On the Stability Analysis of Active Magnetic Bearing With Parametric Uncertainty and Position Tracking Control

2016 ◽  
Author(s):  
Junya Kato ◽  
Kentaro Takagi ◽  
Tsuyoshi Inoue
Keyword(s):  
Tracking Control ◽  
Feedback Linearization ◽  
Disturbance Observer ◽  
Parametric Uncertainty ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Uncertain Parameters ◽  
Rigid Rotor ◽  
Pd Control ◽  
The Stability

This paper considers effect of the parametric uncertainty of an active magnetic bearing which is used to control a rigid rotor. In the feedback control law, PD control and feedback linearization is used. Firstly, this paper shows that one of the two uncertain parameters in the electromagnet model significantly affects the stability of the system. Moreover, this paper analytically shows a method to select the nominal value of the critical parameter affecting the stability. Next, while the shaft is rotating, this paper considers reducing vibration due to rotating unbalance by inversion-based disturbance observer and controlling position by feedforward control, besides PD control and feedback linearization. Based on the linearized model, this paper shows the performance degradation caused by the parametric error and investigates the tracking error experimentally. Finally, in order to improve the tracking performance under the existence of the uncertain parameters, this paper proposes to employ an inversion-based feedforward controller designed from the augmented control object, which includes the controlled object (rigid rotor and magnetic bearing), the disturbance observer and the feedback linearization. The experiment of tracking control of the rotor position is carried out to demonstrate the effectiveness of the proposed method.

Nonlinear Analysis for Influence of Parametric Uncertainty on the Stability of Rotor System With Active Magnetic Bearing Using Feedback Linearization

2018 ◽  
Vol 13 (7) ◽  
Author(s):  
Junya Kato ◽  
Tsuyoshi Inoue ◽  
Kentaro Takagi ◽  
Shota Yabui
Keyword(s):  
Electromagnetic Force ◽  
Feedback Linearization ◽  
Parametric Uncertainty ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Force Model ◽  
Rotating Shaft ◽  
System Nonlinearity ◽  
The Stability ◽  
And Control

Active magnetic bearing (AMB) is the device to support and control rotating shaft. Feedback linearization is one of the methods to compensate the system nonlinearity, and it is often used in the control of AMB. Some parameters in the electromagnetic force model have often been ignored or their parametric uncertainty from the nominal values has been calibrated; however, their influence on the stability has not been investigated. In this paper, the influence of the parametric uncertainty in the electromagnetic force model on the stability of AMB is investigated. The equilibrium positions and their stability are investigated and clarified analytically. Furthermore, the choice of the parameter value for improving the stability of AMB with feedback linearization is proposed, and its effectiveness is explained analytically. It is shown that the proposed choice of the parameter value also reduces the remained nonlinearity significantly. The validity of theoretical results and proposed choice of the parameter value are confirmed by experiment.

A Numerical Study on Effect of Electromagnetic Actuator on Rigid Rotor Supported on Gas Foil Bearing

2017 ◽  
Author(s):  
Kamal Kumar Basumatary ◽  
Gaurav Kumar ◽  
Karuna Kalita ◽  
Sashindra Kumar Kakoty
Keyword(s):  
Numerical Study ◽  
Load Capacity ◽  
Current Trend ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Normal Operation ◽  
Electromagnetic Actuator ◽  
Rigid Rotor ◽  
Magnetic Actuator ◽  
The Stability

Generally, Gas Foil Bearings (GFBs) are used in high speed machineries which are quite prone to instability or wear and tear. The current trend is to develop hybrid bearings which has conventional bearing (GFB) along with active magnetic bearing as an electromagnetic actuator (EMA). The GFBs are used for normal operation and the magnetic actuator can be used for the improvement of the stability and the load capacity of the bearing. In the present work a numerical study has been carried out to study the effects of magnetic actuator on the stability of bump type GFB supported rigid rotor. A rigid rotor supported on two identical GFBs with and without EMA has been investigated. The electromagnetic forces are incorporated in the equation of motion to provide the active control. A PD controller has been used as a controller for the magnetic actuator. It has been observed that the incorporation of EMA to the GFB reduces the sub synchronous vibrations and hence increases the stability.

scholarly journals A new novel six-degree of freedom two-link manipulator using active magnetic bearing: Design, kinematics, and control

