scholarly journals Optimal control for hybrid magnetically suspended flywheel rotor based on state feedback exact linearization model

2020 ◽  
Vol 103 (3) ◽  
pp. 003685042095138
Author(s):  
Tong Wen ◽  
Biao Xiang ◽  
Shilei Zhang
Keyword(s):  
Optimal Control ◽  
Nonlinear Dynamic ◽  
Degrees Of Freedom ◽  
State Feedback ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Exact Linearization ◽  
Dynamic Function ◽  
The Stability ◽  
Flywheel Rotor

For a hybrid magnetically suspended flywheel (MSFW) rotor suspended by permanent magnet biased active magnetic bearing (AMB) and passive magnetic bearing (PMB), the dynamic functions are nonlinear and coupling among different degrees of freedom (DOFs). In this article, the nonlinear dynamic functions in two controllable DOFs of the hybrid MSFW rotor are developed based on the equivalent magnetic circuit, and then the nonlinear dynamic function is linearized by using the state feedback exact linearization (SFEL) in order to minimize the coupling in two controllable DOFs. Furthermore, an optimal control based on the SFEL model is designed to reduce displacement runout and coupling among two controllable DOFs of the hybrid MSFW rotor at the rated speed. Finally, the simulation and experimental results validate the effectiveness of the optimal control based on SFEL model, and the stability of the hybrid MSFW rotor with an impulse-type disturbance is improved.

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.

Stability and Bifurcation of Nonlinear Bearing-Flexible Rotor System with a Single Disk

2010 ◽  
Vol 148-149 ◽  
pp. 141-146
Author(s):  
Di Hei ◽  
Yong Fang Zhang ◽  
Mei Ru Zheng ◽  
Liang Jia ◽  
Yan Jun Lu
Keyword(s):  
Nonlinear Dynamic ◽  
Degrees Of Freedom ◽  
Rotor System ◽  
Dynamic Responses ◽  
Flexible Rotor ◽  
Runge Kutta Method ◽  
Stability And Bifurcation ◽  
Single Disk ◽  
The Stability ◽  
Predictor Corrector

Dynamic model and equation of a nonlinear flexible rotor-bearing system are established based on rotor dynamics. A local iteration method consisting of improved Wilson-θ method, predictor-corrector mechanism and Newton-Raphson method is proposed to calculate nonlinear dynamic responses. By the proposed method, the iterations are only executed on nonlinear degrees of freedom. The proposed method has higher efficiency than Runge-Kutta method, so the proposed method improves calculation efficiency and saves computing cost greatly. Taking the system parameter ‘s’ of flexible rotor as the control parameter, nonlinear dynamic responses of rotor system are obtained by the proposed method. The stability and bifurcation type of periodic responses are determined by Floquet theory and a Poincaré map. The numerical results reveal periodic, quasi-periodic, period-5, jump solutions of rich and complex nonlinear behaviors of the system.

Optimal control for active magnetic bearing with mode

2002 ◽  
Vol 2002.55 (0) ◽  
pp. 345-346
Author(s):  
Masataka MIYAWAKI ◽  
Mochimitsu KOMORI
Keyword(s):  
Optimal Control ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing

Robust Active Chatter Control in Milling Processes With Variable Pitch Cutters

2018 ◽  
Vol 140 (10) ◽  
Author(s):  
Tao Huang ◽  
Lijun Zhu ◽  
Shengli Du ◽  
Zhiyong Chen ◽  
Han Ding
Keyword(s):  
Nonlinear Differential Equations ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Linear Matrix ◽  
Variable Pitch ◽  
Stability Lobe ◽  
Milling Operations ◽  
Controller Gain ◽  
Chatter Control ◽  
The Stability

Milling chatters caused by the regenerative effect is one of the major limitations in increasing the machining efficiency and accuracy of milling operations. This paper studies robust active chatter control for milling processes with variable pitch cutters whose dynamics are governed by multidelay nonlinear differential equations. We propose a state feedback controller based on linear matrix inequality (LMI) approach that can enlarge multiple stability domains in the stability lobe diagram (SLD) while the controller gain is minimized. Numerical simulations of active magnetic bearing systems demonstrate the effectiveness of the proposed method.

Nonlinear Oscillation of a Rotor-AMB System With Time Varying Stiffness and Multi-External Excitations

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
M. Kamel ◽  
H. S. Bauomy
Keyword(s):  
Steady State ◽  
Order Approximation ◽  
Nonlinear Differential Equations ◽  
Steady State Solution ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Multiple Time ◽  
Time Varying ◽  
The Stability ◽  
Amb System

The rotor-active magnetic bearing system subjected to a periodically time-varying stiffness having quadratic and cubic nonlinearities is studied and solved. The multiple time scale technique is applied to solve the nonlinear differential equations governing the system up to the second order approximation. All possible resonance cases are deduced at this approximation and some of them are confirmed by applying the Rung–Kutta method. The main attention is focused on the stability of the steady-state solution near the simultaneous principal resonance and the effects of different parameters on the steady-state response. A comparison is made with the available published work.

