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

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 2

3. Adaptive Controller An adaptive controller is a controller with adjustable parameters and a mechanism for adjusting the parameters (Åström & Wittenmark, 1995) 3 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 4 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 5 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 -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

7. P table (Yamazaki) 7 -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

8. Adaptation law 8 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

9. A modified performance measure 9 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.

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

11. First run 11 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 12 We still get a large dip, but the damping is fine. In the beginning it has difficulties, but then it catches up

13. Control surface after 29 runs 13 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 14

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 15