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The Self-Organizing Controller, SOC

Today, it might be called an adaptive fuzzy controller. The Self-Organizing Controller, SOC. Jan Jantzen jj@inference.dk www.inference.dk 2013. Summary. SOC is a model reference adaptive system, MRAS SOC adapts its control table while it learns from trial runs

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The Self-Organizing Controller, SOC

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  1. Today, it might be called an adaptive fuzzy controller. The Self-Organizing Controller, SOC Jan Jantzen jj@inference.dk www.inference.dk 2013

  2. 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

  3. 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.

  4. 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.

  5. 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.

  6. 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 00000 -5 -6 -6-6-6-6-6-6 -3 -2 -2 0 00 -4 -6 -6-6-6-6-6-6 -5 -4 -2 0 00 -3 -6 -5 -5 -4 -4-4-4 -3 -2 0 000 -2 -6 -5 -4 -3 -2 -2-2 0 00000 -1 -5 -4 -3 -2 -1 -1-1 0 00000 0 -4 -3 -2 -1 0 0000 1 2 3 4 1 0 00000 1 11 2 3 4 5 2 0 00000 2 22 3 4 5 6 3 0 000 2 3 4 444 5 5 6 4 0 00 2 4 5 6 666666 5 0 00 2 2 3 6 666666 6 0 00000 6 666666

  7. 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 00 1 2 3 4 0 -5 -4 -3 -2 -1 0 00 1 2 3 4 5 1 -3 -2 -1 0 000 1 1 2 3 4 5 2 -2 -1 0 00 1 11 2 3 4 5 6 3 -1 0 00 1 2 22 3 4 5 6 6 4 0 00 1 2 3 33 4 5 6 66 5 0 0 1 2 3 4 44 5 6 666 6 0 1 2 3 4 5 6 666666

  8. Adaptation law New control table value Penalty Old control table value Performance value now It is the table value d samples back in time, which is updated.

  9. A modified performance measure 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 Notice how it operates on the error e directly. An adjustable adaptation gain

  10. Example with a long dead time Long dead time compared to the apparent time constant Difficult process The integrator makes it even more difficult

  11. First run The 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

  12. 29th run In the beginning it has difficulties, but then it catches up We still get a large dip, but the damping is fine.

  13. 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

  14. Animation of surface changes

  15. 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

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