parameters.

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

2016 ◽  
Vol 23 (5) ◽  
pp. 770-781 ◽  
Author(s):  
S Mahdi Darbandi ◽  
Mehdi Behzad ◽  
Hassan Salarieh ◽  
Hamid Mehdigholi
Keyword(s):  
Notch Filter ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Disturbance Attenuation ◽  
Test Rig ◽  
Stability Margins ◽  
Periodic Disturbances ◽  
Mass Unbalance ◽  
Gain Margin ◽  
The Stability

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.

Adaptive Virtual Autobalancing for a Rigid Rotor With Unknown Mass Imbalance Supported by Magnetic Bearings

1998 ◽  
Vol 120 (2) ◽  
pp. 557-570 ◽  
Author(s):  
Kai-Yew Lum ◽  
Vincent T. Coppola ◽  
Dennis S. Bernstein
Keyword(s):  
Physical Model ◽  
Magnetic Bearing ◽  
Magnetic Bearings ◽  
Rigid Rotor ◽  
Compensation Scheme ◽  
Elastic Suspension ◽  
Single Plane ◽  
Rotor Imbalance ◽  
Line Identification ◽  
On Line

The objective of this paper is to describe an imbalance compensation scheme for a rigid rotor supported by magnetic bearings that performs on-line identification of rotor imbalance and allows imbalance cancellation under varying speed of rotation. The proposed approach supplements existing magnetic bearing controls which are assumed to achieve elastic suspension of the rotor. By adopting a physical model of imbalance and utilizing measurements of the spin rate, the proposed algorithm allows the computation of the necessary corrective forces regardless of variations in the spin rate. Convergence of the algorithm is analyzed for single-plane balancing, and is supported by simulation in single- and two-plane balancing, as well as by experimental results in single-plane implementation.

Effect of Thrust Magnetic Bearing on Stability and Bifurcation of a Flexible Rotor Active Magnetic Bearing System

2003 ◽  
Vol 125 (3) ◽  
pp. 307-316 ◽  
Author(s):  
Y. S. Ho ◽  
H. Liu ◽  
L. Yu
Keyword(s):  
Periodic Motion ◽  
Magnetic Bearing ◽  
Rotor System ◽  
Magnetic Bearings ◽  
Active Magnetic Bearing ◽  
Flexible Rotor ◽  
Periodic Motions ◽  
Stability And Bifurcation ◽  
Mass Eccentricity ◽  
The Stability

This paper is concerned with the effect of a thrust active magnetic bearing (TAMB) on the stability and bifurcation of an active magnetic bearing rotor system (AMBRS). The shaft is flexible and modeled by using the finite element method that can take the effects of inertia and shear into consideration. The model is reduced by a component mode synthesis method, which can conveniently account for nonlinear magnetic forces and moments of the bearing. Then the system equations are obtained by combining the equations of the reduced mechanical system and the equations of the decentralized PID controllers. This study focuses on the influence of nonlinearities on the stability and bifurcation of T periodic motion of the AMBRS subjected to the influences of both journal and thrust active magnetic bearings and mass eccentricity simultaneously. In the stability analysis, only periodic motion is investigated. The periodic motions and their stability margins are obtained by using shooting method and path-following technique. The local stability and bifurcation behaviors of periodic motions are obtained by using Floquet theory. The results indicate that the TAMB and mass eccentricity have great influence on nonlinear stability and bifurcation of the T periodic motion of system, cause the spillover of system nonlinear dynamics and degradation of stability and bifurcation of T periodic motion. Therefore, sufficient attention should be paid to these factors in the analysis and design of a flexible rotor system equipped with both journal and thrust magnetic bearings in order to ensure system reliability.

Measured and Predicted Force and Stiffness Characteristics of Industrial Magnetic Bearings

1991 ◽  
Vol 113 (4) ◽  
pp. 784-788 ◽  
Author(s):  
J. Imlach ◽  
B. J. Blair ◽  
P. E. Allaire
Keyword(s):  
Critical Speed ◽  
Closed Loop ◽  
Load Capacity ◽  
Magnetic Bearing ◽  
Magnetic Bearings ◽  
Dynamic Loadings ◽  
On Line ◽  
Stiffness Characteristics ◽  
Canned Motor ◽  
Displacement Information

Closed-loop stiffness and load capacity (force) equations have been developed for industrial magnetic bearings. Two sets of magnetic bearings have been constructed using these equations as a design basis. These bearings have been installed in two canned motor pumps. The predicted force and stiffness values from the equations are compared to experimental measurements to determine their validity. When obvious sources of error were eliminated, agreement within 10 percent was obtained for development pump’s magnetic bearings. Agreement was generally better for this pump than for the demonstration pump. By employing these equations, along with easily measured current and displacement information from magnetic bearing equipped machinery, actual stiffness’ and bearing loadings can be determined for operating equipment. Thus, the range of information available from magnetic bearings is extended to include static and dynamic loadings as well as shaft orbits and critical speed and damping information (Humphris et al., 1989). This enhances their use as diagnostic and preventative maintenance tools which are built into machinery and can be used on line.

