Magnetic Levitation System Onemli
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MechatronicsMagnetic Levitation SystemK. Craig1MechatronicsMagnetic Levitation SystemDynamic System InvestigationKevin CraigRensselaer Polytechnic InstituteMechatronicsMagnetic Levitation SystemK. Craig2ElectromagnetInfrared LEDPhototransistorLevitated BallMagnetic Levitation System A Genuine Mechatronic SystemMechatronicsMagnetic Levitation SystemK. Craig3Overall Objective The objective of this exercise is to build and test a one-degree-of-freedom magnetic levitation device, i.e., a device to keep a ferromagnetic object suspended, without contact, beneath an electromagnet, and perform a complete dynamic system investigation. By measuring the location of the object using a non-contact sensor, and adjusting the current in the electromagnet based on this measurement, the levitated object can be maintained at a predetermined location.MechatronicsMagnetic Levitation SystemK. Craig4Dynamic System InvestigationPhysicalSystemExperimentalAnalysisComparisonMathematicalAnalysisMathematicalModelPhysicalModelDesignChangesParameterIdentificationMechatronicsMagnetic Levitation SystemK. Craig5 This system is both inherently nonlinear and open-loop unstable. Steps for a Dynamic System Investigation Physical System Description Physical Modeling (Truth Model vs. Design Model) Model Parameter Identification Mathematical Modeling Dynamic System Behavior Prediction Experiments to Validate Analytical Model Feedback Control System Design and Implementation Testing to Evaluate System Performance Determine Design ImprovementsMechatronicsMagnetic Levitation SystemK. Craig6Required Background Electromechanics: Elementary Electromagnet Linearization of Nonlinear Physical Effects Electronic Components Resistor, Capacitor, Inductor Electrical Impedance & Analogies Potentiometer and Voltage Divider Op-Amp Basics + Buffer, Summer, Difference, Inverting Active Lead / Lag Controller Diode and Light-Emitting Diode (LED) Transistor: npn BJT, pnp BJT, PhototransistorMechatronicsMagnetic Levitation SystemK. Craig7Physical System Description The Magnetic Levitation System consists of the following subsystems: Electromagnet Actuator mounted in a stand Ball-position Sensor: Infrared LED and Phototransistor, positioned in the stand Analog Circuitry on a breadboard Lead Controller (analog implementation) Current Amplifier Assorted op-amps, resistors, capacitors, potentiometers, and diodes for controller implementation, sensor adjustment, buffering, gain adjustment, summing, and inverting.MechatronicsMagnetic Levitation SystemK. Craig8 Required Power Supplies include: 15 volts for op-amps + 15 volts for electromagnet and phototransistor + 15 volts for command and bias voltage generation + 5 volts for infrared LED Current requirements: 300 mA maximum Microcontroller for Digital Control Implementation Blue Earth Micro 485 Microprocessor: Intel 8051 - 12 MHz Digital I/O: 27 bi-directional TTL-compatible pins Analog Inputs: 4 12-bit, 0-5 V, A/D converter channels Serial Communication: RS 232 128K battery-backed RAM; 32K ROMMechatronicsMagnetic Levitation SystemK. Craig9ElectromagnetInfrared LEDPhototransistorVsensor= 5.44 VAt EquilibriumLevitated Ballm = 0.008 kgr = 0.0062 m = 0.24 inMagnetic Levitation System A Genuine Mechatronic SystemEquilibrium Conditionsx0= 0.003 mi0= 0.222 A+xiMechatronicsMagnetic Levitation SystemK. Craig10 Electromagnet Actuator Current flowing through the coil windings of the electromagnet generates a magnetic field. The ferromagnetic core of the electromagnet provides a low-reluctance path in the which the magnetic field is concentrated. The magnetic field induces an attractive force on the ferromagnetic ball.f x i Cix( , ) = FH IK2Electromagnetic ForceProportional to the square of the currentandInversely proportional to the square of the gap distanceMechatronicsMagnetic Levitation SystemK. Craig11CoreWindings1.4"1.5"2.6"0.25" The electromagnet uses a - inch steel bolt as the core with approximately 3000 turns of 26-gauge magnet wire wound around it. The resistance of the electromagnet at room temperature is approximately 32 .MechatronicsMagnetic Levitation SystemK. Craig12InfraredLED+15VPhototransistor+5V+-Unity GainBuffer Op-AmpVsensor62 1 K200 KEmitterDetectorBall-Position SensorLED Blocked: Vsensor = 0 VLED Unblocked: Vsensor = 10 VEquilibrium Position: Vsensor 5.40 VKsensor 4 V/mm Range 1mmiemitter= 15 mAMechatronicsMagnetic Levitation SystemK. Craig13 Ball-Position