1、PDF外文：http:/ of a Didactic Magnetic Levitation System forControl Education Milica B. NaumoviC Absruo The magnetic levitation control system of a metallicsphere is an interesting and visual impressive device successfulfor demonstration many intricate problems for controlengineering research. Th
2、e dynamics of magnetic levitation systemis characterized by its instability, nonlinearity and complexity. Inthis paper some approaches to the levitation sphere modeling areaddressed, that may he validate with experimentalmeasurements. Keywords - magnetic levitation system, control engineeringeducati
3、on, system modelingI. INTRODUCTION Magnetic levitators not only present 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 motivating and su
4、itable' for laboratoryexperiments and classroom demonstrations, as reported in theengineering education literature 1-8.The classic magnetic levitation control experiment is prescnted in the form of laboratory equipment given in Fig.1.The complete purchase of the Feedback Instruments Ltd.Maglev S
5、ystem 33-006 9 is supported by WUS (WorldUniversity Service IO) - Austria under Grant CEP (Centerof Excellence Projects) No. 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 mmdiameter an
6、d 20 g mass. This results in a visuallyappealing 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 analysis of the consideredmagnetic levitation
7、 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. SYSTEMD ESCRIPTION The Magnetic Levitation System (Maglev System 33-006given in Fig. I ) is a relatively new and ef
8、fective laboratory setupvery helpful for control experiments. The basic control goalis to suspend a steel 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 E
9、lectronic Engineering,University of NE, Beogradska 14. 18000 Nil. Yugoslavia, E-mail:nmilicaelfak.ni.ac.yu magnet system, sensors and drivers) with a computer interfacecard, a signal conditioning unit, connecting cables and alaboratory manual. In the analogue mode, the equipment is self-contained wi
10、thinbuilt power supply. Convenient sockets on the enclosurepanel allow for quick changes of analogue controller gain andstructure. The bandwidth of lead compensation may bechanged in order to investigate system stability and timeresponse. Moreover, user-defined analogue controllers may beeasily test
11、ed. Note, that the ,position of the sphere may beadjusted using the set-point control and the stability may bevaried using the gain control. In the digital mode, the Maglev System operates withMATLAB /SlMULrNK' software. Feedback Software forSIMULLNiKs p rovided for the control models and interf
12、acingbetween the PC and the Maglev system hardware. The Maglev System, both in analogue and digital mode,allows the study of various control strategies and other issuesfrom system theory, as follows: Analogue mode .Nonlinear modeling System stabilization Infrared sensor characteristics Closed-loop i
13、dentification Lead-lag compensation Perturbation sensitivity PDcontrol； Linearization about an operating point Digital mode Nonlinear modeling System stabilization Linearization about an operating point A D and DIA conversion Closed-loop identification Perturbation sensitivity State space PD control
14、 Position regulation and tracking control a.S YSTEM MODELINAGN D IDENTIFICATION A schematic diagram of the single-axis magnetic levitationsystem with principal components is depicted in Fig. 2. Theapplied control is voltage, which.is converted into a currentvia the driver within the mechanical
15、 unit. The current passesthrough an electromagnet which creates the correspondingmagnetic field in its vicinity. The sphere is placed along thevertical axis of the electromagnet. The measured position isdetermined from an array of infrared transmitters anddetectors, positioned such that the infrared
16、 beam is intersectedby the sphere. . Using the fundamental principle of dynamics, thebehaviour of the ferromagnetic ball is given by the followingelectromechanical equation wherem is the mass of the levitated ball, g denotes theacceleration due to gravity, x is the distance of the ball f
17、romthe electromagnet, i is the current across the electromagnet,and f ( x , i ) is the magnetic control force. A. Calculating the magnetic control force on the metallicsphere Consider a solenoid with an r radius, an1 length, crossedby an I current. The' sphere is located on the axis of the coila
18、s 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 thesphere is then composed of gravity and the magnetic forceacting on the induced dipole. The magnetic control force between
19、 the solenoid and thesphere can be determined by considering the magnetic field asa function of the ball'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
20、produced by a smallsegment of wire, dl ,canying a current I (see Fig. 4a) isgiven by Whereu0is 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 becomes The magnetic field of a circular contour with an a r
21、adius, asshown in Fig. 4b, is given by Note, that from considerations of symmetry, the fieldcomponent perpendicular to the coil axis dB, must be zero on the axis. In order to 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 distances dx,canying the current n l d x . The total axial field from all turnsof the coil becomes Integrating Eq. (5) within the interval 1 2, gives which can be rewritten in the form
