Marwan K Abbadi Advisor Dr Winfred Anakwa Outline

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Marwan K. Abbadi Advisor: Dr. Winfred Anakwa

Marwan K. Abbadi Advisor: Dr. Winfred Anakwa

Outline • Introduction – Problem definition – Objectives • • • Functional Description System

Outline • Introduction – Problem definition – Objectives • • • Functional Description System Block Diagram System Identification Control Algorithm Software Implementation Hardware Interface Results Conclusions Future work

Introduction • What are Magnetic levitation systems? Maglev. are devices that suspend ferromagnetic materials

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, aerospace shuttles, magnetic bearings and high-precision platforms.

Introduction • Problem definition Maglev. systems based on electromagnetic attraction are characterized by non-linear

Introduction • 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

Project Objectives • Obtain a good model for the magnetic levitation system, maglev model 33 -210 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

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) – Disturbances such as power supply fluctuation, coil temperature variations and external forces applied to the ball. • Output Actual ball position

System Block Diagram

System Block Diagram

System Identification • Importance of modeling the system. • There are two approaches to

System Identification • Importance of modeling the system. • There are two approaches to identify the plant: a) Analytical model- Using differential equations. b) Experimental 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

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, this maglev. system is driven by an active circuit for the coil that adds further non-linearity since I is a non-linear function of e. 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 motion: 2 nd law of Electromagnetic force

System Identification 2) Mechanical equation Using Newton motion: 2 nd law of Electromagnetic force EF= C (i/x)2 Where F= Resultant force m= Mass of the steel ball= 0. 021 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, so linearization is needed. •

System Identification • The previous equation contained non-linear elements, so 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

System Identification • Coil inductance L was approximated as a constant = 296. 74 m. H. • Sensor gain Ks was determined to be 450. 3 volts/meter.

System Identification • Combining the previous equations:

System Identification • Combining the previous equations:

System Identification • The analog controller of the manufacturer was connected to the plant

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 from 0 to 20 Hz.

System Identification • The experimental model of the plant is:

System Identification • The experimental model of the plant is:

System Identification • The experimental model was used instead of the analytical model, since

System Identification • The experimental 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.

System Identification • Frequency response data for controller from the manufacturer:

System Identification • Frequency response data for controller from the manufacturer:

System Identification • Controller from manufacturer: • Approximating to a first order: • Pole

System Identification • Controller from manufacturer: • Approximating to a first order: • Pole at -2827 rad/s and zero at -47 rad/s

System Identification • SIMULINK vs. experimental system response to 0. 6 V step input

System Identification • SIMULINK vs. experimental system response to 0. 6 V step input

System Identification • Bode diagram of Gc_man(s)*Gp_exp(s) PM=30. 5 degrees

System Identification • Bode diagram of Gc_man(s)*Gp_exp(s) PM=30. 5 degrees

System Identification • The analog controller from manufacturer was converted to discrete domain using

System Identification • The analog controller from manufacturer was converted to discrete domain using bilinear (Tustin) transformation with Ts= 5 ms.

Software Implementation • The digital controller was implemented using assembly language program on an

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 • The 8051 microcontroller does not handle floating point arithmetic. • The

Software Implementation • The 8051 microcontroller does not handle floating point arithmetic. • The controller transfer function was approximated for fixed point implementation. • The approximated transfer function: Note: Gain implemented in hardware

Software Implementation

Software Implementation

Hardware Interface • Hardware interface circuitry is needed to level shift and scale the

Hardware Interface • Hardware interface circuitry is needed to level shift and scale the error to the range of the microcontroller A/D. • Furthermore, the control signal generated via the D/A must be readjusted back to the full scale and multiplied by the controller gain.

Hardware Interface 2 E 1(t) = 0 ~ -5 V 3 E 2(t) =

Hardware Interface 2 E 1(t) = 0 ~ -5 V 3 E 2(t) = 0 ~ +5 V Antialiasing filter Ready to be interfaced to the EMAC 1 EMAC Error signal E(t) = ± 5 V Error to A/D

Hardware Interface 2 Shifted signal -2. 5 ~ 2. 5 V Controller gain maglev

Hardware Interface 2 Shifted signal -2. 5 ~ 2. 5 V Controller gain maglev 1 D/A signal 0 ~ 5 V 3 Control signal U D/A to Maglev

Results • The ball was stabilized at the equilibrium point however it was oscillating

Results • The ball was stabilized at the equilibrium point however it was oscillating due to: – Quantization errors of the 8 -bit A/D and D/A. – Truncation errors of coefficients stated in controller transfer function. – Computational truncation errors.

Results Stabilization of steel ball at the nominal equilibrium point Control signal Ball position

Results Stabilization of steel ball at the nominal equilibrium point Control signal Ball position

Results Figure displaying the quantization effects

Results Figure displaying the quantization effects

Results

Results

Results Tracking of sinusoidal reference input: - The steel ball tracked reference sinusoidal and

Results Tracking of sinusoidal reference input: - The steel ball tracked reference sinusoidal and square waveform inputs.

Conclusions • Mathematical modeling of an unstable system is a challenging control engineering problem.

Conclusions • Mathematical modeling of an unstable system is a challenging control engineering problem. Some examples are inverted pendulums and aerospace vehicles. • Implementation of controller algorithm on 8 -bit microcontroller using fixed point arithmetic generates quantization and truncation errors. • These errors, that depend on sampling period and controller gain, cause small oscillations in system response. • The ball tracked reference input signals. Better tracking performance can be achieved using higher resolution A/D and D/A, longer wordlength microcontroller and a higher order controller.

Future work • A user-friendly interface can be developed using the keypad and LCD.

Future work • A user-friendly interface can be developed using the keypad and LCD. • Possible user inputs include sampling period, poles and zeroes locations, settling time etc. • Once implemented, the system will serve as a good apparatus for teaching undergraduate controls students the effect of varying different parameters on overall system response.

END Questions and answers Thank you For more information: visit http: //cegt 201. bradley.

END Questions and answers Thank you For more information: visit http: //cegt 201. bradley. edu/projects/proj 2003/maglev/