By Marwan Karrar Abbadi Date April 22 2004
By Marwan Karrar Abbadi Date: April 22, 2004 Advisor Dr. W. Anakwa
Outline • Introduction – Problem definition – Objectives • • • Functional description System Block diagram System identification Control algorithm Software implementation Hardware interface Results and analysis Conclusions Recommendations and future work
Introduction • What are Magnetic levitation systems? Maglev. are devices that suspend ferromagnetic materials with the aid of electromagnetism. It has wide number of applications such as high-speed trains, magnetic bearings and high-precision platforms. • Problem definition Maglev. systems based on electromagnetic attraction are characterized by non-linear and unstable open-loop dynamics which suggests the need of stabilizing controllers.
Project objectives • Obtain a good model for the magnetic levitation system, maglev model 33 -120 from Feedback Inc. Limited. • Design and implement a microcontroller-based digital controller to stabilize a 21 gram steel ball at a desired vertical position. The overall system should track applied reference input signals.
Functional description • Inputs: Set point (Constant 1. 50 [V] ), corresponds to a distance of 22. 5 mm between the ball and the electromagnet. Reference signal (± 0. 4 Vpp) Internal disturbances such as power supply fluctuation. • Output Actual ball position
System block diagram
System identification • Importance of modeling the system. • There are two approaches to identify the plant: a) Analytical model- Using differential equations. b) Practical model- Bode frequency response data fitting. To obtain a good model for the system, both models were obtained for comparison.
System identification • Analytical model There are two sets of equations that describe magnetic levitation systems. This is the general electrical 1) Electrical: circuit for magnetic levitation systems. However, our maglev. System is driven by an active coil driver that adds further non -linearity since e is a function of i. Where e = Coil input voltage R= Coil resistance i = Coil current L= Coil inductance t = Time L 0= Nominal point inductance x 0= Nominal point pos.
System identification 2) Mechanical equation Using Newton second law of motion Electromagnetic force EF= C (i/x)2 Where F= Resultant force m= Mass of the steel ball= 0. 0021 Kg g= gravitational acceleration = 9. 82 m/s 2 C= Magnetic plant constant Gravitation force GF = m*g
System identification • The previous equation contained non-linear elements, linearization is needed. • Taylor series expansion is used to approximate the equations near the operating point of x 0=22. 5 mm from electromagnet. • Operating region= 18 27 mm from electromagnet. • Magnetic plant constant, C= 1. 477 x 10 -4 N. m 2. A-2
System identification • Coil inductance L was approximated as a constant = 296. 74 m. H. • Sensor calibration was performed. Y(x)= 450. 3*x [V/m]
System identification • Combining the previous equations:
System identification • The analog controller of the manufacturer was connected to the plant to obtain frequency response data. • The data was obtained at the nominal operating point x=x 0=22. 5 mm • The reference input frequency was swept between 0 and 20 Hz.
System identification • The practical model of the plant is:
System identification • The practical model was used instead of the analytical model, since the analytical model did not account for the non-linearity of the active coil driver. • The high-frequency pole at -70. 15 rad/s was omitted in the practical model approximation.
Controller algorithm
Software implementation • The digital controller was implemented using assembly language program on an Intel-80515 microcontroller. • The software code: – Samples the error signal via the A/D. – Computes the control signal. – Sends the control signal to the plant via the D/A.
Software implementation
Hardware interface • Hardware interface circuitry is needed to level shift and scale the error to the scale of the microcontroller A/D. • Furthermore, the control signal generated via the D/A must be readjusted back to the full scale.
Hardware interface 2 E 1(t) = 0 ~ -5 V Since using inverting op-amp 3 E 2(t) = 0 ~ +5 V Ready to be interfaced to the EMAC 1 Error signal E(t) = ± 5 V
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