基于matlab的磁悬浮控制系统研究.docx

MATLABBASEDMAGNETICLEVITATIONCONTROLSYSTEM(基于MATLAB的磁悬浮控制系统的研究)系统介绍磁悬浮系统是一个典型的非线性系统，当前绝大多数磁悬浮控制器都是基于非线性磁悬浮系统在某个平衡点的线性化模型而设计的线性控制律。当系统的平衡点改变时，系统的动态特性会显著改变。MAGNETICLEVITATIONSYSTEMISATYPICALNONLINEARSYSTEMTHECURRENTVASTMAJORITYOFCONTROLLERSWHICHBELONGSTONONLINEARMAGNETICLEVITATIONSYSTEMAREBASEDONALINEAREQUILIBRIUMMODELTODESIGNFORTHELINEARCONTROLLAWWHENTHEEQUILIBRIUMPOINTOFTHESYSTEMCHANGES,THEDYNAMICCHARACTERISTICSOFTHESYSTEMWILLCHANGESIGNIFICANTLY磁悬浮系统是利用电磁力来控制刚体悬浮的空间位置。其工作原理是控制电磁铁绕组的电流，产生与刚体重量等价的电磁力，使得刚体稳定悬浮在平衡位置。由于电磁力与悬浮气隙间存在非线性反比关系，这种平衡并不稳定，一旦受到外界干扰如电压脉动或者风，刚体就会掉下来或被吸上去，因此必须实行闭环控制。MAGNETICLEVITATIONSYSTEMUSESELECTROMAGNETICFORCETOCONTROLTHESUSPENDEDSPATIALPOSITIONOFTHERIGIDBODYITSWORKINGPRINCIPLEISTOCONTROLTHEELECTRICCURRENTOFELECTROMAGNETWINDINGSTOPRODUCEELECTROMAGNETICFORCEWHICHISEQUIVALENTTOTHEWEIGHTOFTHERIGIDBODY,MAKINGTHERIGIDBODYSUSPENDEDINSTABLEEQUILIBRIUMPOSITIONDUETOTHENONLINEARINVERSERELATIONSHIPBETWEENTHEELECTROMAGNETICFORCEANDSUSPENDEDAIR,THISBALANCEISNOTSTABLEINTHEEVENTOFOUTSIDEINTERFERENCESUCHASVOLTAGEFLUCTUATIONORWIND,RIGIDBODYWILLFALLOFFORSUCKUPSOITISNECESSARYTOIMPLEMENTCLOSEDLOOPCONTROL采用位置传感器在线获取刚体位置信号，控制器对位移信号进行处理产生控制信号，功率放大器根据控制信号产生所需电流并送往电磁铁，电磁铁产生相应磁力克服重力使得刚体稳定在平衡点附近。WITHONLINEACCESSTOTHELOCATIONPOSITIONOFTHERIGIDBODYBYTHEUSEOFSENSORSIGNAL,CONTROLLERPRODUCECONTROLSIGNALTHROUGHDISPLACEMENTSIGNALPROCESSINGANDTHEPOWERAMPLIFIERGENERATETHEREQUIREDCURRENTACCORDINGTOCONTROLSIGNALSANDSENTTOELECTROMAGNETSWHICHMAKECORRESPONDINGMAGNETICTOOVERCOMEGRAVITY,RESULTINGINTHESTABILITYOFRIGIDBODYINTHEEQUILIBRIUMPOINT磁悬浮由于其无接触的特点避免了物体之间的摩擦和磨损，能延长设备的使用寿命，改善设备的运行条件，因而在交通、冶金、机械、电器、材料等各个方面有着广阔的应用前景。MAGNETICLEVITATIONSYSTEMCANAVOIDFRICTIONANDWEARBETWEENTHEOBJECTDUETOITSNONCONTACTCHARACTERISTICSITCANALSOEXTENDTHESERVICELIFEOFEQUIPMENTANDIMPROVEOPERATINGCONDITIONSOFTHEEQUIPMENTSOITHASBROADAPPLICATIONPROSPECTSINTHETRANSPORTATION,METALLURGY,MACHINERY,ELECTRICAL,MATERIALSANDOTHERASPECTS模型介绍控制对象是铁磁性材料做成的球体．球的高度为HT，线圈电流为IT．磁悬浮动力学方程以及线圈回路电压方程分别为CONTROLOBJECTISASPHEREMADEOFFERROMAGNETICMATERIALBALLHEIGHTHT,COILCURRENTITMAGLEVKINETICEQUATIONSANDMAGNETICCIRCUITVOLTAGEEQUATIONS22DHTITMGKH1ITLURIT其中M为球的质量，G为重力加速度，L为线圈电感，R为线圈电阻，K为磁场和球之间的耦合系数．系统的输入为线圈电压UT，输出为球的高度HT．WHEREMISTHEBALLQUALITY,GISACCELERATIONDUETOGRAVITY,LISTHECOILINDUCTANCE,RISTHECOILRESISTANCE,KISTHECOUPLINGCOEFFICIENTBETWEENMAGNETICFIELDANDTHEBALLTHESYSTEMISCOILVOLTAGEUT,OUTPUTTHEHEIGHTOFTHEBALLHT球与电磁铁间保持适当的距离时，电磁吸引力与重力平衡．如果球的高度下降太多，则磁场的作用力变弱而使球落下去．如果球离磁铁太近，则磁场作用又会太强而将球拉向磁铁，这也将破坏系统的稳定性。WHENTHEREISANAPPROPRIATEDISTANCEBETWEENTHEBALLANDELECTROMAGNET,THEMAGNETICATTRACTIONANDGRAVITYBALANCEDIFTHEHEIGHTOFTHEBALLDROPTOOMUCH,THEFORCEOFMAGNETICFIELDBECOMEWEAKLEAVINGTHEBALLDROPIFTHEBALLISTOOCLOSETOTHETHEMAGNET,MAGNETICFIELDWILLBETOOSTRONGANDTHEBALLWILLBEPULLEDTOTHEMAGNET,WHICHWILLALSOUNDERMINETHESTABILITYOFTHESYSTEM假定球的期望高度为H。，该位置称为平衡点，此处重力和电磁吸引力相等．令加速度为零，求出维持该位置的期望电流．ASSUMETHATTHEEXPECTATIONHEIGHTOFTHEBALLISH。,THELOCATIONKNOWNASTHEEQUILIBRIUMPOINT,WHEREGRAVITYANDMAGNETICATTRACTIONAREEQUALSOACCELER