Pointwise Optimal Control of Dynamical Systems Described by Constrained Coordinates

1999 ◽  
Vol 121 (4) ◽  
pp. 594-598 ◽  
Author(s):  
V. Radisavljevic ◽  
H. Baruh
Keyword(s):  
Optimal Control ◽  
Dynamical Systems ◽  
Feedback Control ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Control Law ◽  
Algebraic Equations ◽  
The Stability ◽  
The Mathematical Model

A feedback control law is developed for dynamical systems described by constrained generalized coordinates. For certain complex dynamical systems, it is more desirable to develop the mathematical model using more general coordinates then degrees of freedom which leads to differential-algebraic equations of motion. Research in the last few decades has led to several advances in the treatment and in obtaining the solution of differential-algebraic equations. We take advantage of these advances and introduce the differential-algebraic equations and dependent generalized coordinate formulation to control. A tracking feedback control law is designed based on a pointwise-optimal formulation. The stability of pointwise optimal control law is examined.

Isotropic Optimal Control of Active Magnetic Bearing System

1996 ◽  
Vol 118 (4) ◽  
pp. 721-726 ◽  
Author(s):  
Cheol-Soon Kim ◽  
Chong-Won Lee
Keyword(s):  
Optimal Control ◽  
System Analysis ◽  
Control Method ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Control Effort ◽  
Response Component ◽  
Unbalance Response ◽  
Control Scheme ◽  
Bearing System

As a new rotor control scheme, isotropic control of weakly anisotropic rotor bearing system in complex state space is proposed, which utilizes the concepts on the eigenstructure of the isotropic rotor system. Advantages of the scheme are that the controlled system always retains isotropic eigenstructure, leading to circular whirling due to unbalance and that it is efficient for control of unbalance response. And the system analysis and controller design becomes simple and yet comprehensive since the order of the matrices treated in the complex domain approach is half of that in the real approach. The control scheme is applied to a rigid rotor-active magnetic bearing system which is digitally controlled and the control performance is investigated experimentally in relation to unbalance response and control energy. It is found that the isotropic optimal control method, which essentially eliminates the backward unbalance response component, is more efficient than the conventional optimal control in that it gives smaller major whirl radius and yet it often requires less control effort.

Optimal Control of a Nonlinear Magnetic Bearing System Using the Trigonometric Collocation Method

2008 ◽  
Author(s):  
C. Nataraj ◽  
Steven Marx
Keyword(s):  
Optimal Control ◽  
Collocation Method ◽  
Degrees Of Freedom ◽  
Magnetic Bearing ◽  
Degree Of Freedom ◽  
Lookup Table ◽  
Base Excitation ◽  
Strongly Nonlinear ◽  
Trigonometric Collocation ◽  
Bearing System

Magnetic bearings are non-contacting, with the rotor being suspended between electromagnets, and therefore they can eliminate the need for lube oil and reduce machinery wear. The magnetic bearing is naturally unstable, and very nonlinear. This paper proposes a method designed to suppress the motion of a nonlinear magnetic bearing system rotor due to base excitation. The method combines PD feedback with feedforward optimal control, where a measured base motion is used to select a control signal designed to suppress the rotor response. The signal is generated from a combination of subharmonic frequencies and optimized coefficients stored in a lookup table. The trigonometric collocation method (TCM) is used to generate solutions for the four degree-of-freedom system made up of a shaft suspended at each end by a magnetic bearing. The TCM method uses a trigonometric series to simulate the multiharmonic behavior of each degree-of-freedom of strongly nonlinear systems. The method is easy to use and its advantage over numerical methods is that it demands less computation, particularly with higher numbers of degrees-of-freedom.

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.

Design of a Highly Integrated Active Magnetic Bearing With Six Coupled Actuators for High Precision Rotation Applications

1999 ◽  
Author(s):  
M. Kümmerle ◽  
B. Aeschlimann ◽  
J. Zoethout ◽  
T. Belfroid ◽  
R. Vuillemin ◽  
...  
Keyword(s):  
High Precision ◽  
Pid Controller ◽  
Degrees Of Freedom ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
The Other ◽  
Axial Forces ◽  
Functional Prototype ◽  
The One ◽  
Contact Free

Abstract This paper presents the design and the implementation of a contact free Active Magnetic Bearing (AMB) for high precision rotation applications. For controlling five Degrees of Freedom (DOF) of the rotor six coupled reluctance force actuators (creating radial and axial forces at the same time) are used. A method for designing the actuators in order to meet the specifications is described. Two different controller schemes using different sensor configurations have been implemented on a functional prototype: On the one hand a conventional decentralized PID controller, on the other hand a more centralized structure.

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