2018 ◽  
Vol 15 (6) ◽  
pp. 172988141881763 ◽  
Author(s):  
Mohamed Selmy ◽  
Mohamed Fanni ◽  
Abdelfatah M Mohamed ◽  
Tomoyuki Miyashita
Keyword(s):  
High Precision ◽  
Feedback Linearization ◽  
Magnetic Bearing ◽  
Good Choice ◽  
Degree Of Freedom ◽  
Active Magnetic Bearing ◽  
New Novel ◽  
The Stability ◽  
Six Degree Of Freedom ◽  
And Control

Due to the absence of mechanical contact, active magnetic bearing can be electrically controlled in an accuracy of a micrometer. This makes it a good choice to be used for robot manipulation in the micrometer scale, especially in environments that need to be very clean, for example, surgery or clean rooms. Moreover, it can be used in the applications that need high precision micromotion such as semiconductor wafers manipulation. Despite all these benefits, there are few studies that have investigated the application of active magnetic bearing in the robotics field in spotless environments for micromotion applications. This article proposes a new novel six-degree of freedom two-link manipulator using two contactless joints with active magnetic bearing. The key design aspects of the proposed manipulator are presented. The proposed manipulator is designed using finite element method. Each joint roll angle is controlled using a PID-based feedback linearization controller, while a state feedback controller with integral term is used for controlling the active magnetic bearing five-degree of freedom. The stability analysis of the system, under the proposed controller, is carried out. The robustness of the controllers is tested against end effector payload variations. The results demonstrate that the proposed two-link manipulator is feasible and valid for the applications in spotless environments that need high precision accuracy micromotion control. These significant findings have indicated the feasibility of implementing this proposed manipulator in practice and open the door for developing other types of robots with complete contactless joints using active magnetic bearing.

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.

scholarly journals Research on Automatic Balance Control of Active Magnetic Bearing-Rigid Rotor System

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Yang Liu ◽  
Shuaishuai Ming ◽  
Siyao Zhao ◽  
Jiyuan Han ◽  
Yaxin Ma
Keyword(s):  
Vibration Control ◽  
Rotational Speed ◽  
Notch Filter ◽  
Magnetic Bearing ◽  
Rotor System ◽  
Vibration Response ◽  
Active Magnetic Bearing ◽  
Rigid Rotor ◽  
Phase Compensation ◽  
Synchronous Control

In this paper, in order to solve the problem of unbalance vibration of rigid rotor system supported by the active magnetic bearing (AMB), automatic balancing method is applied to suppress the unbalance vibration of the rotor system. Firstly, considering the dynamic and static imbalance of the rotor, the detailed dynamic equations of the AMB-rigid rotor system are established according to Newton’s second law. Then, in order to rotate the rotor around the inertia axis, the notch filter with phase compensation is used to eliminate the synchronous control current. Finally, the variable-step fourth-order Runge–Kutta iteration method is used to solve the unbalanced vibration response of the rotor system in MATLAB simulation. The effects of the rotational speed and phase compensation angle on the unbalanced vibration control are analysed in detail. It is found that the synchronous control currents would increase rapidly with the increase of rotational speed if the unbalance vibration cannot be controlled. When the notch filter with phase shift is used to balance the rotor system automatically, the control current is reduced significantly. It avoids the saturation of the power amplifier and reduces the vibration response of the rotor system. The rotor system can be stabilized over the entire operating speed range by adjusting the compensation phase of the notch filter. The method in the paper is easy to implement, and the research result can provide theoretical support for the unbalance vibration control of AMB-rotor systems.

Adaptive Backstepping Control of the Gripping Process of Heavy Manipulators

2017 ◽  
Author(s):  
Lixin Yang ◽  
Xianmin Zhang
Keyword(s):  
Tracking Control ◽  
Hydraulic Drive ◽  
Adaptive Controller ◽  
Drive System ◽  
Uncertain Parameters ◽  
Backstepping Method ◽  
Nonlinear Characteristics ◽  
Cylinder Model ◽  
Stability Principle ◽  
The Stability

A valve-controlled asymmetrical cylinder model was established to study the gripping hydraulic drive system of the grip device of heavy manipulator. Due to the strong nonlinear characteristics and uncertain parameters of the model, the Lyapunov stability principle was used to design a multistage inversion adaptive controller based on backstepping method and by introducing the virtual control parameter. The simulation results reveal that the tracking control and adaptive of uncertain parameters are very effective, which confirm that the designed controller can guarantee the stability of the closed-loop clamping hydraulic drive system.

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.

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