Performances Comparison for a Rotating Shaft Suspended by 4-Axis Radial ActiveMagnetic Bearings via μ-Synthesis, Loop-Shaping Design, and Sub(H)∞with Uncertainties

The control systems applied on active magnetic bearing are several. A perfect levitation is characterized by maintaining the operating point condition that is characterized by the center of stator coincident with the geometric center of shaft. The first controller implemented for this purpose is PID controller that is characterized by an algorithm that leads the amplifier to produce control current until the operating point condition is not reached, this is obtained by an integration operator. The effect of an integrator is essential but not necessary for a centered levitation for example in the robust control characterized by a dynamic model depended on plant of system so that it depends on angular speed as LQR controller does. In LQR there is not integrator so there is not a perfectly centered section of shaft with center of stator. On contrary PID controller does not depend on angular speed and it can be easily implemented according some simple rules. Predictive control is another interesting controller characterized by a multiple controller operating in different condition in order to get the minimum of cost function, but also in this case the angular speed is introduce for the same reason discussed before

Influence on the Dynamic Behavior of Full Car Equipped by Magnetorheological Damper via Switch on/off and h∞ Controller

This paper shows the influence on dynamic behavior of the car when it is equipped with magneto-rheological dampers controlled by a feedback. The feedback is built up in two ways; the first is implemented by a switch on/off control that is characterized by the injection of magnetic field with a constant value. It happens when a certain value of relative speed between the sprung and unsprung mass is exceeded. The second feedback is characterized by the H-infinity control which is based on the relative displacement in order to vary the magnetic field signal in a continuous manner. At the same time the H-infinity control of vehicle is maintained by taking into account the exceeding of speed signal in order to consider the substantial differences with the switch on/off control. These differences are evaluated in terms of relative displacement and speed between the unsprung and sprung mass. The exogenous excitation is the road disturbances which are introduced as a square wave input in order to emulate those that are commonly encountered on the road. All simulations and results are performed by MATLab-Simulink and Mathematica

ROBUST CONTROL FOR A SUSPENDED ROTATING SHAFT BY RADIAL ACTIVE MAGNETIC BEARINGS

This paper shows a comparison based on dynamic behaviour of a rotating shaft when it is suspended by 4-axis active magnetic bearings under several control systems. The control systems used are μ-synthesis, loop shaping design procedure and Sub(H∞) robust control with the introduction of uncertainties on position and current gains of the actuators. Each of these controllers is characterized by four input signals and four output signals and the introduction of uncertainties on displacement gain and current gain is due to torn and worn of the components during the time, which can lead the entire system to instability phenomena. The comparison of the performances is obtained through the introduction of same weighting function for all three control systems. All simulations and results are performed by MATLab

Sub-Optimal Control Law for Active Magnetic Bearings Suspension

This paper deals with the comparison of three types of sub-optimal control law for the stable levitation of a turbojet shaft, sustained by two radial active magnetic bearings (AMBs). Shaft is considered rigid for the procedure simplification. The utilized approach leads to development of different sub-optimal control laws to use in speed-varying simulations in the angular speed of the shaft. The first control matrix is obtained by explicit relationships of the parameters of the control law vs. speed, obtained using a curve-fitting procedure neglecting the speed-varying elements out of the main diagonal of each single block constituting the entire control matrix. The second control law is obtained by control matrix set to zero angular speed during speed-varying simulations. The third control matrix is obtained by the second neglecting the elements out of main diagonal. Time response to the step input shows difference in performance of the AMBs when varying the control law. All control laws are tested by means of simulation. The study allows showing like a polynomial representation of the control matrix, developed to the variation of angular speed, is able to maintain stable the magnetic levitation

STUDIO DI UN AMMORTIZZATORE ELETTROMAGNETICO A RECUPERO DI ENERGIA

Questo lavoro ha come obiettivo principale lo studio teorico e con supporto di software F.E.M. di un dispositivo che consenta recupero energetico da una sospensione automobilistica. In sostituzione allo smorzatore viscoso, che dissipa l’energia cinetica del veicolo a seguito dell’attraversamento di strade sconnesse o ostacoli più marcati, si è usato uno smorzatore elettromagnetico che svolga le funzioni dello smorzatore viscoso consentendo un recupero di energia elettrica. Lo smorzatore elettromagnetico è di tipo a magneti permanenti e il suo funzionamento si basa sul fenomeno dell’induzione elettromagnetica. Il modello matematico descrive il funzionamento dello smorzatore, restituendo i valori delle grandezze elettriche e meccaniche in funzione della velocità relativa tra stelo e statore. Si è valutato il recupero energetico considerando una minicar elettrica che transita su una strada mediamente sconnessa. La potenza elettrica recuperata ha un valore complessivo di circa 250