scholarly journals Design of a PID Controller for a Linearized Magnetic Bearing

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Theodore K. Psonis ◽  
Pantelis G. Nikolakopoulos ◽  
Epaminondas Mitronikas
Keyword(s):  
Pid Controller ◽  
Closed Loop ◽  
Laboratory Data ◽  
Magnetic Bearing ◽  
Magnetic Bearings ◽  
Controller Performance ◽  
The Stability ◽  
Linearized Model ◽  
And Control ◽  
Linear Controllers

This paper presents the study of magnetic bearings regarding a linear model. Initially, the advantages of magnetic bearings are referenced, in relation to the existing technology. Subsequently, the linearized model of the system is presented and the need for closed loop and control of the system is clarified. This need leads to further analysis of linear controllers like P, I, D, PI, PD, and PID. For each of them, the stability of closed loop system is studied, using the characteristic equation of the system and the Routh-Hurwitz criterion. To this end, the boundary conditions for the existence of the stability of each of them are found and presented. After finding the controllers’ characteristic parameters which could provide stability to the system, simulation tests with existence of white noise follow. Finally, the proposed PID controller performance is examined, based on existing laboratory data, and results concerning the stability of this controller are presented.

scholarly journals A Vibration Sensor-Based Method for Generating the Precise Rotor Orbit Shape with General Notch Filter Method for New Rotor Seal Design Testing and Diagnostics

Sensors ◽  
2021 ◽  
Vol 21 (15) ◽  
pp. 5249
Author(s):  
Karel Kalista ◽  
Jindrich Liska ◽  
Jan Jakl
Keyword(s):  
Notch Filter ◽  
Magnetic Bearing ◽  
Magnetic Bearings ◽  
Harmonic Vibration ◽  
Filter Method ◽  
Vibration Exciter ◽  
Active Magnetic Bearings ◽  
Rotor Vibration ◽  
Seal Design ◽  
Exact Shape

Verification of the behaviour of new designs of rotor seals is a crucial phase necessary for their use in rotary machines. Therefore, experimental equipment for the verification of properties that have an effect on rotor dynamics is being developed in the test laboratories of the manufacturers of these components all over the world. In order to be able to compare the analytically derived and experimentally identified values of the seal parameters, specific requirements for the rotor vibration pattern during experiments are usually set. The rotor vibration signal must contain the specified dominant components, while the others, usually caused by unbalance, must be attenuated. Technological advances have made it possible to use magnetic bearings in test equipment to support the rotor and as a rotor vibration exciter. Active magnetic bearings allow control of the vibrations of the rotor and generate the desired shape of the rotor orbit. This article presents a solution developed for a real test rig equipped with active magnetic bearings and rotor vibration sensors, which is to be used for testing a new design of rotor seals. Generating the exact shape of the orbit is challenging. The exact shape of the rotor orbit is necessary to compare the experimentally and numerically identified properties of the seal. The generalized notch filter method is used to compensate for the undesired harmonic vibrations. In addition, a novel modified generalized notch filter is introduced, which is used for harmonic vibration generation. The excitation of harmonic vibration of the rotor in an AMB system is generally done by injecting the harmonic current into the control loop of each AMB axis. The motion of the rotor in the AMB axis is coupled, therefore adjustment of the amplitudes and phases of the injected signals may be tedious. The novel general notch filter algorithm achieves the desired harmonic vibration of the rotor automatically. At first, the general notch filter algorithm is simulated and the functionality is confirmed. Finally, an experimental test device with an active magnetic bearing is used for verification of the algorithm. The measured data are presented to demonstrate that this approach can be used for precise rotor orbit shape generation by active magnetic bearings.

scholarly journals Online Adaptive Parameter Estimation for Quadrotors

Algorithms ◽  
2018 ◽  
Vol 11 (11) ◽  
pp. 167 ◽  
Author(s):  
Jun Zhao ◽  
Xian Wang ◽  
Guanbin Gao ◽  
Jing Na ◽  
Hongping Liu ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Exponential Convergence ◽  
Estimation Error ◽  
Persistent Excitation ◽  
System Parameters ◽  
Adaptive Parameter ◽  
Adaptive Laws ◽  
Accuracy Parameter ◽  
The Stability ◽  
Quadrotor System

The stability and robustness of quadrotors are always influenced by unknown or immeasurable system parameters. This paper proposes a novel adaptive parameter estimation technology to obtain high-accuracy parameter estimation for quadrotors. A typical mathematical model of quadrotors is first obtained, which can be used for parameter estimation. Then, an expression of the parameter estimation error is derived by introducing a set of auxiliary filtered variables. Moreover, an augmented matrix is constructed based on the obtained auxiliary filtered variables, which is then used to design new adaptive laws to achieve exponential convergence under the standard persistent excitation (PE) condition. Finally, a simulation and an experimental verification for a typical quadrotor system are shown to illustrate the effectiveness of the proposed method.

