外文翻譯---一個(gè)教學(xué)用的磁懸浮控制系統(tǒng)模型

1、Modeling of a Didactic Magnetic Levitation System for Control EducationMilica B. NaumoviCAbsr~uo ~ The magnetic levitation control system of a metallicsphere is an interesting and visual impressive device successfulfor d

2、emonstration many intricate problems for controlengineering research. The dynamics of magnetic levitation systemis characterized by its instability, nonlinearity and complexity. Inthis paper some approaches to the levita

3、tion sphere modeling areaddressed, that may he validate with experimentalmeasurements.Keywords - magnetic levitation system, control engineeringeducation, system modelingI. INTRODUCTIONMagnetic levitators not only presen

4、t intricate problems forcontrol engineering research, but also have many relevantapplications. such as high-speed transportation systems andprecision bearings. From an educational viewpoint, thisprocess is highly motivat

5、ing and suitable' for laboratoryexperiments and classroom demonstrations, as reported in theengineering education literature [1]-[8].The classic magnetic levitation control experiment isprescnted in the form of labor

6、atory equipment given in Fig.1.The complete purchase of the Feedback Instruments Ltd.Maglev System 33-006 [9] is supported by WUS (WorldUniversity Service [IO]) - Austria under Grant CEP (Centerof Excellence Projects) No

7、. 115/2002. This attraction-typelevitator system is a challenging plant because of its nonlinearand unstable nature. The suspended body is a hollow steel ballof 25 mm diameter and 20 g mass. This results in a visuallyapp

8、ealing system with convenient time constants. Both analogueand digital control solutions are implemented. In addition, thesyslem is simple and relatively small, that is portable.This paper deals with the dynamics analysi

9、s of the consideredmagnetic levitation system. Although the gap between the realphysical systcm and the obtained nominal design model hascomplex structure, it should be robust stabilized in spite of modeluncertainties.II

10、. SYSTEMD ESCRIPTIONThe Magnetic Levitation System (Maglev System 33-006given in Fig. I ) is a relatively new and effective laboratory setupvery helpful for control experiments. The basic control goalis to suspend a stee

11、l sphere by means of a magnetic fieldcounteracting the force of gravity. The Maglev Systemconsists of a magnetic levitation mechanical unit (an enclosedMilica B. Nauinovic is with the Faculty of Electronic Engineering,Un

12、iversity of NE, Beogradska 14. 18000 Nil. Yugoslavia, E-mail:nmilica@elfak.ni.ac.yumagnet system, sensors and drivers) with a computer interfacecard, a signal conditioning unit, connecting cables and alaboratory manual.I

13、n the analogue mode, the equipment is self-contained withinbuilt power supply. Convenient sockets on the enclosurepanel allow for quick changes of analogue controller gain andstructure. The bandwidth of lead compensation

14、 may bechanged in order to investigate system stability and timeresponse. Moreover, user-defined analogue controllers may beeasily tested. Note, that Using the fundamental principle of dynamics, thebehaviour of the ferro

15、magnetic ball is given by the followingelectromechanical equationwhere m is the mass of the levitated ball, g denotes theacceleration due to gravity, x is the distance of the ball fromthe electromagnet, i is the current

16、across the electromagnet,and f ( x , i ) is the magnetic control force.A. Calculating the magnetic control force on the metallicsphereConsider a solenoid with an r radius, an 1 length, crossedby an I current. The' sp

17、here is located on the axis of the coilas shown in Fig. 3. The effect of the magnetic field from theelectromagnetic is to introduce a magnetic dipole in the spherewhich itself becomes magnetized. The force acting on thes

18、phere is then composed of gravity and the magnetic forceacting on the induced dipole.The magnetic control force between the solenoid and thesphere can be determined by considering the magnetic field asa function of the b

19、all's distance x from the end of the coil.The magnetic field at some given point (see Fig. 3), maybe calculated according to the Biot-Savar-Laplace formula[ l l ] . Recall, that the magnetic field produced by a small

20、segment of wire, dl , canying a current I (see Fig. 4a) isgiven byWhere u0 is the permeability of the free space and d l x r isthe vector product of vectors dl and r .Hence, the magnitude of the magnetic field becomesThe

21、 magnetic field of a circular contour with an a radius, asshown in Fig. 4b, is given byNote, that from considerations of symmetry, the fieldcomponent perpendicular to the coil axis dB, must be zero onthe axis.In order to

22、 evaluate the field due to the many turns ( N )along the axis of the coil, let n be the number of turns permetre. Also, consider the solenoid given in Fig. 3 as a series ofequidistant circular contours at the mutual dist