Nonlinear Control of a Flexible Rotor Magnetic Bearing System: Robustness and the Indefinate Model

Previously published control strategies for magnetic bearings primarily focus on linear optimal control techniques. While these methods afford many advantages, conspicuously absent from the literature are detailed attempts at nonlinear control. Here, we obtain the equations of motion of an overhung flexible rotor supported in magnetic bearings with two different levels of model sophistication. We derive a generic nonlinear controller in the manner of feedback linearization, and compare the eigenanalysis and transient response of the two rotor models under the action of this >perfect model> controller. We then proceed to obtain a robust nonlinear controller through the sliding mode technique and demonstrate that robustness by implementing it on an uncertain model.Center for Electromechanic

Structural dynamics branch research and accomplishments to FY 1992

This publication contains a collection of fiscal year 1992 research highlights from the Structural Dynamics Branch at NASA LeRC. Highlights from the branch's major work areas--Aeroelasticity, Vibration Control, Dynamic Systems, and Computational Structural Methods are included in the report as well as a listing of the fiscal year 1992 branch publications

Rotors on Active Magnetic Bearings: Modeling and Control Techniques

In the last decades the deeper and more detailed understanding of rotating machinery dynamic behavior facilitated the study and the design of several devices aiming at friction reduction, vibration damping and control, rotational speed increase and mechanical design optimization. Among these devices a promising technology is represented by active magnetic actuators which found a great spread in rotordynamics and in high precision applications due to (a) the absence of all fatigue and tribology issues motivated by the absence of contact, (b) the small sensitivity to the operating conditions, (c) the wide possibility of tuning even during operation, (d) the predictability of the behavior. This technology can be classified as a typical mechatronic product due to its nature which involves mechanical, electrical and control aspects, merging them in a single system. The attractive potential of active magnetic suspensions motivated a considerable research effort for the past decade focused mostly on electrical actuation subsystem and control strategies. Examples of application areas are: (a) Turbomachinery, (b) Vibration isolation, (c) Machine tools and electric drives, (d) Energy storing flywheels, (e) Instruments in space and physics, (f) Non-contacting suspensions for micro-techniques, (g) Identification and test equipment in rotordynamics. This chapter illustrates the design, the modeling, the experimental tests and validation of all the subsystems of a rotors on a five-axes active magnetic suspension. The mechanical, electrical, electronic and control strategies aspects are explained with a mechatronic approach evaluating all the interactions between them. The main goals of the manuscript are: • Illustrate the design and the modeling phases of a five-axes active magnetic suspension; • Discuss the design steps and the practical implementation of a standard suspension control strategy; • Introduce an off-line technique of electrical centering of the actuators; • Illustrate the design steps and the practical implementation of an online rotor selfcentering control technique. The experimental test rig is a shaft (Weight: 5.3 kg. Length: 0.5 m) supported by two radial and one axial cylindrical active magnetic bearings and powered by an asynchronous high frequency electric motor. The chapter starts on an overview of the most common technologies used to support rotors with a deep analysis of their advantages and drawbacks with respect to active magnetic bearings. Furthermore a discussion on magnetic suspensions state of the art is carried out highlighting the research efforts directions and the goals reached in the last years. In the central sections, a detailed description of each subsystem is performed along with the modeling steps. In particular the rotor is modeled with a FE code while the actuators are considered in a linearized model. The last sections of the chapter are focused on the control strategies design and the experimental tests. An off-line technique of actuators electrical centering is explained and its advantages are described in the control design context. This strategy can be summarized as follows. Knowing that: a) each actuation axis is composed by two electromagnets; b) each electromagnet needs a current closed-loop control; c) the bandwidth of this control is depending on the mechanical airgap, then the technique allows to obtain the same value of the closed-loop bandwidth of the current control of both the electromagnets of the same actuation axis. This approach improves performance and gives more steadiness to the control behavior. The decentralized approach of the control strategy allowing the full suspensions on five axes is illustrated from the design steps to the practical implementation on the control unit. Furthermore a selfcentering technique is described and implemented on the experimental test rig: this technique uses a mobile notch filter synchronous with the rotational speed and allows the rotor to spin around its mass center. The actuators are not forced to counteract the unbalance excitation avoiding saturations. Finally, the experimental tests are carried out on the rotor to validate the suspension control, the off-line electrical centering and the selfcentering technique. The numerical and experimental results are superimposed and compared to prove the effectiveness of the modeling approach

Modified Nonlinear Integral Sliding Mode Control for Satellite Attitude Stabilization Using Magnetically Suspended Gimbaled Momentum Wheel

