The Self-Organizing Controller, SOC Jan Jantzen [email protected] 2013 Today, it might be called an adaptive fuzzy controller.

The Self-Organizing Controller, SOC

Jan [email protected]

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