Closed Loop Control of Halbach Array Magnetic Levitation System Height By: Kyle Gavelek Victor Panek Christopher Smith Advised by: Dr. Winfred Anakwa Mr. Steven Gutschlag

Closed Loop Control of Halbach Array Magnetic Levitation System Height Introduction Previous Work Project Summary Halbach Array Inductrack Maglev System Design Equations Preliminary Work Design Tasks Equipment List Schedule Patents References I.Introduction II.Previous Work III.Project Summary IV.Halbach Array V.Inductrack VI.Maglev System VII.Design Equations VIII.Preliminary Work IX.Design Tasks Halbach Array Model DC Motor Model Controller Model uController and Flat Track X.Equipment List XI.Schedule XII.Patents XIII.References

Closed Loop Control of Halbach Array Magnetic Levitation System Height Introduction Previous Work Project Summary Halbach Array Inductrack Maglev System Design Equations Preliminary Work Design Tasks Equipment List Schedule Patents References Maglev technology is applied in various fields today, most prominently in high speed trains.

Closed Loop Control of Halbach Array Magnetic Levitation System Height Introduction Previous Work Project Summary Halbach Array Inductrack Maglev System Design Equations Preliminary Work Design Tasks Equipment List Schedule Patents References Dr. Richard Post Fundamental research in the field of magnetic levitation while at the Lawrence Livermore National Laboratory. He designed the inductrack in the 1990’s. Paul Friend (2004) Determination of levitation equations and successful design of MATLAB GUI software. The GUI software will be used to predict the results with variable input values.

Closed Loop Control of Halbach Array Magnetic Levitation System Height Introduction Previous Work Project Summary Halbach Array Inductrack Maglev System Design Equations Preliminary Work Design Tasks Equipment List Schedule Patents References

Closed Loop Control of Halbach Array Magnetic Levitation System Height Introduction Previous Work Project Summary Halbach Array Inductrack Maglev System Design Equations Preliminary Work Design Tasks Equipment List Schedule Patents References Glen Zomchek (2007) Design and fabrication of inductrack levitation system which achieved.45mm vertical displacement. Dirk DeDecker and Jesse VanIseghem (2012) Re-design of inductrack levitation system with successful vertical displacement of 3.7mm from a starting displacement of 5.0mm

Closed Loop Control of Halbach Array Magnetic Levitation System Height Introduction Previous Work Project Summary Halbach Array Inductrack Maglev System Design Equations Preliminary Work Design Tasks Equipment List Schedule Patents References Current rotary inductrack system

Closed Loop Control of Halbach Array Magnetic Levitation System Height Introduction Previous Work Project Summary Halbach Array Inductrack Maglev System Design Equations Preliminary Work Design Tasks Equipment List Schedule Patents References The objective of CLCML is to model the precious year’s magnetic levitation system and implement closed loop control of the magnetic levitation height.

Closed Loop Control of Halbach Array Magnetic Levitation System Height Introduction Previous Work Project Summary Halbach Array Inductrack Maglev System Design Equations Preliminary Work Design Tasks Equipment List Schedule Patents References Magnetic fields created by Halbach array magnet configuration. Sinusoidal magnetic field generated below the Halbach array. B 0 = Peak Magnetic Field d = Thickness of magnet Br = Individual Magnet’s StrengthM = # of magnets per wavelength

Closed Loop Control of Halbach Array Magnetic Levitation System Height Introduction Previous Work Project Summary Halbach Array Inductrack Maglev System Design Equations Preliminary Work Design Tasks Equipment List Schedule Patents References Φ = Magnetic FluxL = Inductrack Inductance I = CurrentR = Inductrack Resistance λ = magnetic field wavelengthk = wave number = 2π/λ y = vertical distancew = width ω = kv v = ωmr = Tangential Velocity B 0 = Peak Magnetic Field The copper inductrack is fastened to the outside of the rotating wheel making it a rotary inductrack.

Closed Loop Control of Halbach Array Magnetic Levitation System Height Introduction Previous Work Project Summary Halbach Array Inductrack Maglev System Design Equations Preliminary Work Design Tasks Equipment List Schedule Patents References Passing Halbach Array’s Magnetic Field Inherent Track Properties This animation displays the relationship between velocity of a rotary inductrack with a Halbach array as velocity increases.

Closed Loop Control of Halbach Array Magnetic Levitation System Height Introduction Previous Work Project Summary Halbach Array Inductrack Maglev System Design Equations Preliminary Work Design Tasks Equipment List Schedule Patents References As shown above the pole occurs at ω = -R/L

Closed Loop Control of Halbach Array Magnetic Levitation System Height Introduction Previous Work Project Summary Halbach Array Inductrack Maglev System Design Equations Preliminary Work Design Tasks Equipment List Schedule Patents References R = Inductrack Resistance R C = Resistivity of Copper = 1.68 x Ωm ℓ = Length of Inductrack A = Inductrack Cross-sectional Area L = Inductrack Inductance μ 0 = Permeability of free space = 4π H/m λ = Wavelength of magnetic field P C = Mean Perimeter of Inductrack d C = Spacing of Inductors B 0 = Peak Magnetic Field d = Thickness of magnet Br = Individual Magnet’s StrengthM = # of magnets per wavelength

Closed Loop Control of Halbach Array Magnetic Levitation System Height Introduction Previous Work Project Summary Halbach Array Inductrack Maglev System Design Equations Preliminary Work Design Tasks Equipment List Schedule Patents References Using the design equations shown previously, the following values have been calculated in previous work. The accuracy of these values shall be tested through experimentation. B 0 = TR = 1.9 x ΩL = x H