scholarly journals Sliding Mode Output Feedback Control of a Flexible Rotor via Magnetic Bearings

1998 ◽  
Author(s):  
A. S. Lewis ◽  
A. Sinha ◽  
K. W. Wang
Keyword(s):  
Differential Equations ◽  
Sliding Mode ◽  
Output Feedback Control ◽  
Angular Speed ◽  
Magnetic Bearing ◽  
Magnetic Bearings ◽  
Control Parameters ◽  
Flexible Rotor ◽  
Rotor Imbalance ◽  
Feedback Algorithm

A sliding mode feedback algorithm is proposed to control the vibration of a flexible rotor supported by magnetic bearings. It is assumed that the number of states is greater than the number of sensors. A mathematical model of the rotor/magnetic bearing system is presented in terms of partial differential equations. These equations are then discretized into a finite number of ordinary differential equations through Galerkin’s method. The sliding mode control law is designed to be robust to rotor imbalance and transient disturbances. A boundary layer is introduced around each sliding hyperplane to eliminate the chattering phenomenon. The results from numerical simulations are presented which not only corroborate the validity of the proposed controller, but also show the effects of various control parameters as a function of the angular speed of the rotor. In addition, results are presented that indicate how the current required by the magnetic bearings is affected by control parameters and the angular speed of the rotor.

An Evaluation of Stability Indices Using Sensitivity Functions for Active Magnetic Bearing Supported High-Speed Rotor

2006 ◽  
Vol 129 (2) ◽  
pp. 230-238 ◽  
Author(s):  
Naohiko Takahashi ◽  
Hiroyuki Fujiwara ◽  
Osami Matsushita ◽  
Makoto Ito ◽  
Yasuo Fukushima
Keyword(s):  
High Speed ◽  
Transfer Functions ◽  
Mimo System ◽  
Magnetic Bearing ◽  
Singular Value ◽  
Active Magnetic Bearing ◽  
Sensitivity Functions ◽  
Phase Lags ◽  
The Stability ◽  
Stability Indices

In active magnetic bearing (AMB) systems, stability is the most important factor for reliable operation. Rotor positions in radial direction are regulated by four-axis control in AMB, i.e., a radial system is to be treated as a multi-input multioutput (MIMO) system. One of the general indices representing the stability of a MIMO system is “maximum singular value” of a sensitivity function matrix, which needs full matrix elements for calculation. On the other hand, ISO 14839-3 employs “maximum gain” of the diagonal elements. In this concept, each control axis is considered as an independent single-input single-output (SISO) system and thus the stability indices can be determined with just four sensitivity functions. This paper discusses the stability indices using sensitivity functions as SISO systems with parallel/conical mode treatment and/or side-by-side treatment, and as a MIMO system with using maximum singular value; the paper also highlights the differences among these approaches. In addition, a conversion from usual x∕y axis form to forward/backward form is proposed, and the stability is evaluated in its converted form. For experimental demonstration, a test rig diverted from a high-speed compressor was used. The transfer functions were measured by exciting the control circuits with swept signals at rotor standstill and at its 30,000 revolutions/min rotational speed. For stability limit evaluation, the control loop gains were increased in one case, and in another case phase lags were inserted in the controller to lead the system close to unstable intentionally. In this experiment, the side-by-side assessment, which conforms to the ISO standard, indicates the least sensitive results, but the difference from the other assessments are not so great as to lead to inadequate evaluations. Converting the transfer functions to the forward/backward form decouples the mixed peaks due to gyroscopic effect in bode plot at rotation and gives much closer assessment to maximum singular value assessment. If large phase lags are inserted into the controller, the second bending mode is destabilized, but the sensitivity functions do not catch this instability. The ISO standard can be used practically in determining the stability of the AMB system, nevertheless it must be borne in mind that the sensitivity functions do not always highlight the instability in bending modes.

Optimization of Bearing Locations for Rotor Systems With Magnetic Bearings

1995 ◽  
Author(s):  
Sriram Srinivasan ◽  
Eric H. Maslen ◽  
Lloyd E. Barrett
Keyword(s):  
Design Process ◽  
Magnetic Bearing ◽  
Rotating Machinery ◽  
Rotor Systems ◽  
Infinity Norm ◽  
Multi Stage ◽  
Scalar Measure ◽  
Bearing Design ◽  
The Stability ◽  
Practical Measure

This paper presents a method for quickly evaluating the effect of changes in bearing location on bearing design for stability of rotating machinery. This method is intended for use by rotating machinery designers to select the “best” bearing locations prior to the bearing design process. The purpose of the method is to improve the design process by separating the problem of determining the “best” bearing locations from that of determining the actual bearing design. The method is independent of the type of bearing employed. For each candidate bearing configuration, the method provides a scalar measure of the relative ability of bearings to meet stability specifications. Within certain limits, the stability specifications are defined by the designer. The scalar measure is used to rank the candidate bearing locations and thereby select the best one. The scalar measure is compared to a practical measure of magnetic bearing design such as the infinity norm of the controller for an example design of a multi-stage centrifugal compressor.

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