The Self-Organizing Controller, SOC
www.inference.dk2013
Today, it might be called an adaptive fuzzy controller.
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Summary
• SOC is a model reference adaptive system, MRAS• SOC adapts its control table while it learns from trial runs• SOC makes nonlinear, local adjustments
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Adaptive Controller
• An adaptive controller is a controller with adjustable parameters and a mechanism for adjusting the parameters (Åström & Wittenmark, 1995)
This is a loose definition that most people will agree on. The idea is that the closed loop system adapts to changes in the environment; for instance, temperature changes.
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Model reference adaptive system, MRAS
If the process output y behaves differently from what this model prescribes, the controller is re-tuned to more favourable settings. Conceptually, MRAS makes any system behave as desired, but this is not possible in practice; for instance, you cannot make a ferry behave like a sailing boat.
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The self-organizing controller, SOC
This is a performance measure P which plays the role of the model in MRAS. It 'complains' if the performance is undesired. The desired performance is pre-specified.
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P table (Procyk & Mamdani)
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6-6 -6 -6 -6 -6 -6 -6 -6 0 0 0 0 0 0-5 -6 -6 -6 -6 -6 -6 -6 -3 -2 -2 0 0 0-4 -6 -6 -6 -6 -6 -6 -6 -5 -4 -2 0 0 0-3 -6 -5 -5 -4 -4 -4 -4 -3 -2 0 0 0 0-2 -6 -5 -4 -3 -2 -2 -2 0 0 0 0 0 0-1 -5 -4 -3 -2 -1 -1 -1 0 0 0 0 0 0 0 -4 -3 -2 -1 0 0 0 0 0 1 2 3 4 1 0 0 0 0 0 0 1 1 1 2 3 4 5 2 0 0 0 0 0 0 2 2 2 3 4 5 6 3 0 0 0 0 2 3 4 4 4 4 5 5 6 4 0 0 0 2 4 5 6 6 6 6 6 6 6 5 0 0 0 2 2 3 6 6 6 6 6 6 6 6 0 0 0 0 0 0 6 6 6 6 6 6 6
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P table (Yamazaki)
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6-6 -6 -6 -6 -6 -6 -6 -6 -5 -4 -3 -2 -1 0-5 -6 -6 -6 -6 -5 -4 -4 -4 -3 -2 -1 0 0-4 -6 -6 -6 -5 -4 -3 -3 -3 -2 -1 0 0 1-3 -6 -6 -5 -4 -3 -2 -2 -2 -1 0 0 1 2-2 -6 -5 -4 -3 -2 -1 -1 -1 0 0 1 2 3-1 -5 -4 -3 -2 -1 -1 0 0 0 1 2 3 4 0 -5 -4 -3 -2 -1 0 0 0 1 2 3 4 5 1 -3 -2 -1 0 0 0 0 1 1 2 3 4 5 2 -2 -1 0 0 0 1 1 1 2 3 4 5 6 3 -1 0 0 0 1 2 2 2 3 4 5 6 6 4 0 0 0 1 2 3 3 3 4 5 6 6 6 5 0 0 1 2 3 4 4 4 5 6 6 6 6 6 0 1 2 3 4 5 6 6 6 6 6 6 6
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Adaptation law
ndndn jijiji ,,, PFF
New control table value
Old control table value
Penalty
It is the table value d samples back in time, which is updated.
Performance value now
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A modified performance measure
sTnenenp
It is a linear combination of e and de/dt. Setting p = 0 specifies a switching line (Yamazaki style) in the phase plane, where on one side the performance measure is positive and on the other it is negative.
Desired time constant
An adjustable adaptation gain
Notice how it operates on the error e directly.
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Example with a long dead time
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1
1exp
sssG s
Long dead time compared to the apparent time constant
The integrator makes it even more difficult
Difficult process
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First runThe time delay causes the oscillatory behaviour
It is fairly difficult to get it back after the load change
The model prescribes a first order response
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29th run
We still get a large dip, but the damping is fine.
In the beginning it has difficulties, but then it catches up
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Control surface after 29 runs
It will keep on making changes, because the performance is never satisfactory; perfect model following is impossible in this case.
Some parts are raised, some are depressed by the adaptation mechanism
n
snTpISP 2
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Animation of surface changes
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Summary
• The example showed that the SOC could deal with a large time delay.
• The adaptation makes local changes, so it must be allowed to adapt to new conditions.
• A loose tuning is sufficient, the adaptation will do the rest