Closed Loop Control of Halbach Array Magnetic Levitation System Height Introduction Previous Work Project Summary Halbach Array Inductrack Maglev System Design Equations Preliminary Work Design Tasks Equipment List Schedule Patents References F y = Vertical ForceB 0 = Peak Magnetic Field w = Width of Inductrackk = Wave Number = 2π/λ ω = kv v = ω m r = Tangential Velocity y = vertical distance

Closed Loop Control of Halbach Array Magnetic Levitation System Height Introduction Previous Work Project Summary Halbach Array Inductrack Maglev System Design Equations Preliminary Work Design Tasks Equipment List Schedule Patents References ω m = machine rotational speed b = Motor Viscous Friction I A = Armature Current R A = Armature Resistance V S = Source Voltage T C = Columbic Friction K T = K V = Torque Constant = Velocity Constant J A = Moment of Inertia

Closed Loop Control of Halbach Array Magnetic Levitation System Height Introduction Previous Work Project Summary Halbach Array Inductrack Maglev System Design Equations Preliminary Work Design Tasks Equipment List Schedule Patents References The maximum overshoot of the system shall be <10%. The steady state error shall be less than 0.02 cm. The rise time shall be minimized. The settling time shall be less than 50 ms* Controller Design Specifications: *The settling time specification may need to be modified based on the motor’s capabilities.

Closed Loop Control of Halbach Array Magnetic Levitation System Height Introduction Previous Work Project Summary Halbach Array Inductrack Maglev System Design Equations Preliminary Work Design Tasks Equipment List Schedule Patents References μController Specifications: Accept a user-defined levitation height through keypad input. Calculate the vertical displacement of the Halbach array device with a displacement transducer. Calculate an error signal by subtracting the system displacement with the desired displacement from the keypad. Calculate the voltage required by the DC motor to achieve the desired displacement based on the transfer function of the closed loop. Sample displacement not sooner than the settling time (50ms). All calculations within 1ms. The track shall accommodate linear motion of the Halbach array until break velocity is reached. The track shall be designed to minimize break velocity. The track shall be designed to minimize leakage flux and eddy currents. Circular Track Design Specifications:

Closed Loop Control of Halbach Array Magnetic Levitation System Height Introduction Previous Work Project Summary Halbach Array Inductrack Maglev System Design Equations Preliminary Work Design Tasks Equipment List Schedule Patents References Equipment List: Lexan sheets for protective enclosure μController capable of meeting required specifications Materials for fabrication of circular track Materials for fabrication of new Halbach array

Closed Loop Control of Halbach Array Magnetic Levitation System Height Introduction Previous Work Project Summary Halbach Array Inductrack Maglev System Design Equations Preliminary Work Design Tasks Equipment List Schedule Patents References The safety enclosure and all modeling shall be completed before winter break. During winter break each group member will complete some individual work. ChrisKyleVictor Winter BreakController ResearchWebsite Designμcontroller research Week 1-3Controller Designμcontroller code development Week 4-6μcontroller code development incorporating controller and models Week 7-9μcontroller implementation and testing Week 7-9Flat inductrack research when idle Week 10Preparation for Student Expo Week 11Student Expo Week 12-13Final report and project presentation presentation Week 14Final Presentation

Closed Loop Control of Halbach Array Magnetic Levitation System Height Introduction Previous Work Project Summary Halbach Array Inductrack Maglev System Design Equations Preliminary Work Design Tasks Equipment List Schedule Patents References Richard F. Post Magnetic Levitation System for Moving Objects U.S. Patent 5,722,326 March 3, 1998 Richard F. Post Inductrack Magnet Configuration U.S. Patent 6,633,217 B2 October 14, 2003 Richard F. Post Inductrack Configuration U.S. Patent 629,503 B2 October 7, 2003 Richard F. Post Laminated Track Design for Inductrack Maglev System U.S. Patent Pending US 2003/ A1 June 19, 2003 Coffey; Howard T. Propulsion and stabilization for magnetically levitated vehicles U.S. Patent 5,222,436 June 29, 2003 Coffey; Howard T. Magnetic Levitation configuration incorporating levitation, guidance and linear synchronous motor U.S. Patent 5,253,592 October 19, 1993 Levi;Enrico; Zabar;Zivan Air cored, linear induction motor for magnetically levitated systems U.S. Patent 5,270,593 November 10, 1992 Lamb; Karl J. ; Merrill; Toby ; Gossage; Scott D. ; Sparks; Michael T. ;Barrett; Michael S. U.S. Patent 6,510,799 January 28, 2003

Closed Loop Control of Halbach Array Magnetic Levitation System Height Introduction Previous Work Project Summary Halbach Array Inductrack Maglev System Design Equations Preliminary Work Design Tasks Equipment List Schedule Patents References [1] Dirk DeDecker, Jesse VanIseghem. Senior Project. “Development of a Halback Array Magnetic Levitation System”. Final Report, May 2012 [2] Glenn Zomchek. Senior Project. “Redesign of a Rotary Inductrack for Magnetic Levitation Train Demonstration.” Final Report, [3] Paul Friend. Senior Project. Magnetic Levitation Technology 1. Final Report, [4] Post, Richard F., Ryutov, Dmitri D., “The Inductrack Approach to Magnetic Levitation,” Lawrence Livermore National Laboratory. [5] Post, Richard F., Ryutov, Dmitri D., “The Inductrack: A Simpler Approach to Magnetic Levitaiton,” Lawrence Livermore National Laboratory. [6] Post, Richard F., Sam Gurol, and Bob Baldi. "The General Atomics Low Speed Urban Maglev Technology Development Program." Lawrence Livermore National Laboratory and General Atomics.