Sensor The sensor consists of an infrared diode (emitter) and a phototransistor (detector) which are placed facing each other across the gap where the ball is levitated. Infrared light is emitted from the diode and sensed at the base of the phototransistor which then allows a proportional amount of current to flow from the transistor collector to the transistor emitter. When the path between the emitter and detector is completely blocked, no current flows. When no object is placed between the emitter and detector, a maximum amount of current flows. The current flowing through the transistor is converted to a voltage potential across a resistor.MechatronicsMagnetic Levitation SystemK. Craig14 The voltage across the resistor, Vsensor, is sent through a unity-gain, follower op-amp to buffer the signal and avoid any circuit loading effects. Vsensoris proportional to the vertical position of the ball with respect to its operating point; this is compared to the voltage corresponding to the desired ball position. The emitter potentiometer allows for changes in the current flowing through the infrared LED which affects the light intensity, beam width, and sensor gain. The transistor potentiometer adjusts the phototransistor current-to-voltage conversion sensitivity and allows adjustment of the sensors voltage range; a 0 - 10 volt range allows for maximum sensor sensitivity without saturation of the downstream buffer op-amp.MechatronicsMagnetic Levitation SystemK. Craig15From Equilibrium:As i , x, & Vsensor As i , x , & Vsensor +-Vdesired Gc(s)Controller Vbias++ CurrentAmplifier G(s)Magnet + BallH(s)SensorVactual XiMagnetic Levitation System Block DiagramLinear Feedback Control Systemto Levitate Steel Ballabout an Equilibrium Position Corresponding to Equilibrium Gap x0and Equilibrium Current i0MechatronicsMagnetic Levitation SystemK. Craig16Command and Error SignalGenerationFrom Equilibrium:As i , x, & Vsensor As i , x , & Vsensor +-VsensorVcommand-VerrorDifferenceOp-Amp+-Unity GainBuffer Op-AmpVcommand+15V10 K100 K100 K100 K100 KVoltageDividerMechatronicsMagnetic Levitation SystemK. Craig17ActiveLead Controllercontrol 2 1 1 4 4error 1 2 2 3 3V R R C s 1 R R 0.01s 1V R R C s 1 R R 0.001s 1 ( ( ( ( + + (= = ( ( ( ( ( + + Vcontrol-VerrorLead Controller+-InvertingOp-Amp-+1R 100 K = 1C 0.1 F = 2R 100 K = 2C 0.01 F = 51 K1.6 K3R 1.6 K = 4R 50 K = MechatronicsMagnetic Levitation SystemK. Craig18+-VbiasVcontrolVbias +VcontrolSummingOp-Amp+-Vbias withUnity GainBuffer Op-AmpVbias+15VUnity GainInvertingOp-Amp-+10 K10 K10 K10 K5.1 K10 K10 K5.1 KVoltageDividerVbiasGeneration & Summation with VcontrolVbias= 1.77 VAt EquilibriumMechatronicsMagnetic Levitation SystemK. Craig19R1+-Vcontrol+Vbias+-npn BJTTransistorpnp BJTTransistorR2R3Electro-Magnet+Vsupplydiode( )2em control bias1 3Ri V VR R= +iem123R 1000 R 510 R 17.8 (20W)= = = 00i 0.222 Ax 3.0 mm==Current AmplifierRem= 32 Vsupply= 15 Vsupplysatem 3ViR R =+> 9.65 V> 9.65 V< 9.93 mA< 9.93 VMechatronicsMagnetic Levitation SystemK. Craig20+ximgf x i Cix( , ) = FH IK2ElectromagnetBall (mass m)Magnetic Levitation SystemControl System DesignLinearization:2 2 22 2 3 2i i 2i 2iC C C x C ix x x x| | | | | | | | + | | | |\ . \ . \ . \ .Equation of Motion:22imx mg Cx| |= |\ .
2 22 3 2i 2i 2i mx mg C C x C ix x x| | | | | |= + | | |\ . \ . \ .
At Equilibrium:23 22i 2i mx C x C ix x| | | |= | |\ . \ .
22img Cx| |= |\ .MechatronicsMagnetic Levitation SystemK. Craig21+-Vdesired Gc(s)Controller Vbias++ CurrentAmplifier G(s)Magnet + BallH(s)SensorVactual Xi22img Cx| |= |\ .m 0.008g 9.81x 0.003i 0.222====C 1.4332E 5 = 23 22i 2i mx C x C ix x| | | |= | |\ . \ .
x 6540x 88i =
( )2x 88 s 6540 i =Kamp= 0.0287 A/VKsensor 4 V/mmMechatronicsMagnetic Levitation SystemK. Craig22( )( )( )2880.0287 3000s 6540 Open-LoopTransfer Function43R 0.01s 1 0.01s 14R 0.001s 1 0.001s 1 ( + + ( (= ( ( (+ + ControllerMechatronicsMagnetic Levitation SystemK. Craig23 Digital Implementation of Controller The analog controller has a high bandwidth needed to compensate for inherent instability and nonlinearities. Digital controllers have an advantage in that the control systemis implemented in software rather than in hardware, and is therefore much easier to modify. However, a controller implemented digitally has the disadvantages of quantization and limited sampling rate, which can adversely affect system performance.-VerrorScalingCircuit0 5 V12-bit A/DDigitalControllerGc(z)8-bit D/ADAC 08MicrocontrollerWithA/D ConverterScale &OffsetCircuitryTsToBuffer Op-Amp