This paper treats the attitude stabilization problem for satellite using only one MSGMW (Magnetically Suspended Gimbaled Momentum Wheel). To start, the coupled dynamic model of satellite and MSGMW is defined and simplified based on the fact that the attitude errors are small during the mission mode that the MSGMW services. In order to improve the dynamic performance, reduce the steady state error and avoid the chattering phenomenon, a modified integral chattering-free sliding mode controller with a nonlinear integral function and a saturation function is introduced. Lyapunov theory is employed to prove the convergence characteristic outside the boundary layer and the terminal convergence characteristic inside the boundary layer. A numerical simulation example is employed to show the effectiveness and suitability of the proposed controller

Reduced order modeling and sliding mode control of active magnetic bearing

Due to the accelerated growth in the field of power electronics and controller design techniques, the usage of the active magnetic bearing has picked up in industries. Active magnetic bearing helps the rotor to rotate freely without any physical contact. In brief, this paper develops a model of an active magnetic bearing using the finite element method, and its associated reduced order model, followed by the development of a robust control strategy. COMSOL software is used to perform three-dimensional simulation of an active magnetic bearing system. The state space system matrices are extracted from the finite element method, and a linear time-invariant state-space system is generated in MATLAB. Since the original system is large, the reduced order model is constructed. Then, based upon the reduced order model, a sliding mode control is designed to improve the regulation performance of an active magnetic bearing under unmodeled uncertainties. The stability analysis of closed-loop reduced order model with unmodeled uncertainties guarantees the finite time convergence of system states using Lyapunov theory. Further, it is proved that the same control law will also provide satisfactory performance for the original model using the reduced order model as an observer. The numerical simulation is carried out to illustrate the effective performance of the proposed controller for the reduced model as well as the original model with multiple initial conditions. The proposed work offers an alternative approach of using the reduced order model instead of the original model for the controller design of an active magnetic bearing.This publication was made possible by Qatar University High Impact Research Grant # [QUHI-CENG-19/20-2] from the Qatar University. The publication charges are funded by the Qatar National Library, Doha, Qatar.Scopu

Robust Adaptive Cerebellar Model Articulation Controller for 1-DOF Nonlaminated Active Magnetic Bearings

This paper presents a robust adaptive cerebellar model articulation controller (RACMAC) for 1-DOF nonlaminated active magnetic bearings (AMBs) to achieve desired positions for the rotor using a robust sliding mode control based. The dynamic model of 1-DOF nonlaminated AMB is introduced in fractional order equations. However, it is challenging to design a controller based on the model\u27s parameters due to undefined components and external disturbances such as eddy current losses in the actuator, external disturbance, variant parameters of the model while operating. In order to tackle the problem, RACMAC, which has a cerebellar model to estimate nonlinear disturbances, is investigated to resolve this problem. Based on this estimation, a robust adaptive controller that approximates the ideal and compensation controllers is calculated. The online parameters of the neural network are adjusted using Lyapunov\u27s stability theory to ensure the stability of system. Simulation results are presented to demonstrate the effectiveness of the proposed controller.The simulation results indicate that the CMAC multiple nonlinear multiple estimators are close to the actual nonlinear disturbance value, and the effectiveness of the proposed RACMAC method compared with the FOPID and SMC controllers has been studied previously

SIRM 2017

This volume contains selected papers presented at the 12th International Conference on vibrations in rotating machines, SIRM, which took place February 15-17, 2017 at the campus of the Graz University of Technology. By all meaningful measures, SIRM was a great success, attracting about 120 participants (ranging from senior colleagues to graduate students) from 14 countries. Latest trends in theoretical research, development, design and machine maintenance have been discussed between machine manufacturers, machine operators and scientific representatives in the field of rotor dynamics. SIRM 2017 included thematic sessions on the following topics: Rotordynamics, Stability, Friction, Monitoring, Electrical Machines, Torsional Vibrations, Blade Vibrations, Balancing, Parametric Excitation, and Bearings. The papers struck an admirable balance between theory, analysis, computation and experiment, thus contributing a richly diverse set of perspectives and methods to the audience of the conference

Application of Active Magnetic Force Actuator for Control of Flexible Rotor System Vibrations

The purpose of this work was to develop and experimentally demonstrate a novel approach to minimize lateral vibrations of flexible rotor. The applied feed forward control approach employed magnetic force actuator to inject a specially designed force to counteract the rotor unbalance force. By specific selection of frequency and phase as functions of the rotor running speed and rotor natural frequency, the proposed simplified injection waveform has been shown to be effective both in reducing the rotor\u27s vibrations and for hardware implementation. A model of the test rig was constructed using the finite element (FE) method and was validated using experimental data. The effectiveness of the proposed current injection was numerically simulated with FE model and experimentally validated using a residual unbalance force. It was noticed that at a selected constant running speed, just below the first rotor critical speed, the rotor vibrations were reduced approximately by 90 . The method was also implemented during the speed ramp test, which passes through the first critical speed. In this test the proposed force injection also reduced vibrations at various rotor speeds. These results agree well with the results of simulatio