magnetic levitationmfe.scripts.mit.edu/portfolio/img/portfolio/2.171/presentation.pdf · loop...
TRANSCRIPT
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Magnetic LevitationMichael Everett
Wyatt Ubellacker
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OutlineHardware Setup
Linearization
Controller Design
Challenges
Results
Demo
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Hardware SetupLight-based position sensor and coil wound electromagnet
Arduino vs MyRio
- Wanted to implement controller in C-like language with difference equation rather than a transfer function block
- Good documentation, lots of examples
Arduino scaling Op-Amps for sensor and drive
- Arduino analog input is 0-5V- High frequency PWM output to drive
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System Dynamics (non-linear):
Linearization
Linearizing about some operating point and some operating current gives:
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Linearization (cont.)Plugging in for system dynamics gives:
Choosing our operating point and corresponding current to balance the force of gravity gives the final linearized system:
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Linearization (cont.)We need to measure:
We glued the ball to a micrometer and measured change in force for varying height and current around the operating points.
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Linearization (cont.)
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Linearization (cont.)Fitting the measurements results in:
And a linearized transfer function of:
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Linearization (cont.)
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Controller DesignOperating Point
Feedforward Plant
Lead Controller
Sensor
RefHeight
Height Output
++
+-
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Controller DesignDon’t really care about SS error, so we can just use a Lead Compensator:
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Controller Design (cont.)Loop Transmission Bode plot and root locus:
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Controller Design (cont.)Closed Loop transfer function, Bode plot, and pole zero map
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ChallengesArduino hardware limitations
- No DAC (only PWM)- Standard PWM is at 500 Hz (too slow)- Low output resolution (8- and 10-bit)
- High Kp -> high crossover, but lowers output resolution
- RC Filtering PWM output - even enhanced PWM too slow- external DAC chip was only 8-bits - too low resolution- Hard to measure Bode Plot
- Sine calculation slow- Lookup table also slow- Interferes with loop executing @ 4kHz
- 0.1 Hz sensor noise- Significant sensor noise in last few days
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Results
Simulated Experimental
Time Constant 260ms 250ms
Overshoot 5% 3%
S.S. error 20% 16%
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Demohttps://www.youtube.com/watch?v=Chfn8uVCth8