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1、Modeling of a Didactic Magnetic Levitation System for Control EducationMilica B. NaumoviCAbsruo The magnetic levitation control system of a metallicsphere is an interesting and visual impressive device successfulfor demonstration many intricate problems for controlengineering research. The dynamics
2、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 engineeringeducation, system m
3、odelingI. INTRODUCTIONMagnetic 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 suitable for la
4、boratoryexperiments and classroom demonstrations, as reported in theengineering education literature 1-8.The classic magnetic levitation control experiment isprescnted in the form of laboratory equipment given in Fig.1.The complete purchase of the Feedback Instruments Ltd.Maglev System 33-006 9 is s
5、upported 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 mm diameter and 20 g mass. This
6、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 system. Although
7、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 ESCRIPTIONThe Magnetic Levitation System (Maglev System 33-006given in Fig. I ) is a relatively new and effective laboratory s
8、etupvery 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 Electronic Engineerin
9、g,University of NE, Beogradska 14. 18000 Nil. Yugoslavia, E-mail:nmilicaelfak.ni.ac.yumagnet 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 withinbuilt power supply
10、. 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 tested. Note, that the ,po
11、sition 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 interfacingbetween the PC and the
12、 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 modelingSystem stabilizationInfrared sensor characteristicsClosed-loop identificationLead-lag compensat
13、ionPerturbation sensitivityPDcontrol;Linearization about an operating pointDigital mode Nonlinear modelingSystem stabilizationLinearization about an operating pointA D and DIA conversionClosed-loop identificationPerturbation sensitivityState space PD controlPosition regulation and tracking controla.
14、S YSTEM MODELINAGN D IDENTIFICATIONA 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 unit. The current passesthrough an electromagnet w
15、hich 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 beam is intersectedby the sphere. .Using the funda
16、mental principle of dynamics, thebehaviour of the ferromagnetic ball is given by the followingelectromechanical equation where 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 across the electromagnet,and f ( x , i ) is the magnetic control force.A. Calculating the magnetic control force on