ANALISI DEGLI EFFETTI DEL CAMPO MAGNETICO SULLO STATO TENSIONALE INDOTTO IN PIASTRE DI ACCIAIO FORATE

Si è considerata una piastra forata di materiale ferromagnetico opportunamente accoppiata da bobine di filo di rame smaltato alimentato da un alimentatore DC a 30V. Essa è stata analizzata agli Elementi Finiti e successivamente sono state eseguite sperimentazioni per la validazione dei risultati ottenuti. Dopo aver levigato la piastra sono stati installati due estensimetri per misurare la deformazione lungo l’asse x e lungo l’asse z. Si sono ottenuti i valori di deformazione di 5µm in direzione z e -2µm in direzione x. Il confronto numerico-sperimentale mostra che i risultati di laboratorio sono più bassi di quelli numerici, mentre segni e ordini di grandezza sono gli stessi. Si conclude che i risultati dell’analisi FEM possono essere considerati accettabili a causa dell’ortogonalità del piano delle spire rispetto al piano della piastra e a causa del coefficiente di impacchettamento del rame

STUDY OF NEW AUTOMOTIVE REAR SUSPENSION MECHANISM

The paper presents firstly an introduction discussing: the problem’s statement emphasizing the actual problem of research of passenger car suspension to improve driving comfort and dynamic of the vehicle movement; aspects regarding the studies of car suspension mechanisms; the paper’s aims and objectives showing that a new configuration of suspension mechanism having in structure mobile frame and an actuator offering some important operational advantages is proposed. After this, the innovative concept is presented. The motions of mechanism elements and actuator and kinematic displacements are largely presented. The simulation using modern software (MSC Patran 2007, MD R2 Nastran and MSC ADAMS/View) accentuates the actuality of the results, which are presented and discussed for an application. Final conclusions are given

CONTROLLO SUB-OTTIMO PER UN ALBERO ROTANTE IN LEVITAZIONE MAGNETICA ATTIVA

Il presente lavoro ha come scopo quello di mettere in mostra le sostanziali differenze rilevate nel comportamento dinamico di un rotore supportato da cuscinetti radiali in levitazione magnetica attiva. Sono stati rilevati sia gli spostamenti radiali che la risposta in frequenza controllando il rotore dapprima con una legge di ottimo tempo variante e successivamente con una di tipo sub-ottimo, ricavata dalla precedente rendendola stazionaria rispetto alla velocità angolare. È mostrato come la presenza del controllo sub-ottimo annulla la dipendenza del segnale di controllo dalle componenti di spostamento non interessate dal sensore e riduce sensibilmente l’entità degli spostamenti radiali

An estimator algorithm for the rotation time of magnetization vector in nuclear magnetic resonance for imaging (NMRI)

The purpose of this paper is to propose a useful method to investigate the rotation time of the magnetization vector in the nuclear magnetic resonance for imaging (NMRI) system. The ninety degrees rotation of the magnetization vector is the first step in order to establish the free induction decay that radiates electromagnetic energy inside the NMRI chamber. The estimator involved in this research is called Luenberger's observer which is a state estimator of a dynamical system. The Bloch's equation is a dynamical system characterized by a radio frequency (RF) impulse located inside the dynamic matrix, which means the system is not linear. The observer algorithm involved in this paper estimates each vector's component of the Bloch's dynamic model characterized by the magnetizations along the x, y and z direction which are axles located inside the NMRI chamber where the z axis has the same direction of the uniform magnetic field. The result is compared with one shown in the literature which results coincident with estimation. The estimator has been calculated in a closed form except in some cases where the symbolic expression makes the mathematical characterized by a high computational burden. The expression of the solutions is calculated by using the Heaviside expansion once the poles of the dynamical systems characterizing the Bloch's differential equations system are known. A set of simulations is carried out by using different configurations of the observer that have been calculated formerly without considering the RF pulse and subsequently with its introduction showing how the Bloch's dynamical system is affected by the skew symmetric matrix which is typical of a gyroscopic dynamical system. This likelihood produces a time estimation of the rotation vector which is slightly higher than the estimated value offered in the literature

INFLUENCE OF UNCERTAINTIES ON PD TUNING

The aim of this work is to present a method for tuning the parameters of PD controller under the influences of the uncertainties, in order to stabilize the position of a rotor supported by active magnetic bearings (AMBs). The uncertainties are relative to mass, transverse and polar moment of inertia of the rotor. The introduction of the uncertainties is due to an incomplete modeled dynamic of the system or in the case the system being subjected to a parametric variation. The presence of the uncertainties produces a set of differences among the values of the output. Poles displacement method is used to reach the asymptotically stability condition characterized by a periodic oscillation during the transient response as a consequence of the impulse input. In this way we carried out some particular condition under graphical representation which helps making a prevision when the phenomena of instability occurs. In the present approach the poles displacement is obtained by imposing respectively the condition on the real part, which must be negative, and in the discriminant of a second degree equation, which must be less than zero, both depend on the uncertainties and the angular speed of the rotor. All calculations are performed through a 4-axis AMB rigid rotor to validate the PD controller method rule introduced in this work